Zoppellari_Mahfouz_NLP_Project.ipynb

{
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   "source": [
    "# Neural Dependency Parsing Project\n",
    "### Authors:\n",
    "Elena Zoppellari ID: 2076715, email: elena.zoppellari@studenti.unipd.it, MSc: Physics of Data <br>\n",
    "Auriane Mahfouz ID: 2072042, email: auriane.mahfouz@studenti.unipd.it, MSc: Data Science"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "jRutj8WEp-rE"
   },
   "source": [
    "## **Introduction**\n",
    "Dependency parsing is a technique used in natural language processing to identify grammatical and semantic relationships between words in a sentence. <br>\n",
    "An efficient method for parsing is **transition-based parsing** which consists of constructing a dependency tree by applying a sequence of transition actions implemented by **arc-eager**. In order to improve the parser, we incorporate contextual word embeddings and a MultiLayer Percetron for selecting the most suitable parser action. In order to improve performance, the ArcEager is augmented with both **BiLSTM** and **BERT** respectively to perform feature extraction.\n",
    "\n",
    "The neural model will be trained and tested on ***English EWT*** dataset from the *Universal Dependency (UD) project*. The results will be then compared between the two models and with respect to some SotA result.\n",
    "\n",
    "In order to keep the presentation at a simple level, we disregard arc labels in dependency trees.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "FkzvpA8aLNSj"
   },
   "source": [
    "#### Setting up the Environment: Installing and Importing Essential Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "vBdAEm6jKdc-",
    "outputId": "586141f1-5804-4062-9621-f958b9f3f14c"
   },
   "outputs": [
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     "name": "stdout",
     "output_type": "stream",
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    }
   ],
   "source": [
    "!pip install datasets\n",
    "!pip install conllu\n",
    "!pip install transformers\n",
    "!pip install evaluate\n",
    "!pip install textblob"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "fXpE3XkFMagl"
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "from functools import partial\n",
    "from datasets import load_dataset\n",
    "from transformers import AutoTokenizer, AutoModel\n",
    "from torch.optim.lr_scheduler import ReduceLROnPlateau\n",
    "import matplotlib.pyplot as plt\n",
    "from textblob import TextBlob\n",
    "import collections\n",
    "from tabulate import tabulate\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Jthj-_IoKkST"
   },
   "source": [
    "## **Arc-Eager**\n",
    "\n",
    "ArcEager, also known as the Arc-Eager transition-based algorithm, is a popular parsing algorithm used in dependency parsing. It is an efficient and deterministic parsing algorithm that builds a dependency tree by incrementally adding arcs between words in a sentence.\n",
    "\n",
    "In the ArcEager algorithm, each word in the sentence is associated with a stack and a buffer. In particular, consider the following notation:\n",
    "\n",
    "* **$\\sigma$** represents the **stack**;\n",
    "* **$\\beta$** represents the input **buffer**;\n",
    "* **$A$** represents a **set of arcs** constructed so far.\n",
    "\n",
    "$\\sigma$ represents words that have been processed to some extent, while $\\beta$ contains words that are yet to be processed. The algorithm performs a series of transitions until the buffer is empty, and $A$ forms a complete dependency tree.\n",
    "\n",
    "The algorithm starts by taking a sentence of $n$ tokens as input and initializing the following elements:\n",
    "* $\\sigma$  is initially empty;\n",
    "* $\\beta$ contains the indexes representing the tokens, including a special element called `<ROOT>` at position $0$, which represents the root of the dependency tree;\n",
    "* $A$ is initialized with $n+1$ values, all set to $-1$.\n",
    "\n",
    "The first operation involves moving the `<ROOT>` from the buffer to the stack.\n",
    "\n",
    "The goal of the parser is to reach the **final configuration** where:\n",
    "* $\\sigma$ contains only one element: the `<ROOT>`;\n",
    "* $\\beta$ is empty;\n",
    "* $A$ consists of elements that are all different from $-1$, except for the first one (at position $0$) that refers to the `<ROOT>`.\n",
    "\n",
    "To achieve this final configuration, the parser performs **actions** (transitions) that allow the movement of elements from the buffer to the stack and the removal of elements from the stack once the arcs are created.\n",
    "\n",
    "Given a stack of length $m$ and considering $\\sigma_i$ and $\\beta_j$ as the $i$-th and $j$-th element ($i$,$j \\geq 0$)  in the stack and the buffer, respectively, while $a_i$ represents the corresponding arc for the $i$-th element in the stack, the ArcEager algorithm defines the following four actions:\n",
    "\n",
    "* **shift:** removes $\\beta_0$ from the buffer and pushes it into the stack;\n",
    "* **left-arc:** creates an arc  between the topmost element in the stack and the first element in the buffer $(\\sigma_m \\rightarrow \\beta_0)$ and removes $\\sigma_m$ from the stack;\n",
    "* **right-arc:** creates an arc between the first element in the buffer and the topmost element in the stack $(\\beta_0 \\rightarrow \\sigma_m)$ and pushes $\\beta_0$ in the stack;\n",
    "* **reduce:** removes the topmost element in the stack, given that it has an associated arc ($a_m \\neq -1 $).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "sOQpqLVmQZzJ"
   },
   "outputs": [],
   "source": [
    "class ArcEager:\n",
    "  def __init__(self, sentence):\n",
    "    ''' __init__ function initialize the parsing of the sentence initializing the buffer and the stack.\n",
    "    Parameters\n",
    "    sentence: the sentence to parse\n",
    "    '''\n",
    "    self.sentence = sentence\n",
    "    self.buffer = [i for i in range(len(self.sentence))]\n",
    "    self.stack = []\n",
    "    self.arcs = [-1 for _ in range(len(self.sentence))]\n",
    "\n",
    "    # first operation: shift to initialize the stack with the ROOT\n",
    "    self.shift()\n",
    "\n",
    "  def shift(self):\n",
    "    ''' shift function allows the transfer of the first element of the buffer to the stack\n",
    "    '''\n",
    "    b1 = self.buffer[0]\n",
    "    self.buffer = self.buffer[1:]\n",
    "    self.stack.append(b1)\n",
    "\n",
    "  def left_arc(self):\n",
    "    ''' left_arc function allows the creation of an arc between the topmost element in the stack and the first element in the buffer, then pops from the stack the topmost element\n",
    "    '''\n",
    "    o1 = self.stack.pop()\n",
    "    if len(self.buffer) != 0:\n",
    "      o2 = self.buffer[0]\n",
    "      self.arcs[o1] = o2\n",
    "\n",
    "  def right_arc(self):\n",
    "    ''' right_arc function allows the creation of an arc between the first element in the buffer and the topmost element in the stack, then add to the stack the first element of the buffer\n",
    "    '''\n",
    "    o1 = self.stack.pop()\n",
    "    if len(self.buffer) != 0:\n",
    "      o2 = self.buffer[0]\n",
    "      self.arcs[o2] = o1\n",
    "      self.stack.append(o1)\n",
    "      self.shift()\n",
    "\n",
    "  def reduce(self):\n",
    "    ''' reduce function allows to pop the topmost element in the stack, only if it has an arc associated different from default value (-1)\n",
    "    '''\n",
    "    o1= self.stack[-1]\n",
    "    if self.arcs[o1] != -1:\n",
    "        self.stack.pop()\n",
    "\n",
    "  def is_tree_final(self):\n",
    "    ''' is_tree_final function represents the desired final configuration\n",
    "    '''\n",
    "    return len(self.stack) == 1 and len(self.buffer) == 0\n",
    "\n",
    "  def print_configuration(self):\n",
    "    ''' print_configuration allows to print the current configuration of stack, buffer and set of arcs\n",
    "    '''\n",
    "    s = [self.sentence[i] for i in self.stack]\n",
    "    b = [self.sentence[i] for i in self.buffer]\n",
    "    print(s, b)\n",
    "    print(self.arcs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "OtdR3Elcdxdq"
   },
   "source": [
    "## **Oracle**\n",
    "\n",
    "A **static oracle** maps parser configurations $c$ into  actions, and it does so by looking into the gold (reference) tree for the sentence at hand and therefore assumes a correct parsing history. If $c$ does not contain any mistake, then the action provided by the oracle for $c$ is guaranted to be correct.  Furthermore, in cases where there is more than one correct action for $c$, the oracle always chooses a single action, called the **canonical** action. Therefore, it is used as a reference during the training of a dependency parser to provide supervision signals and guide the learning process.\n",
    "\n",
    "We use here the static oracle for the arc-eager parser which is based on the following conditions:\n",
    "* set $A$ if configuration $c$ does not contain any wrong dependency\n",
    "* rigth-arc has precedence over other actions, and can be done only if the buffer is not empty.\n",
    "* left-arc can be done only if the topmost token of the stack $\\sigma_m$ is not the root node and does not already have a head.\n",
    "* shift transition has lowest precedence, and can be done if the buffer is not empty\n",
    "* reduce has a precondition that the top token has a head."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "ImTye0fORmcQ"
   },
   "outputs": [],
   "source": [
    "class Oracle:\n",
    "  def __init__(self, parser, gold_tree):\n",
    "    self.parser = parser\n",
    "    self.gold = gold_tree\n",
    "\n",
    "  def is_left_arc_gold(self):\n",
    "    o1 = self.parser.stack[len(self.parser.stack)-1]\n",
    "    if len(self.parser.buffer) != 0:\n",
    "      o2 = self.parser.buffer[0]\n",
    "\n",
    "      if self.gold[o1] == o2:\n",
    "        return True\n",
    "\n",
    "      return False\n",
    "\n",
    "  def is_right_arc_gold(self):\n",
    "    o1 = self.parser.stack[len(self.parser.stack)-1]\n",
    "    if len(self.parser.buffer) != 0:\n",
    "      o2 = self.parser.buffer[0]\n",
    "\n",
    "      if self.gold[o2] != o1:\n",
    "            return False\n",
    "      return True\n",
    "\n",
    "  def is_reduce_gold(self):\n",
    "    if (self.is_left_arc_gold() or self.is_right_arc_gold()):\n",
    "        return False\n",
    "\n",
    "    else:\n",
    "      miss_nodes = [self.gold[i] for i in range(len(self.gold)) if self.parser.arcs[i] != self.gold[i]]\n",
    "      if(self.parser.arcs[self.parser.stack[-1]] != -1 and self.parser.stack[-1] not in miss_nodes):\n",
    "        return True\n",
    "      else:\n",
    "        return False\n",
    "\n",
    "  def is_shift_gold(self):\n",
    "    if len(self.parser.buffer) == 0:\n",
    "      return False\n",
    "\n",
    "    #This dictates transition precedence of the parser\n",
    "    if (self.is_left_arc_gold() or self.is_right_arc_gold() or self.is_reduce_gold()):\n",
    "      return False\n",
    "\n",
    "    return True"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "xaf_OT5flz2J"
   },
   "source": [
    "### Examples with Static Oracle and gold configuration"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "zGNu-vlR3qww"
   },
   "source": [
    "In this section, we present some examples to demonstrate the effectiveness of the Static Oracle in parsing sentences, using the ArcEager algorithm and the gold configuration as inputs. All the steps in the parsing are shown in order to demonstrate the correct internal mechanism."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "ouJvB_Vx2t3V",
    "outputId": "f210ed66-3580-4fa9-96f8-71a3711690cd"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['<ROOT>'] ['He', 'began', 'to', 'write', 'again', '.']\n",
      "[-1, -1, -1, -1, -1, -1, -1]\n"
     ]
    }
   ],
   "source": [
    "sentence = [\"<ROOT>\", \"He\", \"began\", \"to\", \"write\", \"again\", \".\"]\n",
    "gold = [-1, 2, 0, 4, 2, 4, 2 ]\n",
    "\n",
    "parser = ArcEager(sentence)\n",
    "oracle = Oracle(parser, gold)\n",
    "parser.print_configuration()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "bAafVsFofOyl",
    "outputId": "a14d8b57-aff9-4efa-aaf4-bbe920caa70e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INITIALIZATION:\n",
      "buffer [1, 2, 3, 4, 5, 6]\n",
      "stack [0]\n",
      "[-1, -1, -1, -1, -1, -1, -1]\n",
      "[-1, 2, 0, 4, 2, 4, 2]\n",
      "-------------------------------------\n",
      "SHIFT\n",
      "buffer [2, 3, 4, 5, 6]\n",
      "stack [0, 1]\n",
      "[-1, -1, -1, -1, -1, -1, -1]\n",
      "[-1, 2, 0, 4, 2, 4, 2]\n",
      "-------------------------------------\n",
      "LEFTARC\n",
      "buffer [2, 3, 4, 5, 6]\n",
      "stack [0]\n",
      "[-1, 2, -1, -1, -1, -1, -1]\n",
      "[-1, 2, 0, 4, 2, 4, 2]\n",
      "-------------------------------------\n",
      "RIGHTARC\n",
      "buffer [3, 4, 5, 6]\n",
      "stack [0, 2]\n",
      "[-1, 2, 0, -1, -1, -1, -1]\n",
      "[-1, 2, 0, 4, 2, 4, 2]\n",
      "-------------------------------------\n",
      "SHIFT\n",
      "buffer [4, 5, 6]\n",
      "stack [0, 2, 3]\n",
      "[-1, 2, 0, -1, -1, -1, -1]\n",
      "[-1, 2, 0, 4, 2, 4, 2]\n",
      "-------------------------------------\n",
      "LEFTARC\n",
      "buffer [4, 5, 6]\n",
      "stack [0, 2]\n",
      "[-1, 2, 0, 4, -1, -1, -1]\n",
      "[-1, 2, 0, 4, 2, 4, 2]\n",
      "-------------------------------------\n",
      "RIGHTARC\n",
      "buffer [5, 6]\n",
      "stack [0, 2, 4]\n",
      "[-1, 2, 0, 4, 2, -1, -1]\n",
      "[-1, 2, 0, 4, 2, 4, 2]\n",
      "-------------------------------------\n",
      "RIGHTARC\n",
      "buffer [6]\n",
      "stack [0, 2, 4, 5]\n",
      "[-1, 2, 0, 4, 2, 4, -1]\n",
      "[-1, 2, 0, 4, 2, 4, 2]\n",
      "-------------------------------------\n",
      "REDUCE\n",
      "buffer [6]\n",
      "stack [0, 2, 4]\n",
      "[-1, 2, 0, 4, 2, 4, -1]\n",
      "[-1, 2, 0, 4, 2, 4, 2]\n",
      "-------------------------------------\n",
      "REDUCE\n",
      "buffer [6]\n",
      "stack [0, 2]\n",
      "[-1, 2, 0, 4, 2, 4, -1]\n",
      "[-1, 2, 0, 4, 2, 4, 2]\n",
      "-------------------------------------\n",
      "RIGHTARC\n",
      "buffer []\n",
      "stack [0, 2, 6]\n",
      "[-1, 2, 0, 4, 2, 4, 2]\n",
      "[-1, 2, 0, 4, 2, 4, 2]\n",
      "-------------------------------------\n",
      "REDUCE\n",
      "buffer []\n",
      "stack [0, 2]\n",
      "[-1, 2, 0, 4, 2, 4, 2]\n",
      "[-1, 2, 0, 4, 2, 4, 2]\n",
      "-------------------------------------\n",
      "REDUCE\n",
      "buffer []\n",
      "stack [0]\n",
      "[-1, 2, 0, 4, 2, 4, 2]\n",
      "[-1, 2, 0, 4, 2, 4, 2]\n"
     ]
    }
   ],
   "source": [
    "print(\"INITIALIZATION:\")\n",
    "print(\"buffer\" ,parser.buffer)\n",
    "print(\"stack\" ,parser.stack)\n",
    "print(parser.arcs)\n",
    "print(gold)\n",
    "\n",
    "while not parser.is_tree_final():\n",
    "    print(\"-------------------------------------\")\n",
    "    if oracle.is_shift_gold():\n",
    "      print(\"SHIFT\")\n",
    "      parser.shift()\n",
    "    elif oracle.is_left_arc_gold():\n",
    "      print(\"LEFTARC\")\n",
    "      parser.left_arc()\n",
    "    elif oracle.is_right_arc_gold():\n",
    "      print(\"RIGHTARC\")\n",
    "      parser.right_arc()\n",
    "    elif oracle.is_reduce_gold():\n",
    "      print(\"REDUCE\")\n",
    "      parser.reduce()\n",
    "\n",
    "    print(\"buffer\" ,parser.buffer)\n",
    "    print(\"stack\" ,parser.stack)\n",
    "    print(parser.arcs)\n",
    "    print(gold)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "ksbJIpPUGXYt",
    "outputId": "e7cc36a1-9f31-4773-bb31-96b6174bff46"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['<ROOT>'] ['Book', 'the', 'flight', 'through', 'Houston', '.']\n",
      "[-1, -1, -1, -1, -1, -1, -1]\n"
     ]
    }
   ],
   "source": [
    "sentence = [\"<ROOT>\", \"Book\", \"the\", \"flight\", \"through\", \"Houston\",\".\"]\n",
    "gold = [-1, 0, 3, 1, 5, 3, 1]\n",
    "\n",
    "parser = ArcEager(sentence)\n",
    "oracle = Oracle(parser, gold)\n",
    "\n",
    "parser.print_configuration()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "SWwgOuApHXtR",
    "outputId": "918c4f66-f5f4-47f8-a832-a719062bcb8e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INITIALIZATION:\n",
      "buffer [1, 2, 3, 4, 5, 6]\n",
      "stack [0]\n",
      "[-1, -1, -1, -1, -1, -1, -1]\n",
      "[-1, 0, 3, 1, 5, 3, 1]\n",
      "-------------------------------------\n",
      "RIGHTARC\n",
      "buffer [2, 3, 4, 5, 6]\n",
      "stack [0, 1]\n",
      "[-1, 0, -1, -1, -1, -1, -1]\n",
      "[-1, 0, 3, 1, 5, 3, 1]\n",
      "-------------------------------------\n",
      "SHIFT\n",
      "buffer [3, 4, 5, 6]\n",
      "stack [0, 1, 2]\n",
      "[-1, 0, -1, -1, -1, -1, -1]\n",
      "[-1, 0, 3, 1, 5, 3, 1]\n",
      "-------------------------------------\n",
      "LEFTARC\n",
      "buffer [3, 4, 5, 6]\n",
      "stack [0, 1]\n",
      "[-1, 0, 3, -1, -1, -1, -1]\n",
      "[-1, 0, 3, 1, 5, 3, 1]\n",
      "-------------------------------------\n",
      "RIGHTARC\n",
      "buffer [4, 5, 6]\n",
      "stack [0, 1, 3]\n",
      "[-1, 0, 3, 1, -1, -1, -1]\n",
      "[-1, 0, 3, 1, 5, 3, 1]\n",
      "-------------------------------------\n",
      "SHIFT\n",
      "buffer [5, 6]\n",
      "stack [0, 1, 3, 4]\n",
      "[-1, 0, 3, 1, -1, -1, -1]\n",
      "[-1, 0, 3, 1, 5, 3, 1]\n",
      "-------------------------------------\n",
      "LEFTARC\n",
      "buffer [5, 6]\n",
      "stack [0, 1, 3]\n",
      "[-1, 0, 3, 1, 5, -1, -1]\n",
      "[-1, 0, 3, 1, 5, 3, 1]\n",
      "-------------------------------------\n",
      "RIGHTARC\n",
      "buffer [6]\n",
      "stack [0, 1, 3, 5]\n",
      "[-1, 0, 3, 1, 5, 3, -1]\n",
      "[-1, 0, 3, 1, 5, 3, 1]\n",
      "-------------------------------------\n",
      "REDUCE\n",
      "buffer [6]\n",
      "stack [0, 1, 3]\n",
      "[-1, 0, 3, 1, 5, 3, -1]\n",
      "[-1, 0, 3, 1, 5, 3, 1]\n",
      "-------------------------------------\n",
      "REDUCE\n",
      "buffer [6]\n",
      "stack [0, 1]\n",
      "[-1, 0, 3, 1, 5, 3, -1]\n",
      "[-1, 0, 3, 1, 5, 3, 1]\n",
      "-------------------------------------\n",
      "RIGHTARC\n",
      "buffer []\n",
      "stack [0, 1, 6]\n",
      "[-1, 0, 3, 1, 5, 3, 1]\n",
      "[-1, 0, 3, 1, 5, 3, 1]\n",
      "-------------------------------------\n",
      "REDUCE\n",
      "buffer []\n",
      "stack [0, 1]\n",
      "[-1, 0, 3, 1, 5, 3, 1]\n",
      "[-1, 0, 3, 1, 5, 3, 1]\n",
      "-------------------------------------\n",
      "REDUCE\n",
      "buffer []\n",
      "stack [0]\n",
      "[-1, 0, 3, 1, 5, 3, 1]\n",
      "[-1, 0, 3, 1, 5, 3, 1]\n"
     ]
    }
   ],
   "source": [
    "print(\"INITIALIZATION:\")\n",
    "print(\"buffer\" ,parser.buffer)\n",
    "print(\"stack\" ,parser.stack)\n",
    "print(parser.arcs)\n",
    "print(gold)\n",
    "\n",
    "while not parser.is_tree_final():\n",
    "    print(\"-------------------------------------\")\n",
    "    if oracle.is_shift_gold():\n",
    "      print(\"SHIFT\")\n",
    "      parser.shift()\n",
    "    elif oracle.is_left_arc_gold():\n",
    "      print(\"LEFTARC\")\n",
    "      parser.left_arc()\n",
    "    elif oracle.is_right_arc_gold():\n",
    "      print(\"RIGHTARC\")\n",
    "      parser.right_arc()\n",
    "    elif oracle.is_reduce_gold():\n",
    "      print(\"REDUCE\")\n",
    "      parser.reduce()\n",
    "\n",
    "    print(\"buffer\" ,parser.buffer)\n",
    "    print(\"stack\" ,parser.stack)\n",
    "    print(parser.arcs)\n",
    "    print(gold)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "gaSrWbH_W6wY"
   },
   "source": [
    "## **Dataset:** English EWT from Universal Dependency Project\n",
    "For our task, we selected the **English EWT** dataset from Universal Dependency.\n",
    "The data is sourced from diverse genres of web media, including weblogs, newsgroups, emails, reviews, and Yahoo! Answers. This wide range of genres ensures a varied and representative sample for our analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 328,
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    "id": "3Lh4DhEKgP_I",
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   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6caa7d7ba46e4ba2a13ad1494ded327a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Downloading builder script: 0.00B [00:00, ?B/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b63c111affa446f9853b50be008314a2",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Downloading metadata: 0.00B [00:00, ?B/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c12b7e9530bb42a39d42ebd303e56ee6",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Downloading readme: 0.00B [00:00, ?B/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Downloading and preparing dataset universal_dependencies/en_ewt to /root/.cache/huggingface/datasets/universal_dependencies/en_ewt/2.7.0/1ac001f0e8a0021f19388e810c94599f3ac13cc45d6b5b8c69f7847b2188bdf7...\n"
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       "model_id": "07da84e45a6045aa961905caefa17f29",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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       "model_id": "f58140ddcec143a69a1aec58571ce9c9",
       "version_major": 2,
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      },
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b9a656dce1764901a2d6f2edb1fe80ef",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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       "model_id": "f671d133b30745ee8c1c7d70b0c9616d",
       "version_major": 2,
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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4874c17c8e3848da9dd39a6fa6e196bf",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Extracting data files:   0%|          | 0/3 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0b197b10eb8a4ee1ab5f2983b27092d1",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Generating train split:   0%|          | 0/12543 [00:00<?, ? examples/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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       "model_id": "083dc71799544b6c83fefd911fefc754",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Generating validation split:   0%|          | 0/2002 [00:00<?, ? examples/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e779e96c716940cdadb9ca14c9250a03",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Generating test split:   0%|          | 0/2077 [00:00<?, ? examples/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset universal_dependencies downloaded and prepared to /root/.cache/huggingface/datasets/universal_dependencies/en_ewt/2.7.0/1ac001f0e8a0021f19388e810c94599f3ac13cc45d6b5b8c69f7847b2188bdf7. Subsequent calls will reuse this data.\n"
     ]
    }
   ],
   "source": [
    "dataset = load_dataset('universal_dependencies', 'en_ewt', split=\"train\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "2x1EKX8vjAON",
    "outputId": "41aaae3e-ffab-495e-b18a-cb42b778c141"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dataset length: 12543\n",
      "dataset keys: dict_keys(['idx', 'text', 'tokens', 'lemmas', 'upos', 'xpos', 'feats', 'head', 'deprel', 'deps', 'misc'])\n",
      "\n",
      "Example of sentence's tokens and gold dependency tree:\n",
      "['Two', 'of', 'them', 'were', 'being', 'run', 'by', '2', 'officials', 'of', 'the', 'Ministry', 'of', 'the', 'Interior', '!']\n",
      "['6', '3', '1', '6', '6', '0', '9', '9', '6', '12', '12', '9', '15', '15', '12', '6']\n"
     ]
    }
   ],
   "source": [
    "# info about dataset\n",
    "print(f\"dataset length: {len(dataset)}\")\n",
    "print(f\"dataset keys: {dataset[1].keys()}\")\n",
    "\n",
    "# we look into a sentence in the dataset and print its tokens and (gold) dependency tree\n",
    "print(\"\\nExample of sentence's tokens and gold dependency tree:\")\n",
    "print(dataset[3][\"tokens\"])\n",
    "print(dataset[3][\"head\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "rPkahOr3VXKP"
   },
   "source": [
    "To be sure to don't have to deal with misspelled words, a spell checker has been used to check all the tokens in the dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "pxJQjcJ3jDV4",
    "outputId": "184df857-d197-4362-d714-8f56d2b2c462"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N. of errors found: 0\n"
     ]
    }
   ],
   "source": [
    "# Spell checker\n",
    "errors = 0\n",
    "for i, sentence in enumerate(dataset[\"tokens\"]): # for each sentence in the dataset\n",
    "  for j, token in enumerate(sentence): # for each token in a sentence\n",
    "    token_new = TextBlob(token) # check for errors in spelling\n",
    "    if token_new != token:\n",
    "      dataset[\"tokens\"][i][j] = token_new\n",
    "      errors += 1\n",
    "print(f\"N. of errors found:\", errors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "bhSov9QT-Eo-",
    "outputId": "6d596974-30e9-40f8-a951-aed7a5308691"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Dimension of the vocabulary: 20132\n",
      "\n",
      "Dimension of the vocabulary of lemmas: 14796\n",
      "\n",
      "Max length of a sentence: 160, \n",
      "Min length of a sentence: 1\n",
      "\n",
      "Frequency of POS: {0: 34786, 1: 23676, 2: 17625, 3: 3996, 4: 643, 5: 4502, 6: 12459, 7: 5567, 8: 16284, 9: 6703, 10: 12924, 11: 18584, 12: 845, 13: 2444, 14: 9903, 15: 688, 16: 23028, 17: 12396}\n"
     ]
    }
   ],
   "source": [
    "# Vocabulary:\n",
    "vocabulary = {}\n",
    "for sentence in dataset[\"tokens\"]:\n",
    "  for token in sentence:\n",
    "    if token not in vocabulary:\n",
    "      vocabulary[token] = 1\n",
    "    else:\n",
    "      vocabulary[token] += 1\n",
    "\n",
    "print(f\"\\nDimension of the vocabulary: {len(vocabulary)}\")\n",
    "\n",
    "# Lemmas vocabulary\n",
    "voc_lemma = {}\n",
    "for sentence in dataset[\"lemmas\"]:\n",
    "  for lemma in sentence:\n",
    "    if lemma not in voc_lemma:\n",
    "      voc_lemma[lemma] = 1\n",
    "    else:\n",
    "      voc_lemma[lemma] += 1\n",
    "\n",
    "print(f\"\\nDimension of the vocabulary of lemmas: {len(voc_lemma)}\")\n",
    "\n",
    "# Sentence length\n",
    "len_sentence = {}\n",
    "for i, sentence in enumerate(dataset[\"tokens\"]):\n",
    "  len_sentence[i] = len(sentence)\n",
    "\n",
    "max_key = max(len_sentence, key=len_sentence.get)\n",
    "min_key = min(len_sentence, key=len_sentence.get)\n",
    "\n",
    "print(f\"\\nMax length of a sentence: {len_sentence[max_key]}, \\nMin length of a sentence: {len_sentence[min_key]}\")\n",
    "\n",
    "# POS frequency\n",
    "voc_pos = {}\n",
    "for sentence in dataset[\"upos\"]:\n",
    "  for pos in sentence:\n",
    "    if pos not in voc_pos:\n",
    "      voc_pos[pos] = 1\n",
    "    else:\n",
    "      voc_pos[pos] += 1\n",
    "\n",
    "POS = list(voc_pos.keys())\n",
    "POS.sort()\n",
    "sorted_pos = {i: voc_pos[i] for i in POS}\n",
    "\n",
    "print(f\"\\nFrequency of POS: {sorted_pos}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 400
    },
    "id": "IFbyJMUQiAJv",
    "outputId": "129c016d-b9a7-4e48-97a9-3cd48b87aaed"
   },
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 2500x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Word frequencies in the vocabulary\n",
    "# we provide also a comparison with Zipf/Mandelbrot law, the coefficient has been calculated in order to interpolate the frequency of the most frequent word\n",
    "def zipf(r):\n",
    "  return [23328 / (x + 2.7) for x in r]\n",
    "\n",
    "sorted_freq_w = sorted(vocabulary.items(), key=lambda x: x[1], reverse=True)\n",
    "top_50 = sorted_freq_w[:50]\n",
    "\n",
    "keys_word = [pair[0] for pair in top_50]\n",
    "values_word = [pair[1] for pair in top_50]\n",
    "\n",
    "x = [i for i in range(50)]\n",
    "y = zipf(x)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(25, 6))\n",
    "ax.bar(keys_word, values_word)\n",
    "ax.plot(keys_word, y, label = \"Zipf/Mandelbrot law\", color = \"red\")\n",
    "\n",
    "# Add labels and title\n",
    "ax.set_xlabel('Word')\n",
    "ax.set_ylabel('Frequency')\n",
    "ax.set_title('Top 50 Word Frequencies in the Vocabulary')\n",
    "\n",
    "# Show the plot\n",
    "ax.legend()\n",
    "ax.grid(alpha=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Abs_SfmQVtzo"
   },
   "source": [
    "From the plot above we can observe that the frequencies of the tokens follows approximately well the Zipf/Mandelbrot law."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 400
    },
    "id": "3J7T5M0QsTCy",
    "outputId": "78141da7-b7d6-4913-9d98-61a41ffcb99d"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 2500x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Lemmas frequencies in the vocabulary\n",
    "\n",
    "sorted_freq_l = sorted(voc_lemma.items(), key=lambda x: x[1], reverse=True)\n",
    "top_50_l = sorted_freq_l[:50]\n",
    "\n",
    "keys_lemma = [pair[0] for pair in top_50_l]\n",
    "values_lemma = [pair[1] for pair in top_50_l]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(25, 6))\n",
    "ax.bar(keys_lemma, values_lemma)\n",
    "\n",
    "# Add labels and title\n",
    "ax.set_xlabel('Lemma')\n",
    "ax.set_ylabel('Frequency')\n",
    "ax.set_title('Top 50 Lemma Frequencies in the Vocabulary')\n",
    "\n",
    "# Show the plot\n",
    "ax.grid(alpha=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1AHJJRqAurUv"
   },
   "source": [
    "For POS tags in Universal Dependency the numerical list in range [1:18] corresponds to:\n",
    "0. ADJ: Adjective\n",
    "1. ADP: Adposition\n",
    "2. ADV: Adverb\n",
    "3. AUX: Auxiliary\n",
    "4. CCONJ: Coordinating Conjunction\n",
    "5. DET: Determiner\n",
    "6. INTJ: Interjection\n",
    "7. NOUN: Noun\n",
    "8. NUM: Numeral\n",
    "9. PART: Particle\n",
    "10. PRON: Pronoun\n",
    "11. PROPN: Proper Noun\n",
    "12. PUNCT: Punctuation\n",
    "13. SCONJ: Subordinating Conjunction\n",
    "14. SYM: Symbol\n",
    "15. VERB: Verb\n",
    "16. X: Other\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 872
    },
    "id": "Lic-OfNltP0w",
    "outputId": "cde82502-ae5f-4b88-d82d-1470e7316368"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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798XH/XweuVeUse6Yq/tZb731su++++aZZ55ZZjt///vfc/TRR2eDDTZI69at06NHj5x44ol544036o3r379/qqqq8pvf/Kbe8ksuuaT82l7ds1VVVaVt27bp3bt3LrvssvL6uuf8o//eeuutt1JVVZX77ruvUbJ+2tdj586d8/bbb9cb16dPn4waNareshdffDGDBw9Ot27d0qZNm/Tq1SuHHnpoHn/88c/t+H799ddzwgknZKONNkqbNm3StWvX1NbW1nufrYR/VyQfvy/uv//+dO3aNf/93/+9zH2+853vZKeddsqSJUvK/65Y3t8DF1xwQaqqqtK/f//PIcn/Wdm/Tz7uGHv00UeTLPv33Prrr5+DDz44M2fOrLfND7+Gq6qq0qVLl3z729/O//7v/zZ61s9iyZIl2XnnnXPggQfWWz5//vx07949//mf/1nQzJoX5RyN5sorr8wPfvCDPPDAA3nttdeWWX/33Xdn1qxZeeqpp/Lf//3f+etf/5rtttuu3h/RTV1DZayurs6sWbPyyiuv5Be/+EXuuOOOfPe73/28YqyUz5p1yJAhmThxYl555ZVl7nv11Vdnhx12yLbbbtvoOVbGJ2X9JNttt11GjhyZ4447rvwP67lz5+b444/PmWeema233rqhp0w++Ed/3759c8899+SCCy7IM888kzvvvDN77LFHhg4dmiS57bbbstNOO2XRokW57rrr8te//jW/+tWvUlNTkx//+Mflbf3whz/M9773vRx88MF5+umn89hjj2WXXXbJN7/5zVx66aXLPPbLL7+ca6+99nPLujL23nvvzJo1KzNmzMgdd9yRPfbYIyeeeGK+/vWv1/vD/6yzzsqsWbPq/fzgBz/ID3/4w3rLunXrtszYpqpt27Y577zzMm/evOWuHz169DI5rr766vLt5ZUgn7dPylAqlXLIIYfkrLPOyoknnpi//vWvue+++9K9e/f079+//MfwqmgKx/Mn5f+0Ntxww2UyXXPNNdlwww0bZPufRd1r9YUXXsi///u/Z9SoUbnggguSJDNnzswjjzySYcOG5aqrrlrh/V9++eVcfPHF+fnPf54zzjgjBx98cL3jvF+/fjn22GPrLevevXvhGZPk+eefz6xZs/6/9u49LKpq/x/4m6vDRdCQR44KhCIMkFHeUswvaSpw8oIXAtNCAa8cgyIy0sILJKlIaoia3Cw1IKXQ05G84MlLxzsqpUBJWZl3AgFDwPX7w99MjjODA84wiO/X8/A8uvdae9Znz9p71lp77b2Rn5+P2tpavPTSS7h9+7Z8/fnz59G3b1+UlpZiy5Yt+PHHH7F27Vrs2bMHAwcOxI0bNxQ+TyKRYP78+airq2tzscm+wx9++AEvv/wywsPDsWXLFvl6Y2Nj7N69GwUFBS0eq6Zu3ryJ5cuXN5rm2LFj6NOnD0pKSrBu3Tr88MMPyM3NhVQqRVRUVIvV7/Hjx+PkyZPIzMxESUkJ8vLy8MILL8jbd49Tu0LdvqioqMD69euxcOFChcHnnJwc7NixA5mZmTAyMgIA/OMf/0BBQYFSfyAtLQ0ODg4tGg+gWf/EysoKwN99nXv/+vTpI08v68/9/vvv2Lp1K4qLixEQEKC0XVk9vXjxIr766iv8+uuvmDx5su6C1AIjIyNkZGRg586d2LRpk3z5nDlz8MQTTyA2NlaPpWtDBJEO3Lx5U1haWopz586JwMBAER8fL19XVlYmAIiTJ08q5GloaBAvvPCCcHR0FPX19UIIIdLT04W1tXULllxzuowxPj5eGBoaipqaGl2HoRFtxFpXVyc6d+4sFi9erHLbKSkpLRHKAzUWa0FBgQAgysvLlfI5OjqKpKQk+f/r6+tFv379RGBgoBBCCH9/fzFw4ED5907a5+fnJ7p27SqqqqqU1pWXl4vq6mrRqVMn4e/vrzK/7Hv97rvvBACxatUqpTRvvvmmMDExERcuXBBC/F0noqOjhb29vfjrr7/kaa2trUV6err8//fXEV0KDg4WY8aMUVq+Z88eAUB88sknTS5TS5a/qe6NNzg4WIwcOVJIpVIRHR0tT5ObmyvUNXsAiNzcXKXl3t7eIiIiQgclbpwmMXz++ecCgMjLy1PKP27cOGFjYyM/FmJjY4Wnp6dSuvvP302pz7qkSfyNtQ/u/T5lMc6fP1/07NlTIZ2Li4t47733BABRVlami1AeSNWxOnz4cDFgwAAhhBALFiwQQUFB4uzZs8La2lqpXaAq/7hx48Szzz6r9Fn6rM/qYlT1u5qXlycAiFOnTsmX+fr6im7duinF/8cffwhzc3Mxc+ZM+TJvb28xdepUYWNjI5KTk+XLk5KShKOj4yMf2/3fYc+ePUVQUJAQ4u/jYtq0aaJ///7yNOXl5QKAKCgo0EmsTT0eo6OjhaWlpbh8+bI8naenp4iNjRVCCHHnzh3h4eEh+vTpIxoaGpS2qaodpov6Ldtv+/btU7n+cWpXPGhfCCHElClTxLPPPitu374trly5ImxtbcXKlSvl62W/RSNHjhRxcXHy5QcPHhSdOnUSs2bNEt7e3roMQ4km/RN1fZ17qToGVq1aJQCIiooK+TJV9fTTTz8V5ubmDxtKi1i5cqXo2LGjuHjxovjyyy+FiYmJKCws1Hex2gzOnCOdyM7OhlQqhaurKyZPnoy0tDQIIRrNY2hoiIiICPzyyy84fvx4C5W0+XQZo5mZGe7cuaMwu0WftBGrsbExXnvtNWRkZCjkzcnJQUNDAyZOnKjrMDTSnFhVMTIyQmZmJr766iu88soryM/PR0ZGhvzKIWnXjRs3sHPnToSHh8PCwkJpfYcOHZCfn49r167h7bffVrkN2S05W7ZsgaWlJWbMmKGUJioqCnV1ddi6davC8sjISNTX12P16tUPH4wODR06FJ6enti2bZu+i6JTRkZG+OCDD7B69WqVV8MfBQ+KYfPmzXBxccGoUaOU1kVFReH69evYtWtXsz67NdRnbX+Ho0ePRnl5OQ4cOAAAOHDgAMrLy1XuP30zMzPD7du3IYRAeno6Jk+eDKlUCmdnZ3zxxReN5i0qKsKhQ4dgamraQqVtHlmM96uoqJDfjiqL4caNG8jPz8fs2bNhZmamkN7Ozg6TJk1CVlaWwm+1lZUV5s2bh0WLFqG6ulqHkSjTdWyafN6CBQtw5syZB9aXh6Uu1geZOHGi/LZYVQoLC/H9998jKioKhobK3dWWeuSNpaUlLC0t8eWXX6K2tlZp/ePUrnjQvgDuzkq/fv06Fi9ejNmzZ+Opp57CnDlzlNKFhIQo3J6blpaGSZMm6eW8pav+yZUrV5CbmwsjI6NG2/43btxAdnY2nnvuuWZ9TkubM2cOPD098eqrr2L69Ol4//334enpqe9itRkcnCOdSE1NlU/P9fX1RUVFBf773/8+MJ9UKgUAvT37pSl0FWNpaSnWrl2Lvn37on379lor78PQVqwhISH46aefFPKmp6dj/PjxsLa21n7Bm6G5sari5uaGyMhIbNmyBQsWLICLi4s2i0r3+PHHHyGEkNc5VWTPQGwsDQCUlJSgR48eKhuJXbp0gZWVldJzZMzNzREbG4slS5agoqKiGRG0HKlUqnD+mTt3rrzRLfvbv3+//gqoJWPHjsUzzzzzSN9q0VgMJSUlcHNzU5lPtvz+eqqp1lKftfkdmpiYyC+4AHc7g5MnT4aJiclDb1tbhBDYvXs38vPzMXToUOzevRs1NTXw8fEBAEyePBmpqalK+Xbs2AFLS0tIJBL06tULV65cQXR0dEsXXyP3xyjTrVs3WFpaokOHDti8eTNGjx4tP1eXlpZCCNFofS8vL8fVq1cVls+ePRsSiQQrVqzQXUD3aMnYgLvPgPrss89w+vRphc8D7v5WRUREYN68eTq50KsuVk3Jnim5fv16/PTTT0rrNf291jVjY2NkZGQgMzMTHTp0wKBBg/Duu+/Kn5H8OLUrHrQvgLuD4unp6fjggw/wzTffID09XeXzaUeOHInKykp8++23qK6uRnZ2NkJCQloyHAWa9k+8vLyU2kv3qqiogKWlJSwsLNC5c2cUFBSovGi8Zs0aeTobGxsUFxerfWxBa2NgYICUlBTs2bMHnTt3xjvvvKPvIrUpHJwjrSsuLsaRI0fkVxqMjY0RGBioskF5P9kVi9b0oHFVtB2j7GRubm4OV1dXdO7cWeF+fn3SZqxSqRReXl7yH6Aff/wR+/fvR2hoqI5K3zQPE6sqVVVVyMrKgrm5eZsY7GjNNJnd2JQZkM2ZLRkaGgobGxt8+OGHTc7bkoQQCuef6OhoFBYWKvz17dtXjyXUng8//BCZmZk4e/asvovSbI3F0Jx6qqnWUp+1+R2GhIQgJycHly5dQk5Ojl47g/e6d3DNz88PgYGBWLBgAdLS0hAYGAhjY2MAd2cbHTx4UGkwY8iQISgsLMThw4cRHByMqVOnYvz48foIRS11Mcrs378fx48fR0ZGBlxcXLB27VqlbTS1vrdr1w6LFi3C8uXLce3atYcNQa2Wjk3WsTczM8O0adPwxhtvYNasWUrp5s6di6tXr2q10/+gWJvCx8cHzz//vMJz2WR0eW5rqvHjx+PixYvIy8uDr68v9u3bh969eyvNtHqQttCuaGxfyAwdOhQDBgzAq6++CkdHR5XbkV0sSU9PR05ODlxcXPT63GlN+ydZWVlK7aV7tW/fHoWFhTh27BgSExPRu3dvxMfHK33epEmTUFhYiFOnTuHAgQNwdnbGiBEjlF6S0lqlpaXB3NwcZWVlj+zdCa0VB+dI61JTU1FfX48uXbrA2NgYxsbGSElJwdatWx945UfW+HZycmqJojabtmOUncyLiopQXV2Nb7/9ttXMstJ2rKGhodi6dStu3ryJ9PR09OjRA97e3jqNQVMPilX2QFhVcf/5559Ks/+io6MhkUhw6NAh7N69u9U92Lct6dmzJwwMDHDu3Dm1aWTHVGNpZOnOnz+v8ladixcvorKyUuXxaWxsjPj4eKxcubJZLxJpKWfPnlU4Jjt16gRnZ2eFv/tvr3pU/d///R98fHwQExOj76I0m7oYXFxc1A5YyZbL6qmVlZXa8xYAlTOXW0t9Vhe/lZUVqqurFd4+DDQeU69evSCVSjFx4kS4ubm1mpfzyAbXSktLcevWLWRmZqK2tha5ublYs2aN/Peoa9euqK+vVxpssbCwgLOzMzw9PZGWlobDhw83+6KSrqiK8d7ZJE5OTnB1dUVwcDDCwsIQGBgoX+fs7AwDA4NG63vHjh1ha2urtG7y5MlwdHREXFyc9oP6/1o6NlnHvqysDNXV1VixYoXaWz9jYmKwcOFC1NTU6DTW5hyPAJCQkICsrCycPHlSYbmmv9ctRSKRYPjw4Xjvvfdw6NAhTJkyBbGxsY9lu0LdvriX7JzVGNnFkuTk5FZxoUST/om9vb1Se+lehoaGcHZ2hpubG958800MGDBA5cC5tbW1PP+gQYOQmpqK0tJSZGVl6TRGbTh06BCSkpKwY8cO9O/fH6Ghoa1qMP1Rx8E50qr6+nps3LgRiYmJClcVTp06hS5duii8Tep+d+7cwapVq+Dk5IRnn322BUvdNLqIUXYy7969e6vqFOsi1pdffhmGhobYvHkzNm7ciJCQkFYxU1KTWHv27AlDQ0Ol5wWeP38eFRUVCg2rXbt2YcOGDcjMzISnpyfi4uIQGRnZqt9w+Sh74okn4OPjg+TkZJXPF/rzzz8xYsQIdOrUCUuXLlW5DVknIigoCFVVVVi3bp1SmuXLl8PExETtrJSAgAB4eHhg4cKFzQ9Gh/bu3YszZ860ulk1upSQkIDt27fju+++03dRmk1VDEFBQSgtLcX27duV0icmJsLGxgbDhw8HALi6uuK3337D5cuXFdKdOHECEolE7RvyWkt9VhW/q6sr6uvrlWYunDhxAgDUXuAKCQnBvn37WkVnUEY2uObg4CDv0G7atAndunXDqVOnFH6TEhMTkZGRgYaGBpXbMjQ0xLvvvov58+fj1q1bLRlGo1TFqE54eDiKioqQm5sLAPK6vGbNGqWYLl26hE2bNiEwMFBlW8LQ0BBLlixBSkqKzh6Z0tKxyTr2Xbt2VTkod685c+bA0NAQK1eubGZ0itTF2tzjsX///hg3bpzSrXHPPPMM3N3dkZiYqDTgB/z9e60v7u7uqK6uZrsCf++LpvLw8ICHhweKiorwyiuv6KBkTaOL/sk777yDrKws+XGgjuyZdK3pnK1KTU0NpkyZglmzZmHIkCFITU3FkSNHVM4GpuZp/BeEqIl27NiB8vJyhIaGKl0lGz9+PFJTU+Hr6wsAuH79Oi5duoSamhoUFRXho48+wpEjR/Dvf/+7VT80/3GIUUYXsVpaWiIwMBAxMTGorKzElClTWjIktTSJdebMmQgLC0NUVBSMjY3Rq1cv/Prrr5g7dy4GDBgALy8vAEBlZSVCQ0MRHR2Nfv36AQDeeOMN5ObmYvr06So70/TwkpOTMWjQIPTv3x+LFi3C008/jfr6euzatQspKSk4e/YsNmzYgICAAIwePRqvv/46nJ2dce3aNWRnZ+PChQv4/PPPMXDgQERERCA6Ohq3b9+Gv78/6urq8Nlnn2HlypX46KOPYG9vr7YcCQkJ8mdE6VNtbS0uXbqEhoYGXL58GTt37sSSJUswcuRIvPbaa/J0N2/exKVLlxTympuby2eKPup69eqFSZMmYdWqVfouSrOpiiEoKAg5OTkIDg7GsmXL8OKLL6KyshLJycnIy8tDTk6OfPaOj48PXF1dMXHiRMTFxcHOzg4nTpzA/PnzERER0ejvUWuoz6ri9/DwwIgRIxASEoLExER0794dxcXFiIyMRGBgILp27apyW9OmTUNAQECLPVC+uVJTUzFhwgSl2X329vaIiYnBzp078dJLL6nMGxAQgOjoaCQnJ+Ott95qieJqlbm5OaZNm4bY2Fj4+/vDwMAAH3/8Mby8vODj44O4uDg4OTnh+++/R3R0NLp27ary1jGZl156Cc899xzWrVuHzp07t2AkyrQd24NIJBIsXLgQ4eHhWoxCWXOPRwCIj4+Hh4eHwmCfgYEB0tPTMWzYMAwePBjz5s2DVCpFVVUVtm/fjm+++abZzwNuiuvXryMgIAAhISF4+umn0b59exw7dgxLly7FmDFjYGFh8di0Kx60L5pj7969qKuraxXnY036J7K+zr06dOgAiUSicpv29vYYO3Ys3n//fezYsUO+vKamRr6dy5cvY/HixZBIJBgxYoT2AtKBmJgYCCGQkJAAAHjyySexfPlyvPXWW/Dz88OTTz6p3wK2BS3wRlh6jIwcOVL885//VLnu8OHD8tfHA5D/mZubCzc3NzF79mxRWlqqkCc1NVXY2Ni0RNE1pu0YG3v9vL5pO1aZQ4cOCQBqt60PmsZ669YtERsbK6RSqTAzMxNOTk5i+vTp4urVq/L0U6dOFU899ZSora1V2E5JSYkwNzcXmZmZOo3lcXbx4kURHh4uHB0dhampqejatasYPXq0KCgokKc5evSoGDdunLC1tRXt2rUTzs7OYvr06SrPP3369BESiURYWFiIwYMHi7y8PIU0BQUFAoAoLy9XWD5ixAgBQKSnp8uX2dvbi9WrV2s7ZJWCg4Plx6SxsbGwtbUVw4YNE2lpaaKhoUGeztHRUeH4lf3NmDFDaZuOjo4iKSmpRcrfVMHBwWLMmDFK/5YpKysTpqamQl2zB4DIzc1VWj548GARFRWl5dI+mKYx1NXViWXLlgkPDw9hamoqrKyshI+Pjzhw4IDSNn///XcRHBwsHBwchJmZmXB3dxcJCQni9u3b8jRNqc+6pGn85eXl4vXXXxc9evQQZmZmomfPnuLtt98WN2/eVMgHQJw8eVLlZ508eVIAEGVlZTqI5MFUxXrs2DEBQBw5ckRlHj8/PzF27Fi1+YUQYsmSJcLW1lZUVVXJl3l7e4uIiAhtFV1j6soohPo6d+HCBWFsbCyysrLky37++WcRHBwsOnfuLExMTIS9vb2YM2eOuHbtmkJeVXHK2h2Ojo5aiOhvrSG2e6lqU9bX1wt3d3cBQOG3sKkai1WIhzsep0+fLgCI2NhYheXFxcXitddeE126dBGmpqbC0dFRTJw4UZw4cULp83VRv//66y/xzjvviN69ewtra2thbm4uXF1dxfz580VNTY083ePQrtB0Xwih/ruIjY0Vnp6eaj8jIiJCeHt7a7fgTaCufyKrt6r+tmzZIoRQ35/77rvvBABx+PBhIcTdfXNv/o4dOwpvb2+xd+9encf3MPbt2yeMjIzE/v37ldaNGDFCDB06VNy5c0cPJWtbDITgTcLUeiUkJOCzzz5DUVGRvotCRNRsDQ0NsLKyQmZmJiZMmKDv4pCGpFIpwsLCHsnZR0RE1HaxXUHU9vC2VmqVampqcO7cOaSnp8PPz0/fxSEiarbffvsNGzduRENDA55//nl9F4c0cOXKFfznP/9BcXExXnzxRX0Xh4iISI7tCqK2iYNz1CqtX78eixYtwrBhw/D+++/ruzhERM32zDPPwMbGBp9++ins7Oz0XRzSgK+vL8rLy7Fq1apW/YIiIiJ6/LBdQdQ28bZWIiIiIiIiIiIiPWn8/dtERERERERERESkMxycIyIiIiIiIiIi0hMOzhEREREREREREekJB+eIiIiIiIiIiIj0hINzREREREREREREesLBOSIiIiIiIiIiIj3h4BwRERFRGzVlyhQYGBjAwMAApqamcHZ2xqJFi1BfXy9P09DQgKSkJPTq1QsSiQQdO3aEn58fDh48qLCthoYGJCQkQCqVwszMDE888QSee+45bNiwQe3nZ2RkoEOHDroKj4iIiKhNMNZ3AYiIiIhId3x9fZGeno7a2lp8/fXXCA8Ph4mJCWJiYiCEQFBQEHbv3o1ly5bhxRdfRGVlJZKTk/HCCy8gJycH/v7+AICFCxdi3bp1+Pjjj9G3b19UVlbi2LFjKC8v12+ARERERI84zpwjIiIiasPatWsHOzs7ODo6YtasWRg2bBjy8vIAANnZ2fjiiy+wceNGhIWFwcnJCZ6enli/fj1Gjx6NsLAwVFdXAwDy8vIwe/ZsBAQEyNOFhobirbfeUvm5+/btw9SpU1FRUSGfvbdgwQIAwKeffoq+ffuiffv2sLOzwyuvvIIrV64o5M/Ly0PPnj0hkUgwZMgQZGZmwsDAAH/++ScA4JdffsGoUaPQsWNHWFhYwMPDA19//bVudiIRERGRDnFwjoiIiOgxYmZmhtu3bwMANm/eDBcXF4waNUopXVRUFK5fv45du3YBAOzs7LB3715cvXpVo8/x8vLCRx99BCsrK/zxxx/4448/5AN5dXV1WLx4MU6dOoUvv/wSP//8M6ZMmSLPW1ZWhgkTJsDf3x+nTp3CjBkzMG/ePIXth4eHo7a2Ft9++y3OnDmDDz/8EJaWls3ZJURERER6xdtaiYiIiB4DQgjs2bMH+fn5mDNnDgCgpKQEbm5uKtPLlpeUlAAAVqxYgQkTJsDOzg4eHh7w8vLCmDFj4OfnpzK/qakprK2tYWBgADs7O4V1ISEh8n93794dq1atQr9+/VBVVQVLS0usW7cOrq6uWLZsGQDA1dUVRUVFiI+Pl+e7cOECxo8fj169esm3Q0RERPQo4sw5IiIiojZsx44dsLS0hEQigZ+fHwIDA+W3lwJ3B+004e7ujqKiIvzvf/9DSEgIrly5glGjRiEsLKzJZTp+/DhGjRoFBwcHtG/fHt7e3gDuDrgBQHFxMfr166eQp3///gr/f/311xEXF4dBgwYhNjYWp0+fbnI5iIiIiFoDDs4RERERtWFDhgxBYWEhSktLcevWLWRmZsLCwgIA4OLigrNnz6rMJ1vu4uIiX2ZoaIh+/fohMjIS27ZtQ0ZGBlJTU1FWVqZxeaqrq+Hj4wMrKyts2rQJR48eRW5uLgDIb7fVRFhYGM6fP49XX30VZ86cQd++fbF69WqN8xMRERG1FhycIyIiImrDLCws4OzsDAcHBxgbKz7RJCgoCKWlpdi+fbtSvsTERNjY2GD48OFqt+3u7g4A8pdG3M/U1BQNDQ0Ky86dO4fr168jISEBgwcPhlQqVXoZhKurK44dO6aw7OjRo0rbt7e3x8yZM7Ft2zZERUXhk08+UVtWIiIiotaKg3NEREREj6mgoCCMHTsWwcHBSE1Nxc8//4zTp09jxowZyMvLw4YNG+Sz7CZMmICkpCQcPnwYv/zyC/bt24fw8HC4uLhAKpWq3P6TTz6Jqqoq7NmzB9euXUNNTQ0cHBxgamqK1atX4/z588jLy8PixYsV8s2YMQPnzp3D3LlzUVJSguzsbGRkZAAADAwMAACRkZHIz89HWVkZTpw4gYKCArXPzyMiIiJqzTg4R0RERPSYMjAwQHZ2Nt59910kJSXB1dUVgwcPlg+++fv7y9P6+Phg+/btGDVqFFxcXBAcHAypVIpvvvlGaUaejJeXF2bOnInAwEDY2tpi6dKlsLW1RUZGBnJycuDu7o6EhAQsX75cIZ+TkxO++OILbNu2DU8//TRSUlLkb2tt164dAKChoQHh4eFwc3ODr68vXFxcsGbNGt3sKCIiIiIdMhCaPgWYiIiIiEhP4uPjsXbtWvz666/6LgoRERGRVqm+zElEREREpEdr1qxBv379YGNjg4MHD2LZsmX417/+pe9iEREREWkdB+eIiIiIqNUpLS1FXFwcbty4AQcHB0RFRSEmJkbfxSIiIiLSOt7WSkREREREREREpCd8IQQREREREREREZGecHCOiIiIiIiIiIhITzg4R0REREREREREpCccnCMiIiIiIiIiItITDs4RERERERERERHpCQfniIiIiIiIiIiI9ISDc0RERERERERERHrCwTkiIiIiIiIiIiI9+X+ULCThvdco3wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1500x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# POS frequencies in the vocabulary\n",
    "\n",
    "keys_pos = [\"ADJ\", \"ADP\", \"ADV\", \"AUX\", \"\", \"CCONJ\", \"DET\", \"INTJ\", \"NOUN\", \"NUM\", \"PART\", \"PRON\", \"PROPN\", \"PUNCT\", \"SCONJ\", \"SYM\", \"VERB\", \"X\"]\n",
    "values_pos = list(sorted_pos.values())\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(15, 10))\n",
    "ax.bar(keys_pos, values_pos)\n",
    "\n",
    "# Add labels and title\n",
    "ax.set_xlabel('POS tags')\n",
    "ax.set_ylabel('Frequency')\n",
    "ax.set_title('POS Frequencies in the Vocabulary')\n",
    "\n",
    "# Show the plot\n",
    "ax.grid(alpha=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 401
    },
    "id": "0LFSRKfzwZjm",
    "outputId": "0eaaef87-5df6-4f6c-c0d2-344613155a6a"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2500x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sentence length distribution\n",
    "lengths = list(len_sentence.values())\n",
    "frequency = collections.Counter(lengths)\n",
    "\n",
    "sorted_freq = sorted(frequency.items(), key=lambda x: x[1], reverse=True)\n",
    "#top_50_l = sorted_freq_l[:50]\n",
    "\n",
    "keys = [pair[0] for pair in sorted_freq]\n",
    "values = [pair[1] for pair in sorted_freq]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(25, 6))\n",
    "ax.bar(keys, values)\n",
    "\n",
    "# Add labels and title\n",
    "ax.set_xlabel('Sentence length')\n",
    "ax.set_ylabel('Frequency')\n",
    "ax.set_title('Sentence length distribution')\n",
    "\n",
    "# Show the plot\n",
    "ax.grid(alpha=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6J-UGfCo4p1e"
   },
   "source": [
    "## **BiLSTM and MLP for Neural Dependency Parsing**\n",
    "\n",
    "In the first part of project, we augmented the parser with a Bidirectional Long Short-Term Memory (BiLSTM) model and a Multi-Layer Perceptron (MLP) to enhance the dependency parsing capabilities of the parser.\n",
    "\n",
    "### **BiLSTM: Capturing Contextual Information**\n",
    "A BiLSTM is a type of recurrent neural network (RNN) that can capture sequential dependencies in input data. It consists of two LSTM (Long Short-Term Memory) layers: one processes the input sequence in the forward direction, and the other processes it in the backward direction. The output of each LSTM layer at each time step is given by:\n",
    "\n",
    "* Forward LSTM: $h_f(t) = LSTM_f(x(t), h_f(t-1))$\n",
    "\n",
    "* Backward LSTM: $h_b(t) = LSTM_b(x(t), h_b(t+1))$\n",
    "\n",
    "Here, $x(t)$ represents the input at time step $t$, $h_f(t)$ denotes the hidden state of the forward LSTM, and $h_b(t)$ denotes the hidden state of the backward LSTM.\n",
    "\n",
    "In the context of neural dependency parsing, the BiLSTM serves as a contextual encoder, allowing us to capture the contextual information from input sentence. By utilizing two LSTM layers, one in the forward direction and the other in the backward direction, the BiLSTM can effectively model the dependencies between words. The hidden states from both directions are concatenated to provide comprehensive representations that consider the preceding and succeeding words:\n",
    "\n",
    "$h(t) = [h_f(t); h_b(t)]$\n",
    "\n",
    "where $[;]$ denotes the concatenation operation.\n",
    "\n",
    "### **MLP: Transition Evaluation based on Features**\n",
    "The MLP, also known as a Multi-Layer Perceptron, is a feedforward neural network composed of interconnected nodes or neurons. It is designed to learn non-linear mappings between inputs and outputs.\n",
    "\n",
    "The MLP acts as the decision-making component of the parser. It takes as input various features, including representations of the top-most token from the stack and the first token in the buffer, which capture the essential information about the current parsing state. The MLP learns to map these input features to scores for each possible transition, aiding in the decision-making process.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "9MYiXYSxW1-H"
   },
   "source": [
    "#### Data preparation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Z3FxlGC9eGrY"
   },
   "source": [
    "Firstly, we define a function to remove non-projective trees. Additionally, we create a dictionary of word/index pairs to be used later when generating word embeddings. Words with fewer than three occurrences are not encoded and will be mapped to the special token `<unk>`.\n",
    "\n",
    "In the word/index dictionary, the special tokens `<pad>`, `<ROOT>` and `<unk>` are indexed as 0, 1, and 2, respectively.\n",
    "\n",
    "Furthermore, a function is provided to preprocess the data by removing tokens associated with `None` heads."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "SX1Wbw2w5Goz"
   },
   "outputs": [],
   "source": [
    "# the function returns whether a tree is projective or not. It is currently\n",
    "# implemented inefficiently by brute checking every pair of arcs.\n",
    "def is_projective(tree):\n",
    "  for i in range(len(tree)):\n",
    "    if tree[i] == -1:\n",
    "      continue\n",
    "    left = min(i, tree[i])\n",
    "    right = max(i, tree[i])\n",
    "\n",
    "    for j in range(0, left):\n",
    "      if tree[j] > left and tree[j] < right:\n",
    "        return False\n",
    "    for j in range(left+1, right):\n",
    "      if tree[j] < left or tree[j] > right:\n",
    "        return False\n",
    "    for j in range(right+1, len(tree)):\n",
    "      if tree[j] > left and tree[j] < right:\n",
    "        return False\n",
    "\n",
    "  return True\n",
    "\n",
    "# the function creates a dictionary of word/index pairs: our embeddings vocabulary\n",
    "# threshold is the minimum number of appearance for a token to be included in the embedding list\n",
    "def create_dict(dataset, threshold=3):\n",
    "  dic = {}  # dictionary of word counts\n",
    "  for sample in dataset:\n",
    "    for word in sample['tokens']:\n",
    "      if word in dic:\n",
    "        dic[word] += 1\n",
    "      else:\n",
    "        dic[word] = 1\n",
    "\n",
    "  map = {}  # dictionary of word/index pairs. This is our embedding list\n",
    "  map[\"<pad>\"] = 0\n",
    "  map[\"<ROOT>\"] = 1\n",
    "  map[\"<unk>\"] = 2 #used for words that do not appear in our list\n",
    "\n",
    "  next_indx = 3\n",
    "  for word in dic.keys():\n",
    "    if dic[word] >= threshold:\n",
    "      map[word] = next_indx\n",
    "      next_indx += 1\n",
    "\n",
    "  return map\n",
    "\n",
    "def remove_None(examples):\n",
    "    new_head = []\n",
    "    new_tokens = []\n",
    "\n",
    "    for i, sample in enumerate(examples[\"head\"]):\n",
    "        if sample != \"None\":\n",
    "            new_head.append(sample)\n",
    "            new_tokens.append(examples[\"tokens\"][i])\n",
    "\n",
    "    examples[\"head\"] = new_head\n",
    "    examples[\"tokens\"] = new_tokens\n",
    "    return examples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "VZ-N9t3GFM5W"
   },
   "source": [
    "The next function is responsible for processing our data and generating the actual training samples.\n",
    "\n",
    "For each sentence in the dataset, we utilize the oracle to compute the canonical action sequence that leads to the gold tree. Subsequently, we pair the configurations with their corresponding canonical actions. Since our neural classifier only considers $\\sigma_m$ and $\\beta_0$, it is unnecessary to record the complete parser configuration.\n",
    "\n",
    "The function returns a processed version of the input sample, which includes the encoded batch of all samples, the gold configurations ($\\sigma_m$, $\\beta_0$) for each sentence, the gold moves for each step in the golden parsing process, and the final golden configuration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "b1ogbuYz-4IX"
   },
   "outputs": [],
   "source": [
    "def process_sample(sample, get_gold_path = False):\n",
    "\n",
    "  # put sentence and gold tree in our format\n",
    "  sentence = [\"<ROOT>\"] + sample[\"tokens\"]\n",
    "  gold = [-1] + [int(i) for i in sample[\"head\"]]  #heads in the gold tree are strings, we convert them to int\n",
    "\n",
    "  # embedding ids of sentence words\n",
    "  enc_sentence = [emb_dictionary[word] if word in emb_dictionary else emb_dictionary[\"<unk>\"] for word in sentence]\n",
    "\n",
    "  # gold_path and gold_moves are parallel arrays whose elements refer to parsing steps\n",
    "  gold_path = []   # record two topmost stack tokens and first buffer token for current step\n",
    "  gold_moves = []  # contains oracle (canonical) move for current step: 0 is left, 1 right, 3 shift, 2 reduce\n",
    "\n",
    "  if get_gold_path:  # only for training\n",
    "    parser = ArcEager(sentence)\n",
    "    oracle = Oracle(parser, gold)\n",
    "\n",
    "    while not parser.is_tree_final():\n",
    "\n",
    "      # save configuration\n",
    "      configuration = [parser.stack[len(parser.stack)-1]]\n",
    "      if len(parser.buffer) == 0:\n",
    "        configuration.append(-1)\n",
    "      else:\n",
    "        configuration.append(parser.buffer[0])\n",
    "      gold_path.append(configuration)\n",
    "\n",
    "      # save gold move\n",
    "      if oracle.is_left_arc_gold():\n",
    "        gold_moves.append(0)\n",
    "        parser.left_arc()\n",
    "      elif oracle.is_right_arc_gold():\n",
    "        parser.right_arc()\n",
    "        gold_moves.append(1)\n",
    "      elif oracle.is_shift_gold():\n",
    "        parser.shift()\n",
    "        gold_moves.append(2)\n",
    "      elif oracle.is_reduce_gold():\n",
    "        parser.reduce()\n",
    "        gold_moves.append(3)\n",
    "\n",
    "  return enc_sentence, gold_path, gold_moves, gold"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "KxbnXRwJ-93d"
   },
   "source": [
    "Next function used to batch the training data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "5uhOyPuj-t1c"
   },
   "outputs": [],
   "source": [
    "def prepare_batch(batch_data, get_gold_path=False):\n",
    "  data = [process_sample(s, get_gold_path=get_gold_path) for s in batch_data]\n",
    "  # sentences, paths, moves, trees are parallel arrays, each element refers to a sentence\n",
    "  sentences = [s[0] for s in data]\n",
    "  paths = [s[1] for s in data]\n",
    "  moves = [s[2] for s in data]\n",
    "  trees = [s[3] for s in data]\n",
    "  return sentences, paths, moves, trees"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "W20DIPzkOjMW"
   },
   "source": [
    "During the model training, we exclusively focus on non-projective trees. In order to maintain consistency, we also eliminate non-projective trees from the evaluation and test datasets. However, after training, the model will be tested on data containing non-projective trees as well, allowing for a comprehensive comparison of the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "BSY8aixm-Aj2",
    "outputId": "f972e66e-4ebd-4406-8670-49e22de92971"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:datasets.builder:Found cached dataset universal_dependencies (/root/.cache/huggingface/datasets/universal_dependencies/en_ewt/2.7.0/1ac001f0e8a0021f19388e810c94599f3ac13cc45d6b5b8c69f7847b2188bdf7)\n",
      "WARNING:datasets.builder:Found cached dataset universal_dependencies (/root/.cache/huggingface/datasets/universal_dependencies/en_ewt/2.7.0/1ac001f0e8a0021f19388e810c94599f3ac13cc45d6b5b8c69f7847b2188bdf7)\n",
      "WARNING:datasets.builder:Found cached dataset universal_dependencies (/root/.cache/huggingface/datasets/universal_dependencies/en_ewt/2.7.0/1ac001f0e8a0021f19388e810c94599f3ac13cc45d6b5b8c69f7847b2188bdf7)\n"
     ]
    }
   ],
   "source": [
    "train_dataset = load_dataset('universal_dependencies', 'en_ewt', split=\"train\")\n",
    "dev_dataset = load_dataset('universal_dependencies', 'en_ewt', split=\"validation\")\n",
    "test_dataset = load_dataset('universal_dependencies', 'en_ewt', split=\"test\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 17,
     "referenced_widgets": [
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      "904d29eec0234e1580300ad3a90311ff",
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      "9d0881114f39420fb6e3906161c0c560",
      "e36e05f32f574333a8898e727d0d7fae",
      "e1e6fd5eb62f41e485b22aa158364725",
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    },
    "id": "U4qZf_1fM2mI",
    "outputId": "061d911c-ea87-4ec3-f67c-984e97365e58"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6a1025ed34ca4225a4969aa47122ad62",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Map:   0%|          | 0/12543 [00:00<?, ? examples/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e1e6fd5eb62f41e485b22aa158364725",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Map:   0%|          | 0/2002 [00:00<?, ? examples/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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       "Map:   0%|          | 0/2077 [00:00<?, ? examples/s]"
      ]
     },
     "metadata": {},
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    }
   ],
   "source": [
    "train_dataset = train_dataset.map(remove_None, batched=False)\n",
    "dev_dataset = dev_dataset.map(remove_None, batched=False)\n",
    "test_dataset = test_dataset.map(remove_None, batched=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "lu_feq9hfuYM",
    "outputId": "b3d70a0b-ae05-4949-f02e-41fb4eafe34a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of samples:\n",
      "Train:\t 11887\n",
      "Dev:\t 1947\n",
      "Test:\t 2023\n"
     ]
    }
   ],
   "source": [
    "# remove non-projective sentences: heads in the gold tree are strings, we convert them to int\n",
    "train_dataset = [sample for sample in train_dataset if is_projective([-1] + [int(head) for head in sample[\"head\"]])]\n",
    "dev_dataset = [sample for sample in dev_dataset if is_projective([-1] + [int(head) for head in sample[\"head\"]])]\n",
    "test_dataset = [sample for sample in test_dataset if is_projective([-1] + [int(head) for head in sample[\"head\"]])]\n",
    "\n",
    "# create the embedding dictionary\n",
    "emb_dictionary = create_dict(train_dataset)\n",
    "\n",
    "print(\"Number of samples:\")\n",
    "print(\"Train:\\t\", len(train_dataset)) #(train is the number of samples without the non-projective)\n",
    "print(\"Dev:\\t\", len(dev_dataset))\n",
    "print(\"Test:\\t\", len(test_dataset))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "nue1YPrTfGXw"
   },
   "source": [
    "### **Model implementation**\n",
    "The model implemented in the `Net` class follows this structure:\n",
    "1. The embedding layer, BiLSTM, and MLP layer are initialized.\n",
    "2. The input sentences given to the model are transformed using the embedding layer, and dropout is applied.\n",
    "3. The created embeddings are packed and fed into the BiLSTM.\n",
    "4. The model's output, which contains a concatenation of the forward and reverse hidden states at each time step in the sequence, is unpacked and returned with a size of $h$: `(len(sentences), batch, output_{hidden-units})`;\n",
    "5. The input for the MLP is prepared by concatenating, for each possible true configuration $(\\sigma_m, \\beta_0)$ (where $m$ is the stack size):\n",
    "  * the `output_{hidden-units}` identified by the first element in the given configuration `[j[0]]` and the index of the batch `[i]`, or a zero tensor if `[j[0]] = -1`  \n",
    "  * the `output_{hidden-units}` identified by the second element in the given configuration `[j[1]]` and the index of the batch `[i]`, or a zero tensor if `[j[1]] = -1`  \n",
    "6. The prepared tensor is passed into the MLP model, where it goes through the following layers:\n",
    "\n",
    "<center>\n",
    "\n",
    "| Layer   | input | output |\n",
    "| ------- | ----- | ------ |\n",
    "| dropout | `4 x LSTM_SIZE` | `4 x LSTM_SIZE` |\n",
    "| linear layer | `4 x LSTM_SIZE`| `MLP_SIZE` |\n",
    "| $\\tanh$ | `MLP_SIZE` | `MLP_SIZE` |\n",
    "| linear layer | `MLP_SIZE` | $4$ |\n",
    "| $softmax$ | $4$ | $4$ |\n",
    "\n",
    "</center>\n",
    "\n",
    "The final number of outputs, 4, is chosen to cover the four possible ArcEager transitions, and softmax is used to produce probabilities.\n",
    "7. To test the obtained results, the parser configurations for each sentence in the batch from the evaluation set are initialized using ArcEager. Then, the sentences are prepared and passed through the BiLSTM network.\n",
    "8. For each obtained parser in the batch, the configurations are created, and the input for the MLP is prepared following the method described in point 5. These inputs are then passed through the MLP model, returning probabilities for each ArcEager transition for each parser.\n",
    "9. The `parse_step()` function is called to perform the chosen transition on the parser configuration. This process described in points 8 and 9 continues until all the dependency trees created from the batch have reached the final configuration, i.e., only `<ROOT>` remains in the stack, and the buffer is empty.\n",
    "10. In the mentioned function, various conditions are taken into consideration to avoid getting the configuration stuck and enable reaching the final configuration. Sometimes, the `parse_step()` function performs a different action than the suggested one. This can be the second most suggested action or a specific action in case there is only one possibility for the current parser configuration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "zwsgidl04fzP"
   },
   "outputs": [],
   "source": [
    "class Net(nn.Module):\n",
    "\n",
    "  def __init__(self, device, EMBEDDING_SIZE, DROPOUT, LSTM_LAYERS, LSTM_SIZE):\n",
    "    ''' __init__ function initialize both the biLSTM and the MLP\n",
    "    Parameters\n",
    "    device: device (CPU or GPU) on which the model will be executed.\n",
    "    EMBEDDING_SIZE: size of the word embeddings\n",
    "    DROPOUT: dropout rate, which add regulatization in order to prevent overfitting\n",
    "    LSTM_LAYERS: number of LSTM layers in the bidirectional LSTM model.\n",
    "    LSTM_SIZE: size of the LSTM hidden state\n",
    "    '''\n",
    "    super(Net, self).__init__()\n",
    "\n",
    "    # input parameters are collected by Net\n",
    "    self.device = device\n",
    "    self.EMBEDDING_SIZE = EMBEDDING_SIZE\n",
    "    self.DROPOUT = DROPOUT\n",
    "    self.LSTM_LAYERS = LSTM_LAYERS\n",
    "    self.LSTM_SIZE = EMBEDDING_SIZE\n",
    "\n",
    "    # initialize embedding layer\n",
    "    self.embeddings = nn.Embedding(len(emb_dictionary), self.EMBEDDING_SIZE, padding_idx=emb_dictionary[\"<pad>\"])\n",
    "\n",
    "    # initialize bi-LSTM\n",
    "    self.lstm = nn.LSTM(self.EMBEDDING_SIZE, self.LSTM_SIZE, num_layers=self.LSTM_LAYERS, bidirectional=True, dropout=self.DROPOUT)\n",
    "\n",
    "    # initialize feedforward MLP\n",
    "    self.w1 = torch.nn.Linear(4 * self.LSTM_SIZE, MLP_SIZE, bias=True) # input size: 1 biLSTM layer (2 LSTM layers) x 2 configuration size x LSTM_SIZE, output size: MLP_SIZE\n",
    "    self.activation = torch.nn.Tanh()\n",
    "    self.w2 = torch.nn.Linear(MLP_SIZE, 4, bias=True)  # input size: LSTM_SIZE, output size: 4 transitions\n",
    "    self.softmax = torch.nn.Softmax(dim=-1)\n",
    "\n",
    "    self.dropout = torch.nn.Dropout(self.DROPOUT)\n",
    "\n",
    "  def forward(self, x, paths):\n",
    "    ''' forward function defines the forward pass of the model.\n",
    "    Parameters\n",
    "    x: input sentences tokenized\n",
    "    paths: given configurations\n",
    "    '''\n",
    "\n",
    "    # get the embeddings\n",
    "    x = [self.dropout(self.embeddings(torch.tensor(i).to(self.device))) for i in x]\n",
    "\n",
    "    # run the bi-lstm\n",
    "    h = self.lstm_pass(x)\n",
    "\n",
    "    # for each parser configuration that we need to score we arrange from the\n",
    "    # output of the bi-lstm the correct input for the feedforward\n",
    "    mlp_input = self.get_mlp_input(paths, h)\n",
    "\n",
    "    # run the feedforward and get the scores for each possible action\n",
    "    out = self.mlp(mlp_input)\n",
    "\n",
    "    return out\n",
    "\n",
    "  def lstm_pass(self, x):\n",
    "    ''' lstm_pass function packs the input sentence to pass it through the biLSTM and then unpack the output to obtain the hidden states\n",
    "    Parameters\n",
    "    x: input sentences tokenized\n",
    "    '''\n",
    "    x = torch.nn.utils.rnn.pack_sequence(x, enforce_sorted=False)\n",
    "    h, (h_0, c_0) = self.lstm(x)\n",
    "\n",
    "    # packed output is unpacked\n",
    "    h, h_sizes = torch.nn.utils.rnn.pad_packed_sequence(h)  # size h: (length_sentences, batch, output_hidden_units)\n",
    "    return h\n",
    "\n",
    "  def get_mlp_input(self, configurations, h):\n",
    "    ''' get_mlp_input function constructs the input tensor for the MLP using the information obtained by the biLSTM\n",
    "    Parameters\n",
    "    configurations: given configurations\n",
    "    h: hidden states obtained from the biLSTM, aka the contextual information retrieved by the net\n",
    "    '''\n",
    "    mlp_input = []\n",
    "    zero_tensor = torch.zeros(2 * self.LSTM_SIZE, requires_grad=False).to(self.device)\n",
    "    for i in range(len(configurations)):\n",
    "        for j in configurations[i]:  # for each configuration of a sentence\n",
    "            mlp_input.append(\n",
    "                torch.cat([zero_tensor if j[0] == -1 else h[j[0]][i], zero_tensor if j[1] == -1 else h[j[1]][i]]))\n",
    "    mlp_input = torch.stack(mlp_input).to(self.device)\n",
    "    return mlp_input\n",
    "\n",
    "  def mlp(self, x):\n",
    "    ''' mlp function applies the feedforward network to the input tensor x, obtaining the final output probabilities using the softmax function.\n",
    "    Parameters\n",
    "    x: mlp_input, a tensor prepared using get_mlp_input function\n",
    "    '''\n",
    "    return self.softmax(self.w2(self.dropout(self.activation(self.w1(self.dropout(x))))))\n",
    "\n",
    "  def infere(self, x):\n",
    "    ''' infer function performs the inference process using the trained model and returns the predicted dependency trees\n",
    "    Parameters\n",
    "    x: input sentences tokenized\n",
    "    '''\n",
    "    parsers = [ArcEager(i) for i in x]\n",
    "\n",
    "    x = [self.embeddings(torch.tensor(i).to(self.device)) for i in x]\n",
    "\n",
    "    # retrive the current contextual information given by the net\n",
    "    h = self.lstm_pass(x)\n",
    "\n",
    "    while not self.parsed_all(parsers):\n",
    "        # get the current configuration and score next moves\n",
    "        configurations = self.get_configurations(parsers)\n",
    "        # prepare the mlp_input and fed it into the MLP\n",
    "        mlp_input = self.get_mlp_input(configurations, h)\n",
    "        mlp_out = self.mlp(mlp_input)\n",
    "        # take the next parsing step based on the scores returned by the MLP\n",
    "        self.parse_step(parsers, mlp_out)\n",
    "\n",
    "    # return the predicted dependency tree\n",
    "    return [parser.arcs for parser in parsers]\n",
    "\n",
    "  def get_configurations(self, parsers):\n",
    "    ''' get_configurations function returns the configurations for each parser in a batch.\n",
    "    Since we are considering ArcEager, the transitions involves only the state of the topmost element in the stack and the first element in the buffer, therefore only these two are considered.\n",
    "    Parameters\n",
    "    parsers: parsers configuration given by ArcEager over input sentences\n",
    "    '''\n",
    "    configurations = []\n",
    "\n",
    "    for parser in parsers:\n",
    "        if parser.is_tree_final():\n",
    "            conf = [-1, -1]\n",
    "        else:\n",
    "            conf = [parser.stack[-1]]\n",
    "            if len(parser.buffer) == 0:\n",
    "                conf.append(-1)\n",
    "            else:\n",
    "                conf.append(parser.buffer[0])\n",
    "        configurations.append([conf])\n",
    "\n",
    "    return configurations\n",
    "\n",
    "  def parsed_all(self, parsers):\n",
    "    ''' parsed_all function is used to check if all the parser configurations in the batch have reached the final configuration.\n",
    "    Parameters\n",
    "    parsers: parsers configuration given by ArcEager over input sentences and processed using parse_step function\n",
    "    '''\n",
    "    for parser in parsers:\n",
    "        if not parser.is_tree_final():\n",
    "            return False\n",
    "    return True\n",
    "\n",
    "  def parse_step(self, parsers, moves):\n",
    "      ''' parse_step function performs the suggested move by the MLP taking into considerations the contraints given by ArcEager.\n",
    "      In fact, in order to perform the suggested move we must be sure to not be in some peculiar situation, for example if the buffer has only one element and we perform\n",
    "      a shift or a right-arc we risk to empty it without having completed the parsing process, that in this case will be stuck and could not reach the wanted final configuration.\n",
    "      The function addresses all possible cases for each suggested move, making the correct decision in problematic scenarios or choosing the second most suggested move\n",
    "      in case of indecision.\n",
    "      Parameters\n",
    "      parsers:  parsers configuration given by ArcEager over input sentences and processed using parse_step function\n",
    "      moves: scores obtained from MLP\n",
    "      '''\n",
    "      moves_argm = moves.argmax(-1)\n",
    "\n",
    "      for i in range(len(parsers)):\n",
    "        if parsers[i].is_tree_final():\n",
    "          continue\n",
    "        else:\n",
    "          if moves_argm[i] == 0:\n",
    "            if len(parsers[i].stack) > 1:\n",
    "              parsers[i].left_arc()\n",
    "            else:\n",
    "              if len(parsers[i].buffer) == 1:\n",
    "                if parsers[i].arcs[parsers[i].buffer[0]] == -1:\n",
    "                  parsers[i].right_arc()\n",
    "                else:\n",
    "                  parsers[i].shift()\n",
    "              elif len(parsers[i].buffer) > 1:\n",
    "                if parsers[i].arcs[parsers[i].buffer[0]] != -1:\n",
    "                  parsers[i].shift()\n",
    "                else: # we perform the second suggested move\n",
    "                  if (moves[i][1] > moves[i][2]):\n",
    "                    parsers[i].right_arc()\n",
    "                  elif (moves[i][2] > moves[i][1]):\n",
    "                    parsers[i].shift()\n",
    "\n",
    "          elif moves_argm[i] == 1:\n",
    "            if len(parsers[i].buffer) > 0:\n",
    "              if len(parsers[i].buffer) != 1:\n",
    "                parsers[i].right_arc()\n",
    "\n",
    "              else:\n",
    "                if (parsers[i].arcs[parsers[i].stack[-1]] != -1 and parsers[i].arcs[parsers[i].buffer[0]] != -1): # case: both topmost in the stack and element in the buffer have a head\n",
    "                  arcs_of_stack = [parsers[i].arcs[j] for j in parsers[i].stack] # list of all the arcs of the elements in the stack\n",
    "                  if (-1 not in arcs_of_stack[1:]): # if all the elements in the stack have a head we can do shift\n",
    "                    parsers[i].shift()\n",
    "                  else: # if there are elements in the stack that don't have a head, let's do reduce so the buffer is not empty\n",
    "                    parsers[i].reduce()\n",
    "                elif (parsers[i].arcs[parsers[i].buffer[0]] != -1 and len(parsers[i].stack)==1): # case: only root in the stack and 1 element in the buffer WITH head\n",
    "                  parsers[i].shift()\n",
    "                elif (parsers[i].arcs[parsers[i].buffer[0]] == -1 and len(parsers[i].stack)==1): # case: only root in the stack abd 1 element in the buffer WITHOUT head\n",
    "                  parsers[i].right_arc()\n",
    "                elif (parsers[i].arcs[parsers[i].stack[-1]] != -1 and parsers[i].arcs[parsers[i].buffer[0]] == -1 and len(parsers[i].stack)>1): # case: topmost element in the stack WITH head and one element in the buffer WITHOUT head\n",
    "                  arcs_of_stack = [parsers[i].arcs[j] for j in parsers[i].stack] # list of all the arcs of the elements in the stack\n",
    "                  if (-1 not in arcs_of_stack[1:]): # if all the elements in the stack have a head we can do rightarc (that do also a shift)\n",
    "                    parsers[i].right_arc()\n",
    "                  else: # if there are elements in the stack that don't have a head, let's do reduce so the buffer is not empty\n",
    "                    parsers[i].reduce()\n",
    "                elif (parsers[i].arcs[parsers[i].stack[-1]] == -1 and parsers[i].arcs[parsers[i].buffer[0]] != -1): # case: topmost element in the stack don't have a root but the only element in the buffer has it --> leftarc\n",
    "                    parsers[i].left_arc()\n",
    "                elif (parsers[i].arcs[parsers[i].stack[-1]] == -1 and parsers[i].arcs[parsers[i].buffer[0]] == -1): # case: both topmost element in the stack and first in the buffer don't have a head\n",
    "                    parsers[i].left_arc()\n",
    "            else:\n",
    "              if parsers[i].arcs[parsers[i].stack[-1]] != -1:\n",
    "                parsers[i].reduce()\n",
    "          elif moves_argm[i] == 2:\n",
    "            if len(parsers[i].buffer) > 0:\n",
    "              if len(parsers[i].buffer) != 1:\n",
    "                parsers[i].shift()\n",
    "              else:\n",
    "                if (parsers[i].arcs[parsers[i].stack[-1]] != -1 and parsers[i].arcs[parsers[i].buffer[0]] != -1): # case: both topmost in the stack and element in the buffer have a head\n",
    "                  arcs_of_stack = [parsers[i].arcs[j] for j in parsers[i].stack] # list of all the arcs of the elements in the stack\n",
    "                  if (-1 not in arcs_of_stack[1:]): # if all the elements in the stack have a head we can do shift\n",
    "                    parsers[i].shift()\n",
    "                  else: # if there are elements in the stack that don't have a head, let's do reduce so the buffer is not empty\n",
    "                    parsers[i].reduce()\n",
    "                elif (parsers[i].arcs[parsers[i].buffer[0]] != -1 and len(parsers[i].stack)==1): # case: only root in the stack and 1 element in the buffer WITH head\n",
    "                  parsers[i].shift()\n",
    "                elif (parsers[i].arcs[parsers[i].buffer[0]] == -1 and len(parsers[i].stack)==1): # case: only root in the stack abd 1 element in the buffer WITHOUT head\n",
    "                  parsers[i].right_arc()\n",
    "                elif (parsers[i].arcs[parsers[i].stack[-1]] != -1 and parsers[i].arcs[parsers[i].buffer[0]] == -1 and len(parsers[i].stack)>1): # case: topmost element in the stack WITH head and one element in the buffer WITHOUT head\n",
    "                  arcs_of_stack = [parsers[i].arcs[j] for j in parsers[i].stack] # list of all the arcs of the elements in the stack\n",
    "                  if (-1 not in arcs_of_stack[1:]): # if all the elements in the stack have a head we can do rightarc (that do also a shift)\n",
    "                    parsers[i].right_arc()\n",
    "                  else: # if there are elements in the stack that don't have a head, let's do reduce so the buffer is not empty\n",
    "                    parsers[i].reduce()\n",
    "                elif (parsers[i].arcs[parsers[i].stack[-1]] == -1 and parsers[i].arcs[parsers[i].buffer[0]] != -1): # case: topmost element in the stack don't have a root but the only element in the buffer has it --> leftarc\n",
    "                    parsers[i].left_arc()\n",
    "                elif (parsers[i].arcs[parsers[i].stack[-1]] == -1 and parsers[i].arcs[parsers[i].buffer[0]] == -1): # case: both topmost element in the stack and first in the buffer don't have a head\n",
    "                    parsers[i].left_arc()\n",
    "            else:\n",
    "              if parsers[i].arcs[parsers[i].stack[-1]] != -1:\n",
    "                parsers[i].reduce()\n",
    "          elif moves_argm[i] == 3:\n",
    "            if parsers[i].arcs[parsers[i].stack[-1]] != -1:\n",
    "              parsers[i].reduce()\n",
    "            else:\n",
    "              if len(parsers[i].buffer) == 1: # case: there's only one element in the buffer and the topmost in the stack doesn't have a root ---> leftarc\n",
    "                if len(parsers[i].stack) > 1:\n",
    "                  parsers[i].left_arc()\n",
    "                else:\n",
    "                  parsers[i].right_arc()\n",
    "              else: # we perform the second suggested move\n",
    "                if (moves[i][0] > moves[i][1] and moves[i][0] > moves[i][2]):\n",
    "                  if len(parsers[i].stack) > 1:\n",
    "                    parsers[i].left_arc()\n",
    "                  else:\n",
    "                    if (moves[i][1] > moves[i][2]):\n",
    "                      parsers[i].right_arc()\n",
    "                    elif (moves[i][1] <= moves[i][2]):\n",
    "                      parsers[i].shift()\n",
    "                elif (moves[i][1] > moves[i][0] and moves[i][1] > moves[i][2]):\n",
    "                  parsers[i].right_arc()\n",
    "                elif (moves[i][2] >= moves[i][0] and moves[i][2] > moves[i][1]):\n",
    "                  parsers[i].shift()\n",
    "                elif (moves[i][2] > moves[i][0] and moves[i][2] >= moves[i][1]):\n",
    "                  parsers[i].shift()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "q4zLAUc85gS4"
   },
   "source": [
    "#### Train and Test\n",
    "\n",
    "We use **UAS (Unlabeled Accuracy Score)** for evaluation of the predicted trees from the model, which is the percentage of\n",
    "words in the input that are attached to the correct head,\n",
    "ignoring the dependency label.\n",
    "\n",
    "UAS estimate is returned by the test function, which takes as input model\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "RF4v0UTrDAUs"
   },
   "outputs": [],
   "source": [
    "def evaluate(gold, preds):\n",
    "  total = 0\n",
    "  correct = 0\n",
    "\n",
    "  for g, p in zip(gold, preds):\n",
    "    for i in range(1,len(g)):\n",
    "      total += 1\n",
    "      if g[i] == p[i]:\n",
    "        correct += 1\n",
    "\n",
    "  return correct/total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "bhutul7I5irm"
   },
   "outputs": [],
   "source": [
    "def train(model, dataloader, criterion, optimizer):\n",
    "  model.train()\n",
    "  total_loss = 0\n",
    "  count = 0\n",
    "\n",
    "  for batch in dataloader:\n",
    "    optimizer.zero_grad()\n",
    "    sentences, paths, moves, trees = batch\n",
    "\n",
    "    out = model(sentences, paths)\n",
    "    labels = torch.tensor(sum(moves, [])).to(device) #sum(moves, []) flatten the array\n",
    "    loss = criterion(out, labels)\n",
    "\n",
    "    count +=1\n",
    "    total_loss += loss.item()\n",
    "\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "\n",
    "  return total_loss/count\n",
    "\n",
    "def test(model, dataloader):\n",
    "  model.eval()\n",
    "\n",
    "  gold = []\n",
    "  preds = []\n",
    "\n",
    "  for batch in dataloader:\n",
    "    sentences, paths, moves, trees = batch\n",
    "    with torch.no_grad():\n",
    "      pred = model.infere(sentences)\n",
    "      gold += trees\n",
    "      preds += pred\n",
    "\n",
    "  return evaluate(gold, preds)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "jBScmvI_S_H3"
   },
   "source": [
    "The parameters for the model `EMBEDDING_SIZE = 400`,\n",
    "`DROPOUT = 0.1`, `LR = 0.001`, `LSTM_LAYERS = 2`, `BATCH_SIZE = 16` have been chosen using a gridsearch function that considered only 5 epochs for the evaluation of the loss and the UAS for computational reasons."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "vSyAEZLWJMcs"
   },
   "outputs": [],
   "source": [
    "EMBEDDING_SIZE = 400\n",
    "LSTM_SIZE = EMBEDDING_SIZE\n",
    "DROPOUT = 0.1\n",
    "LR = 0.001\n",
    "LSTM_LAYERS = 2\n",
    "BATCH_SIZE = 16\n",
    "MLP_SIZE = 200\n",
    "train_dataloader = torch.utils.data.DataLoader(train_dataset, batch_size=BATCH_SIZE, shuffle=True, collate_fn=partial(prepare_batch, get_gold_path=True))\n",
    "dev_dataloader = torch.utils.data.DataLoader(dev_dataset, batch_size=BATCH_SIZE, shuffle=False, collate_fn=partial(prepare_batch))\n",
    "test_dataloader = torch.utils.data.DataLoader(test_dataset, batch_size=BATCH_SIZE, shuffle=False, collate_fn=partial(prepare_batch))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8Q8Q22aETuEp"
   },
   "source": [
    "The model training was performed using the GPU offered by Colab Tesla 4 T4. The number of epochs was set to `EPOCHS = 30`, to avoid exceeding computational time.\n",
    "During the training, it was observed that the UAS value did not show significant improvement after some epochs. To address this issue, an adaptive learning rate approach was employed using the `ReduceLROnPlateau` function from `torch`. This function reduced the learning rate by a factor of 0.5 after 3 epochs without any improvement in the UAS value. Here, \"improvement\" was defined as a difference greater than $0.002$ between the current best UAS value and the next one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "VE7pvCBADdHu",
    "outputId": "74a9b310-cccc-40b6-e28b-485fa9f8023a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Device: cuda\n",
      "Epoch:   0 | avg_train_loss: 0.933 | dev_uas: 0.704 |\n",
      "Epoch:   1 | avg_train_loss: 0.862 | dev_uas: 0.746 |\n",
      "Epoch:   2 | avg_train_loss: 0.836 | dev_uas: 0.759 |\n",
      "Epoch:   3 | avg_train_loss: 0.821 | dev_uas: 0.763 |\n",
      "Epoch:   4 | avg_train_loss: 0.810 | dev_uas: 0.777 |\n",
      "Epoch:   5 | avg_train_loss: 0.803 | dev_uas: 0.781 |\n",
      "Epoch:   6 | avg_train_loss: 0.797 | dev_uas: 0.781 |\n",
      "Epoch:   7 | avg_train_loss: 0.792 | dev_uas: 0.784 |\n",
      "Epoch:   8 | avg_train_loss: 0.789 | dev_uas: 0.789 |\n",
      "Epoch:   9 | avg_train_loss: 0.786 | dev_uas: 0.791 |\n",
      "Epoch:  10 | avg_train_loss: 0.783 | dev_uas: 0.793 |\n",
      "Epoch:  11 | avg_train_loss: 0.781 | dev_uas: 0.795 |\n",
      "Epoch:  12 | avg_train_loss: 0.779 | dev_uas: 0.790 |\n",
      "Epoch:  13 | avg_train_loss: 0.778 | dev_uas: 0.792 |\n",
      "Epoch 00014: reducing learning rate of group 0 to 5.0000e-04.\n",
      "Epoch:  14 | avg_train_loss: 0.773 | dev_uas: 0.797 |\n",
      "Epoch:  15 | avg_train_loss: 0.769 | dev_uas: 0.795 |\n",
      "Epoch:  16 | avg_train_loss: 0.767 | dev_uas: 0.798 |\n",
      "Epoch:  17 | avg_train_loss: 0.766 | dev_uas: 0.798 |\n",
      "Epoch 00018: reducing learning rate of group 0 to 2.5000e-04.\n",
      "Epoch:  18 | avg_train_loss: 0.765 | dev_uas: 0.801 |\n",
      "Epoch:  19 | avg_train_loss: 0.763 | dev_uas: 0.801 |\n",
      "Epoch:  20 | avg_train_loss: 0.763 | dev_uas: 0.798 |\n",
      "Epoch:  21 | avg_train_loss: 0.762 | dev_uas: 0.801 |\n",
      "Epoch 00022: reducing learning rate of group 0 to 1.2500e-04.\n",
      "Epoch:  22 | avg_train_loss: 0.761 | dev_uas: 0.800 |\n",
      "Epoch:  23 | avg_train_loss: 0.761 | dev_uas: 0.803 |\n",
      "Epoch:  24 | avg_train_loss: 0.760 | dev_uas: 0.800 |\n",
      "Epoch:  25 | avg_train_loss: 0.760 | dev_uas: 0.802 |\n",
      "Epoch:  26 | avg_train_loss: 0.760 | dev_uas: 0.802 |\n",
      "Epoch 00027: reducing learning rate of group 0 to 6.2500e-05.\n",
      "Epoch:  27 | avg_train_loss: 0.759 | dev_uas: 0.802 |\n",
      "Epoch:  28 | avg_train_loss: 0.759 | dev_uas: 0.802 |\n",
      "Epoch:  29 | avg_train_loss: 0.759 | dev_uas: 0.801 |\n"
     ]
    }
   ],
   "source": [
    "from torch.optim.lr_scheduler import ReduceLROnPlateau\n",
    "\n",
    "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n",
    "print(\"Device:\", device)\n",
    "model = Net(device, EMBEDDING_SIZE, DROPOUT, LSTM_LAYERS, LSTM_SIZE)\n",
    "model.to(device)\n",
    "\n",
    "criterion = nn.CrossEntropyLoss()\n",
    "optimizer = torch.optim.Adam(model.parameters(), lr=LR)\n",
    "scheduler = ReduceLROnPlateau(optimizer, mode='max', factor=0.5, patience=2, threshold_mode='abs', threshold = 0.002,\n",
    "                              cooldown = 1, min_lr = 1e-8, verbose=True)\n",
    "EPOCHS = 30\n",
    "loss = []\n",
    "dev_uas = []\n",
    "\n",
    "for epoch in range(EPOCHS):\n",
    "  avg_train_loss = train(model, train_dataloader, criterion, optimizer)\n",
    "  loss.append(avg_train_loss)\n",
    "  val_uas = test(model, dev_dataloader)\n",
    "  dev_uas.append(val_uas)\n",
    "  print(\"Epoch: {:3d} | avg_train_loss: {:5.3f} | dev_uas: {:5.3f} |\".format(epoch, avg_train_loss, val_uas))\n",
    "  scheduler.step(val_uas)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 449
    },
    "id": "oE-JbvTXCaC_",
    "outputId": "84f4a542-73b1-4ee3-8eb0-3d357062cad4"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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04nA4tK01QVlZGbt27SI1NZXg4OB6rzX197dGgixUOxKUX1pFfon3J5uJiIjI8SkEWSgkwI+ESPOvJE2OFhERaVkKQRbTvCARERFrKARZLDVWl88QERGxgkKQxVJizMPkNRIkIm2NjruR5uDN7UohyGKp7gupKgSJSNtQe/hz7VXORbyptLQUwzC8cpi9zhhtsdrdYel5JbhcBna7DpMUkdbN4XAQFRXlvv5TSEiIDgFvgA6RbxrDMCgtLeXgwYOEhobWO5GlpxSCLJYYFYy/w0ZltYv9h8tIim78dW5ERHxVfHw8QItdCLO1crlc7ktwSONERkYec34gTykEWczPYadbx1B25BSTnluiECQibYLNZiMhIYFOnTrVuzin1DEMg6KiIsLDwzUS1Ej+/v7Y7XYKCgq8sj6FIB+QEmOGoF0HixnZK9bqckREvMbhcHhlt0VbZBgGFRUVBAUFKQQ1gSZGtzHueUE6QkxERKTFKAT5APcRYgpBIiIiLUYhyAekxprnCtJh8iIiIi1HIcgH1F4640BBGeVVTourERERaR8UgnxAx9AAIoL8MAzYnafRIBERkZZgeQh66aWXSE5OJigoiLS0NFauXHnc91ZVVfH444/TvXt3goKCGDhwIAsXLjyldfoCm81GSs0usXTtEhMREWkRloag+fPnM23aNB599FHWrFnDwIEDGTNmzHFPrvXII4/wj3/8gxdffJFNmzZx6623ctlll7F27VqP1+krumtytIiISIuyNAQ999xzTJ06lRtuuIHTTjuNOXPmEBISwssvv9zg+19//XUeeughxo0bR2pqKrfddhvjxo3j2Wef9XidviJF1xATERFpUZadLLGyspLVq1czffp09zK73c7o0aNZvnx5g5+pPanUkYKDg1m6dKnH66xdb0VFhft5YWEhYJ6QydtXQa5d59HrTYmtDUHFuvLyUY7XMzkx9c0z6ptn1LemU888c6K+NbWXloWg3NxcnE4ncXFx9ZbHxcWxZcuWBj8zZswYnnvuOUaOHEn37t1ZvHgx77//Pk6n0+N1AsyePZtZs2Yds7ygoKBZQlBxcTFAvTOExgaaP2fXwWKvnQ68rThez+TE1DfPqG+eUd+aTj3zzIn6VjuI0Vit6rIZf/nLX5g6dSp9+vTBZrPRvXt3brjhhlPe1TV9+nSmTZvmfl5YWEhSUhKRkZFEREScatn11IaqyMjIev/x+gebE6MLyqtx+gUTHRrg1Z/bmh2vZ3Ji6ptn1DfPqG9Np5555kR9a2ofLQtBMTExOBwOsrOz6y3Pzs52X334aLGxsXz44YeUl5eTl5dH586defDBB0lNTfV4nQCBgYEEBgYes9xmszXLhlm73iPXHRLoR+fIIA4UlLM7r4SOYcfW05411DM5OfXNM+qbZ9S3plPPPHO8vjW1j5ZNjA4ICGDw4MEsXrzYvczlcrF48WKGDRt2ws8GBQWRmJhIdXU17733HhMmTDjldfqC2jNH79TkaBERkWZn6e6wadOmMWXKFIYMGcLQoUN5/vnnKSkp4YYbbgBg8uTJJCYmMnv2bABWrFjB/v37GTRoEPv37+exxx7D5XLxwAMPNHqdviwlJpSlO3J1IVUREZEWYGkImjRpEgcPHmTmzJlkZWUxaNAgFi5c6J7YnJGRgd1eN1hVXl7OI488wq5duwgLC2PcuHG8/vrrREVFNXqdviz1iCPEREREpHnZDB2bd4zCwkIiIyMpKCholonRBQUFDU7oWrI1h+tf+YFecWEsuuc8r/7c1uxEPZPjU988o755Rn1rOvXMMyfqW1N/f1t+2Qyp071mTtDuvFKcLmVTERGR5qQQ5EM6RwUT4LBTWe3iwOEyq8sRERFp0xSCfIjDbqNbxxAAdmpekIiISLNSCPIxtZOjdYSYiIhI81II8jEpMea8IF1IVUREpHkpBPkYjQSJiIi0DIUgH5Mao3MFiYiItASFIB9Te+mMAwXllFU6La5GRESk7VII8jEdQvyJDPYHYHeedomJiIg0F4UgH2Oz2Y64fIZCkIiISHNRCPJBKTG1k6M1L0hERKS5KAT5oNrLZ2gkSEREpPkoBPmg2pGgXTpMXkREpNkoBPmgujlBxRiGLqQqIiLSHBSCfFByx1BsNigsr+ZQSaXV5YiIiLRJCkE+KMjfQefIYEC7xERERJqLQpCPcl8+Q5OjRUREmoVCkI+qvXzGTh0mLyIi0iwUgnyU+1xBGgkSERFpFgpBPqr2GmKaEyQiItI8FIJ8VO1I0J68EpwuHSYvIiLibQpBPioxKpgAPztVToN9+aVWlyMiItLmKAT5KLvdRkpHnTlaRESkuSgE+TBdTV5ERKT5KAT5MF1NXkREpPkoBPkw94VUNRIkIiLidQpBPqz2MPl0zQkSERHxOoUgH1Z71ujMgnJKK6strkZERKRtUQjyYR1CA+gQ4g9oNEhERMTbFIJ8XN3kaIUgERERb1II8nHuy2docrSIiIhXKQT5OI0EiYiINA+FIB/X3X3CRJ0rSERExJsUgnxcSkzd1eQNQxdSFRER8RaFIB/XrWMINhsUlVeTW1xpdTkiIiJthkKQjwvyd5AYFQxoXpCIiIg3KQS1AnVHiGlekIiIiLcoBLUCqTpCTERExOsUglqB1JojxHbqXEEiIiJeoxDUCtSdK0i7w0RERLxFIagVqJ0TlHGolGqny+JqRERE2gaFoFYgISKIIH87VU6DffllVpcjIiLSJigEtQJ2u43kjjVnjtYuMREREa9QCGolUt2Xz9DkaBEREW9QCGolUo+4fIaIiIicOoWgVsJ9hJhGgkRERLxCIaiVcO8O05wgERERr1AIaiVqd4dlF1ZQUlFtcTUiIiKtn0JQKxEZ4k+n8EAAlu/Ms7gaERGR1k8hqBWZeEYiAG+uzLC4EhERkdZPIagVuXpoVwC+2prD3kOlFlcjIiLSuikEtSIpMaGc2yMGw4B5P2g0SERE5FQoBLUy16aZo0Hzf9hHZbWuIyYiIuIphaBWZvRpcXQKDyS3uIIvNmVbXY6IiEirpRDUyvg77Fx1VhIAb6zYY3E1IiIirZdCUCs0aWhX7Db4bmceOw/q5IkiIiKeUAhqhRKjgrmwTycA3lyhCdIiIiKeUAhqpa5N6wbAu6v3UV7ltLgaERGR1kchqJUa2SuWxKhgCsqqWLA+0+pyREREWh2FoFbKYbdxTc3h8pogLSIi0nQKQa3YL4ck4We3sSbjMJsOFFpdjoiISKuiENSKxYYHMub0eECjQSIiIk2lENTK1Z5B+sO1+ymuqLa4GhERkdbD8hD00ksvkZycTFBQEGlpaaxcufKE73/++efp3bs3wcHBJCUlcc8991BeXu5+/bHHHsNms9W79enTp7m/hmWGpXYkNTaUkkon//1xv9XliIiItBqWhqD58+czbdo0Hn30UdasWcPAgQMZM2YMOTk5Db7/zTff5MEHH+TRRx9l8+bNzJ07l/nz5/PQQw/Ve1+/fv3IzMx035YuXdoSX8cSNpvNfbj8f77PwDAMiysSERFpHfys/OHPPfccU6dO5YYbbgBgzpw5LFiwgJdffpkHH3zwmPd/9913nHPOOVxzzTUAJCcnc/XVV7NixYp67/Pz8yM+Pr7RdVRUVFBRUeF+XlhoTjI2DMProaJ2nd5c7+VndOaZhVvYnFnI2ozDnNE1ymvr9gXN0bP2QH3zjPrmGfWt6dQzz5yob03tpWUhqLKyktWrVzN9+nT3MrvdzujRo1m+fHmDnxk+fDj/+c9/WLlyJUOHDmXXrl18+umnXHfddfXet337djp37kxQUBDDhg1j9uzZdO3a9bi1zJ49m1mzZh2zvKCgoFlCUHGxeakLm83mlXXagIv6xPDxxhxe+XYHqZf29Mp6fUVz9Kw9UN88o755Rn1rOvXMMyfqW+0gRmNZFoJyc3NxOp3ExcXVWx4XF8eWLVsa/Mw111xDbm4u5557LoZhUF1dza233lpvd1haWhqvvvoqvXv3JjMzk1mzZjFixAg2btxIeHh4g+udPn0606ZNcz8vLCwkKSmJyMhIIiIivPBt69SGqsjISK9u9DeM6M7HG3NYtCWXxy8bQFRIgNfWbbXm6llbp755Rn3zjPrWdOqZZ07Ut6b20dLdYU21ZMkSnnzySf72t7+RlpbGjh07uOuuu3jiiSeYMWMGABdffLH7/QMGDCAtLY1u3brx9ttvc9NNNzW43sDAQAIDA49ZXjux2tuOnLTtLWd07UDfhAg2Zxby/toD3HRuitfW7Quao2ftgfrmGfXNM+pb06lnnjle35raR8smRsfExOBwOMjOzq63PDs7+7jzeWbMmMF1113HzTffTP/+/bnssst48sknmT17Ni6Xq8HPREVF0atXL3bs2OH17+BLzAnSdWeQ1j5mERGRE7MsBAUEBDB48GAWL17sXuZyuVi8eDHDhg1r8DOlpaXY7fVLdjgcwPEnQxUXF7Nz504SEhK8VLnvmnhGIqEBDnYdLOH7XYesLkdERMSnWXqI/LRp0/jnP//Ja6+9xubNm7ntttsoKSlxHy02efLkehOnx48fz9///nfmzZtHeno6X3zxBTNmzGD8+PHuMHTffffx9ddfs3v3br777jsuu+wyHA4HV199tSXfsSWFBfox8YxEQGeQFhERORlL5wRNmjSJgwcPMnPmTLKyshg0aBALFy50T5bOyMioN/LzyCOPYLPZeOSRR9i/fz+xsbGMHz+eP/zhD+737Nu3j6uvvpq8vDxiY2M599xz+f7774mNjW3x72eFa9O68caKDD7/KYuDRRXEhh8710lERETAZmjyyDEKCwuJjIykoKCgWY4OKygoaNajAS772zLWZhzm/jG9uf2CHs3yM1pSS/SsLVLfPKO+eUZ9azr1zDMn6ltTf39bftkM8b7aM0i/tTIDp0sZV0REpCEKQW3QpQMSiAz2Z19+Gd9sP2h1OSIiIj5JIagNCvJ38IvBXQB44/sMi6sRERHxTQpBbdQ1NecM+nJLNvsPl1lcjYiIiO9RCGqjuseGMSy1Iy4D5q/UaJCIiMjRFILasGvPNkeD5v2wlypnw2fUFhERaa8Ugtqwi06LJyYskJyiChZvzj75B0RERNoRhaA2LMDPzqSzaiZIr9AuMRERkSMpBLVxV53VFZsNvt2ey+7cEqvLERER8RkKQW1cUnQI5/cyLxnypiZIi4iIuCkEtQO1Z5B+Z9VeyqucFlcjIiLiGxSC2oEL+nSic2QQ+aVVLNyYZXU5IiIiPkEhqB1w2G1cPdQ8XP6FL7drNEhERASFoHZj8rBkOoUHsutgCX/6fKvV5YiIiFhOIaidiAzx56kr+gMwd1k6K9MPWVyRiIiItRSC2pEL+8Rx5eAuGAbc/+46SiurrS5JRETEMgpB7cyM8afROTKIPXmlPP3ZFqvLERERsYxCUDsTEeTP078YAMBry/fw3Y5ciysSERGxhkJQOzSiZyzXpplHi93/7nqKyqssrkhERKTlKQS1Uw+N60uXDsHsP1zGk59utrocERGRFqcQ1E6FBvrxx18MBOCtlXtZsjXH4opERERalkJQOzase0euH54MwIPvbaCgTLvFRESk/VAIaud+N7YPKTGhZBWW8/jHm6wuR0REpMV4HIJ27NjB559/TllZGQCGYXitKGk5wQEO/nTlAOw2eG/NPr7YlG11SSIiIi2iySEoLy+P0aNH06tXL8aNG0dmZiYAN910E/fee6/XC5TmN7hbNFNHpAIw/f0N5JdUWlyRiIhI82tyCLrnnnvw8/MjIyODkJAQ9/JJkyaxcOFCrxYnLeeen/WiR6cwcosrmPnRT1aXIyIi0uyaHIIWLVrE008/TZcuXeot79mzJ3v27PFaYdKygvwdPHvlQBx2Gx+vO8CnGzKtLklERKRZNTkElZSU1BsBqnXo0CECAwO9UpRYY2BSFLed1x2ARz7cSG5xhcUViYiINJ8mh6ARI0bw73//2/3cZrPhcrl45plnuOCCC7xanLS8O0f1pE98OIdKKnn4gw2a8C4iIm2WX1M/8MwzzzBq1ChWrVpFZWUlDzzwAD/99BOHDh1i2bJlzVGjtKAAPzvP/nIgE/66jM9/yuajdQeYMCjR6rJERES8rskjQaeffjrbtm3j3HPPZcKECZSUlHD55Zezdu1aunfv3hw1Sgvr1zmSO0f1BGDmf38iu7Dc4opERES8r8kjQQCRkZE8/PDD3q5FfMht53fni03ZbNhfwPT3NzB3yhBsNpvVZYmIiHhNk0PQN998c8LXR44c6XEx4jv8HeZusUtfWMqXW3J4Z/U+fjkkyeqyREREvKbJIej8888/ZtmRIwROp/OUChLf0SsunHt+1ounF27hiY83cW6PGDpHBVtdloiIiFc0eU5Qfn5+vVtOTg4LFy7krLPOYtGiRc1Ro1jolpGpnNE1iqKKan733nodLSYiIm1Gk0NQZGRkvVtMTAw/+9nPePrpp3nggQeao0axkMNu409XDiTQz86323OZ9fEmBSEREWkTvHYV+bi4OLZu3eqt1YkP6R4bxuzL+wPw6ne7+cOCzQpCIiLS6jV5TtD69evrPTcMg8zMTJ566ikGDRrkrbrEx1x+ZhfKq1w89MEG/rU0HX8/Ow+M6a0jxkREpNVqcggaNGgQNpvtmJGAs88+m5dfftlrhYnvuSatK9UuFzP/+xN/X7ITf4edaT/rZXVZIiIiHmlyCEpPT6/33G63ExsbS1BQkNeKEt81eVgyVU6DJz7ZxAuLt+Nvt/HbmhMrioiItCZNDkHdunVrjjqkFbnp3BSqnS5mf7aFZ7/Yhp/Dzm3n62zhIiLSujQqBL3wwguNXuGdd97pcTHSevz6vO5Uuwz++PlWnl64BX+HjZtHpFpdloiISKM1KgT9+c9/btTKbDabQlA7cvsFPaisdvGXxdv5/YLN+DvsTBmebHVZIiIijdKoEHT0PCCRWneP7km1y8VLX+3k0Y9+ws9h49o07TIVERHf57XzBEn7ZLPZuO+i3vx6pLkr7OEPNvL2D3strkpEROTkPLqK/L59+/joo4/IyMigsrKy3mvPPfecVwqT1sNms/HgxX2odLp4Zdlufvf+evwcNi4/s4vVpYmIiBxXk0PQ4sWL+fnPf05qaipbtmzh9NNPZ/fu3RiGwZlnntkcNUorYLPZmHnpaVQ7DV7/fg/3vbMOh93GhEGJVpcmIiLSoCbvDps+fTr33XcfGzZsICgoiPfee4+9e/dy3nnnceWVVzZHjdJK2Gw2Zv28H1cPTcJlwLS31/HphkyryxIREWlQk0PQ5s2bmTx5MgB+fn6UlZURFhbG448/ztNPP+31AqV1sdtt/GFif34xuAtOl8Gdb61l0U9ZVpclIiJyjCaHoNDQUPc8oISEBHbu3Ol+LTc313uVSatlt9t4+ooBXHZGItUug9vfXMOXW7KtLktERKSeJoegs88+m6VLlwIwbtw47r33Xv7whz9w4403cvbZZ3u9QGmdHHYbf/zFAC4dkECV0+DW19fwv00KQiIi4juaPDH6ueeeo7i4GIBZs2ZRXFzM/Pnz6dmzp44Mk3r8HHb+PGkQTpfBZxuzuPnfq7h6aBIPjetLeJC/1eWJiEg71+SRoCeffJJDhw4B5q6xOXPmsH79et577z1dV0yO4e+w85erzuD6mjNJv7VyL2P+/A1fbztobWEiItLuNTkEHTx4kLFjx5KUlMT999/PunXrmqMuaUMC/Ow89vN+zLvlbLpGh3CgoJwpL6/kd++up7C8yuryRESknWpyCPrvf/9LZmYmM2bM4IcffuDMM8+kX79+PPnkk+zevbsZSpS24uzUjiy8e4R7VGj+KnNU6KutOdYWJiIi7ZJHl83o0KEDt9xyC0uWLGHPnj1cf/31vP766/To0cPb9UkbExLgx2M/78fbvx5GcscQMgvKueGVH7j/nXUUlGlUSEREWs4pXTusqqqKVatWsWLFCnbv3k1cXJy36pI2bmhKNJ/dNZIbz0nBZoN3Vu/joj9/zVdbNCokIiItw6MQ9NVXXzF16lTi4uK4/vrriYiI4JNPPmHfvn3erk/asOAABzPHn8bbvx5GSkwo2YUV3PDqD9z79joKSjUqJCIizavJISgxMZFx48aRm5vL//3f/5Gdnc3LL7/MqFGjsNlszVGjtHFnJUfz6Z0juPlcc1TovTX7uOj5r1m8WecVEhGR5tPk8wQ99thjXHnllURFRTVDOdJeBQc4eOTS07i4fzz3v7OeXbkl3PTaKi4/I5GZ40+zujwRaasqiqDsMER2Af0h3+40OQRNnTq1OeoQAWBwt2g+vWsEz32xjX99u4v31+5n6Y5cHroohQlDIq0uT0Tagqoy2PY5bHwXti0CZwVEdYMeo81bykgIDLO6SmkBNsMwDKuL8DWFhYVERkZSUFBARESEV9dtGAYFBQVERkZq9+FJrN6Tz/3vrmPXwRIALuwdy0OX9KVHp3CLK2sdtK15Rn3zjM/3zVkFO78yg8+WBVBZXPeazQ6Gq+653R+6DYMePzNDUae+3h0lMgwo2IuRs4Wy7J0Eh0di8wsCvyDwr7n3C6y5r30cXLfM0eTxi6bXV1kMZfl1t9JD9Z+X5YPdD8ITIDzOvA+ruQ+NbdYaT7StNfX3t+Uh6KWXXuKPf/wjWVlZDBw4kBdffJGhQ4ce9/3PP/88f//738nIyCAmJoZf/OIXzJ49m6CgII/XeTSFIN9RXuXkz19sY+7SdKpdBg67jV+ldeWu0b2IDg2wujyfpm3NM+2uby4nlBeYt6BICIn2aDU+2TeXE/Z8ZwafTf81f3HXiuwKp18Op18B0amweyns+AK2fwGH99RfT0Qi9BhlBqLU880+NYZhQME+OLjFvOVsgYOb4eDW+iGsqWyOI8JRIDj8wREIjoCaxwH1H/sFHLvMEQDYoPxww0HHdSoHp9ggrFNdKDo6JNU+D+3kUVhqMyFo/vz5TJ48mTlz5pCWlsbzzz/PO++8w9atW+nUqdMx73/zzTe58cYbefnllxk+fDjbtm3j+uuv56qrrnJft6yp62yIQpBvMQyD9elZvPjtPv632TyEPjzIjzsv7Mnk4d0I9HNYXKFv0rbmmVbbt+oKyNth/gKrDTVlh+selxeYv/COfq2y6IiV2CBhIHS/AFIvgK5nm79kG8GjvlUUw/5VkPG9WU9EZ3NuTu0tLA7sTfz3bRiwf40ZfH76AIoy614L7QT9LjODT9LQhkd3DAMO7TLD0I7/we5vobq87nWbA5LSzFDU82cQ199cT+H+I0JObeDZelR/j2D3x+jYg+qwBPzsNmzVFebPqa6A6rKa+/K6e2dl0/rgDY4ACI42g3Fwh2NvzkooyjJvxVlQlA3F2WA4G7f+obfAuD82uaw2E4LS0tI466yz+Otf/wqAy+UiKSmJ3/72tzz44IPHvP+OO+5g8+bNLF682L3s3nvvZcWKFe4r2zd1nQ1RCPItR/Zs+c48nliwmc2ZhQB06xjC9Iv7MKZfvPp5FG1rnmkVfXO5zMCzf3XdLWvDqf317h8CVaX1l/kFQ/I5ZiDqfuEJdws1qm9F2bD3ezP0ZCyHzPUn/oVp94PwzhCZaIaiiMT6ISki0fxlbLNB9iYz+Gx8D/J3160jKBL6/twMPskjmj7yUFUGe5bBjsVmKMrdVv/1kBgzDFQUHv87dOwJnfpAbM2tU1+ITsWw+zV+W3O5zLlLVUcGpJpw5KyquT/qcXVlw8trHxtOsz/BNSGnXtiJBv/gpu8GdDmhNM8Mn0XZ5n1x9rHPi7PhgodgxL1NWz/eDUHNvGPx+CorK1m9ejXTp093L7Pb7YwePZrly5c3+Jnhw4fzn//8h5UrVzJ06FB27drFp59+ynXXXefxOgEqKiqoqKhwPy8sNDdmwzDwdkasXaemYjXekT0b1r0jH99xDu+t2cefFm1jT14pt/5nDUNTonnkkr70T9Tk6Vra1jzjk30ryqwJO2vM+wNrsTXwS9cIijRHO4IiITjKvA884rH7dsTz4CgIjDB3kxRlwa4lsOtL2LkEW0mO+Yt/x//M9YfFQ+p5NaHoAnOkpvZnH903w4BDO82wk7EcMr7HdmjXsTVHdoGuw8ywU3TA3H1UsBcKM7G5qqEgw7wdh+EfCkGR2IoOHLEsBHqPM3d3dR9VfzSrqf9d/YLMdXQfBWOeNAPWzi/NnqR/g60011yt3Q869qgLOrF9zOAT3d3sbUO1N2Vbs9nq5gi1pKb2y2Y35wSFxkL8idbrMsOYB//OTtS3pv67tSwE5ebm4nQ6jznLdFxcHFu2bGnwM9dccw25ubmce+65GIZBdXU1t956Kw899JDH6wSYPXs2s2bNOmZ5QUFBs4Sg4mJzX7DP/pXpYxrq2ZieEYzodgavfr+P11YeYGX6IX7+12Vcenosvz2vG3HhjRvCb8u0rXnG8r5VFOGXsx5H1jocWT/il70Oe3HWMW8z/IJwdupPdfxAnHGDcMYPxBWR1PS/3Ks4YgQoGJIvNm8XGNjztuK/5xv8Mpbit38FtuIsWD/fvAHOmD5UdT2X6q4jqYo/g8oDGynP/wm/Az/gd2AV9rK8+jVjwxXTh+rOQ6jufBbVnYdgRCQ2XJfLia0kB3vRAfNWbN7bijKxF+3HXpSJvSwPW1UJVJVgOAKo7nY+lb3HU5U62hzZAigpB8ob/hmesHeAnleYN2cljuwNGIHhuKKSa+bZHKW49NhlNSzf1nxC0//bnKhvtYMYjWVZCPLEkiVLePLJJ/nb3/5GWloaO3bs4K677uKJJ55gxowZHq93+vTpTJs2zf28sLCQpKQkIiMjm2V3GODbQ+0+5ng9iwSmj49myoie/PHzrXz44wE+2XiQ/23N49cjU7llZCohAa1qE/cqbWueOeW+GYa5m6K8wNxFUl54nMcFUFFgLqt9Xl4ABfuxUf+PL8NmN0cWEodA4mBIPBM69cVh96NZZ8RFpUH3NOB+qC7HyFgBu76CXV9hy1yHI3cLjtwtsOZfDbfCEWjW2nWYOb8oaSj2oCgCgEYd1tAhGuhz3JeNqjJzLk5xDsSdhl9QVMv/Uou+0OOP6t+oZ07Ut6b20bLfEDExMTgcDrKz658VODs7m/j4hsfQZsyYwXXXXcfNN98MQP/+/SkpKeGWW27h4Ycf9midAIGBgQQGHjtyYLPZmmXDrF2vNvrGO1HPEjuE8PxVZ3D9OSn8/pNNrNqTz18W72DeD3u5f0wfLj8jEbu9ffa63W1rhmHuqshaD3Gnm4HBg6OdmtS38gJzjsvub2H3MsjeeOqTWKO61oSdwdD5TGwJA60/b41/MHQ/37wxC0pya3adfQU7l0DhPlyBkdi6DcPWdRh0HYat86BGT6z2SEAIxPQ0b61Uu/s36iXH61urCUEBAQEMHjyYxYsXM3HiRMCcxLx48WLuuOOOBj9TWlqK3V7/Sh8Oh/l3kGEYHq1T2o5BSVG8c+swPtuYxezPNrP3UBn3vbOOV79L596LenNez9h2G4baPMOA7Yvg66fNOTNH6tgDupwFXYaY9536ndo5TEoPmXNcdi+DPUvNCclHnmOmls0OgeHmnJygSAiKMOfenPBxpBmAwhp3JKulQmOg/y/Mm2FglORSWOUgMqqDzrwsrYal+wqmTZvGlClTGDJkCEOHDuX555+npKSEG264AYDJkyeTmJjI7NmzARg/fjzPPfccZ5xxhnt32IwZMxg/frw7DJ1sndK22Ww2xvVP4MI+nXjtu9389csdbNxfyA2v/EBSdDBXndWVK4d0oVN4C08ulOZhGLD1UzP8ZK4zl/kFm4cvH9xiHkFVe1v3lvm6fwh0PrMuFHU5yzxvyfGU5JlHB+1ZVjfSc9TuKqJTods5kHyuub7QWAgIg6P+aGuzbDYzFBUUWF2JSJNYGoImTZrEwYMHmTlzJllZWQwaNIiFCxe6JzZnZGTUG/l55JFHsNlsPPLII+zfv5/Y2FjGjx/PH/7wh0avU9qHIH8Hvz6vO78Y3IWXvtrJO6v3svdQGX/8fCt//mIbF/WL45qh3RjevaNGh1ojlwu2fAJfPwPZG8xl/qEw9GYY9lsIizWXlR4yR4b2/VBzW23Ow9mz1LzViuxaF4o6n4F/9i44uNYMPjmbjv35Mb3qQk+3cyAiofm/s4h4neVnjPZFOk+Qb/FGz8oqnXyy/gBvrsxgbcZh9/JuHUPco0MxYW3riDKP+2YY5gn3SnIhOuW4h/dawuWCzf+Fr/8IOT+ZywLCzJOuDbsDQjue/PO5244IRatqQs5J/jcY29c8X063mtuJRo7aKf2/renUM8+0mZMl+iqFIN/i7Z5tzizkzRUZfLh2P0UV1QD4O2xc1C+ea4d25ezUtjE6dMK+VRTB4QzI32NeIuDox7XnoIlMgrN/A2dOtnZirstpnv33mz+au7nAnEeTdiucfZvHl3oAzF7sX+MORcaBtbiCOmBPHYkt+VzoNtzc1SMnpP+3NZ165hmFoGamEORbmqtnpZXVfLIukzdWZrBu72H38uSOIVw9tCu/GNyFjq11dMgwMA5nULJ7DaFVedgOHxV2yg6dfB2OQPMMtWBO2B1ykxk6WnIUxFltngH4mz9C3va6Ws7+DaT92jyzrZfp36hn1LemU888oxDUzBSCfEtL9OynAwW8uSKD//54gOKa0aEAh50xp8dzzdCupKVE+/boUGUJHFhbt4tn3w/maelPJLgDRHUzj0bq0K3mcTfzcWSSeXTTurdg+V/NicVgngxu4FXmvJvYXs33fZzVsOFt+OZP5lmHwTzL8bA7IO2Wxl/A0gP6N+oZ9a3p1DPPKAQ1M4Ug39KSPSupqObjdebcofX76o50SYoO5rJBiVx2ZhdSYkKbtYaTMgwzlLjntfxgXjfpqGswGXY/XB26Y49JxRaVXBN0utYFn6BGbtsul3kE1ncvwN4Vdct7j4Phd5onwfPGf5eCfeYVv2uv01Sw11weHA3D74Czpja+5lOgf6OeUd+aTj3zjEJQM1MI8i1W9Wzj/gLeXJnBR0eMDgGc0TWKy8/swvgBCUSFNOq8t6emLL/mCKdVdSM95YePfV9EYr3Dvo34ARSUVnq3bxnfw7IXzFBUO5m4y1lwzl1mKGrsFb9rr9S957ua21JzV92RQmJg+G/hrJtbdD6S/o16Rn1rOvXMMwpBzUwhyLdY3bOySieLNmXxwdr9fLPtIK6afzH+DhsX9unE5Wd24YLenQjwO4VzwhgGlBysOafNzrpz2+RuO/aq1WBeRLHzGXWhJ3GIeaXteqtsxr7lbofvXoR18+rmDUV3N0dsBl5tnl34SC4X5G6F3Uvrgs/R18Oy2SFhYM0RWMMh9XwIaPlRN6u3t9ZKfWs69cwzCkHNTCHIt/hSz3KKyvnoxwO8v2Y/mzLrLtQXFeLP+AGdufzMRAYlRR2/zvKCmoCzqy7oHNppBp8GrgruFp1ad2K/LkPMS0Kc5ND1FulbUTas/Af88C/zu4E5gpP2azPE7PuhLvQcPRnbEWBeFqLbcPOWlGaeYdlivrS9tSbqW9OpZ55RCGpmCkG+xVd7tiWrkA/W7OeDtfvJKapwL0+NCeWyMxK5rH80XfZ+DHt/qAk6O8zRnuOyQVSSeZmH6O7mfcce0HmQR4dot2jfKoph7euw/KW6uTxH8wuGpKE1Jxgcbgago0eMfICvbm++Tn1rOvXMM94MQe33Etsip6hPfATTx0XwwNg+LNuRywdr97NwYxZZuXkUfjmfgG8+BdvhYz8YFlcTdFLrgk7HHtAhGfxb6eU8AsPM8/WcdTP89KF5RNnhDHPkqttwcxdXwkDwa4E5VCIijaQQJHKKHHYbI3vFMjLJj6diPoPv/05glblraJ8Rw3vOEexwJVIRmUpKr/6k9e3G2akdCQlog//8HP4w4ErzJiLi49rg/4VFWljxQfj+JVj5LwIri8xl0d05POQOPq0YzrKt+azOyMeZb8CKg/xjxUECHHbOSunAyJ6xjOwVS5/4cA2Hi4i0MIUgEU8V7DfPnbP6NaguM5d16gcj74XTJhJld3ALcMsFUFhexXc78vhm+0G+2XaQffllLNuRx7Idecz+bAudwgPN0aResYzoEUOHUO02EhFpbgpBIk11aBcsfR5+fBNcVeayxMEw4j7oNRbsxx4qHxHkz9jT4xl7ejyGYZCeW8LX28xA9P2uQ+QUVfDu6n28u3ofNhsMSIzkvJpQNCgpCj/HKRx+LyIiDVIIEmmsnC3w7bOw8V0wXOaybueaIz+pFzT6rMk2m43U2DBSY8O44ZwUKqqdrNqd7w5FW7KKWLevgHX7Cnjhyx2EB/pxdveOjOwZw7k9Y0nuGKJdZyIiXqAQJHIyB36Eb/8Emz+uW9ZjtDny023YKa8+0M/BOT1iOKdHDA+N60t2YTnfbDvI19sOsnRHLodLq/hiUzZfbDKvBdalQzAjesYwomcsw7t3bJmzVouItEEKQSJHqyozr1+18yvY+SXkbKp7re94GHGvebbmZhIXEcSVQ5K4ckgSTpfBTwcK+HZ7Lt9uP8jqPfnsyy/jrZV7eWvlXuw26N8lihE9YhjRM4YzunY4tTNXi4i0IwpBIoZhBp0di83Qs+e7uktBANgccPoVMGIadOrboqU57DYGdIliQJcobr+gByUV1axMP+QORdtzilm39zDr9h7mr1/tICTAwbDUjpzbM4YRPWLoGKBzoYqIHI9CkLRPxQdh1xLYWRN8irPrvx6RCN0vNG+p50NItBVVHiM00I8L+nTigj6dAMgqKOfb7eZus6Xbc8krqWTxlhwWb8kBIDrEn76dI+gTH0Hv+HD6xIfTs1M4wQGNvNCpiEgbphAk7UN1BexdUTfak7W+/ut+weblHLpfCD1GQUyvRk90tlJ8ZN2uM5fLYFNmIUt3mKNEP+zO51BplftQ/Fo2GyR3DKV3XDh9Esxg1Ds+gq7RITjsvv+dRUS8RSFIfJ/LiT0/HUptUF0OlSXmvJ2qMqgqPeJWs8z9es2yymLIXGc+P1J8/7rRnqSzW+8lK2rY7TZOT4zk9MRIbj2vO2WV1azakcn+YoOt2UVszTJveSWVpOeWkJ5bwsKf6q7kHuRvp1dcOL3jwmtGjSLoFR9GbFigjkYTkTZJIUh8V95OWPsfWPcWEUWZp76+0E71d3GFx536On1YkL+D/p3DOfeoiwweLKpga1YRW7IK2VITjLZlF1Fe5WL9vgLW7yuot56oEH96dQqnZ1wYveLq7mPCAlv6K4mIeJVCkPiWimLY9KEZfjKWA2ADDL8gCO6AzT8E/EPMq4/7B5uPA0LqHrvvj1rWsQfEnd7giQzbm9jwQGLDAzm3Z92V6Z0ugz15JTXhqGbUKLuIPXklHC6tYuXuQ6zcfajeeqJDA+jZKYze8eH0jAunVyczHOls1yLSWigEifUMw5yvs/Z12PgBVJWYy2126DEaY9C1FMQPJzI6tlXM02mNHPa6Ezhe3D/Bvby8ysnOg8Vszy5ma3YR27OL2JZdzN78Ug6VVLIi/RAr0uuHo5iwQHrFhdGzUxgpMaGkxpr3naOCNedIRHyKQpBYpzAT1r0FP74BeTvqlkd3hzN+BQOvgojOZkgqKDj+eqTZBPk76Nc5kn6dI+stL6t0siOnmG3ZRWzLKWJ7tvl4X34ZucUV5BZX8N3OvHqfCfCzk9wxhJSYUFJiwkiNDSU1JpSUmFCiQwM070hEWpxCkLSs6krYttDc3bXji7rLT/iHQr/LzPDT9WyN+Pi44AAH/btE0r9L/XBUUlHN9ppwtPNgMekHzQnYe/JKqax2sS27mG3ZxUD9UxJEBPmREhtGakxNMIoNZXj3GKK1a01EmpFCkLSMnC2w5jVYPx9Kjxgh6DrMDD6nTYTAMMvKE+8IDfRjUFIUg5Ki6i13ugz255exK7fYfWRaem4Juw6WcKCgjMLyavdJH2sF+tm57IxEbjgnhd7x4S37RUSkXVAIkua3/Qt4cxIYTvN5WDwMuhoG/Qpielhbm7QIh91G144hdO0Ywvm9679WXuVkT14p6bnF7KwZOdq4v4AtWUXM+2Ev837Yy4ieMdx4Tgrn9YrFrnlFIuIlCkHSvAr2wftTzQCUch4Mux26jwKHNj0xBfk76B0fXm+0xzAMVu/J5+Vl6SzcmFVzmZBcUmNCueGcZC4/swuhgdqGROTU6P8i0nycVfDODVCWb15w9Np3wE/nlpGTs9lsDEmOZkhyNHsPlfLv5buZt3Ivu3JLmPHfn/jj51u5emhXJg9PJjEq2OpyRaSV0klTpPksngX7VkJgJFz5qgKQeCQpOoSHLzmN5Q+NYtbP+5HcMYTC8mr+8c0uRj7zFbe/uYbVe/IxDF0sVkSaRiNB0jy2fArfvWg+nvgSdEi2tBxp/cIC/ZgyPJnrzu7GV1tzmLs0ne925rFgfSYL1mcyMCmKG89JZlz/BPwd+vtORE5OIUi8L38PfHir+fjs26HveGvrkTbFbrcxqm8co/rGsTmzkFeWpfPhjwdYt/cwd837kdmfbuFXZ3dlwqBEkqJDrC5XRHyY/lwS76quhHdvgPICSBwCox+zuiJpw/omRPDMLwby3YMXMu1nvYgJCySrsJw/LdrGiGe+YsJLy/jnN7vYf7jM6lJFxAdpJEi864uZsH81BEXBla+An052J80vJiyQO0f15NfnpfLJukzeXb2PFel57nMP/eHTzZzZNYpLBnTmkv4JxEcGWV2yiPgAhSDxnk0fwYq/m48v+wdEdbW2Hml3Av0cXDG4C1cM7kJOUTmfb8zi4/WZ/LD7EGsyDrMm4zBPfLKJs5I7cEn/BMb1T6BThAKRSHulECTecWgX/PcO8/HwO6H3WGvrkXavU3gQ1w1L5rphyWQXlvPZhkw+WZ/Jqj35/LDbvM36ZBNDk6O5dEACY09PIDZcRzCKtCcKQXLqqsrhneuhogCS0mDUTKsrEqknLiKI689J4fpzUsgsKOPTDVl8sv4AazMOsyL9ECvSD/HoRz9xdmpHLumfwIC4AMLDI3A4dHZqkbZMIUhO3aKHIXMdBEfDL14Bh7/VFYkcV0JkMDedm8JN56awL7+UzzZk8cmGTNbtPcx3O/P4bqd5bbtgfwc948LoFRdO77hwesWb93ERgbrivUgboRAkp2bje/DDv8zHl/8fRCZaW49IE3TpEMLUkalMHZnK3kOlLNiQycKNWWw6UEBZlZP1+wpYv6+g3mcigvzoHR9Or7hw+tTc94oLp4OueC/S6igEiefydsJHd5mPz50GPX9mbT0ipyApOoRbz+vOr0emkpd/mIJqP7bnFLM1q5ht2UVszS4iPbeEwvJq95yiI3UKD6R3fDg9OoWRGBVMfGQQ8RFBxEcGERcRpBM4ivgghSDxTFUZvD0FKoug2zlwwcNWVyTiNX52G6mxYXTvFM7Y0+uWV1Q72XWwxAxFWUXucLT3UBk5RRXkFFXw7fbcY9Zns5mH8SfUBKOEyCDiI4Nr7s3ncRFBBPk7WvBbiohCkHhm4YOQvQFCYuCKuboqvLQLgX4O+iZE0Dchot7ykopqtucUsy2riJ0Hi8ksKCeroJzMwjKyCyqodLo4WFTBwaIK1lNwnLVDdGgAnaOCSOoQQlJ0CF06BNc8DqZLhxCFJBEv028uabr1b8PqVwEbXPEviEiwuiIRS4UG+jEoKYpBSVHHvGYYBodKKo8IRuVkFZS5n2cVlHOgoIzyKheHSio5VFLJxv2FDf6c2PBAkjoEkxQdUi8cJXUIISFKu9xEmkohSJrm4Db4+G7z8XkPQPcLLC1HxNfZbDY6hgXSMSyQ0xMjG3yPYRgUllVzoKCM/fll7M0vZe8h835ffhn7DpVSVFHtHk1ak3H4mHU47DYSIoNIiQmle2wYqbF19/ERQTqiTaQBCkHSeJWl8M4UqCqBlJFw3u+srkikTbDZbESG+BMZ4n/MrjYwQ1JBWZU7GO09VHpMUKqsdpmBKb/smHlJIQEOUmNDSY2pH45SY8IIDtAuNmm/FIKk8T69H3I2QWgnuPxfYNf/PEVags1mIyokgKiQAPp3OXY0yeUyOFhcQcahUnYdLGbXwRJ21tzvOVRKaaWTjfsLG9zNlhgVXBOIQukcFUx4kD/hQX5EBNfcB/m5lwX7OzSiJG2KQpCcXHEOrHoZfvwP2Ozwi7kQHmd1VSJSw263ERdhHmF2VnJ0vdcqq1114Si3hJ05NfcHizlcWsX+w2XsP3zs6FFD/Ow2woL8iKgJReFHBKSIIH+C7U7io8OJDg2kQ0gAHUL96RASQHRogCZ1i09SCJKGFR+EzR/BTx/AnmVguMzl5083d4WJSKsQ4GenR6cwenQKO+a1QyWV9UaOcooqKCqvorC8mqLyaorKq9z3LgOqXQaHS6s4XFrV5DqC/O1EhwTQITSgJiAF0CHEDEkdQvzpEBpARJA/EcH+RAb7ExHsR2SwP4F+Ck/SfBSCpE5Jbl3w2b20LvgAdD4DBl4DZ91sXX0i4lXRoQFEh0Yz5KjRo6MZhkFppZPCI0LR0UGpsKyK7MPFlFTbyC+p5HBpFYdKK8kvqaTaZVBe5eJAQTkHCsqbVGOQv52IIDMYmeHoiMc1u+1ql9e+LyLYXB4W4Ifdrt13cnwKQe1dSS5s/rgm+Hx7bPA5bSL0mwgdki0qUESsZrPZCA30IzTQj4SGD3AzJ28XFBAZGVlv3pBhGBRXVJNfUkV+aSWHSis5XFrJoZKqmvtK8kvN0FRQVkVheRUFpVUUVVRjGFBe5aK8yjwRZdPrhvDAI4JSUE1ACqoLTRHBfoQF+hHk76i52c17PweB/naC/MxlgTWvBTjsmhfVhigEtUclebClJvikfwuGs+61hEHQ7zI4bQJEp1hWooi0DTabrWbekD9dO4Y0+nMul2GOMJWb4aigrIrCsiMeu5dXU1BWRVF57XvMUalKpwvDgMLyagrLq9mXX+al7wOBfnVBKcjfjr/DjsNuO+Lehp/djp/Dhp/dhp/D7r73t9tw1Dx22MGoriIiNJiAmtAV6Ocg0M9OoJ+dAL+a5/5297K6149cbi7TqFfTKQS1Fy4XrJ9nnugw/Zujgs/AmuAzUcFHRHyC3V532oAkDz5fXmXuvissq665rw1PZkg68rXi8mrKq5yUV7uoqHJSXuWkotplLqtyUV7txDDM9daNTrmAps+Nak4BDrs7SNWOaNUGtuPd14azAEdNWHPYCDgitAXULHO/x173ntrQZQP36JjNVvu8tiqbexk176t93CkikITI4JZrUAMUgtqLL2bA8r/WPU8YWLerKzrVqqpERJpF7e6tTuGnvi7DMKh0msGnooGAVOV0Ue00qHbV3htUOV04XQbVToMql/m4ymngdLmochru9xeXlmFz+FNR7aKi2kVltYuKavNnVFS5qHTWPK99XHXE69XmemtVOs33FFF96l+6Bfzm/O48MLaPpTUoBLUH6+bVBaCR98PAq6Fjd2trEhFpJWw2W80uJwcE+3ttvcebR9UU1U6XO5QdGc4qqo+9r2hgeVVNcKty1oYzl/nYVfvYcIe8+stduAzzO7hjmAFGzfeqeYphQO07DAP3iBpAhBd76SmFoLZu/xr46E7z8Yj74MJHrK1HRES8xtyFZSc0UL/OPaGr7bVlxTkw/1fgrIBeY+GCh62uSERExGcoBLVV1ZXw9mQo3A8de8Ll/wd2/ecWERGppd+KbdXC30HGcgiMgKvfgqDjnNxDRESknVIIaotWvWJe6wsbXPEviOlpdUUiIiI+RyGorcn43rzaO5iToHuNsbYeERERH6UQ1JYU7If514Gryjzj84h7ra5IRETEZykEtRVV5eaRYCU50KkfTPjbkafsFBERkaMoBLUFhgGf3A0H1kBwB7j6TQgMs7oqERERn+YTIeill14iOTmZoKAg0tLSWLly5XHfe/7555vXHjnqdskll7jfc/311x/z+tixY1viq1hjxRxY9xbY7HDlq7riu4iISCNYforJ+fPnM23aNObMmUNaWhrPP/88Y8aMYevWrXTq1OmY97///vtUVla6n+fl5TFw4ECuvPLKeu8bO3Ysr7zyivt5YGBg830JK+1aAp/XnATxot9D6vlWViMiItJqWB6CnnvuOaZOncoNN9wAwJw5c1iwYAEvv/wyDz744DHvj46Orvd83rx5hISEHBOCAgMDiY+Pb1QNFRUVVFRUuJ8XFhYCNddEOfJCJ15Qu06vrDd/N7xzPTbDiTFgEqTdVv/CLG2EV3vWjqhvnlHfPKO+NZ165pkT9a2pvbQ0BFVWVrJ69WqmT5/uXma32xk9ejTLly9v1Drmzp3LVVddRWhoaL3lS5YsoVOnTnTo0IELL7yQ3//+93Ts2LHBdcyePZtZs2Yds7ygoKBZQlBxcTGAxxfMA6CqlPD5V+Moy6c6bgDFIx+HmvDW1nitZ+2M+uYZ9c0z6lvTqWeeOVHfCpv4e9DSEJSbm4vT6SQuLq7e8ri4OLZs2XLSz69cuZKNGzcyd+7cesvHjh3L5ZdfTkpKCjt37uShhx7i4osvZvny5TgcjmPWM336dKZNm+Z+XlhYSFJSEpGRkURERHj47RpWG6pO5arBGAa8exe23M0YobE4rnmLyIi4k3+ulfJKz9oh9c0z6ptn1LemU888c6K+NbWPlu8OOxVz586lf//+DB06tN7yq666yv24f//+DBgwgO7du7NkyRJGjRp1zHoCAwMbnDNUO6na246csO2Rpc/Bpg/B7o/tl69DZBev1ueLTrln7ZT65hn1zTPqW9OpZ545Xt+a2kdLjw6LiYnB4XCQnZ1db3l2dvZJ5/OUlJQwb948brrpppP+nNTUVGJiYtixY8cp1esTtn0Oi58wH497BroNs7YeERGRVsrSEBQQEMDgwYNZvHixe5nL5WLx4sUMG3biX+7vvPMOFRUV/OpXvzrpz9m3bx95eXkkJCSccs2Wyt0O790MGDD4Bhhyo9UViYiItFqWnydo2rRp/POf/+S1115j8+bN3HbbbZSUlLiPFps8eXK9idO15s6dy8SJE4+Z7FxcXMz999/P999/z+7du1m8eDETJkygR48ejBnTyq+j9f5UqCiEpLPh4mesrkZERKRVs3xO0KRJkzh48CAzZ84kKyuLQYMGsXDhQvdk6YyMDOz2+llt69atLF26lEWLFh2zPofDwfr163nttdc4fPgwnTt35qKLLuKJJ55o3ecKKjwAB9bWnRDRL8DqikRERFo1y0MQwB133MEdd9zR4GtLliw5Zlnv3r2Pe+h6cHAwn3/+uTfL8w27l5n38QMgopXv1hMREfEBlu8Ok0ba/Y15nzLC2jpERETaCIWg1mL3UvM+WSFIRETEGxSCWoOC/XBolzkfqOvZVlcjIiLSJigEtQZ7auYDJQyEoEhraxEREWkjFIJag93fmvfJ51pbh4iISBuiENQapNeGIM0HEhER8RaFIF9XsA/y02vmA+kSGSIiIt6iEOTras8PlDAIgrx7RXsREZH2TCHI12k+kIiISLNQCPJ1Oj+QiIhIs1AI8mXu+UAOnR9IRETEyxSCfFntKFDnQZoPJCIi4mUKQb5M84FERESajUKQL9N8IBERkWajEOSrDu+F/N3mfKCkNKurERERaXMUgnxV7fXCNB9IRESkWSgE+ap0zQcSERFpTgpBvso9KXqktXWIiIi0UQpBvuhwBhzeU3N+IM0HEhERaQ4KQb6o9nphnc+AwHBraxEREWmjFIJ8kfvQeM0HEhERaS4KQb5o9zfmvc4PJCIi0mwUgnxN/h5zTpDmA4mIiDQrhSBfU3t+oMQzNR9IRESkGSkE+RrNBxIREWkRCkG+RhdNFRERaREKQb7kyPlASWdbXY2IiEibphDkS2p3hSWeCYFh1tYiIiLSxikE+RL3fCAdGi8iItLcFIJ8iSZFi4iItBiFIF+RvwcKMsDuB0k6P5CIiEhzUwjyFbVHhXXWfCAREZGWoBDkK7QrTEREpEUpBPkCw1AIEhERaWEKQb7g8B4o2GvOB+qq8wOJiIi0BIUgX+A+P9BgCAi1thYREZF2QiHIF2hXmIiISItTCLKaYUC6rhcmIiLS0hSCrJa/Gwr3gd1f5wcSERFpQQpBVtN8IBEREUsoBFlN84FEREQsoRBkJZ0fSERExDIKQVbKTz9iPtBQq6sRERFpVxSCrKT5QCIiIpZRCLKSdoWJiIhYRiHIKkfOB0oZYW0tIiIi7ZBCkFXyd0PhfnM+UBfNBxIREWlpCkFW2V1zluguQyAgxNpaRERE2iGFIKtoPpCIiIilFIKsoPMDiYiIWE4hyAL2gj3Yig5oPpCIiIiFFIIs4Ldvufmgy1maDyQiImIRhSAL+O2tCUHaFSYiImIZhaCWZhj47fvefKwQJCIiYhmFoJZ2aBf2kmwMR4C5O0xEREQsoRDU0updL0zzgURERKyiENTS9tQeGq9LZYiIiFhJIagl6fxAIiIiPkMhqCXl7cRWlKn5QCIiIj5AIagl1VwvzBl/BvgHW1yMiIhI+6YQ1JLKDmH4h1Dd5WyrKxEREWn3/KwuoF0ZcS8Mu4PyvBwCra5FRESknfOJkaCXXnqJ5ORkgoKCSEtLY+XKlcd97/nnn4/NZjvmdskll7jfYxgGM2fOJCEhgeDgYEaPHs327dtb4qucnCMAAsOtrkJERKTdszwEzZ8/n2nTpvHoo4+yZs0aBg4cyJgxY8jJyWnw/e+//z6ZmZnu28aNG3E4HFx55ZXu9zzzzDO88MILzJkzhxUrVhAaGsqYMWMoLy9vqa8lIiIiPs7yEPTcc88xdepUbrjhBk477TTmzJlDSEgIL7/8coPvj46OJj4+3n374osvCAkJcYcgwzB4/vnneeSRR5gwYQIDBgzg3//+NwcOHODDDz9swW8mIiIivszSOUGVlZWsXr2a6dOnu5fZ7XZGjx7N8uXLG7WOuXPnctVVVxEaGgpAeno6WVlZjB492v2eyMhI0tLSWL58OVddddUx66ioqKCiosL9vLCwEDADlWEYHn2346ldp7fX25apZ55R3zyjvnlGfWs69cwzJ+pbU3tpaQjKzc3F6XQSFxdXb3lcXBxbtmw56edXrlzJxo0bmTt3rntZVlaWex1Hr7P2taPNnj2bWbNmHbO8oKCgWUJQcXExADabzavrbqvUM8+ob55R3zyjvjWdeuaZE/WtdhCjsVr10WFz586lf//+DB069JTWM336dKZNm+Z+XlhYSFJSEpGRkURERJxqmfXUhqrIyEht9I2knnlGffOM+uYZ9a3p1DPPnKhvTe2jpSEoJiYGh8NBdnZ2veXZ2dnEx8ef8LMlJSXMmzePxx9/vN7y2s9lZ2eTkJBQb52DBg1qcF2BgYEEBh570HrtkWfeduRRbdI46pln1DfPqG+eUd+aTj3zzPH61tQ+WjoxOiAggMGDB7N48WL3MpfLxeLFixk2bNgJP/vOO+9QUVHBr371q3rLU1JSiI+Pr7fOwsJCVqxYcdJ1ioiISPth+e6wadOmMWXKFIYMGcLQoUN5/vnnKSkp4YYbbgBg8uTJJCYmMnv27Hqfmzt3LhMnTqRjx471lttsNu6++25+//vf07NnT1JSUpgxYwadO3dm4sSJLfW1RERExMdZHoImTZrEwYMHmTlzJllZWQwaNIiFCxe6JzZnZGRgt9cfsNq6dStLly5l0aJFDa7zgQceoKSkhFtuuYXDhw9z7rnnsnDhQoKCgpr9+4iIiEjrYDN0bN4xCgsLiYyMpKCgoFkmRhcUFGgiXBOoZ55R3zyjvnlGfWs69cwzJ+pbU39/W36yRBERERErKASJiIhIu6QQJCIiIu2S5ROjfVHtNKmmnnmysesuLCzUeSGaQD3zjPrmGfXNM+pb06lnnjlR34687FVjKAQ1oKioCICkpCSLKxEREZGmKioqIjIy8qTv09FhDXC5XBw4cIDw8HCvp/PaS3Ls3bvX60eetVXqmWfUN8+ob55R35pOPfPMifpmGAZFRUV07tz5mNPrNEQjQQ2w2+106dKlWX9GRESENvomUs88o755Rn3zjPrWdOqZZ47Xt8aMANXSxGgRERFplxSCREREpF1SCGphgYGBPProow1etV4app55Rn3zjPrmGfWt6dQzz3izb5oYLSIiIu2SRoJERESkXVIIEhERkXZJIUhERETaJYUgERERaZcUglrQSy+9RHJyMkFBQaSlpbFy5UqrS/Jpjz32mPvaMLW3Pn36WF2Wz/nmm28YP348nTt3xmaz8eGHH9Z73TAMZs6cSUJCAsHBwYwePZrt27dbU6wPOVnfrr/++mO2v7Fjx1pTrI+YPXs2Z511FuHh4XTq1ImJEyeydevWeu8pLy/n9ttvp2PHjoSFhXHFFVeQnZ1tUcW+oTF9O//884/Z3m699VaLKrbe3//+dwYMGOA+IeKwYcP47LPP3K97aztTCGoh8+fPZ9q0aTz66KOsWbOGgQMHMmbMGHJycqwuzaf169ePzMxM923p0qVWl+RzSkpKGDhwIC+99FKDrz/zzDO88MILzJkzhxUrVhAaGsqYMWMoLy9v4Up9y8n6BjB27Nh6299bb73VghX6nq+//prbb7+d77//ni+++IKqqiouuugiSkpK3O+55557+Pjjj3nnnXf4+uuvOXDgAJdffrmFVVuvMX0DmDp1ar3t7ZlnnrGoYut16dKFp556itWrV7Nq1SouvPBCJkyYwE8//QR4cTszpEUMHTrUuP32293PnU6n0blzZ2P27NkWVuXbHn30UWPgwIFWl9GqAMYHH3zgfu5yuYz4+Hjjj3/8o3vZ4cOHjcDAQOOtt96yoELfdHTfDMMwpkyZYkyYMMGSelqLnJwcAzC+/vprwzDMbcvf399455133O/ZvHmzARjLly+3qkyfc3TfDMMwzjvvPOOuu+6yrqhWoEOHDsa//vUvr25nGglqAZWVlaxevZrRo0e7l9ntdkaPHs3y5cstrMz3bd++nc6dO5Oamsq1115LRkaG1SW1Kunp6WRlZdXb9iIjI0lLS9O21whLliyhU6dO9O7dm9tuu428vDyrS/IpBQUFAERHRwOwevVqqqqq6m1vffr0oWvXrtrejnB032q98cYbxMTEcPrppzN9+nRKS0utKM/nOJ1O5s2bR0lJCcOGDfPqdqYLqLaA3NxcnE4ncXFx9ZbHxcWxZcsWi6ryfWlpabz66qv07t2bzMxMZs2axYgRI9i4cSPh4eFWl9cqZGVlATS47dW+Jg0bO3Ysl19+OSkpKezcuZOHHnqIiy++mOXLl+NwOKwuz3Iul4u7776bc845h9NPPx0wt7eAgACioqLqvVfbW52G+gZwzTXX0K1bNzp37sz69ev53e9+x9atW3n//fctrNZaGzZsYNiwYZSXlxMWFsYHH3zAaaedxo8//ui17UwhSHzWxRdf7H48YMAA0tLS6NatG2+//TY33XSThZVJe3DVVVe5H/fv358BAwbQvXt3lixZwqhRoyyszDfcfvvtbNy4UfP0muh4fbvlllvcj/v3709CQgKjRo1i586ddO/evaXL9Am9e/fmxx9/pKCggHfffZcpU6bw9ddfe/VnaHdYC4iJicHhcBwzcz07O5v4+HiLqmp9oqKi6NWrFzt27LC6lFajdvvStnfqUlNTiYmJ0fYH3HHHHXzyySd89dVXdOnSxb08Pj6eyspKDh8+XO/92t5Mx+tbQ9LS0gDa9fYWEBBAjx49GDx4MLNnz2bgwIH85S9/8ep2phDUAgICAhg8eDCLFy92L3O5XCxevJhhw4ZZWFnrUlxczM6dO0lISLC6lFYjJSWF+Pj4etteYWEhK1as0LbXRPv27SMvL69db3+GYXDHHXfwwQcf8OWXX5KSklLv9cGDB+Pv719ve9u6dSsZGRntens7Wd8a8uOPPwK06+3taC6Xi4qKCu9uZ96duy3HM2/ePCMwMNB49dVXjU2bNhm33HKLERUVZWRlZVldms+69957jSVLlhjp6enGsmXLjNGjRxsxMTFGTk6O1aX5lKKiImPt2rXG2rVrDcB47rnnjLVr1xp79uwxDMMwnnrqKSMqKsr473//a6xfv96YMGGCkZKSYpSVlVlcubVO1LeioiLjvvvuM5YvX26kp6cb//vf/4wzzzzT6Nmzp1FeXm516Za57bbbjMjISGPJkiVGZmam+1ZaWup+z6233mp07drV+PLLL41Vq1YZw4YNM4YNG2Zh1dY7Wd927NhhPP7448aqVauM9PR047///a+RmppqjBw50uLKrfPggw8aX3/9tZGenm6sX7/eePDBBw2bzWYsWrTIMAzvbWcKQS3oxRdfNLp27WoEBAQYQ4cONb7//nurS/JpkyZNMhISEoyAgAAjMTHRmDRpkrFjxw6ry/I5X331lQEcc5syZYphGOZh8jNmzDDi4uKMwMBAY9SoUcbWrVutLdoHnKhvpaWlxkUXXWTExsYa/v7+Rrdu3YypU6e2+z9aGuoXYLzyyivu95SVlRm/+c1vjA4dOhghISHGZZddZmRmZlpXtA84Wd8yMjKMkSNHGtHR0UZgYKDRo0cP4/777zcKCgqsLdxCN954o9GtWzcjICDAiI2NNUaNGuUOQIbhve3MZhiG4eHIlIiIiEirpTlBIiIi0i4pBImIiEi7pBAkIiIi7ZJCkIiIiLRLCkEiIiLSLikEiYiISLukECQiIiLtkkKQiIiItEsKQSIijbBkyRJsNtsxF20UkdZLIUhERETaJYUgERERaZcUgkSkVXC5XMyePZuUlBSCg4MZOHAg7777LlC3q2rBggUMGDCAoKAgzj77bDZu3FhvHe+99x79+vUjMDCQ5ORknn322XqvV1RU8Lvf/Y6kpCQCAwPp0aMHc+fOrfee1atXM2TIEEJCQhg+fDhbt25t3i8uIs1GIUhEWoXZs2fz73//mzlz5vDTTz9xzz338Ktf/Yqvv/7a/Z7777+fZ599lh9++IHY2FjGjx9PVVUVYIaXX/7yl1x11VVs2LCBxx57jBkzZvDqq6+6Pz958mTeeustXnjhBTZv3sw//vEPwsLC6tXx8MMP8+yzz7Jq1Sr8/Py48cYbW+T7i4j36SryIuLzKioqiI6O5n//+x/Dhg1zL7/55pspLS3llltu4YILLmDevHlMmjQJgEOHDtGlSxdeffVVfvnLX3Lttddy8OBBFi1a5P78Aw88wIIFC/jpp5/Ytm0bvXv35osvvmD06NHH1LBkyRIuuOAC/ve//zFq1CgAPv30Uy655BLKysoICgpq5i6IiLdpJEhEfN6OHTsoLS3lZz/7GWFhYe7bv//9b3bu3Ol+35EBKTo6mt69e7N582YANm/ezDnnnFNvveeccw7bt2/H6XTy448/4nA4OO+8805Yy4ABA9yPExISAMjJyTnl7ygiLc/P6gJERE6muLgYgAULFpCYmFjvtcDAwHpByFPBwcGNep+/v7/7sc1mA8z5SiLS+mgkSER83mmnnUZgYCAZGRn06NGj3i0pKcn9vu+//979OD8/n23bttG3b18A+vbty7Jly+qtd9myZfTq1QuHw0H//v1xuVz15hiJSNumkSAR8Xnh4eHcd9993HPPPbhcLs4991wKCgpYtmwZERERdOvWDYDHH3+cjh07EhcXx8MPP0xMTAwTJ04E4N577+Wss87iiSeeYNKkSSxfvpy//vWv/O1vfwMgOTmZKVOmcOONN/LCCy8wcOBA9uzZQ05ODr/85S+t+uoi0owUgkSkVXjiiSeIjY1l9uzZ7Nq1i6ioKM4880weeugh9+6op556irvuuovt27czaNAgPv74YwICAgA488wzefvtt5k5cyZPPPEECQkJPP7441x//fXun/H3v/+dhx56iN/85jfk5eXRtWtXHnroISu+roi0AB0dJiKtXu2RW/n5+URFRVldjoi0EpoTJCIiIu2SQpCIiIi0S9odJiIiIu2SRoJERESkXVIIEhERkXZJIUhERETaJYUgERERaZcUgkRERKRdUggSERGRdkkhSERERNolhSARERFpl/4fENAi7dAdk2kAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "epochs = [i for i in range(EPOCHS)]\n",
    "import matplotlib.pyplot as plt\n",
    "plt.plot(epochs, loss, label = \"loss\")\n",
    "plt.plot(epochs, dev_uas, label = \"uas evaluation\")\n",
    "plt.xlabel(\"epoch\")\n",
    "plt.ylabel(\"value\")\n",
    "plt.legend()\n",
    "plt.grid(alpha=0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "rB7ELXrCLu1A"
   },
   "source": [
    "In the previous plot, it can be observed that the UAS evaluation metric reaches a plateau, making it difficult for further improvement. This suggests that the maximum value has been reached, indicating that additional training epochs may not be necessary. Moreover, extending the training could potentially lead to overfitting, as indicated by the decreasing pattern of the loss on the training set.\n",
    "\n",
    "Finally, the model is also tested on the test set:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Kn_SMghyGTDX"
   },
   "source": [
    "**Testing the model on only projective sentences**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "FDvW7TqgpoC3",
    "outputId": "ac9c6c70-97d2-4fbe-9c5c-a93d9bc52ac4"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test_uas: 0.817\n"
     ]
    }
   ],
   "source": [
    "test_uas = test(model, test_dataloader)\n",
    "print(\"test_uas: {:5.3f}\".format(test_uas))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "iFKw60U_aZXv"
   },
   "source": [
    "**Testing the model on projective and non-projective sentences**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "XNiHjprXabJ1",
    "outputId": "cac81cb5-b0ac-4f1f-9f25-db36d87b1865"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:datasets.builder:Found cached dataset universal_dependencies (/root/.cache/huggingface/datasets/universal_dependencies/en_ewt/2.7.0/1ac001f0e8a0021f19388e810c94599f3ac13cc45d6b5b8c69f7847b2188bdf7)\n"
     ]
    }
   ],
   "source": [
    "test_dataset = load_dataset('universal_dependencies', 'en_ewt', split=\"test\")\n",
    "test_dataset = test_dataset.map(remove_None, batched=False)\n",
    "test_dataloader_2 = torch.utils.data.DataLoader(test_dataset, batch_size=BATCH_SIZE, shuffle=False, collate_fn=partial(prepare_batch))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "XYze8UiDgPRz",
    "outputId": "12c7654a-3fcb-49bd-adbc-89e843e7ef26"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test_uas: 0.812\n"
     ]
    }
   ],
   "source": [
    "test_uas_2 = test(model, test_dataloader_2)\n",
    "print(\"test_uas: {:5.3f}\".format(test_uas_2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "lujTPapvGfzq"
   },
   "source": [
    "These latest results demonstrate that our model exhibits efficient performance in producing dependency trees, even for non-projective samples."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "oRJtcQikgtZR"
   },
   "source": [
    "## **BERT and MLP for Neural Dependency Parsing**\n",
    "BERT (Bidirectional Encoder Representations from Transformers) is an NLP algorithm based on the encoder component of the Transformer architecture. It leverages self-attention mechanisms to capture contextual relationships between words in a sentence, followed by a feed-forward neural network.\n",
    "\n",
    "The input to BERT undergoes sub-tokenization and positional embeddings. It then passes through a series of standard Transformer blocks, which include self-attention and feed-forward layers. These blocks are augmented with residual connections and layer normalization to improve the flow of information and facilitate effective training.\n",
    "\n",
    "It is designed to generate contextualized word embeddings by considering jointly the preceding and following words within a sentence.\n",
    "\n",
    "Here's a brief overview of the BERT algorithm:\n",
    "\n",
    "* **Pre-training:** BERT is initially pre-trained on a large corpus of unlabeled text data during which the model learns to predict masked words based on the surrounding context using masked language modeling. This pre-training phase helps BERT develop a deep understanding of language semantics and syntax.\n",
    "\n",
    "* **Fine-tuning:** After pre-training, BERT is fine-tuned on specific downstream tasks. This involves training the model on labeled datasets for NLP tasks. Fine-tuning allows BERT to adapt to the specific requirements of the target task.\n",
    "\n",
    "We have augmented arc-eager using BERT as an encoder in hope of improving the accuracy of arc-eager parsing by providing more nuanced and precise representations of words.\n",
    "\n",
    "As for the biLSTM, the features extracted from BERT are passed through a MultiLayer Perceptron that will return a score for each possible transition."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TK4Yk_66ofHA"
   },
   "source": [
    "#### Loading and Preprocessing data\n",
    "First of all, the `AutoTokenizer` function of BERT uncased is loaded as `tokenizer`. This function is called inside `tokenize_and_align_labels` function, which prepare the sample for BERT, producing the BERT's indices corresponding to each token in the sentence (`input_ids`), the attention mask, indicating whether the token should be attented by the model or not, and providing also a tool useful to identify the subtokens: `word_ids`. These quantities are padded to have all the same length, which has been chosen as a trade-off with computational efficienty and max length of sentences in the dataset: `max_len = 200`.\n",
    "\n",
    "The goal of the `process_sample` function is to process the data and create the actual training examples as mentioned before. The oracle is used to compute the canonical action sequence for each sentence leading to the gold tree. We then pair configurations and canonical actions.\n",
    "The function returns as before the encoded batch of all the samples, the gold configuration for all the sentences, the gold moves and the final golden configuration, but provides also additional quantities since the samples are now prepared from the `tokenizer`: the input ids, the processed word_ids, the attention mask."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
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    {
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       "Downloading (…)solve/main/vocab.txt: 0.00B [00:00, ?B/s]"
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       "Downloading (…)/main/tokenizer.json: 0.00B [00:00, ?B/s]"
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   ],
   "source": [
    "tokenizer = AutoTokenizer.from_pretrained(\"bert-base-uncased\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "KPv5Jr37pJX0"
   },
   "outputs": [],
   "source": [
    "# we put our samples in input (every batch in the train/ev/test dataset) and extract its tokens\n",
    "# we should return a new dictionary with all the informations given by bert\n",
    "# in the example from hugginface they are doing operations with labels but we are not interested in it because we have an unsupervised task\n",
    "def tokenize_and_align_labels(examples):\n",
    "    tokenized_inputs = tokenizer(examples[\"tokens\"], truncation=True, is_split_into_words=True, padding='max_length', max_length=200)\n",
    "    tokenized_inputs[\"word_ids\"] = tokenized_inputs.word_ids()\n",
    "    return tokenized_inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "5KowQe7_ozLj"
   },
   "outputs": [],
   "source": [
    "def process_sample(sample, get_gold_path = False):\n",
    "\n",
    "  # put sentence and gold tree in our format\n",
    "  sentence = [\"<ROOT>\"] + sample[\"tokens\"]\n",
    "  input_ids = sample[\"input_ids\"]\n",
    "  attention_mask = sample[\"attention_mask\"]\n",
    "  word_id_org = []\n",
    "  for i in sample[\"word_ids\"]: # remove None from word_ids\n",
    "    if i != None:\n",
    "      word_id_org.append(i)\n",
    "  gold = [-1] + [int(i) for i in sample[\"head\"]]  # heads in the gold tree are strings, we convert them to int\n",
    "  word_id = []\n",
    "  word_id.append(1) # append 1 to refer to the root coherent with enc_sentence\n",
    "  for i, word in enumerate(sample[\"tokens\"]):\n",
    "    if i in word_id_org:\n",
    "      word_id.append(word_id_org.index(i)) # we keep only the index of the leftmost token\n",
    "    elif i not in word_id_org: # to prevent errors\n",
    "      word_id.append(i)\n",
    "\n",
    "  # embedding ids of sentence words\n",
    "  enc_sentence = [emb_dictionary[word] if word in emb_dictionary else emb_dictionary[\"<unk>\"] for word in sentence]\n",
    "\n",
    "  # gold_path and gold_moves are parallel arrays whose elements refer to parsing steps\n",
    "  gold_path = []   # record topmost stack token and first buffer token for current step\n",
    "  gold_moves = []  # contains oracle (canonical) move for current step: 0 is left, 1 right, 2 shift, 3 reduce\n",
    "\n",
    "  if get_gold_path:  # only for training\n",
    "    parser = ArcEager(sentence)\n",
    "    oracle = Oracle(parser, gold)\n",
    "\n",
    "    while not parser.is_tree_final():\n",
    "      # save configuration\n",
    "      configuration = [parser.stack[len(parser.stack)-1]]\n",
    "      if len(parser.buffer) == 0:\n",
    "        configuration.append(-1)\n",
    "      else:\n",
    "        configuration.append(parser.buffer[0])\n",
    "      gold_path.append(configuration)\n",
    "\n",
    "      # save gold move\n",
    "      if oracle.is_left_arc_gold():\n",
    "        gold_moves.append(0)\n",
    "        parser.left_arc()\n",
    "      elif oracle.is_right_arc_gold():\n",
    "        parser.right_arc()\n",
    "        gold_moves.append(1)\n",
    "      elif oracle.is_shift_gold():\n",
    "        parser.shift()\n",
    "        gold_moves.append(2)\n",
    "      elif oracle.is_reduce_gold():\n",
    "        parser.reduce()\n",
    "        gold_moves.append(3)\n",
    "\n",
    "  return enc_sentence, gold_path, gold_moves, gold, input_ids, word_id, attention_mask"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "i21JfTLMjKpL"
   },
   "source": [
    "The next function is used to batch the training data. Since we are dealing with BERT, we need to return as well the input ids, word ids and the attention mask."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "UdO5J-aAq3wx"
   },
   "outputs": [],
   "source": [
    "def prepare_batch_bert(batch_data, get_gold_path=False):\n",
    "  data = [process_sample(s, get_gold_path=get_gold_path) for s in batch_data]\n",
    "  # sentences, paths, moves, trees are parallel arrays, each element refers to a sentence\n",
    "  sentences = [s[0] for s in data]\n",
    "  paths = [s[1] for s in data]\n",
    "  moves = [s[2] for s in data]\n",
    "  trees = [s[3] for s in data]\n",
    "  input_ids = [s[4] for s in data]\n",
    "  word_id =  [s[5] for s in data]\n",
    "  attention_mask = [s[6] for s in data]\n",
    "  return sentences, paths, moves, trees, input_ids, word_id, attention_mask"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1qgSsOaqlSeg"
   },
   "source": [
    "In order to provide a consistent comparison with BiLSTM, we choose again *English EWT* from Universal Dependencies Project to train and test the model that includes BERT."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "zO6xEW_43HfY",
    "outputId": "1c5ffe9b-85b2-4f8c-e5f2-8e58e17c2e3a"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:datasets.builder:Found cached dataset universal_dependencies (/root/.cache/huggingface/datasets/universal_dependencies/en_ewt/2.7.0/1ac001f0e8a0021f19388e810c94599f3ac13cc45d6b5b8c69f7847b2188bdf7)\n",
      "WARNING:datasets.builder:Found cached dataset universal_dependencies (/root/.cache/huggingface/datasets/universal_dependencies/en_ewt/2.7.0/1ac001f0e8a0021f19388e810c94599f3ac13cc45d6b5b8c69f7847b2188bdf7)\n",
      "WARNING:datasets.builder:Found cached dataset universal_dependencies (/root/.cache/huggingface/datasets/universal_dependencies/en_ewt/2.7.0/1ac001f0e8a0021f19388e810c94599f3ac13cc45d6b5b8c69f7847b2188bdf7)\n"
     ]
    }
   ],
   "source": [
    "train_dataset = load_dataset('universal_dependencies', 'en_ewt', split=\"train\")\n",
    "dev_dataset = load_dataset('universal_dependencies', 'en_ewt', split=\"validation\")\n",
    "test_dataset = load_dataset('universal_dependencies', 'en_ewt', split=\"test\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_bHCiGS4uE_M"
   },
   "source": [
    "As before, the  `None ` are removed from the dataset and the  `tokenize_and_align_labels ` function is applied to prepare data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 54,
     "referenced_widgets": [
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   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:datasets.arrow_dataset:Loading cached processed dataset at /root/.cache/huggingface/datasets/universal_dependencies/en_ewt/2.7.0/1ac001f0e8a0021f19388e810c94599f3ac13cc45d6b5b8c69f7847b2188bdf7/cache-5c6116a0f4b7949c.arrow\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "034ffac0bba64c9b97f2565a18a2880a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Map:   0%|          | 0/12543 [00:00<?, ? examples/s]"
      ]
     },
     "metadata": {},
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    }
   ],
   "source": [
    "train_dataset = train_dataset.map(remove_None, batched=False)\n",
    "train_dataset = train_dataset.map(tokenize_and_align_labels, batched=False)\n",
    "dev_dataset = dev_dataset.map(remove_None, batched=False)\n",
    "dev_dataset = dev_dataset.map(tokenize_and_align_labels, batched=False)\n",
    "test_dataset = test_dataset.map(remove_None, batched=False)\n",
    "test_dataset = test_dataset.map(tokenize_and_align_labels, batched=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5Vyg3Fa9gtBU"
   },
   "source": [
    "Similarly to the biLSTM training, we have excluded sentences with non-projective trees from the training dataset. However, for the evaluation phase, we have chosen to include sentences with non-projective trees.\n",
    "As a result, we anticipate that the UAS value obtained during training will be smaller compared to the UAS value obtained during second phase of the testing, where non-projective sentences will be removed from the test dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "VcR7r35LrYbn",
    "outputId": "8866f0da-740d-4fb0-a56e-c6540f1a3d51"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of samples:\n",
      "Train:\t 11887\n",
      "Dev:\t 2002\n",
      "Test:\t 2077\n"
     ]
    }
   ],
   "source": [
    "# remove non-projective sentences: heads in the gold tree are strings, we convert them to int\n",
    "train_dataset = [sample for sample in train_dataset if is_projective([-1] + [int(head) for head in sample[\"head\"]])]\n",
    "# create the embedding dictionary\n",
    "emb_dictionary = create_dict(train_dataset)\n",
    "\n",
    "print(\"Number of samples:\")\n",
    "print(\"Train:\\t\", len(train_dataset)) #(train is the number of samples without the non-projective)\n",
    "print(\"Dev:\\t\", len(dev_dataset))\n",
    "print(\"Test:\\t\", len(test_dataset))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "l1xlu1IkuRWk"
   },
   "source": [
    "#### **Model Implementation with BERT**\n",
    "The `Bert` class implements the model as follows:\n",
    "\n",
    "1. The pre-trained BERT model is initialized.\n",
    "2. The linear layers and activation functions for the MLP are defined.\n",
    "3. The input x and attention are converted into a PyTorch tensor, reshaped then passed through the BERT model to generate the output containing various BERT outputs, including the hidden states.\n",
    "4. The 13 hidden states are averaged to obtain h1. This choice has been made because each hidden layer in BERT captures different levels of linguistic information. By averaging the representations from all layers, we can capture a more comprehensive understanding of the input text. In fact, lower layers tend to capture more surface-level features, while higher layers capture more abstract and semantic information. Our hope is that averaging could help incorporate these diverse representations into a single unified representation. Another advantage of this choice can be reducing reliace on a single specific layer and consequently prevent overfitting.\n",
    "5. The dimensions of h1 are permuted using `h1.permute(1, 0, 2)` to obtain h.\n",
    "6. The `paths`, `h`, and `word_id` are used to get the input for the MLP layer which is passed through the MLP layer considering only the leftmost embedding from each subtoken. Similarly as in `Net` class the resulting tensor out represents the output probabilities for the parse configurations.\n",
    "7. The parse steps are calculated as in `Net` class in order to achieve the final configuration for each parser in the evaluation set.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "mSkiJ4iKrieM"
   },
   "outputs": [],
   "source": [
    "class Bert(nn.Module):\n",
    "    def __init__(self, device, DROPOUT):\n",
    "        '''__init__ fucntion initializes both BERT and MLP\n",
    "      Parameters:\n",
    "      device: (CPU or GPU) on which the model will be executed\n",
    "      DROPOUT: dropout rate which acts as a regularization to avoid overfitting\n",
    "      '''\n",
    "        super(Bert, self).__init__()\n",
    "        self.device = device\n",
    "        self.DROPOUT = DROPOUT\n",
    "        self.model_name = 'bert-base-uncased'\n",
    "\n",
    "        # Load the pretrained BERT model with hidden states output\n",
    "        self.bert = AutoModel.from_pretrained(self.model_name, output_hidden_states=True)\n",
    "\n",
    "        # Define the linear layers and activation functions\n",
    "        self.w1 = torch.nn.Linear(2 * BERT_HIDD, MLP_SIZE, bias=True)\n",
    "        self.activation = torch.nn.Tanh()\n",
    "        self.w2 = torch.nn.Linear(MLP_SIZE, 4, bias=True)\n",
    "\n",
    "        # Softmax activation function for output probabilities\n",
    "        self.softmax = torch.nn.Softmax(dim=-1)\n",
    "\n",
    "        # Dropout layers for regularization\n",
    "        self.dropout = torch.nn.Dropout(self.DROPOUT)\n",
    "\n",
    "\n",
    "    def forward(self, x, paths, word_id, attention):\n",
    "        '''The forward function defines the forward pass of the model\n",
    "      Parameters:\n",
    "      x: tokenized input sequence\n",
    "      paths: sequence of actions taken by the parser during the parsing process\n",
    "      word_id: index of each subtoken in an input sentence\n",
    "      attention: attention mask which is a binary tensor of the same shape as the input sequence,\n",
    "      where each element indicates whether the corresponding token should be attended to or not.\n",
    "      '''\n",
    "        x = torch.tensor([x]).to(self.device) # (1, 8, 200)\n",
    "        x = torch.squeeze(x, 0) # we remove dimension 1 (batch_size, padding) = (8, 200)\n",
    "        attention = torch.tensor([attention]).to(self.device) # (1, 8, 200)\n",
    "        attention = torch.squeeze(attention, 0)\n",
    "        output = self.bert(input_ids=x, attention_mask=attention)\n",
    "        h1 =  sum(output.hidden_states)/13\n",
    "        h = h1.permute(1,0,2)\n",
    "\n",
    "        mlp_input = self.get_mlp_input(paths, h, word_id)\n",
    "        out = self.mlp(mlp_input)\n",
    "\n",
    "        return out\n",
    "\n",
    "    def get_mlp_input(self, configurations, h, word_id): # configurations = paths\n",
    "        '''Parameters:\n",
    "        configurations: the given configurations\n",
    "        h: tensor containing the hidden states\n",
    "        word_id: index of each token in the input\n",
    "         '''\n",
    "        mlp_input = []\n",
    "        zero_tensor = torch.zeros(BERT_HIDD, requires_grad=False).to(self.device) # it needs to have the same size of the last dimension of the output of the model\n",
    "\n",
    "        for i in range(len(configurations)): # i is the index, belongs to [0,batch_size-1]\n",
    "            for j in configurations[i]: # for each configuration [a,b]\n",
    "\n",
    "                # concatenate zero tensor if the element is -1 (the root, zero prob), otherwise the output from the model (h)\n",
    "                # h[a][i] where i is the index through the bert_hidd elements\n",
    "                # a = word_id[i][j[0]] ---> corresponds to the index of the token for the piece of token\n",
    "                mlp_input.append(\n",
    "                    torch.cat([zero_tensor if j[0] == -1 else h[word_id[i][j[0]]][i],\n",
    "                               zero_tensor if j[1] == -1 else h[word_id[i][j[1]]][i]])\n",
    "                )\n",
    "\n",
    "        mlp_input = torch.stack(mlp_input).to(self.device)\n",
    "        return mlp_input\n",
    "\n",
    "    def mlp(self, x):\n",
    "        return self.softmax(self.w2(self.dropout(self.activation(self.w1(self.dropout(x))))))\n",
    "\n",
    "    def infere(self, x, sentences, word_id, attention, test=False):\n",
    "        '''performs the inference process using the trained model and returns the predicted dependency trees\n",
    "        x: input tokens\n",
    "        sentences: input sentences\n",
    "        word_id: index of each token in the input\n",
    "        attention: attention mask\n",
    "        test: boolean, if equal True it saves the parse step suggested moves in order to perform a statistical analysis on the results\n",
    "        '''\n",
    "        parsers = [ArcEager(i) for i in sentences]\n",
    "        x = torch.tensor([x]).to(self.device) # (1, 16, 100)\n",
    "        x = torch.squeeze(x, 0) # we remove dimension 1\n",
    "        attention = torch.tensor([attention]).to(self.device) # (1, 16, 100)\n",
    "        attention = torch.squeeze(attention,0)\n",
    "        output = self.bert(input_ids=x, attention_mask=attention)\n",
    "\n",
    "        h1 =  sum(output.hidden_states)/13\n",
    "        h = h1.permute(1,0,2)\n",
    "\n",
    "        pred_moves = []\n",
    "        while not self.parsed_all(parsers):\n",
    "            configurations = self.get_configurations(parsers)\n",
    "            mlp_input = self.get_mlp_input(configurations, h, word_id)\n",
    "            mlp_out = self.mlp(mlp_input)\n",
    "            if test == True:\n",
    "              step = self.parse_step(parsers, mlp_out, test=True)\n",
    "              pred_moves.append(step)\n",
    "            else:\n",
    "              self.parse_step(parsers, mlp_out, test=False)\n",
    "\n",
    "        if test == True:\n",
    "          return pred_moves\n",
    "        else:\n",
    "          return [parser.arcs for parser in parsers]\n",
    "\n",
    "    def get_configurations(self, parsers):\n",
    "      '''returns the configuration of each parser in the batch\n",
    "      takes only into configuration the top most element of the stack and the first element of the buffer\n",
    "      Parameters:\n",
    "      parsers: parsers configuration given by arc-eager over the input sentences\n",
    "      '''\n",
    "      configurations = []\n",
    "\n",
    "      for parser in parsers:\n",
    "          if parser.is_tree_final():\n",
    "              conf = [-1, -1]\n",
    "          else:\n",
    "              if len(parser.stack) == 0:\n",
    "                print(\"hhh\")\n",
    "              conf = [parser.stack[-1]]\n",
    "              if len(parser.buffer) == 0:\n",
    "                  conf.append(-1)\n",
    "              else:\n",
    "                  conf.append(parser.buffer[0])\n",
    "          configurations.append([conf])\n",
    "\n",
    "      return configurations\n",
    "\n",
    "    def parsed_all(self, parsers):\n",
    "      '''checks if all the parser configurations in the batch have reached the final configuration.\n",
    "      Parameter:\n",
    "      parsers: parsers configuration given by arc-eager over the input sentences and processed using parse_step function\n",
    "      test: boolean, if equal True it saves the parse step suggested moves in order to perform a statistical analysis on the results\n",
    "      '''\n",
    "      for parser in parsers:\n",
    "          if not parser.is_tree_final():\n",
    "              return False\n",
    "      return True\n",
    "\n",
    "    def parse_step(self, parsers, moves, test=False):\n",
    "      '''This function performs the suggested move by mlp taking into consideration the constraints of arc-eager.\n",
    "      It addresses all of the cases for each suggested move of the 4 moves by making the correct decision in certain scenarios based on the oracle\n",
    "      or by choosing the second best choice depending on the score in case of indecision.\n",
    "      Parameter:\n",
    "      parsers: parsers configuration given by arc-eager over the input sentences and processed using parse_step function\n",
    "      moves: scores obtained from mlp'''\n",
    "      moves_argm = moves.argmax(-1)\n",
    "      steps = []\n",
    "      for i in range(len(parsers)):\n",
    "        if parsers[i].is_tree_final():\n",
    "          steps.append(None)\n",
    "          continue\n",
    "        else:\n",
    "          if moves_argm[i] == 0:\n",
    "            if len(parsers[i].stack) > 1:\n",
    "              parsers[i].left_arc()\n",
    "              steps.append(0)\n",
    "            else:\n",
    "              if len(parsers[i].buffer) == 1:\n",
    "                if parsers[i].arcs[parsers[i].buffer[0]] == -1:\n",
    "                  parsers[i].right_arc()\n",
    "                  steps.append(1)\n",
    "                else:\n",
    "                  parsers[i].shift()\n",
    "                  steps.append(2)\n",
    "              elif len(parsers[i].buffer) > 1:\n",
    "                if parsers[i].arcs[parsers[i].buffer[0]] != -1:\n",
    "                  parsers[i].shift()\n",
    "                  steps.append(2)\n",
    "                else: # we perform the second suggested move\n",
    "                  if (moves[i][1] > moves[i][2]):\n",
    "                    parsers[i].right_arc()\n",
    "                    steps.append(1)\n",
    "                  elif (moves[i][2] > moves[i][1]):\n",
    "                    parsers[i].shift()\n",
    "                    steps.append(2)\n",
    "\n",
    "          elif moves_argm[i] == 1:\n",
    "            if len(parsers[i].buffer) > 0:\n",
    "              if len(parsers[i].buffer) != 1:\n",
    "                parsers[i].right_arc()\n",
    "                steps.append(1)\n",
    "\n",
    "              else:\n",
    "                if (parsers[i].arcs[parsers[i].stack[-1]] != -1 and parsers[i].arcs[parsers[i].buffer[0]] != -1): # case: both topmost in the stack and element in the buffer have a head\n",
    "                  arcs_of_stack = [parsers[i].arcs[j] for j in parsers[i].stack] # list of all the arcs of the elements in the stack\n",
    "                  if (-1 not in arcs_of_stack[1:]): # if all the elements in the stack have a head we can do shift\n",
    "                    parsers[i].shift()\n",
    "                    steps.append(2)\n",
    "                  else: # if there are elements in the stack that don't have a head, let's do reduce so the buffer is not empty\n",
    "                    parsers[i].reduce()\n",
    "                    steps.append(3)\n",
    "                elif (parsers[i].arcs[parsers[i].buffer[0]] != -1 and len(parsers[i].stack)==1): # case: only root in the stack and 1 element in the buffer WITH head\n",
    "                  parsers[i].shift()\n",
    "                  steps.append(2)\n",
    "                elif (parsers[i].arcs[parsers[i].buffer[0]] == -1 and len(parsers[i].stack)==1): # case: only root in the stack abd 1 element in the buffer WITHOUT head\n",
    "                  parsers[i].right_arc()\n",
    "                  steps.append(1)\n",
    "                elif (parsers[i].arcs[parsers[i].stack[-1]] != -1 and parsers[i].arcs[parsers[i].buffer[0]] == -1 and len(parsers[i].stack)>1): # case: topmost element in the stack WITH head and one element in the buffer WITHOUT head\n",
    "                  arcs_of_stack = [parsers[i].arcs[j] for j in parsers[i].stack] # list of all the arcs of the elements in the stack\n",
    "                  if (-1 not in arcs_of_stack[1:]): # if all the elements in the stack have a head we can do rightarc (that do also a shift)\n",
    "                    parsers[i].right_arc()\n",
    "                    steps.append(1)\n",
    "                  else: # if there are elements in the stack that don't have a head, let's do reduce so the buffer is not empty\n",
    "                    parsers[i].reduce()\n",
    "                    steps.append(3)\n",
    "                elif (parsers[i].arcs[parsers[i].stack[-1]] == -1 and parsers[i].arcs[parsers[i].buffer[0]] != -1): # case: topmost element in the stack don't have a root but the only element in the buffer has it --> leftarc\n",
    "                    parsers[i].left_arc()\n",
    "                    steps.append(0)\n",
    "                elif (parsers[i].arcs[parsers[i].stack[-1]] == -1 and parsers[i].arcs[parsers[i].buffer[0]] == -1): # case: both topmost element in the stack and first in the buffer don't have a head\n",
    "                    parsers[i].left_arc()\n",
    "                    steps.append(0)\n",
    "            else:\n",
    "              if parsers[i].arcs[parsers[i].stack[-1]] != -1:\n",
    "                parsers[i].reduce()\n",
    "                steps.append(3)\n",
    "          elif moves_argm[i] == 2:\n",
    "            if len(parsers[i].buffer) > 0:\n",
    "              if len(parsers[i].buffer) != 1:\n",
    "                parsers[i].shift()\n",
    "                steps.append(2)\n",
    "              else:\n",
    "                if (parsers[i].arcs[parsers[i].stack[-1]] != -1 and parsers[i].arcs[parsers[i].buffer[0]] != -1): # case: both topmost in the stack and element in the buffer have a head\n",
    "                  arcs_of_stack = [parsers[i].arcs[j] for j in parsers[i].stack] # list of all the arcs of the elements in the stack\n",
    "                  if (-1 not in arcs_of_stack[1:]): # if all the elements in the stack have a head we can do shift\n",
    "                    parsers[i].shift()\n",
    "                    steps.append(2)\n",
    "                  else: # if there are elements in the stack that don't have a head, let's do reduce so the buffer is not empty\n",
    "                    parsers[i].reduce()\n",
    "                    steps.append(3)\n",
    "                elif (parsers[i].arcs[parsers[i].buffer[0]] != -1 and len(parsers[i].stack)==1): # case: only root in the stack and 1 element in the buffer WITH head\n",
    "                  parsers[i].shift()\n",
    "                  steps.append(2)\n",
    "                elif (parsers[i].arcs[parsers[i].buffer[0]] == -1 and len(parsers[i].stack)==1): # case: only root in the stack abd 1 element in the buffer WITHOUT head\n",
    "                  parsers[i].right_arc()\n",
    "                  steps.append(1)\n",
    "                elif (parsers[i].arcs[parsers[i].stack[-1]] != -1 and parsers[i].arcs[parsers[i].buffer[0]] == -1 and len(parsers[i].stack)>1): # case: topmost element in the stack WITH head and one element in the buffer WITHOUT head\n",
    "                  arcs_of_stack = [parsers[i].arcs[j] for j in parsers[i].stack] # list of all the arcs of the elements in the stack\n",
    "                  if (-1 not in arcs_of_stack[1:]): # if all the elements in the stack have a head we can do rightarc (that do also a shift)\n",
    "                    parsers[i].right_arc()\n",
    "                  else: # if there are elements in the stack that don't have a head, let's do reduce so the buffer is not empty\n",
    "                    parsers[i].reduce()\n",
    "                    steps.append(3)\n",
    "                elif (parsers[i].arcs[parsers[i].stack[-1]] == -1 and parsers[i].arcs[parsers[i].buffer[0]] != -1): # case: topmost element in the stack don't have a root but the only element in the buffer has it --> leftarc\n",
    "                    parsers[i].left_arc()\n",
    "                    steps.append(0)\n",
    "                elif (parsers[i].arcs[parsers[i].stack[-1]] == -1 and parsers[i].arcs[parsers[i].buffer[0]] == -1): # case: both topmost element in the stack and first in the buffer don't have a head\n",
    "                    parsers[i].left_arc()\n",
    "                    steps.append(0)\n",
    "            else:\n",
    "              if parsers[i].arcs[parsers[i].stack[-1]] != -1:\n",
    "                parsers[i].reduce()\n",
    "                steps.append(3)\n",
    "          elif moves_argm[i] == 3:\n",
    "            if parsers[i].arcs[parsers[i].stack[-1]] != -1:\n",
    "              parsers[i].reduce()\n",
    "              steps.append(3)\n",
    "            else:\n",
    "              if len(parsers[i].buffer) == 1: # case: there's only one element in the buffer and the topmost in the stack doesn't have a root ---> leftarc\n",
    "                if len(parsers[i].stack) > 1:\n",
    "                  parsers[i].left_arc()\n",
    "                  steps.append(0)\n",
    "                else:\n",
    "                  parsers[i].right_arc()\n",
    "                  steps.append(1)\n",
    "              else: # we perform the second suggested move\n",
    "                if (moves[i][0] > moves[i][1] and moves[i][0] > moves[i][2]):\n",
    "                  if len(parsers[i].stack) > 1:\n",
    "                    parsers[i].left_arc()\n",
    "                    steps.append(0)\n",
    "                  else:\n",
    "                    if (moves[i][1] > moves[i][2]):\n",
    "                      parsers[i].right_arc()\n",
    "                      steps.append(1)\n",
    "                    elif (moves[i][1] <= moves[i][2]):\n",
    "                      parsers[i].shift()\n",
    "                      steps.append(2)\n",
    "                elif (moves[i][1] > moves[i][0] and moves[i][1] > moves[i][2]):\n",
    "                  parsers[i].right_arc()\n",
    "                  steps.append(1)\n",
    "                elif (moves[i][2] >= moves[i][0] and moves[i][2] > moves[i][1]):\n",
    "                  parsers[i].shift()\n",
    "                  steps.append(2)\n",
    "                elif (moves[i][2] > moves[i][0] and moves[i][2] >= moves[i][1]):\n",
    "                  parsers[i].shift()\n",
    "                  steps.append(2)\n",
    "      if test == True:\n",
    "        return steps\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "4qaeA5Otl5mg"
   },
   "source": [
    "Also for BERT evaluation we will use **UAS** score, then the *evaluation* function that we will use is the same as before. The train and test function instead need to be updated to fit the `Bert` class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "NxlqVrl-1hfO"
   },
   "outputs": [],
   "source": [
    "def train_bert(model, dataloader, criterion, optimizer):\n",
    "    model.train()\n",
    "    total_loss = 0\n",
    "    count = 0\n",
    "\n",
    "    for batch in dataloader:\n",
    "        optimizer.zero_grad()\n",
    "        sentences, paths, moves, trees, input, words_id, attention = batch\n",
    "\n",
    "        out = model(input, paths, words_id, attention)\n",
    "        labels = torch.tensor(sum(moves, [])).to(device) #sum(moves, []) flatten the array\n",
    "        loss = criterion(out, labels)\n",
    "\n",
    "        count += 1\n",
    "        total_loss += loss.item()\n",
    "\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "\n",
    "    return total_loss / count\n",
    "\n",
    "\n",
    "def test_bert(model, dataloader):\n",
    "    model.eval()\n",
    "\n",
    "    gold = []\n",
    "    preds = []\n",
    "\n",
    "    for batch in dataloader:\n",
    "        sentences, paths, moves, trees, input, words_id, attention = batch\n",
    "\n",
    "        with torch.no_grad():\n",
    "            pred = model.infere(input, sentences, words_id, attention, test=False) # x, sentences, word_id, attention\n",
    "            gold += trees\n",
    "            preds += pred\n",
    "\n",
    "    return evaluate(gold, preds)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "SzziI5Vjm2bk"
   },
   "source": [
    "Grid search was used on 5 epochs to check the best parameters for evaluating the model using UAS. The parameters found to be the best are `DROPOUT = 0.1`, `LR = 5e-5`, `BATCH_SIZE = 8`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "UYkGEURr9OUr"
   },
   "outputs": [],
   "source": [
    "MLP_SIZE = 200\n",
    "BERT_HIDD = 768\n",
    "DROPOUT = 0.1\n",
    "LR = 5e-5\n",
    "BATCH_SIZE = 8\n",
    "train_dataloader_bert = torch.utils.data.DataLoader(train_dataset, batch_size=BATCH_SIZE, shuffle=True, collate_fn=partial(prepare_batch_bert, get_gold_path=True))\n",
    "dev_dataloader_bert = torch.utils.data.DataLoader(dev_dataset, batch_size=BATCH_SIZE, shuffle=False, collate_fn=partial(prepare_batch_bert))\n",
    "test_dataloader_bert = torch.utils.data.DataLoader(test_dataset, batch_size=BATCH_SIZE, shuffle=False, collate_fn=partial(prepare_batch_bert))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "YWfpo563nAA7"
   },
   "source": [
    "**Training the model**\n",
    "\n",
    "For training the model, the number of epochs was set to `EPOCHS = 15`, to avoid exceeding computational time.\n",
    "During the training, it was observed that the UAS value did not show significant improvement after some epochs. To address this issue, also for this training an adaptive learning rate approach was employed using the `ReduceLROnPlateau` function from `torch`. This function reduced the learning rate by a factor of 0.5 after 5 epochs without any improvement in the UAS value. As before, \"improvement\" is defined as a difference greater than $0.002$ between the current best UAS value and the next one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "WUxrLOu5-kUH",
    "outputId": "fa42ab00-2d52-49bb-9f5e-73796e4ba3fc"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Device: cuda\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Some weights of the model checkpoint at bert-base-uncased were not used when initializing BertModel: ['cls.predictions.bias', 'cls.seq_relationship.bias', 'cls.predictions.transform.LayerNorm.weight', 'cls.predictions.transform.LayerNorm.bias', 'cls.predictions.transform.dense.weight', 'cls.seq_relationship.weight', 'cls.predictions.transform.dense.bias']\n",
      "- This IS expected if you are initializing BertModel from the checkpoint of a model trained on another task or with another architecture (e.g. initializing a BertForSequenceClassification model from a BertForPreTraining model).\n",
      "- This IS NOT expected if you are initializing BertModel from the checkpoint of a model that you expect to be exactly identical (initializing a BertForSequenceClassification model from a BertForSequenceClassification model).\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch:   0 | avg_train_loss: 0.879 | dev_uas: 0.792 |\n",
      "Epoch:   1 | avg_train_loss: 0.811 | dev_uas: 0.845 |\n",
      "Epoch:   2 | avg_train_loss: 0.799 | dev_uas: 0.808 |\n",
      "Epoch:   3 | avg_train_loss: 0.793 | dev_uas: 0.824 |\n",
      "Epoch:   4 | avg_train_loss: 0.790 | dev_uas: 0.814 |\n",
      "Epoch:   5 | avg_train_loss: 0.788 | dev_uas: 0.794 |\n",
      "Epoch 00007: reducing learning rate of group 0 to 2.5000e-05.\n",
      "Epoch:   6 | avg_train_loss: 0.786 | dev_uas: 0.789 |\n",
      "Epoch:   7 | avg_train_loss: 0.781 | dev_uas: 0.806 |\n",
      "Epoch:   8 | avg_train_loss: 0.777 | dev_uas: 0.826 |\n",
      "Epoch:   9 | avg_train_loss: 0.775 | dev_uas: 0.817 |\n",
      "Epoch:  10 | avg_train_loss: 0.775 | dev_uas: 0.809 |\n",
      "Epoch:  11 | avg_train_loss: 0.774 | dev_uas: 0.796 |\n",
      "Epoch 00013: reducing learning rate of group 0 to 1.2500e-05.\n",
      "Epoch:  12 | avg_train_loss: 0.773 | dev_uas: 0.818 |\n",
      "Epoch:  13 | avg_train_loss: 0.771 | dev_uas: 0.818 |\n",
      "Epoch:  14 | avg_train_loss: 0.770 | dev_uas: 0.840 |\n"
     ]
    }
   ],
   "source": [
    "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n",
    "print(\"Device:\", device)\n",
    "model_bert = Bert(device, DROPOUT)\n",
    "model_bert.to(device)\n",
    "\n",
    "criterion = nn.CrossEntropyLoss()\n",
    "optimizer = torch.optim.Adam(model_bert.parameters(), lr=LR)\n",
    "scheduler = ReduceLROnPlateau(optimizer, mode='max', factor=0.5, patience=4, threshold_mode='abs', threshold = 0.002,\n",
    "                              cooldown = 1, min_lr = 1e-8, verbose=True)\n",
    "\n",
    "EPOCHS_bert = 15\n",
    "loss_bert = []\n",
    "dev_uas_bert = []\n",
    "\n",
    "for epoch in range(EPOCHS_bert):\n",
    "  avg_train_loss = train_bert(model_bert, train_dataloader_bert, criterion, optimizer)\n",
    "  loss_bert.append(avg_train_loss)\n",
    "  val_uas = test_bert(model_bert, dev_dataloader_bert)\n",
    "  dev_uas_bert.append(val_uas)\n",
    "  scheduler.step(val_uas)\n",
    "\n",
    "  print(\"Epoch: {:3d} | avg_train_loss: {:5.3f} | dev_uas: {:5.3f} |\".format(epoch, avg_train_loss, val_uas))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "23jfH8GMuZ_F"
   },
   "source": [
    "**Testing the model on non-projective and projective sentences**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "JYEZ0oZk-pPn",
    "outputId": "a042318b-17c7-4eed-8bf1-62876a535012"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test_uas: 0.845\n"
     ]
    }
   ],
   "source": [
    "test_uas_bert = test_bert(model_bert, test_dataloader_bert)\n",
    "print(\"test_uas: {:5.3f}\".format(test_uas_bert))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 430
    },
    "id": "MNZuw67C-stT",
    "outputId": "b6e62fe2-1789-4341-9e58-8556ea50059b"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "epochs = [i for i in range(EPOCHS_bert)]\n",
    "import matplotlib.pyplot as plt\n",
    "plt.plot(epochs, loss_bert, label = \"loss\")\n",
    "plt.plot(epochs, dev_uas_bert, label = \"uas evaluation\")\n",
    "plt.legend()\n",
    "plt.grid(alpha=0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5eIOAbjx02XG"
   },
   "source": [
    "**Testing the model only on projective sentences**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "7dt1pKdc07oI",
    "outputId": "2e0a336a-6839-45f2-ffa1-eba332a4dfd1"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:datasets.builder:Found cached dataset universal_dependencies (/root/.cache/huggingface/datasets/universal_dependencies/en_ewt/2.7.0/1ac001f0e8a0021f19388e810c94599f3ac13cc45d6b5b8c69f7847b2188bdf7)\n",
      "WARNING:datasets.arrow_dataset:Loading cached processed dataset at /root/.cache/huggingface/datasets/universal_dependencies/en_ewt/2.7.0/1ac001f0e8a0021f19388e810c94599f3ac13cc45d6b5b8c69f7847b2188bdf7/cache-f3378a650a701b6d.arrow\n",
      "WARNING:datasets.arrow_dataset:Loading cached processed dataset at /root/.cache/huggingface/datasets/universal_dependencies/en_ewt/2.7.0/1ac001f0e8a0021f19388e810c94599f3ac13cc45d6b5b8c69f7847b2188bdf7/cache-698be1b7e7fd628c.arrow\n"
     ]
    }
   ],
   "source": [
    "test_dataset = load_dataset('universal_dependencies', 'en_ewt', split=\"test\")\n",
    "test_dataset = test_dataset.map(remove_None, batched=False)\n",
    "test_dataset = test_dataset.map(tokenize_and_align_labels, batched=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "yScQHXoV1FZr",
    "outputId": "2aa7fbf2-1c26-4fa7-be78-d3dff52e0b04"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test:\t 2023\n"
     ]
    }
   ],
   "source": [
    "# remove non-projective sentences: heads in the gold tree are strings, we convert them to int\n",
    "test_dataset = [sample for sample in test_dataset if is_projective([-1] + [int(head) for head in sample[\"head\"]])]\n",
    "\n",
    "print(\"Test:\\t\", len(test_dataset))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "zL-Vsp0D1VoH"
   },
   "outputs": [],
   "source": [
    "BATCH_SIZE = 8\n",
    "\n",
    "test_dataloader_bert_2 = torch.utils.data.DataLoader(test_dataset, batch_size=BATCH_SIZE, shuffle=False, collate_fn=partial(prepare_batch_bert))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "OQCyNvDF-42H",
    "outputId": "c3ec9bf5-c171-4f0a-e940-409af4b6e816"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test_uas: 0.848\n"
     ]
    }
   ],
   "source": [
    "test_uas_bert_2 = test_bert(model_bert, test_dataloader_bert_2)\n",
    "print(\"test_uas: {:5.3f}\".format(test_uas_bert_2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "qxKajp30_EsJ"
   },
   "source": [
    "As noticed for the biLSTM, the test on only projective sentences returns a slightly better result, but the two are still comparable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-sG20HSpgQKy"
   },
   "source": [
    "## **Predicted moves analysis for Bert model**\n",
    "In this section a further analysis on the moves predicted from the model with BERT as feature encoder is provided.\n",
    "\n",
    "For the test dataset with only non-projective samples the true positives ($tp$), true negatives ($tn$), false positive ($fp$) and false negatives ($fn$) are extracted in order to evaluate the following scores:\n",
    "* $Accuracy = \\frac{tp + tn}{tp + tn + fp + fn}$, which represents how well the model is able to correctly predict or correctily discard a transition.\n",
    "* $Precision = \\frac{tp}{tp+fp}$ which represents the number of correct predictions over all the prediction for the specific class.\n",
    "* $Recall = \\frac{tp}{tp+fn}$, which measures the proportion of actual positive instances that are correctly identified by the classifier.\n",
    "* $F1 = 2 * \\frac{Precision * Recall }{Precision + Recall}$, which is the harmonic mean of precision and recall, providing a balanced measure that takes into account both false positives and false negatives.\n",
    "\n",
    "In particular the following notation will be used for each transition $t$:\n",
    "* $tp$: number of correct $t$ identification\n",
    "* $tn$: number of correct $\\bar{t}$ (all classes except from $t$) identification\n",
    "* $fp$: number of wrong $t$ identification\n",
    "* $fn$: number of wrong $\\bar{t}$ identification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "A49lwz-lwSdf"
   },
   "outputs": [],
   "source": [
    "test_dataloader_analysis = torch.utils.data.DataLoader(test_dataset, batch_size=BATCH_SIZE, shuffle=True, collate_fn=partial(prepare_batch_bert, get_gold_path=True))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "IebVj3OzlyOZ"
   },
   "outputs": [],
   "source": [
    "confusion_matrix_0 = np.zeros((2,2)) # 4 evaluation: tp, tn, fp, fn for leftarc\n",
    "confusion_matrix_1 = np.zeros((2,2)) # 4 evaluation: tp, tn, fp, fn for rightarc\n",
    "confusion_matrix_2 = np.zeros((2,2)) # 4 evaluation: tp, tn, fp, fn for shift\n",
    "confusion_matrix_3 = np.zeros((2,2)) # 4 evaluation: tp, tn, fp, fn for reduce\n",
    "\n",
    "for batch in test_dataloader_analysis:\n",
    "  sentences, paths, moves, trees, input, words_id, attention = batch\n",
    "\n",
    "  with torch.no_grad():\n",
    "    moves_unord = model_bert.infere(input, sentences, words_id, attention, test=True) # x, sentences, word_id, attention\n",
    "    ord = np.zeros((len(moves),len(moves_unord))) # batch_size x max_parser moves\n",
    "    for i, sequence in enumerate(moves_unord):\n",
    "      for j, elem in enumerate(sequence):\n",
    "        ord[j][i] = elem\n",
    "\n",
    "    gold = np.zeros((len(moves),len(moves_unord)))\n",
    "    for i, sequence in enumerate(moves):\n",
    "      for j, elem in enumerate(sequence):\n",
    "        gold[i][j] = elem + 1 # in this way we will remove the 0 without removing left_arc moves\n",
    "\n",
    "    for index in range(len(moves)): # for each element in the batch\n",
    "      pred = ord[index]\n",
    "      pred = pred[~np.isnan(pred)] # remove nan\n",
    "      true = gold[index]\n",
    "      true = true[true != 0]-1 # remove padding 0 and subtract 1 in order to recover the gold configuration\n",
    "\n",
    "      # Now we check for correct move prediction\n",
    "      for (p, t) in zip(pred, true):\n",
    "        if p == 0:\n",
    "          if t == 0:\n",
    "            confusion_matrix_0[0][0] += 1 # tp\n",
    "          else:\n",
    "            confusion_matrix_0[1][0] += 1 # fp\n",
    "        elif p == 1:\n",
    "          if t == 1:\n",
    "            confusion_matrix_1[0][0] += 1 # tp\n",
    "          else:\n",
    "            confusion_matrix_1[1][0] += 1 # fp\n",
    "        elif p == 2:\n",
    "          if t == 2:\n",
    "            confusion_matrix_2[0][0] += 1 # tp\n",
    "          else:\n",
    "            confusion_matrix_2[1][0] += 1 # fp\n",
    "        elif p == 3:\n",
    "          if t == 3:\n",
    "            confusion_matrix_3[0][0] += 1 # tp\n",
    "          else:\n",
    "            confusion_matrix_3[1][0] += 1 # fp\n",
    "        if p != 0:\n",
    "          if t == 0:\n",
    "            confusion_matrix_0[0][1] += 1 # fn\n",
    "          else:\n",
    "            confusion_matrix_0[1][1] += 1 # tn\n",
    "        if p != 1:\n",
    "          if t == 1:\n",
    "            confusion_matrix_1[0][1] += 1 # fn\n",
    "          else:\n",
    "            confusion_matrix_1[1][1] += 1 # tn\n",
    "        if p != 2:\n",
    "          if t == 2:\n",
    "            confusion_matrix_2[0][1] += 1 # fn\n",
    "          else:\n",
    "            confusion_matrix_2[1][1] += 1 # tn\n",
    "        if p != 3:\n",
    "          if t == 3:\n",
    "            confusion_matrix_3[0][1] += 1 # fn\n",
    "          else:\n",
    "            confusion_matrix_3[1][1] += 1 # tn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6rr9MB2i-2sZ"
   },
   "source": [
    "**Left-arc transition**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "Lnxkn0AA-18b",
    "outputId": "4b77ee34-efce-4ce4-c7dd-e809d169d466"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LEFT-ARC TRANSITION\n",
      "The confusion matrix is:\n",
      "+---------+---------------+-------------------+\n",
      "| x       |   Predicted 0 |   Predicted non-0 |\n",
      "+=========+===============+===================+\n",
      "| True 0  |          7738 |              5423 |\n",
      "+---------+---------------+-------------------+\n",
      "| False 0 |          5523 |             29046 |\n",
      "+---------+---------------+-------------------+\n",
      "Accuracy: 0.770668342761366\n",
      "Precision: 0.5835155719779805\n",
      "Recall: 0.5879492439784211\n",
      "F1 score: 0.5857240178639013\n"
     ]
    }
   ],
   "source": [
    "print(\"LEFT-ARC TRANSITION\\nThe confusion matrix is:\")\n",
    "labels0 = [\"True 0\", \"False 0\"]\n",
    "# Convert NumPy array to a 2D list\n",
    "matrix_2d_list0 = confusion_matrix_0.tolist()\n",
    "\n",
    "# Create a new 2D list for the table data\n",
    "table_data0 = [[labels0[i]] + row for i, row in enumerate(matrix_2d_list0)]\n",
    "table0 = tabulate(table_data0, tablefmt=\"grid\",  headers=[\"x\",\"Predicted 0\", \"Predicted non-0\"])\n",
    "print(table0)\n",
    "\n",
    "# Accuracy\n",
    "acc0 = (confusion_matrix_0[0][0] + confusion_matrix_0[1][1])/(confusion_matrix_0[0][0] + confusion_matrix_0[1][0] + confusion_matrix_0[0][1] + confusion_matrix_0[1][1])\n",
    "print(\"Accuracy:\", acc0)\n",
    "\n",
    "# Precision\n",
    "pr0 = confusion_matrix_0[0][0] / (confusion_matrix_0[0][0] + confusion_matrix_0[1][0])\n",
    "print(\"Precision:\", pr0)\n",
    "\n",
    "# Recall\n",
    "rec0 = confusion_matrix_0[0][0] / (confusion_matrix_0[0][0] + confusion_matrix_0[0][1])\n",
    "print(\"Recall:\", rec0)\n",
    "\n",
    "# F1 score\n",
    "f0 = 2 * pr0 * rec0 / (pr0 + rec0)\n",
    "print(\"F1 score:\", f0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "lmVkHObaIG1V"
   },
   "source": [
    "**Right-arc transition**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "B7ClTt45IKY_",
    "outputId": "29fcae5c-060d-418e-a5d5-e282436480ce"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RIGHT-ARC TRANSITION\n",
      "The confusion matrix is:\n",
      "+---------+---------------+-------------------+\n",
      "| x       |   Predicted 1 |   Predicted non-1 |\n",
      "+=========+===============+===================+\n",
      "| True 1  |          5692 |              5012 |\n",
      "+---------+---------------+-------------------+\n",
      "| False 1 |          5065 |             31961 |\n",
      "+---------+---------------+-------------------+\n",
      "Accuracy: 0.7888749214330609\n",
      "Precision: 0.5291438133308544\n",
      "Recall: 0.5317638266068759\n",
      "F1 score: 0.530450584781697\n"
     ]
    }
   ],
   "source": [
    "from tabulate import tabulate\n",
    "print(\"RIGHT-ARC TRANSITION\\nThe confusion matrix is:\")\n",
    "labels1 = [\"True 1\", \"False 1\"]\n",
    "# Convert NumPy array to a 2D list\n",
    "matrix_2d_list1 = confusion_matrix_1.tolist()\n",
    "\n",
    "# Create a new 2D list for the table data\n",
    "table_data1 = [[labels1[i]] + row for i, row in enumerate(matrix_2d_list1)]\n",
    "table1 = tabulate(table_data1, tablefmt=\"grid\",  headers=[\"x\",\"Predicted 1\", \"Predicted non-1\"])\n",
    "print(table1)\n",
    "\n",
    "# Accuracy\n",
    "acc1 = (confusion_matrix_1[0][0] + confusion_matrix_1[1][1])/(confusion_matrix_1[0][0] + confusion_matrix_1[1][0] + confusion_matrix_1[0][1] + confusion_matrix_1[1][1])\n",
    "print(\"Accuracy:\", acc1)\n",
    "\n",
    "# Precision\n",
    "pr1 = confusion_matrix_1[0][0] / (confusion_matrix_1[0][0] + confusion_matrix_1[1][0])\n",
    "print(\"Precision:\", pr1)\n",
    "\n",
    "# Recall\n",
    "rec1 = confusion_matrix_1[0][0] / (confusion_matrix_1[0][0] + confusion_matrix_1[0][1])\n",
    "print(\"Recall:\", rec1)\n",
    "\n",
    "# F1 score\n",
    "f1 = 2 * pr1 * rec1 / (pr1 + rec1)\n",
    "print(\"F1 score:\", f1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "zLs9NzUII7Oc"
   },
   "source": [
    "**Shift transition**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "zpv5eT_EI_zN",
    "outputId": "45ebfb56-da55-4fb9-d117-ba7817825de0"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SHIFT TRANSITION\n",
      "The confusion matrix is:\n",
      "+---------+---------------+-------------------+\n",
      "| x       |   Predicted 2 |   Predicted non-2 |\n",
      "+=========+===============+===================+\n",
      "| True 2  |          8977 |              4184 |\n",
      "+---------+---------------+-------------------+\n",
      "| False 2 |          4131 |             30438 |\n",
      "+---------+---------------+-------------------+\n",
      "Accuracy: 0.825790907186256\n",
      "Precision: 0.684848947207812\n",
      "Recall: 0.6820910265177418\n",
      "F1 score: 0.6834672046899386\n"
     ]
    }
   ],
   "source": [
    "from tabulate import tabulate\n",
    "print(\"SHIFT TRANSITION\\nThe confusion matrix is:\")\n",
    "labels2 = [\"True 2\", \"False 2\"]\n",
    "# Convert NumPy array to a 2D list\n",
    "matrix_2d_list2 = confusion_matrix_2.tolist()\n",
    "\n",
    "# Create a new 2D list for the table data\n",
    "table_data2 = [[labels2[i]] + row for i, row in enumerate(matrix_2d_list2)]\n",
    "table2 = tabulate(table_data2, tablefmt=\"grid\",  headers=[\"x\",\"Predicted 2\", \"Predicted non-2\"])\n",
    "print(table2)\n",
    "\n",
    "# Accuracy\n",
    "acc2 = (confusion_matrix_2[0][0] + confusion_matrix_2[1][1])/(confusion_matrix_2[0][0] + confusion_matrix_2[1][0] + confusion_matrix_2[0][1] + confusion_matrix_2[1][1])\n",
    "print(\"Accuracy:\", acc2)\n",
    "\n",
    "# Precision\n",
    "pr2 = confusion_matrix_2[0][0] / (confusion_matrix_2[0][0] + confusion_matrix_2[1][0])\n",
    "print(\"Precision:\", pr2)\n",
    "\n",
    "# Recall\n",
    "rec2 = confusion_matrix_2[0][0] / (confusion_matrix_2[0][0] + confusion_matrix_2[0][1])\n",
    "print(\"Recall:\", rec2)\n",
    "\n",
    "# F1 score\n",
    "f2 = 2 * pr2 * rec2 / (pr2 + rec2)\n",
    "print(\"F1 score:\", f2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "E-Wp9--EJedo"
   },
   "source": [
    "**Reduce transition**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "v92jP0x0JjAZ",
    "outputId": "77c38e42-9f20-4b87-983e-807c66d4921a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "REDUCE TRANSITION\n",
      "The confusion matrix is:\n",
      "+---------+---------------+-------------------+\n",
      "| x       |   Predicted 3 |   Predicted non-3 |\n",
      "+=========+===============+===================+\n",
      "| True 3  |          7475 |              3229 |\n",
      "+---------+---------------+-------------------+\n",
      "| False 3 |          3129 |             33897 |\n",
      "+---------+---------------+-------------------+\n",
      "Accuracy: 0.866792373769118\n",
      "Precision: 0.7049226706903056\n",
      "Recall: 0.6983370702541106\n",
      "F1 score: 0.7016144171203303\n"
     ]
    }
   ],
   "source": [
    "from tabulate import tabulate\n",
    "print(\"REDUCE TRANSITION\\nThe confusion matrix is:\")\n",
    "labels3 = [\"True 3\", \"False 3\"]\n",
    "# Convert NumPy array to a 2D list\n",
    "matrix_2d_list3 = confusion_matrix_3.tolist()\n",
    "\n",
    "# Create a new 2D list for the table data\n",
    "table_data3 = [[labels3[i]] + row for i, row in enumerate(matrix_2d_list3)]\n",
    "table3 = tabulate(table_data3, tablefmt=\"grid\",  headers=[\"x\",\"Predicted 3\", \"Predicted non-3\"])\n",
    "print(table3)\n",
    "\n",
    "# Accuracy\n",
    "acc3 = (confusion_matrix_3[0][0] + confusion_matrix_3[1][1])/(confusion_matrix_3[0][0] + confusion_matrix_3[1][0] + confusion_matrix_3[0][1] + confusion_matrix_3[1][1])\n",
    "print(\"Accuracy:\", acc3)\n",
    "\n",
    "# Precision\n",
    "pr3 = confusion_matrix_3[0][0] / (confusion_matrix_3[0][0] + confusion_matrix_3[1][0])\n",
    "print(\"Precision:\", pr3)\n",
    "\n",
    "# Recall\n",
    "rec3 = confusion_matrix_3[0][0] / (confusion_matrix_3[0][0] + confusion_matrix_3[0][1])\n",
    "print(\"Recall:\", rec3)\n",
    "\n",
    "# F1 score\n",
    "f3 = 2 * pr3 * rec3 / (pr3 + rec3)\n",
    "print(\"F1 score:\", f3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "VsZZGfVBCLlz"
   },
   "source": [
    "From this analysis we can see that the two actions that assign dependencies (left-arc and right-arc) have similar scores since they reach around 78% of accuracy, 53-58% of precision, 53-58% of recall and 53-58% of F1 scores. That is because right-arc has similar number of true positive, false positive and false negative, while left-arc has a higher number of true positive but lower true negative values.\n",
    "\n",
    "Shift and reduce instead have higher scores, shift reaches 83% while reduce 87%. The precision, recall and F1 score for both are around 70%."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1VPOLJG8ueaW"
   },
   "source": [
    "## Comparison of the results between BILSTM and BERT\n",
    "\n",
    "As mentioned before, in order to evaluate the performance of each model, we used Unlabeled Attachment Score (UAS) as the evaluation metric. UAS is the percentage of\n",
    "words in the input that are attached to the correct head, ignoring the dependency labels.\n",
    "As reported in the provious steps, we tested biLSTM and BERT models both on only projective sentences and on all the sentences (projective and non-projective).\n",
    "\n",
    "For biLSTM, taking only the projective sentences into consideration resulted in 81.2% UAS while taking both the projective and non-projective sentences gave a UAS of 81.7%.\n",
    "\n",
    "Regarding BERT, taking only the projective sentences resulted in 84.8% UAS while taking both the projective and non-projective sentences gave a 84.5% UAS.\n",
    "\n",
    "We notice that the results of each model are comparable which means that the model works as good with the non-projective sentences.\n",
    "However this is expected: BERT performed better than BiLSTM. This is due to the architecture of BERT. For instance, BERT is based on the transformer architecture, which uses self-attention mechanisms to capture global dependencies in the input sequence. It makes it more effective in capturing contextual information compared to BiLSTM, which relies on recurrent connections. Moreover, BERT is pre-trained on large scale unlabeled dataset and then fine-tuned on the parameters to make the model more specific to the dependency task. Bilstm, on the other hand, does not employ pre-training, thus it may need more labeled data to achieve a performance similar to BERT's."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TgedzJdNvN7o"
   },
   "source": [
    "## Comparison with SotA\n",
    "The dataset used for the analysis is the English EWT dataset for which a leaderboard of State-of-the-Art (SotA) result showed a range between 89.63 and 93.27% UAS, as reported from Altintas et al. *Improving the performance of graph based dependency parsing by guiding bi-affine layer with augmented global and local features*, 2023 [reference](https://pdf.sciencedirectassets.com/779210/1-s2.0-S2667305323X00027/1-s2.0-S2667305323000157/main.pdf?X-Amz-Security-Token=IQoJb3JpZ2luX2VjEKz%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaCXVzLWVhc3QtMSJHMEUCIQDhvEYfuxw5aLBLYEb39khYk6PHk1TASvsTOd3NWdpg%2FQIgSo%2FadUCYzckq4jRyLIa8cAab2sBMLWl6btV%2F4YlqEr8qswUIFBAFGgwwNTkwMDM1NDY4NjUiDGe%2FW11FfsXq3fHE5yqQBUYt4UMHxjbJoCEnoIOPzCcSw4lEED0VDilI135J1UF7qWoAAIn5De3eY%2BBMKSzcIXB0U9YF1LCZ4HYJrw%2FmeLwuXrixeDIJkmszkSAu8Ow0CUdbB%2Bs8YVRxfdtnP4VmRPHbcaxZDCd9UUjkD5LxrEd%2BwQzu26y7tj2BjTn%2FdEw2xwyATeOOuWKFTfvPF16aNvN1feiyh07%2BXAfRSDGcERMB3y5Zu%2BzT4jqpOEwyXf7zIbRk%2BWwddvGdL1qODyxS%2FAqgRluAgLaKtBjhEnl%2FMzRaCWNRZl2ZJrwHV4ePqypciIpT0qR2ydGIKkg1NK7OMbY5rVuR9Ds82VBcYrO%2FIFv4QkYwFbFKaHeJpFYv9x63DJ4%2BdJYf1feEHC9rTBH8tV%2Fm8A%2FueScuugGsnj1%2FaSduP%2Fjzndnb3K%2F8mX7%2Fx0z9NWB24w1NIC2syLJspIl%2Fb2T%2BOzi%2BKesIzx%2FTxID3JVjmvBgdj3xz1DjF1NS2YUQTo3bgtyAzMvoE%2FihuRuEXE0HHuyg7bqPaVaHrRqAtwhw%2Fs9HAj21N7m06ZvdMMW0O5W%2Bbc4HDL3C4IyPGCQDdP64J%2B6nPcxYor4XZNdycXqwNvve5%2B77D3xw%2BWq73AMd87ysK0SvVke2VgQCDh07N8GQfxQN%2BuvPb%2BetX%2F2YpWDsyUcPIle4PlzMWjQNhtALALlgGHqQ5w1dyH9us9zaoQM7ECl9V%2FwuSTWRBL5GLRw76vNXbwMC8DGGrzXaMnGxA4ICwmmwWWOSTjzVJfvJCYAzgQufCN1Ds5dnjya1uU9nZiJlXtBeY9PtdR078NShC3OQyEEyyKNiNNGJmtK7L2hZQn1pj9F8EsvIcauJbQBqv6VQLWPrEL9uV0aN4VfAkMJKh26QGOrEB9ROdcGrI4nfLvTLMndEez8LwqbF82BOROZ5K0SxClGBfAREMwb4XbQjLiIyjq0D5Fa2Pjkm8ZRTEXgeSGJG3e3Yy0TECpPtByBVZmBJ47eWP5AbW0X57mErJw8dnW87YcIB6zavfPknazbiTKIekwYrdSOcTD0ZJEQBdHLfWEXiOJwQkIhbfZRBPoWUBVTYC2hkwMgivJ7AQYgarkf4EEmwqXye45%2FqMSCe6MrfghoLz&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Date=20230624T125342Z&X-Amz-SignedHeaders=host&X-Amz-Expires=300&X-Amz-Credential=ASIAQ3PHCVTYSLVU5FLF%2F20230624%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Signature=d0bd3d2944657ad59152ef0009a87fade3c8db38901963579f4e87baa72fb034&hash=f964c9e8566cdf928d3d2058cc3a123f8039a1d41c3542c81154301528930515&host=68042c943591013ac2b2430a89b270f6af2c76d8dfd086a07176afe7c76c2c61&pii=S2667305323000157&tid=spdf-768893de-1c26-46c3-9495-eeffa6160c30&sid=402e8fed9919584d622bad293fbeaf2aee38gxrqb&type=client&tsoh=d3d3LnNjaWVuY2VkaXJlY3QuY29t&ua=0f165100065b5001560a&rr=7dc51d7e4a02bb03&cc=it). With BERT, we were able to attain around 85%. The most recent version of SotA used Sentence Representation and Super Token Features in order to enhance the performance the base model.\n",
    "\n",
    "Some limitations and suggestions concerning our model:\n",
    "* It would be a good practice to improve our model using methods like sentence represention and super token features (get additional features derived from dividing a token into subword units).\n",
    "* The limited number of computational resources used for training. With Google Colab's GPU Tesla 4 we trained the model for a small number of epochs, but we got signs of overfitting. Using a more resourful device and increasing the number of epochs to up to 50-80 epochs could have given better results.\n",
    "* As mentioned, a main problem we faced is overfitting. We notice that the training loss curve decreases fatser than the UAS increases. Maybe adding further regularization techiques could prevent it. A more resourceful device could also allow a more fine-tuned research on the hyperparameters.\n",
    "\n"
   ]
  }
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