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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "view-in-github",
    "colab_type": "text"
   },
   "source": [
    "<a href=\"https://colab.research.google.com/github/danielpatrickhug/GitModel/blob/main/bottom_up_vs_top_down.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Quick review of kernels and message passing"
   ],
   "metadata": {
    "id": "yY0KniATGCYE"
   }
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "6GoWfmE5EYVy"
   },
   "outputs": [],
   "source": [
    "%%capture\n",
    "%%bash\n",
    "\n",
    "pip install sentence-transformers"
   ]
  },
  {
   "cell_type": "code",
   "source": [
    "import numpy as np\n",
    "from sentence_transformers import SentenceTransformer\n",
    "import torch\n",
    "from torch import Tensor\n",
    "import pandas as pd\n",
    "import math"
   ],
   "metadata": {
    "id": "m8YO9qknEkIc"
   },
   "execution_count": 4,
   "outputs": []
  },
  {
   "cell_type": "code",
   "source": [
    "def embed_data(data, key=\"query\", model_name=\"all-MiniLM-L6-v2\", cores=1, gpu=False, batch_size=128):\n",
    "    \"\"\"\n",
    "    Embed the sentences/text using the MiniLM language model (which uses mean pooling)\n",
    "    \"\"\"\n",
    "    print(\"Embedding data\")\n",
    "    model = SentenceTransformer(model_name)\n",
    "    print(\"Model loaded\")\n",
    "\n",
    "    sentences = data[key].tolist()\n",
    "    unique_sentences = data[key].unique()\n",
    "    print(\"Unique sentences\", len(unique_sentences))\n",
    "\n",
    "    if cores == 1:\n",
    "        embeddings = model.encode(unique_sentences, show_progress_bar=True, batch_size=batch_size)\n",
    "    else:\n",
    "        devices = [\"cpu\"] * cores\n",
    "        if gpu:\n",
    "            devices = None  # use all CUDA devices\n",
    "\n",
    "        # Start the multi-process pool on multiple devices\n",
    "        print(\"Multi-process pool starting\")\n",
    "        pool = model.start_multi_process_pool(devices)\n",
    "        print(\"Multi-process pool started\")\n",
    "\n",
    "        chunk_size = math.ceil(len(unique_sentences) / cores)\n",
    "\n",
    "        # Compute the embeddings using the multi-process pool\n",
    "        embeddings = model.encode_multi_process(unique_sentences, pool, batch_size=batch_size, chunk_size=chunk_size)\n",
    "        model.stop_multi_process_pool(pool)\n",
    "\n",
    "    print(\"Embeddings computed\")\n",
    "\n",
    "    mapping = {sentence: embedding for sentence, embedding in zip(unique_sentences, embeddings)}\n",
    "    embeddings = np.array([mapping[sentence] for sentence in sentences])\n",
    "\n",
    "    return embeddings"
   ],
   "metadata": {
    "id": "im3g772qEyl0"
   },
   "execution_count": 28,
   "outputs": []
  },
  {
   "cell_type": "code",
   "source": [
    "sentences = [\n",
    "    \"This framework generates embeddings for each input sentence\",\n",
    "    \"Sentences are passed as a list of string.\",\n",
    "    \"The quick brown fox jumps over the lazy dog.\",\n",
    "    \"Where was Marie Curie born?\",\n",
    "    \"Maria Sklodowska, later known as Marie Curie, was born on November 7, 1867.\",\n",
    "    \"Born in Paris on 15 May 1859, Pierre Curie was the son of Eugène Curie, a doctor of French Catholic origin from Alsace.\",\n",
    "]\n",
    "\n",
    "data = [(i, sent) for i, sent in enumerate(sentences)]\n",
    "data = pd.DataFrame(data, columns=[\"id\", \"query\"])"
   ],
   "metadata": {
    "id": "ZsmEW2rmSr47"
   },
   "execution_count": 113,
   "outputs": []
  },
  {
   "cell_type": "code",
   "source": [
    "# Bottom up adj matrix\n",
    "def cosine_similarity(a, b):\n",
    "    \"\"\"\n",
    "    inner product between two vectors divided by the norm\n",
    "    :a: n-dim feature vector\n",
    "    :b: n-dim feature vector\n",
    "    :return: the cosine similarity of the two embeddings\n",
    "    \"\"\"\n",
    "    if not isinstance(a, torch.Tensor):\n",
    "        a = torch.tensor(np.array(a))\n",
    "\n",
    "    if not isinstance(b, torch.Tensor):\n",
    "        b = torch.tensor(np.array(b))\n",
    "    return torch.dot(a, b) / (torch.norm(a) * torch.norm(b))\n",
    "\n",
    "\n",
    "def adjaceny_matrix(sentence_embeddings):\n",
    "    A = torch.zeros((sentence_embeddings.shape[0], sentence_embeddings.shape[0]))\n",
    "    for i in range(sentence_embeddings.shape[0]):\n",
    "        for j in range(sentence_embeddings.shape[0]):\n",
    "            i_j_sim = cosine_similarity(sentence_embeddings[i], sentence_embeddings[j])\n",
    "            A[i, j] = i_j_sim\n",
    "    return A\n",
    "\n",
    "\n",
    "# kernel\n",
    "def cos_sim(a: Tensor, b: Tensor):\n",
    "    \"\"\"\n",
    "    Computes the cosine similarity cos_sim(a[i], b[j]) for all i and j.\n",
    "    :return: Matrix with res[i][j]  = cos_sim(a[i], b[j])\n",
    "    \"\"\"\n",
    "    if not isinstance(a, torch.Tensor):\n",
    "        a = torch.tensor(np.array(a))\n",
    "\n",
    "    if not isinstance(b, torch.Tensor):\n",
    "        b = torch.tensor(np.array(b))\n",
    "\n",
    "    if len(a.shape) == 1:\n",
    "        a = a.unsqueeze(0)\n",
    "\n",
    "    if len(b.shape) == 1:\n",
    "        b = b.unsqueeze(0)\n",
    "\n",
    "    a_norm = torch.nn.functional.normalize(a, p=2, dim=1)\n",
    "    b_norm = torch.nn.functional.normalize(b, p=2, dim=1)\n",
    "    return torch.mm(a_norm, b_norm.transpose(0, 1))"
   ],
   "metadata": {
    "id": "TRBVy9XYElKr"
   },
   "execution_count": 67,
   "outputs": []
  },
  {
   "cell_type": "code",
   "source": [
    "MODEL_NAME = \"all-MiniLM-L6-v2\"  # \"allenai-specter\"#\n",
    "embs = embed_data(data, model_name=MODEL_NAME)"
   ],
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 121,
     "referenced_widgets": [
      "e436712117fd41d890d8a1578072b6e8",
      "af4183da7f9c44d8904170066a9f78c9",
      "2fdbc6e4d162405e9f18b92b63ec642b",
      "bcbd0ecb528b4727b842a523cddd0606",
      "1ddf9189d5934239bc61eddfbecac25c",
      "df3f8df495aa48979aeff1e5f4bb91ce",
      "33e12eace4b34552a428a9c13db45449",
      "09ae39c4fdc9433f9cb7a3be7a3383d7",
      "442f2862e8a34c30893af7beba356579",
      "564c483c5e3d4af2ad6a2d0bbd52b4a7",
      "0b964214e72e4cd4a18c54d90bd93cab"
     ]
    },
    "id": "d8A8KLfKFA3t",
    "outputId": "5a999e75-51ca-4ad6-df54-278775b78273"
   },
   "execution_count": 68,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Embedding data\n",
      "Model loaded\n",
      "Unique sentences 6\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "Batches:   0%|          | 0/1 [00:00<?, ?it/s]"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "e436712117fd41d890d8a1578072b6e8"
      }
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Embeddings computed\n"
     ]
    }
   ]
  },
  {
   "cell_type": "code",
   "source": [
    "threshold = 0.7"
   ],
   "metadata": {
    "id": "XOAr9wrnIGok"
   },
   "execution_count": 69,
   "outputs": []
  },
  {
   "cell_type": "markdown",
   "source": [
    "##kernel\n"
   ],
   "metadata": {
    "id": "rmi8ey-tGLZY"
   }
  },
  {
   "cell_type": "code",
   "source": [
    "A = cos_sim(embs, embs)\n",
    "adj_matrix = torch.zeros_like(A)\n",
    "adj_matrix[A > threshold] = 1\n",
    "adj_matrix[A <= threshold] = 0"
   ],
   "metadata": {
    "id": "UXpJ5wNUH0q6"
   },
   "execution_count": 70,
   "outputs": []
  },
  {
   "cell_type": "markdown",
   "source": [
    "##bottom-up"
   ],
   "metadata": {
    "id": "0JDHOlBoGN-p"
   }
  },
  {
   "cell_type": "code",
   "source": [
    "A_b = adjaceny_matrix(embs)\n",
    "adj_matrix_b = torch.zeros_like(A_b)\n",
    "adj_matrix_b[A_b > threshold] = 1\n",
    "adj_matrix_b[A_b <= threshold] = 0"
   ],
   "metadata": {
    "id": "MjSPHdpPGZtv"
   },
   "execution_count": 71,
   "outputs": []
  },
  {
   "cell_type": "markdown",
   "source": [
    "### thresholded map connections are equal "
   ],
   "metadata": {
    "id": "msGUPbl0GTF3"
   }
  },
  {
   "cell_type": "code",
   "source": [
    "adj_matrix == adj_matrix_b"
   ],
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "q8agMWLgG0fH",
    "outputId": "3153ce1b-0fc6-47d5-cd1a-b5a63da13c0c"
   },
   "execution_count": 72,
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "tensor([[True, True, True, True, True, True],\n",
       "        [True, True, True, True, True, True],\n",
       "        [True, True, True, True, True, True],\n",
       "        [True, True, True, True, True, True],\n",
       "        [True, True, True, True, True, True],\n",
       "        [True, True, True, True, True, True]])"
      ]
     },
     "metadata": {},
     "execution_count": 72
    }
   ]
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Message Passing"
   ],
   "metadata": {
    "id": "3MiBkmPAIOxU"
   }
  },
  {
   "cell_type": "code",
   "source": [
    "def k_hop_message_passing(A, node_features, k):\n",
    "    \"\"\"\n",
    "    Compute the k-hop adjacency matrix and aggregated features using message passing.\n",
    "\n",
    "    Parameters:\n",
    "    A (numpy array): The adjacency matrix of the graph.\n",
    "    node_features (numpy array): The feature matrix of the nodes.\n",
    "    k (int): The number of hops for message passing.\n",
    "\n",
    "    Returns:\n",
    "    A_k (numpy array): The k-hop adjacency matrix.\n",
    "    agg_features (numpy array): The aggregated feature matrix for each node in the k-hop neighborhood.\n",
    "    \"\"\"\n",
    "\n",
    "    print(\"Compute the k-hop adjacency matrix\")\n",
    "    A_k = np.linalg.matrix_power(A, k)\n",
    "\n",
    "    print(\"Aggregate the messages from the k-hop neighborhood:\")\n",
    "    agg_features = node_features.copy()\n",
    "\n",
    "    for i in range(k):\n",
    "        agg_features += np.matmul(np.linalg.matrix_power(A, i + 1), node_features)\n",
    "\n",
    "    return A_k, agg_features"
   ],
   "metadata": {
    "id": "oaJWX-6NTVI-"
   },
   "execution_count": 143,
   "outputs": []
  },
  {
   "cell_type": "code",
   "source": [
    "A_k, agg = k_hop_message_passing(adj_matrix, embs, 2)\n",
    "A_k"
   ],
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "2kK8pqd_QyGX",
    "outputId": "df80c8c4-a5b6-4718-e240-7267141fa594"
   },
   "execution_count": 144,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Compute the k-hop adjacency matrix\n",
      "Aggregate the messages from the k-hop neighborhood:\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[2., 2., 0., 0., 0., 0.],\n",
       "       [2., 2., 0., 0., 0., 0.],\n",
       "       [0., 0., 1., 0., 0., 0.],\n",
       "       [0., 0., 0., 3., 3., 3.],\n",
       "       [0., 0., 0., 3., 3., 3.],\n",
       "       [0., 0., 0., 3., 3., 3.]], dtype=float32)"
      ]
     },
     "metadata": {},
     "execution_count": 144
    }
   ]
  },
  {
   "cell_type": "code",
   "source": [
    "U, S, VT = np.linalg.svd(adj_matrix)\n",
    "print(f\"U: {U.shape}\\n\")\n",
    "print(f\"S: {S.shape}\\n\")\n",
    "print(f\"VT: {VT.shape}\\n\")\n",
    "plt.plot(np.diag(S))\n",
    "plt.xlabel(\"Singular value index\")\n",
    "plt.ylabel(\"Singular value\")\n",
    "plt.title(\"Singular values of A\")\n",
    "plt.show()"
   ],
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 403
    },
    "id": "mOhoojeGJ_vQ",
    "outputId": "9be58a8a-d7b4-482b-b13e-14d29fb3b627"
   },
   "execution_count": 154,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "U: (6, 6)\n",
      "\n",
      "S: (6,)\n",
      "\n",
      "VT: (6, 6)\n",
      "\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ]
  },
  {
   "cell_type": "code",
   "source": [
    "agg == embs"
   ],
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "7q8575a-ISYj",
    "outputId": "8d8bdcc2-b3e9-446c-c414-acb557f59cc0"
   },
   "execution_count": 127,
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[False, False, False, ..., False, False, False],\n",
       "       [False, False, False, ..., False, False, False],\n",
       "       [ True,  True,  True, ...,  True,  True,  True],\n",
       "       [False, False, False, ..., False, False, False],\n",
       "       [False, False, False, ..., False, False, False],\n",
       "       [False, False, False, ..., False, False, False]])"
      ]
     },
     "metadata": {},
     "execution_count": 127
    }
   ]
  },
  {
   "cell_type": "code",
   "source": [
    "embs == embs"
   ],
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "mjzPNx_xIVOM",
    "outputId": "31fde23b-f3e8-463d-a0fb-98f5cd6ee920"
   },
   "execution_count": 128,
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[ True,  True,  True, ...,  True,  True,  True],\n",
       "       [ True,  True,  True, ...,  True,  True,  True],\n",
       "       [ True,  True,  True, ...,  True,  True,  True],\n",
       "       [ True,  True,  True, ...,  True,  True,  True],\n",
       "       [ True,  True,  True, ...,  True,  True,  True],\n",
       "       [ True,  True,  True, ...,  True,  True,  True]])"
      ]
     },
     "metadata": {},
     "execution_count": 128
    }
   ]
  },
  {
   "cell_type": "code",
   "source": [
    "import torch\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "def k_hop_message_passing(A, node_features, exp):\n",
    "    # Convert adjacency matrix and node features to PyTorch tensors\n",
    "    A = torch.tensor(A)\n",
    "    node_features = torch.tensor(node_features)\n",
    "\n",
    "    # Compute the k-hop adjacency matrix using PyTorch\n",
    "    A_k = A.clone().detach().float()\n",
    "    for i in range(int(exp) - 1):\n",
    "        A_k = torch.matmul(A_k, A)\n",
    "\n",
    "    # Compute the aggregated features using PyTorch\n",
    "    agg_features = torch.matmul(A_k, node_features)\n",
    "\n",
    "    # Exponentiate the k-hop adjacency matrix by exp using PyTorch\n",
    "    A_k_exp = A_k**exp\n",
    "\n",
    "    # Return the exponentiated matrix and aggregated features as NumPy arrays\n",
    "    return A_k_exp.numpy(), agg_features.numpy()"
   ],
   "metadata": {
    "id": "zoI8pMbQUTtN"
   },
   "execution_count": 146,
   "outputs": []
  },
  {
   "cell_type": "code",
   "source": [
    "# Our sentences we like to encode\n",
    "sentences = [\n",
    "    \"This framework generates embeddings for each input sentence\",\n",
    "    \"Sentences are passed as a list of string.\",\n",
    "    \"The quick brown fox jumps over the lazy dog.\",\n",
    "    \"Where was Marie Curie born?\",\n",
    "    \"Maria Sklodowska, later known as Marie Curie, was born on November 7, 1867.\",\n",
    "    \"Born in Paris on 15 May 1859, Pierre Curie was the son of Eugène Curie, a doctor of French Catholic origin from Alsace.\",\n",
    "]\n",
    "\n",
    "data = [(i, sent) for i, sent in enumerate(sentences)]\n",
    "data = pd.DataFrame(data, columns=[\"id\", \"query\"])\n",
    "embs = embed_data(data)\n",
    "print(embs.shape)\n",
    "A = cos_sim(embs, embs)\n",
    "adj_matrix = torch.zeros_like(A)\n",
    "adj_matrix[A > 0.5] = 1\n",
    "adj_matrix[A <= 0.5] = 0\n",
    "A_k, agg_features = k_hop_message_passing(adj_matrix, embs, math.e)\n",
    "A_k"
   ],
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 391,
     "referenced_widgets": [
      "ff4e0fca8b414c9bb0fda07f3f0dfbe2",
      "3229ac6de10d47eebc9fcfafaf13d5bc",
      "7b5bcce897a64934ae9116f1e1fc8580",
      "adcf3fffa5644f67b41da731979df7f3",
      "46e7143835fa4f138651aa50191c65e0",
      "bbcf3c71b39c4438aca359404b88c068",
      "f991e1a906f443ae8b243219b8a8472b",
      "367d10ae54364d2fac10a20e731aadd1",
      "1fec02eac5c24fe58edce9ae7fcda8b4",
      "ccff51e5c3e74bf3810c499b55d55551",
      "c18ed581cafb46d29edb53110afe013e"
     ]
    },
    "id": "F8H3HLmLTeF_",
    "outputId": "a5b2956f-0b93-48c7-d0e5-8075dff45899"
   },
   "execution_count": 147,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Embedding data\n",
      "Model loaded\n",
      "Unique sentences 6\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "Batches:   0%|          | 0/1 [00:00<?, ?it/s]"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "ff4e0fca8b414c9bb0fda07f3f0dfbe2"
      }
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Embeddings computed\n",
      "(6, 384)\n"
     ]
    },
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "<ipython-input-146-755027329b31>:7: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor).\n",
      "  A = torch.tensor(A)\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[ 6.5808854,  6.5808854,  0.       ,  0.       ,  0.       ,\n",
       "         0.       ],\n",
       "       [ 6.5808854,  6.5808854,  0.       ,  0.       ,  0.       ,\n",
       "         0.       ],\n",
       "       [ 0.       ,  0.       ,  1.       ,  0.       ,  0.       ,\n",
       "         0.       ],\n",
       "       [ 0.       ,  0.       ,  0.       , 19.812988 , 19.812988 ,\n",
       "        19.812988 ],\n",
       "       [ 0.       ,  0.       ,  0.       , 19.812988 , 19.812988 ,\n",
       "        19.812988 ],\n",
       "       [ 0.       ,  0.       ,  0.       , 19.81299  , 19.81299  ,\n",
       "        19.81299  ]], dtype=float32)"
      ]
     },
     "metadata": {},
     "execution_count": 147
    }
   ]
  },
  {
   "cell_type": "code",
   "source": [
    "U, S, VT = np.linalg.svd(A_k)\n",
    "print(f\"U: {U.shape}\\n\")\n",
    "print(f\"S: {S.shape}\\n\")\n",
    "print(f\"VT: {VT.shape}\\n\")\n",
    "plt.plot(np.diag(S))\n",
    "plt.xlabel(\"Singular value index\")\n",
    "plt.ylabel(\"Singular value\")\n",
    "plt.title(\"Singular values of A\")\n",
    "plt.show()"
   ],
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 403
    },
    "id": "4ustgQkeJjOA",
    "outputId": "f43b7c07-d6d4-4f8f-b369-ae4171f36654"
   },
   "execution_count": 148,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "U: (6, 6)\n",
      "\n",
      "S: (6,)\n",
      "\n",
      "VT: (6, 6)\n",
      "\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ]
  },
  {
   "cell_type": "code",
   "source": [
    "A_k, agg_features = k_hop_message_passing(adj_matrix, embs, math.pi)\n",
    "A_k"
   ],
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "wJWW7QahT24e",
    "outputId": "d18cb2aa-1ad4-4ea9-caa4-8f16146b8ce4"
   },
   "execution_count": 150,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "<ipython-input-146-755027329b31>:7: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor).\n",
      "  A = torch.tensor(A)\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[ 77.88024,  77.88024,   0.     ,   0.     ,   0.     ,   0.     ],\n",
       "       [ 77.88024,  77.88024,   0.     ,   0.     ,   0.     ,   0.     ],\n",
       "       [  0.     ,   0.     ,   1.     ,   0.     ,   0.     ,   0.     ],\n",
       "       [  0.     ,   0.     ,   0.     , 995.0418 , 995.0418 , 995.0418 ],\n",
       "       [  0.     ,   0.     ,   0.     , 995.0418 , 995.0418 , 995.0418 ],\n",
       "       [  0.     ,   0.     ,   0.     , 995.0416 , 995.0416 , 995.0416 ]],\n",
       "      dtype=float32)"
      ]
     },
     "metadata": {},
     "execution_count": 150
    }
   ]
  },
  {
   "cell_type": "code",
   "source": [
    "U, S, VT = np.linalg.svd(A_k)\n",
    "print(f\"U: {U.shape}\\n\")\n",
    "print(f\"S: {S.shape}\\n\")\n",
    "print(f\"VT: {VT.shape}\\n\")\n",
    "plt.plot(np.diag(S))\n",
    "plt.xlabel(\"Singular value index\")\n",
    "plt.ylabel(\"Singular value\")\n",
    "plt.title(\"Singular values of A\")\n",
    "plt.show()"
   ],
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 403
    },
    "id": "j3k1KjtAK3GW",
    "outputId": "0306cc99-dc12-4c54-eef2-25d5f9a6f76a"
   },
   "execution_count": 151,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "U: (6, 6)\n",
      "\n",
      "S: (6,)\n",
      "\n",
      "VT: (6, 6)\n",
      "\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ]
  },
  {
   "cell_type": "code",
   "source": [
    "import math\n",
    "\n",
    "phi = (1 + math.sqrt(5)) / 2\n",
    "A_k, agg_features = k_hop_message_passing(adj_matrix, embs, phi)\n",
    "A_k"
   ],
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "C6ltDiQOU4_7",
    "outputId": "74c22032-78d0-4eaa-fc5f-d8eed6b7dc27"
   },
   "execution_count": 152,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "<ipython-input-146-755027329b31>:7: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor).\n",
      "  A = torch.tensor(A)\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[1., 1., 0., 0., 0., 0.],\n",
       "       [1., 1., 0., 0., 0., 0.],\n",
       "       [0., 0., 1., 0., 0., 0.],\n",
       "       [0., 0., 0., 1., 1., 1.],\n",
       "       [0., 0., 0., 1., 1., 1.],\n",
       "       [0., 0., 0., 1., 1., 1.]], dtype=float32)"
      ]
     },
     "metadata": {},
     "execution_count": 152
    }
   ]
  },
  {
   "cell_type": "code",
   "source": [
    "U, S, VT = np.linalg.svd(A_k)\n",
    "print(f\"U: {U.shape}\\n\")\n",
    "print(f\"S: {S.shape}\\n\")\n",
    "print(f\"VT: {VT.shape}\\n\")\n",
    "plt.plot(np.diag(S))\n",
    "plt.xlabel(\"Singular value index\")\n",
    "plt.ylabel(\"Singular value\")\n",
    "plt.title(\"Singular values of A\")\n",
    "plt.show()"
   ],
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 403
    },
    "id": "Y_ZYJ_6gLelg",
    "outputId": "38c7b8b5-fb6c-47cb-843b-58045a69c825"
   },
   "execution_count": 153,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "U: (6, 6)\n",
      "\n",
      "S: (6,)\n",
      "\n",
      "VT: (6, 6)\n",
      "\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ]
  },
  {
   "cell_type": "code",
   "source": [
    "adj_matrix"
   ],
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "5jdlFdHsFqyA",
    "outputId": "2d7313b4-a66a-4fc6-a3e4-d1791ca0f426"
   },
   "execution_count": 99,
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "tensor([[1., 1., 0., 0., 0., 0.],\n",
       "        [1., 1., 0., 0., 0., 0.],\n",
       "        [0., 0., 1., 0., 0., 0.],\n",
       "        [0., 0., 0., 1., 1., 1.],\n",
       "        [0., 0., 0., 1., 1., 1.],\n",
       "        [0., 0., 0., 1., 1., 1.]])"
      ]
     },
     "metadata": {},
     "execution_count": 99
    }
   ]
  },
  {
   "cell_type": "code",
   "source": [
    "cos_sim(agg_features, embs)"
   ],
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "WeIzb_2tFvGm",
    "outputId": "a973976e-a2ca-4ba7-d405-a53209b5c1e8"
   },
   "execution_count": 100,
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "tensor([[ 0.8769,  0.8769,  0.1264,  0.0061, -0.0484, -0.0160],\n",
       "        [ 0.8769,  0.8769,  0.1264,  0.0061, -0.0484, -0.0160],\n",
       "        [ 0.1181,  0.1036,  1.0000, -0.0194, -0.0224, -0.0172],\n",
       "        [ 0.0307, -0.0703, -0.0228,  0.9048,  0.8509,  0.8294],\n",
       "        [ 0.0307, -0.0703, -0.0228,  0.9048,  0.8509,  0.8294],\n",
       "        [ 0.0307, -0.0703, -0.0228,  0.9048,  0.8509,  0.8294]])"
      ]
     },
     "metadata": {},
     "execution_count": 100
    }
   ]
  },
  {
   "cell_type": "code",
   "source": [
    "cos_sim(embs, embs)"
   ],
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "tiSM4gHuF3N_",
    "outputId": "19585dbd-d811-4d26-a191-f3c5d306e36d"
   },
   "execution_count": 102,
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "tensor([[ 1.0000,  0.5381,  0.1181,  0.0364, -0.0141,  0.0571],\n",
       "        [ 0.5381,  1.0000,  0.1036, -0.0257, -0.0708, -0.0852],\n",
       "        [ 0.1181,  0.1036,  1.0000, -0.0194, -0.0224, -0.0172],\n",
       "        [ 0.0364, -0.0257, -0.0194,  1.0000,  0.6973,  0.6416],\n",
       "        [-0.0141, -0.0708, -0.0224,  0.6973,  1.0000,  0.5024],\n",
       "        [ 0.0571, -0.0852, -0.0172,  0.6416,  0.5024,  1.0000]])"
      ]
     },
     "metadata": {},
     "execution_count": 102
    }
   ]
  },
  {
   "cell_type": "code",
   "source": [
    "from typing import List, Tuple\n",
    "\n",
    "\n",
    "def linearly_sum_gnn_heads(\n",
    "    matrices: List[Tuple[np.ndarray, np.ndarray]], normalization_fn: str = \"max\"\n",
    ") -> Tuple[np.ndarray, np.ndarray]:\n",
    "    \"\"\"\n",
    "    Linearly sum a list of adjacency matrices and normalize the result. Also computes the average of the node embeddings\n",
    "    and checks that the number of documents in the adjacency matrices matches the number of documents in the embeddings set.\n",
    "\n",
    "    Parameters:\n",
    "    matrices (List of Tuple): List of tuples where each tuple contains an adjacency matrix and its\n",
    "        corresponding node embeddings.\n",
    "\n",
    "    Returns:\n",
    "    normalized_matrix (numpy array): The linearly summed and normalized adjacency matrix.\n",
    "    avg_embeddings (numpy array): The average node embeddings.\n",
    "    \"\"\"\n",
    "    if len(matrices) == 1:\n",
    "        return matrices[0]\n",
    "    # Compute the average of the embeddings\n",
    "    avg_embeddings = np.mean([t[1] for t in matrices], axis=0)\n",
    "\n",
    "    # Check that the number of documents in the adjacency matrices matches the number of documents in the embeddings set\n",
    "    num_docs_adj = matrices[0][0].shape[0]\n",
    "    num_docs_embs = avg_embeddings.shape[0]\n",
    "    if num_docs_adj != num_docs_embs:\n",
    "        raise ValueError(\n",
    "            \"Number of documents in adjacency matrix does not match number of documents in embeddings set.\"\n",
    "        )\n",
    "\n",
    "    # Linearly sum the adjacency matrices and normalize the matrix by dividing it by the maximum value\n",
    "    summed_matrix = sum([t[0] for t in matrices])\n",
    "    if normalization_fn == \"max\":\n",
    "        max_value = np.max(summed_matrix)\n",
    "        normalized_matrix = summed_matrix / max_value\n",
    "    elif normalization_fn == \"sum\":\n",
    "        normalized_matrix = summed_matrix / len(matrices)\n",
    "    elif normalization_fn == \"min-max\":\n",
    "        min_value = np.min(summed_matrix)\n",
    "        max_value = np.max(summed_matrix)\n",
    "        normalized_matrix = (summed_matrix - min_value) / (max_value - min_value)\n",
    "    elif normalization_fn == \"z_score\":\n",
    "        mean = np.mean(summed_matrix)\n",
    "        std = np.std(summed_matrix)\n",
    "        normalized_matrix = (summed_matrix - mean) / std\n",
    "    elif normalization_fn == \"circular\":\n",
    "        min_value = np.min(summed_matrix)\n",
    "        max_value = np.max(summed_matrix)\n",
    "        normalized_matrix_linear = (summed_matrix - min_value) / (max_value - min_value)\n",
    "        normalized_matrix = np.sin(2 * np.pi * normalized_matrix_linear)\n",
    "    else:\n",
    "        raise ValueError(f\"Normalization function {normalization_fn} not supported.\")\n",
    "\n",
    "    A_k, agg_embs = k_hop_message_passing(normalized_matrix, avg_embeddings, 1)\n",
    "    print(f\"adj matrix shape: {A_k.shape}\")\n",
    "    print(f\"agg embeddings shape: {agg_embs.shape}\")\n",
    "    return A_k, agg_embs"
   ],
   "metadata": {
    "id": "mpMRQNaRF77B"
   },
   "execution_count": 105,
   "outputs": []
  },
  {
   "cell_type": "code",
   "source": [
    "matricies = [\n",
    "    k_hop_message_passing(adj_matrix, embs, math.e),\n",
    "    k_hop_message_passing(adj_matrix, embs, math.pi),\n",
    "    k_hop_message_passing(adj_matrix, embs, phi),\n",
    "]\n",
    "A_k, agg_embs = linearly_sum_gnn_heads(matricies, \"sum\")"
   ],
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "-QQ_c7RQHBlK",
    "outputId": "47b6b96d-735e-457a-c97d-25a959133d99"
   },
   "execution_count": 140,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "adj matrix shape: (6, 6)\n",
      "agg embeddings shape: (6, 384)\n"
     ]
    },
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "<ipython-input-139-755027329b31>:7: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor).\n",
      "  A = torch.tensor(A)\n"
     ]
    }
   ]
  },
  {
   "cell_type": "code",
   "source": [
    "A_k"
   ],
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "yzfXkQcrHV08",
    "outputId": "757c99f5-9497-45a9-ff69-765db954ca1a"
   },
   "execution_count": 141,
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[ 28.487043,  28.487043,   0.      ,   0.      ,   0.      ,\n",
       "          0.      ],\n",
       "       [ 28.487043,  28.487043,   0.      ,   0.      ,   0.      ,\n",
       "          0.      ],\n",
       "       [  0.      ,   0.      ,   1.      ,   0.      ,   0.      ,\n",
       "          0.      ],\n",
       "       [  0.      ,   0.      ,   0.      , 338.61826 , 338.61826 ,\n",
       "        338.61826 ],\n",
       "       [  0.      ,   0.      ,   0.      , 338.61826 , 338.61826 ,\n",
       "        338.61826 ],\n",
       "       [  0.      ,   0.      ,   0.      , 338.6182  , 338.6182  ,\n",
       "        338.6182  ]], dtype=float32)"
      ]
     },
     "metadata": {},
     "execution_count": 141
    }
   ]
  },
  {
   "cell_type": "code",
   "source": [
    "U, S, VT = np.linalg.svd(A_k)\n",
    "print(f\"U: {U.shape}\\n\")\n",
    "print(f\"S: {S.shape}\\n\")\n",
    "print(f\"VT: {VT.shape}\\n\")\n",
    "plt.plot(np.diag(S))\n",
    "plt.xlabel(\"Singular value index\")\n",
    "plt.ylabel(\"Singular value\")\n",
    "plt.title(\"Singular values of A\")\n",
    "plt.show()"
   ],
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 403
    },
    "id": "fHn_WdaiHYtR",
    "outputId": "89d7ab5d-bf2d-48c7-d610-e0fbb63f9939"
   },
   "execution_count": 142,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "U: (6, 6)\n",
      "\n",
      "S: (6,)\n",
      "\n",
      "VT: (6, 6)\n",
      "\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ]
  },
  {
   "cell_type": "code",
   "source": [],
   "metadata": {
    "id": "s_Zr8R9oKsFk"
   },
   "execution_count": null,
   "outputs": []
  }
 ]
}