W6_MoreOptimization.ipynb

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  "cells": [
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      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
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      "source": [
        "<a href=\"https://colab.research.google.com/github/arashash/Deep-Learning-Course-Tutorials/blob/main/W6_MoreOptimization.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "AZQL5C34b81C"
      },
      "source": [
        "# Week 6: Optimization techniques\n",
        "**By Arash Ash, adapted from Neuromatch Academy [contents](https://github.com/NeuromatchAcademy/course-content-dl)**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "ZyvLcFnZb81E"
      },
      "source": [
        "---\n",
        "# Tutorial Objectives\n",
        "\n",
        "Objectives:\n",
        "*   Necessity and importance of optimization\n",
        "*   Introduction to commonly used optimization techniques\n",
        "*   Optimization in non-convex loss landscapes \n",
        "*   'Adaptive' hyperparameter tuning \n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "qCgFV_rnb81G"
      },
      "source": [
        "---\n",
        "# Setup"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "BU6_R_T2b81G"
      },
      "source": [
        "# Imports\n",
        "import time\n",
        "import copy\n",
        "import torch\n",
        "import torchvision\n",
        "\n",
        "import numpy as np\n",
        "import ipywidgets as widgets\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "import torch.nn as nn\n",
        "import torch.optim as optim\n",
        "import torch.nn.functional as F\n",
        "import torchvision.datasets as datasets\n",
        "\n",
        "from tqdm.auto import tqdm"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "execution": {},
        "id": "z2lLhSoGb81H"
      },
      "source": [
        "# @title Figure settings\n",
        "import ipywidgets as widgets       # interactive display\n",
        "%config InlineBackend.figure_format = 'retina'\n",
        "plt.style.use(\"https://raw.githubusercontent.com/NeuromatchAcademy/content-creation/main/nma.mplstyle\")\n",
        "plt.rc('axes', unicode_minus=False)"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "execution": {},
        "id": "Ye-ldqYLb81H"
      },
      "source": [
        "# @title Helper functions\n",
        "def print_params(model):\n",
        "  for name, param in model.named_parameters():\n",
        "    if param.requires_grad:\n",
        "      print(name, param.data)"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "execution": {},
        "id": "5pnQr7Vvb81I"
      },
      "source": [
        "# @title Set random seed\n",
        "\n",
        "# @markdown Executing `set_seed(seed=seed)` you are setting the seed\n",
        "\n",
        "# for DL its critical to set the random seed so that students can have a\n",
        "# baseline to compare their results to expected results.\n",
        "# Read more here: https://pytorch.org/docs/stable/notes/randomness.html\n",
        "\n",
        "# Call `set_seed` function in the exercises to ensure reproducibility.\n",
        "import random\n",
        "import torch\n",
        "\n",
        "def set_seed(seed=None, seed_torch=True):\n",
        "  if seed is None:\n",
        "    seed = np.random.choice(2 ** 32)\n",
        "  random.seed(seed)\n",
        "  np.random.seed(seed)\n",
        "  if seed_torch:\n",
        "    torch.manual_seed(seed)\n",
        "    torch.cuda.manual_seed_all(seed)\n",
        "    torch.cuda.manual_seed(seed)\n",
        "    torch.backends.cudnn.benchmark = False\n",
        "    torch.backends.cudnn.deterministic = True\n",
        "\n",
        "  print(f'Random seed {seed} has been set.')\n",
        "\n",
        "\n",
        "# In case that `DataLoader` is used\n",
        "def seed_worker(worker_id):\n",
        "  worker_seed = torch.initial_seed() % 2**32\n",
        "  np.random.seed(worker_seed)\n",
        "  random.seed(worker_seed)"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "execution": {},
        "id": "ETijYn14b81I"
      },
      "source": [
        "# @title Set device (GPU or CPU). Execute `set_device()`\n",
        "# especially if torch modules used.\n",
        "\n",
        "# inform the user if the notebook uses GPU or CPU.\n",
        "\n",
        "def set_device():\n",
        "  device = \"cuda\" if torch.cuda.is_available() else \"cpu\"\n",
        "  if device != \"cuda\":\n",
        "    print(\"WARNING: For this notebook to perform best, \"\n",
        "        \"if possible, in the menu under `Runtime` -> \"\n",
        "        \"`Change runtime type.`  select `GPU` \")\n",
        "  else:\n",
        "    print(\"GPU is enabled in this notebook.\")\n",
        "\n",
        "  return device"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "AxTEk7SYb81J",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6bfb364a-272c-41a9-da97-b0a100678d13"
      },
      "source": [
        "SEED = 2021\n",
        "set_seed(seed=SEED)\n",
        "DEVICE = set_device()"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Random seed 2021 has been set.\n",
            "GPU is enabled in this notebook.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "Lf0FtHZWb81J"
      },
      "source": [
        "---\n",
        "# Section 1. Introduction"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "8TJ8W7iCb81J",
        "cellView": "form"
      },
      "source": [
        "# @title Video 1: Introduction\n",
        "from ipywidgets import widgets\n",
        "\n",
        "out2 = widgets.Output()\n",
        "with out2:\n",
        "  from IPython.display import IFrame\n",
        "  class BiliVideo(IFrame):\n",
        "    def __init__(self, id, page=1, width=400, height=300, **kwargs):\n",
        "      self.id=id\n",
        "      src = \"https://player.bilibili.com/player.html?bvid={0}&page={1}\".format(id, page)\n",
        "      super(BiliVideo, self).__init__(src, width, height, **kwargs)\n",
        "\n",
        "  video = BiliVideo(id=f\"BV1VB4y1K7Vr\", width=854, height=480, fs=1)\n",
        "  print(\"Video available at https://www.bilibili.com/video/{0}\".format(video.id))\n",
        "  display(video)\n",
        "\n",
        "out1 = widgets.Output()\n",
        "with out1:\n",
        "  from IPython.display import YouTubeVideo\n",
        "  video = YouTubeVideo(id=f\"zm9oekdkJbQ\", width=854, height=480, fs=1, rel=0)\n",
        "  print(\"Video available at https://youtube.com/watch?v=\" + video.id)\n",
        "  display(video)\n",
        "\n",
        "out = widgets.Tab([out1, out2])\n",
        "out.set_title(0, 'Youtube')\n",
        "out.set_title(1, 'Bilibili')"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "Bf6pvjS_b81K"
      },
      "source": [
        "## Discuss: Unexpected consequences\n",
        "\n",
        "Can you think of examples from your own experience/life where poorly chosen incentives or objectives have lead to unexpected consequences?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "xMCdVrT0b81K"
      },
      "source": [
        "---\n",
        "# Section 2: Case study: successfully training an MLP for image classification"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "nl36MeFCb81K"
      },
      "source": [
        "Many of the core ideas (and tricks) in modern optimization for deep learning can be illustrated in the simple setting of training an MLP to solve an image classification task. In this tutorial we will guide you through the key challenges that arise when optimizing high-dimensional, non-convex$^\\dagger$ problems. We will use these challenges to motivate and explain some commonly used solutions.\n",
        "\n",
        "**Disclaimer:** Some of the functions you will code in this tutorial are already implemented in Pytorch and many other libraries. For pedagogical reasons, we decided to bring these simple coding tasks into the spotlight and place a relatively higher emphasis in your understanding of the algorithms, rather than the use of a specific library. \n",
        "\n",
        "In 'day-to-day' research projects you will likely to rely on the community-vetted, optimized libraries rather than the 'manual implementations' you will write today. In Section 8 you will have a chance to 'put it all together' and use the full power of Pytorch to tune the parameters of an MLP to classify handwritten digits."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "j0QCMCypb81K"
      },
      "source": [
        "$^\\dagger$: A **convex** function has one, global minimum - a nice property, as an optimization algorithm won't get stuck in a local minimum that isn't a global one (e.g., $f(x)=x^2 + 2x + 1$). A **non-convex** function is wavy - has some 'valleys' (local minima) that aren't as deep as the overall deepest 'valley' (global minimum). Thus, the optimization algorithms can get stuck in the local minimum, and it can be hard to tell when this happens (e.g., $f(x) = x^4 + x^3 - 2x^2 - 2x$). See also **Section 5** for more details."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "REeodkbnb81L",
        "cellView": "form"
      },
      "source": [
        "# @title Video 2: Case Study - MLP Classification\n",
        "from ipywidgets import widgets\n",
        "\n",
        "out2 = widgets.Output()\n",
        "with out2:\n",
        "  from IPython.display import IFrame\n",
        "  class BiliVideo(IFrame):\n",
        "    def __init__(self, id, page=1, width=400, height=300, **kwargs):\n",
        "      self.id=id\n",
        "      src = \"https://player.bilibili.com/player.html?bvid={0}&page={1}\".format(id, page)\n",
        "      super(BiliVideo, self).__init__(src, width, height, **kwargs)\n",
        "\n",
        "  video = BiliVideo(id=f\"BV1GB4y1K7Ha\", width=854, height=480, fs=1)\n",
        "  print(\"Video available at https://www.bilibili.com/video/{0}\".format(video.id))\n",
        "  display(video)\n",
        "\n",
        "out1 = widgets.Output()\n",
        "with out1:\n",
        "  from IPython.display import YouTubeVideo\n",
        "  video = YouTubeVideo(id=f\"pJc2ENhYbqA\", width=854, height=480, fs=1, rel=0)\n",
        "  print(\"Video available at https://youtube.com/watch?v=\" + video.id)\n",
        "  display(video)\n",
        "\n",
        "out = widgets.Tab([out1, out2])\n",
        "out.set_title(0, 'Youtube')\n",
        "out.set_title(1, 'Bilibili')\n"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "wdhnQnmKb81L"
      },
      "source": [
        "## Section 2.1: Data\n",
        "\n",
        "We will use the MNIST dataset of handwritten digits. We load the data via the Pytorch `datasets` module, as you learned in W1D1.\n",
        "\n",
        "**Note:** Although we can download the MNIST dataset directly from `datasets` using the optional argument `download=True`, we are going to download them from NMA directory on OSF to ensure network reliability.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "RKkoiMVTb81L",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "cellView": "form",
        "outputId": "a27c43a2-732a-4942-db82-fc45df23dcfd"
      },
      "source": [
        "# @title Download MNIST dataset\n",
        "import tarfile, requests, os\n",
        "\n",
        "fname = 'MNIST.tar.gz'\n",
        "name = 'MNIST'\n",
        "url = 'https://osf.io/y2fj6/download'\n",
        "\n",
        "if not os.path.exists(name):\n",
        "  print('\\nDownloading MNIST dataset...')\n",
        "  r = requests.get(url, allow_redirects=True)\n",
        "  with open(fname, 'wb') as fh:\n",
        "    fh.write(r.content)\n",
        "  print('\\nDownloading MNIST completed.')\n",
        "\n",
        "if not os.path.exists(name):\n",
        "  with tarfile.open(fname) as tar:\n",
        "    tar.extractall()\n",
        "    os.remove(fname)\n",
        "else:\n",
        "  print('MNIST dataset has been dowloaded.')"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Downloading MNIST dataset...\n",
            "\n",
            "Downloading MNIST completed.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "-wztVns7b81L"
      },
      "source": [
        "def load_mnist_data(change_tensors=False, download=False):\n",
        "  \"\"\"Load training and test examples for the MNIST digits dataset\n",
        "\n",
        "  Returns:\n",
        "    train_data (tensor): training input tensor of size (train_size x 784)\n",
        "    train_target (tensor): training 0-9 integer label tensor of size (train_size)\n",
        "    test_data (tensor): test input tensor of size (70k-train_size x 784)\n",
        "    test_target (tensor): training 0-9 integer label tensor of size (70k-train_size)\n",
        "\n",
        "  \"\"\"\n",
        "  # Load train and test sets\n",
        "  train_set = datasets.MNIST(root='.', train=True, download=download,\n",
        "                             transform=torchvision.transforms.ToTensor())\n",
        "  test_set = datasets.MNIST(root='.', train=False, download=download,\n",
        "                            transform=torchvision.transforms.ToTensor())\n",
        "\n",
        "  # Original data is in range [0, 255]. We normalize the data wrt its mean and std_dev.\n",
        "  ## Note that we only used *training set* information to compute mean and std\n",
        "  mean = train_set.data.float().mean()\n",
        "  std = train_set.data.float().std()\n",
        "\n",
        "  if change_tensors:\n",
        "    # Apply normalization directly to the tensors containing the dataset\n",
        "    train_set.data = (train_set.data.float() - mean) / std\n",
        "    test_set.data = (test_set.data.float() - mean) / std\n",
        "  else:\n",
        "    tform = torchvision.transforms.Compose([torchvision.transforms.ToTensor(),\n",
        "                                            torchvision.transforms.Normalize(mean=[mean / 255.], std=[std / 255.])\n",
        "                                            ])\n",
        "    train_set = datasets.MNIST(root='.', train=True, download=download,\n",
        "                               transform=tform)\n",
        "    test_set = datasets.MNIST(root='.', train=False, download=download,\n",
        "                              transform=tform)\n",
        "\n",
        "  return train_set, test_set\n",
        "\n",
        "\n",
        "train_set, test_set = load_mnist_data(change_tensors=True)"
      ],
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "1DzXnoEDb81M"
      },
      "source": [
        "As we are just getting started, we will concentrate on a small subset of only 500 examples out of the 60.000 data points contained in the whole training set.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "tynIXd5ib81M"
      },
      "source": [
        "# Sample a random subset of 500 indices\n",
        "subset_index = np.random.choice(len(train_set.data), 500)\n",
        "\n",
        "# We will use these symbols to represent the training data and labels, to stay\n",
        "# as close to the mathematical expressions as possible.\n",
        "X, y = train_set.data[subset_index, :], train_set.targets[subset_index]"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "flLNVmzJb81M"
      },
      "source": [
        "Run the following cell to visualize the content of three examples in our training set. Note how the pre-processing we applied to the data changes the range of pixel values after normalization.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "DBHsPdFyb81M",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 374
        },
        "cellView": "form",
        "outputId": "cbc682c2-f2c2-4e94-a22f-90db4fcb46a3"
      },
      "source": [
        "# @title Run me!\n",
        "num_figures = 3\n",
        "fig, axs = plt.subplots(1, num_figures, figsize=(5 * num_figures, 5))\n",
        "\n",
        "for sample_id, ax in enumerate(axs):\n",
        "  # Plot the pixel values for each image\n",
        "  ax.matshow(X[sample_id, :], cmap='gray_r')\n",
        "  # 'Write' the pixel value in the corresponding location\n",
        "  for (i, j), z in np.ndenumerate(X[sample_id, :]):\n",
        "    text = '{:.1f}'.format(z)\n",
        "    ax.text(j, i, text, ha='center',\n",
        "            va='center', fontsize=6, c='steelblue')\n",
        "\n",
        "  ax.set_title('Label: ' + str(y[sample_id].item()))\n",
        "  ax.axis('off')\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 1080x360 with 3 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "width": 1032,
              "height": 357
            },
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "Rkr33Vgab81M"
      },
      "source": [
        "## Section 2.2: Model\n",
        "\n",
        "As you will see next week, there are specific model architectures that are better suited to image-like data, such as Convolutional Neural Networks (CNNs). For simplicity, in this tutorial we will focus exclusively on Multi-Layer Perceptron (MLP) models as they allow us to highlight many important optimization challenges shared with more advanced neural network designs."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "97ZMF298b81M"
      },
      "source": [
        "class MLP(nn.Module):\n",
        "  \"\"\" This class implements MLPs in Pytorch of an arbitrary number of hidden\n",
        "  layers of potentially different sizes. Since we concentrate on classification\n",
        "  tasks in this tutorial, we have a log_softmax layer at prediction time.\n",
        "  \"\"\"\n",
        "\n",
        "  def __init__(self, in_dim=784, out_dim=10, hidden_dims=[], use_bias=True):\n",
        "    \"\"\"Constructs a MultiLayerPerceptron\n",
        "\n",
        "    Args:\n",
        "        in_dim (int): dimensionality of input data\n",
        "        out_dim (int): number of classes\n",
        "        hidden_dims (list): contains the dimensions of the hidden layers, an empty\n",
        "            list corresponds to a linear model (in_dim, out_dim)\n",
        "    \"\"\"\n",
        "\n",
        "    super(MLP, self).__init__()\n",
        "\n",
        "    self.in_dim = in_dim\n",
        "    self.out_dim = out_dim\n",
        "\n",
        "    # If we have no hidden layer, just initialize a linear model (e.g. in logistic regression)\n",
        "    if len(hidden_dims) == 0:\n",
        "      layers = [nn.Linear(in_dim, out_dim, bias=use_bias)]\n",
        "    else:\n",
        "      # 'Actual' MLP with dimensions in_dim - num_hidden_layers*[hidden_dim] - out_dim\n",
        "      layers = [nn.Linear(in_dim, hidden_dims[0], bias=use_bias), nn.ReLU()]\n",
        "\n",
        "      # Loop until before the last layer\n",
        "      for i, hidden_dim in enumerate(hidden_dims[:-1]):\n",
        "        layers += [nn.Linear(hidden_dim, hidden_dims[i + 1], bias=use_bias),\n",
        "                   nn.ReLU()]\n",
        "\n",
        "      # Add final layer to the number of classes\n",
        "      layers += [nn.Linear(hidden_dims[-1], out_dim, bias=use_bias)]\n",
        "\n",
        "    self.main = nn.Sequential(*layers)\n",
        "\n",
        "  def forward(self, x):\n",
        "    # Flatten the images into 'vectors'\n",
        "    transformed_x = x.view(-1, self.in_dim)\n",
        "    hidden_output = self.main(transformed_x)\n",
        "    output = F.log_softmax(hidden_output, dim=1)\n",
        "    return output"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "7rioW_cGb81N"
      },
      "source": [
        "Linear models constitute a very special kind of MLPs: they are equivalent to an MLP with *zero* hidden layers. This is simply an affine transformation, in other words a 'linear' map $W x$ with an 'offset' $b$; followed by a softmax function.\n",
        "\n",
        "$$f(x) = \\text{softmax}(W x + b)$$\n",
        "\n",
        "Here $x \\in \\mathbb{R}^{784}$, $W \\in \\mathbb{R}^{10 \\times 784}$ and $b \\in \\mathbb{R}^{10}$. Notice that the dimensions of the weight matrix are $10 \\times 784$ as the input tensors are flattened images, i.e., $28 \\times 28 = 784$-dimensional tensors and the output layer consists of $10$ nodes."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "BTvKTHgfb81N",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6dfe4e3d-65f2-4ee5-a3b1-c45a04933b2f"
      },
      "source": [
        "# Empty hidden_dims means we take a model with zero hidden layers.\n",
        "model = MLP(in_dim=784, out_dim=10, hidden_dims=[])\n",
        "\n",
        "# We print the model structure with 784 inputs and 10 outputs\n",
        "print(model)"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "MLP(\n",
            "  (main): Sequential(\n",
            "    (0): Linear(in_features=784, out_features=10, bias=True)\n",
            "  )\n",
            ")\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "SUfIN-BIb81N"
      },
      "source": [
        "## Section 2.3: Loss\n",
        "\n",
        "While we care about the accuracy of the model, the 'discrete' nature of the 0-1 loss makes it challenging to optimize. In order to learn good parameters for this model, we will use the cross entropy loss (negative log-likelihood), which you saw in last lecture, as a surrogate objective to be minimized. \n",
        "\n",
        "This particular choice of model and optimization objective leads to a *convex* optimization problem with respect to the parameters $W$ and $b$. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "dKE7UEwAb81N"
      },
      "source": [
        "loss_fn = F.nll_loss"
      ],
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "Z5GQSEARb81N"
      },
      "source": [
        "## Section 2.4: Interpretability"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "588fJLmtb81N"
      },
      "source": [
        "In last lecture, you saw that inspecting the weights of a model can provide insights on what 'concepts' the model has learned. Here we show the weights of a partially trained model. The weights corresponding to each class 'learn' to _fire_ when an input of the class is detected.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "execution": {},
        "id": "E99_P8iGb81N"
      },
      "source": [
        "#@markdown Run _this cell_ to train the model. If you are curious about how the training\n",
        "#@markdown takes place, double-click this cell to find out. At the end of this tutorial\n",
        "#@markdown you will have the opportunity to train a more complex model on your own.\n",
        "\n",
        "cell_verbose = False\n",
        "partial_trained_model = MLP(in_dim=784, out_dim=10, hidden_dims=[])\n",
        "\n",
        "if cell_verbose:\n",
        "  print('Init loss', loss_fn(partial_trained_model(X), y).item()) # This matches around np.log(10 = # of classes)\n",
        "\n",
        "optimizer = optim.Adam(partial_trained_model.parameters(), lr=7e-4)\n",
        "for _ in range(200):\n",
        "  loss = loss_fn(partial_trained_model(X), y)\n",
        "  optimizer.zero_grad()\n",
        "  loss.backward()\n",
        "  optimizer.step()\n",
        "\n",
        "if cell_verbose:\n",
        "  print('End loss', loss_fn(partial_trained_model(X), y).item()) # This should be less than 1e-2"
      ],
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "GnS0wNRGb81N",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 141
        },
        "outputId": "8d855e7f-ee65-44de-fc48-6b87e758d1fa"
      },
      "source": [
        "# Show class filters of a trained model\n",
        "W = partial_trained_model.main[0].weight.data.numpy()\n",
        "\n",
        "fig, axs = plt.subplots(1, 10, figsize=(15, 4))\n",
        "for class_id in range(10):\n",
        "  axs[class_id].imshow(W[class_id, :].reshape(28, 28), cmap='gray_r')\n",
        "  axs[class_id].axis('off')\n",
        "  axs[class_id].set_title('Class ' + str(class_id) )\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 1080x288 with 10 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "width": 1062,
              "height": 124
            },
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "YWlvEhzgb81O"
      },
      "source": [
        "---\n",
        "# Section 3: High dimensional search"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "GGfov9lIb81O"
      },
      "source": [
        "We now have a model with its corresponding trainable parameters as well as an objective to optimize. Where do we go to next? How do we find a 'good' configuration of parameters?\n",
        "\n",
        "One idea is to choose a random direction and move only if the objective is reduced. However, this is inefficient in high dimensions and you will see how gradient descent (with a suitable step-size) can guarantee consistent improvement in terms of the objective function."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "RAdvEluib81O",
        "cellView": "form"
      },
      "source": [
        "# @title Video 3: Optimization of an Objective Function\n",
        "from ipywidgets import widgets\n",
        "\n",
        "out2 = widgets.Output()\n",
        "with out2:\n",
        "  from IPython.display import IFrame\n",
        "  class BiliVideo(IFrame):\n",
        "    def __init__(self, id, page=1, width=400, height=300, **kwargs):\n",
        "      self.id=id\n",
        "      src = \"https://player.bilibili.com/player.html?bvid={0}&page={1}\".format(id, page)\n",
        "      super(BiliVideo, self).__init__(src, width, height, **kwargs)\n",
        "\n",
        "  video = BiliVideo(id=f\"BV1aL411H7Ce\", width=854, height=480, fs=1)\n",
        "  print(\"Video available at https://www.bilibili.com/video/{0}\".format(video.id))\n",
        "  display(video)\n",
        "\n",
        "out1 = widgets.Output()\n",
        "with out1:\n",
        "  from IPython.display import YouTubeVideo\n",
        "  video = YouTubeVideo(id=f\"aSJTRdjRvvw\", width=854, height=480, fs=1, rel=0)\n",
        "  print(\"Video available at https://youtube.com/watch?v=\" + video.id)\n",
        "  display(video)\n",
        "\n",
        "out = widgets.Tab([out1, out2])\n",
        "out.set_title(0, 'Youtube')\n",
        "out.set_title(1, 'Bilibili')"
      ],
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "DzzcKAPmb81O"
      },
      "source": [
        "## Coding Exercise 3: Implement gradient descent\n",
        "\n",
        "In this exercise you will use PyTorch automatic differentiation capabilities to compute the gradient of the loss with respect to the parameters of the model. You will then use these gradients to implement the update performed by the gradient descent method.  "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "XPt_LAuNb81O"
      },
      "source": [
        "def zero_grad(params):\n",
        "  \"\"\"Clear up gradients as Pytorch automatically accumulates gradients from\n",
        "  successive backward calls\n",
        "  \"\"\"\n",
        "  for par in params:\n",
        "    if not(par.grad is None):\n",
        "      par.grad.data.zero_()\n",
        "\n",
        "\n",
        "def random_update(model, noise_scale=0.1, normalized=False):\n",
        "  \"\"\" Performs a random update on the parameters of the model\n",
        "  \"\"\"\n",
        "  for par in model.parameters():\n",
        "    noise = torch.randn_like(par)\n",
        "    if normalized:\n",
        "      noise /= torch.norm(noise)\n",
        "    par.data +=  noise_scale * noise"
      ],
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "LI4oPSiYb81O",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7b7198fe-6cfa-458e-c99f-82535a985e99"
      },
      "source": [
        "def gradient_update(loss, params, lr=1e-3):\n",
        "  \"\"\"Perform a gradient descent update on a given loss over a collection of parameters\n",
        "\n",
        "  Args:\n",
        "    loss (tensor): A scalar tensor containing the loss whose gradient will be computed\n",
        "    params (iterable): Collection of parameters with respect to which we compute gradients\n",
        "    lr (float): Scalar specifying the learning rate or step-size for the update\n",
        "  \"\"\"\n",
        "  # Clear up gradients as Pytorch automatically accumulates gradients from\n",
        "  # successive backward calls\n",
        "  zero_grad(params)\n",
        "\n",
        "  # Compute gradients on given objective\n",
        "  loss.backward()\n",
        "\n",
        "  with torch.no_grad():\n",
        "    for par in params:\n",
        "      #################################################\n",
        "      ## TODO for students: update the value of the parameter ##\n",
        "      raise NotImplementedError(\"Student exercise: implement gradient update\")\n",
        "      #################################################\n",
        "      # Here we work with the 'data' attribute of the parameter rather than the\n",
        "      # parameter itself.\n",
        "      par.data -= ...\n",
        "\n",
        "\n",
        "set_seed(seed=SEED)\n",
        "model1 = MLP(in_dim=784, out_dim=10, hidden_dims=[])\n",
        "print('\\n The model1 parameters before the update are: \\n')\n",
        "print_params(model1)\n",
        "loss = loss_fn(model1(X), y)\n",
        "\n",
        "## Uncomment below to test your function\n",
        "# gradient_update(loss, list(model1.parameters()), lr=1e-1)\n",
        "# print('\\n The model1 parameters after the update are: \\n')\n",
        "# print_params(model1)"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Random seed 2021 has been set.\n",
            "\n",
            " The model1 parameters before the update are: \n",
            "\n",
            "main.0.weight tensor([[-0.0264,  0.0010,  0.0173,  ...,  0.0297,  0.0278, -0.0221],\n",
            "        [-0.0040, -0.0295, -0.0086,  ..., -0.0070,  0.0254, -0.0233],\n",
            "        [ 0.0240, -0.0231,  0.0342,  ...,  0.0124,  0.0270, -0.0180],\n",
            "        ...,\n",
            "        [-0.0005,  0.0157,  0.0111,  ...,  0.0144, -0.0301, -0.0144],\n",
            "        [ 0.0181,  0.0303,  0.0255,  ..., -0.0110, -0.0175,  0.0205],\n",
            "        [ 0.0208, -0.0353, -0.0183,  ..., -0.0271,  0.0099,  0.0003]])\n",
            "main.0.bias tensor([-0.0290, -0.0033,  0.0100, -0.0320,  0.0022,  0.0221,  0.0307,  0.0243,\n",
            "         0.0159, -0.0064])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "KYC7_8TJb81O"
      },
      "source": [
        "```\n",
        " The model1 parameters after the update are: \n",
        "\n",
        "main.0.weight tensor([[-0.0263,  0.0010,  0.0174,  ...,  0.0298,  0.0278, -0.0220],\n",
        "        [-0.0047, -0.0302, -0.0093,  ..., -0.0077,  0.0248, -0.0240],\n",
        "        [ 0.0234, -0.0237,  0.0335,  ...,  0.0117,  0.0263, -0.0187],\n",
        "        ...,\n",
        "        [-0.0006,  0.0156,  0.0110,  ...,  0.0143, -0.0302, -0.0145],\n",
        "        [ 0.0164,  0.0286,  0.0238,  ..., -0.0127, -0.0191,  0.0188],\n",
        "        [ 0.0206, -0.0354, -0.0184,  ..., -0.0272,  0.0098,  0.0002]])\n",
        "main.0.bias tensor([-0.0292, -0.0018,  0.0115, -0.0370,  0.0054,  0.0155,  0.0317,  0.0246,\n",
        "         0.0198, -0.0061])\n",
        "```"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "tdzPJo8Gb81P"
      },
      "source": [
        "## Comparing updates\n",
        "\n",
        "These plots compare the effectiveness of updating random directions for the problem of optimizing the parameters of a high-dimensional linear model. We contrast the behavior at initialization and during an intermediate stage of training by showing the histograms of change in loss over 100 different random directions vs the changed in loss induced by the gradient descent update\n",
        "\n",
        "**Remember:** since we are trying to minimize, here negative is better!\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "execution": {},
        "id": "p_CRpt-mb81P",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 620
        },
        "outputId": "69cdfb2c-ee38-431c-e835-cdc3c124877e"
      },
      "source": [
        "# @markdown _Run this cell_ to visualize the results\n",
        "fig, axs = plt.subplots(1, 2, figsize=(10, 4))\n",
        "\n",
        "for id, (model_name, my_model) in enumerate([('Initialization', model),\n",
        "                                              ('Partially trained', partial_trained_model)]):\n",
        "  # Compue the loss we will be comparing to\n",
        "  base_loss = loss_fn(my_model(X), y)\n",
        "\n",
        "  # Compute the improvement via gradient descent\n",
        "  dummy_model = copy.deepcopy(my_model)\n",
        "  loss1 = loss_fn(dummy_model(X), y)\n",
        "  gradient_update(loss1, list(dummy_model.parameters()), lr=1e-2)\n",
        "  gd_delta = loss_fn(dummy_model(X), y) - base_loss\n",
        "\n",
        "  deltas = []\n",
        "  for trial_id in range(100):\n",
        "    # Compute the improvement obtained with a random direction\n",
        "    dummy_model = copy.deepcopy(my_model)\n",
        "    random_update(dummy_model, noise_scale=1e-2)\n",
        "    deltas.append((loss_fn(dummy_model(X), y) - base_loss).item())\n",
        "\n",
        "  # Plot histogram for random direction and vertical line for gradient descent\n",
        "  axs[id].hist(deltas, label='Random Directions', bins=20)\n",
        "  axs[id].set_title(model_name)\n",
        "  axs[id].set_xlabel('Change in loss')\n",
        "  axs[id].set_ylabel('% samples')\n",
        "  axs[id].axvline(0, c='green', alpha=0.5)\n",
        "  axs[id].axvline(gd_delta.item(), linestyle='--', c='red', alpha=1,\n",
        "                  label='Gradient Descent')\n",
        "\n",
        "\n",
        "handles, labels = axs[id].get_legend_handles_labels()\n",
        "fig.legend(handles, labels, loc='upper center',\n",
        "           bbox_to_anchor=(0.5, 1.05),\n",
        "           fancybox=False, shadow=False, ncol=2)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "error",
          "ename": "NotImplementedError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mNotImplementedError\u001b[0m                       Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-22-dab15ede1b6e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     10\u001b[0m   \u001b[0mdummy_model\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcopy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdeepcopy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmy_model\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m   \u001b[0mloss1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mloss_fn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdummy_model\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 12\u001b[0;31m   \u001b[0mgradient_update\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mloss1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdummy_model\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mparameters\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlr\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1e-2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     13\u001b[0m   \u001b[0mgd_delta\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mloss_fn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdummy_model\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mbase_loss\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     14\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m<ipython-input-21-d2914420fd74>\u001b[0m in \u001b[0;36mgradient_update\u001b[0;34m(loss, params, lr)\u001b[0m\n\u001b[1;32m     18\u001b[0m       \u001b[0;31m#################################################\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     19\u001b[0m       \u001b[0;31m## TODO for students: update the value of the parameter ##\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 20\u001b[0;31m       \u001b[0;32mraise\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Student exercise: implement gradient update\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     21\u001b[0m       \u001b[0;31m#################################################\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     22\u001b[0m       \u001b[0;31m# Here we work with the 'data' attribute of the parameter rather than the\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mNotImplementedError\u001b[0m: Student exercise: implement gradient update"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "width": 702,
              "height": 270
            },
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "x6EDRzDLb81P"
      },
      "source": [
        "## Think! 3: Gradient descent vs. random search\n",
        "\n",
        "Compare the behavior of gradient descent and random search based on the histograms above. Is any of the two methods more reliable? How can you explain the changes between behavior of the methods at initialization vs during training?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "Vy1Bxg2Xb81P"
      },
      "source": [
        "---\n",
        "# Section 4: Poor conditioning"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "8Udtqm3ub81P"
      },
      "source": [
        "Already in this 'simple' logistic regression problem, the issue of bad conditioning is haunting us. Not all parameters are created equal and the sensitivity of the network to changes on the parameters will have a big impact in the dynamics of the optimization.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "SOa4VnZRb81P",
        "cellView": "form"
      },
      "source": [
        "# @title Video 4: Momentum\n",
        "from ipywidgets import widgets\n",
        "\n",
        "out2 = widgets.Output()\n",
        "with out2:\n",
        "  from IPython.display import IFrame\n",
        "  class BiliVideo(IFrame):\n",
        "    def __init__(self, id, page=1, width=400, height=300, **kwargs):\n",
        "      self.id=id\n",
        "      src = \"https://player.bilibili.com/player.html?bvid={0}&page={1}\".format(id, page)\n",
        "      super(BiliVideo, self).__init__(src, width, height, **kwargs)\n",
        "\n",
        "  video = BiliVideo(id=f\"BV1NL411H71t\", width=854, height=480, fs=1)\n",
        "  print(\"Video available at https://www.bilibili.com/video/{0}\".format(video.id))\n",
        "  display(video)\n",
        "\n",
        "out1 = widgets.Output()\n",
        "with out1:\n",
        "  from IPython.display import YouTubeVideo\n",
        "  video = YouTubeVideo(id=f\"3ES5O58Y_2M\", width=854, height=480, fs=1, rel=0)\n",
        "  print(\"Video available at https://youtube.com/watch?v=\" + video.id)\n",
        "  display(video)\n",
        "\n",
        "out = widgets.Tab([out1, out2])\n",
        "out.set_title(0, 'Youtube')\n",
        "out.set_title(1, 'Bilibili')\n"
      ],
      "execution_count": 23,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "Y2HaO21fb81Q"
      },
      "source": [
        "We illustrate this issue in a 2-dimensional setting. We freeze all but two parameters of the network: one of them is an element of the weight matrix (filter) for class 0, while the other is the bias for class 7. This results in an optimization with two decision variables.\n",
        "\n",
        "How much difference is there in the behavior of these two parameters under gradient descent? What is the effect of momentum in bridging that gap?\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "execution": {},
        "id": "AytZ2nerb81Q"
      },
      "source": [
        "# @markdown _Run this cell_ to setup some helper functions.\n",
        "\n",
        "def loss_2d(model, u, v, mask_idx=(0, 378), bias_id=7):\n",
        "  \"\"\"Defines a 2-dim function by freezing all but two parameters of a linear\n",
        "  model.\n",
        "\n",
        "  Args:\n",
        "    model (torch module): a pytorch 0-hidden layer (linear) model\n",
        "    u (scalar): first free parameter\n",
        "    v (scalar): second free parameter\n",
        "    mask_idx (tuple): selects parameter in weight matrix replaced by u\n",
        "    bias_idx (int): selects parameter in bias vector replaced by v\n",
        "\n",
        "  Returns:\n",
        "    scalar: loss of the 'new' model over inputs X, y (defined externally)\n",
        "  \"\"\"\n",
        "\n",
        "  # We zero out the element of the weight tensor that will be\n",
        "  # replaced by u\n",
        "  mask = torch.ones_like(model.main[0].weight)\n",
        "  mask[mask_idx[0], mask_idx[1]] = 0.\n",
        "  masked_weights = model.main[0].weight * mask\n",
        "\n",
        "  # u is replacing an element of the weight matrix\n",
        "  masked_weights[mask_idx[0], mask_idx[1]] = u\n",
        "\n",
        "  res = X.reshape(-1, 784) @ masked_weights.T + model.main[0].bias\n",
        "\n",
        "  # v is replacing a bias for class 7\n",
        "  res[:, 7] += v - model.main[0].bias[7]\n",
        "  res =  F.log_softmax(res, dim=1)\n",
        "\n",
        "  return loss_fn(res, y)\n",
        "\n",
        "\n",
        "def plot_surface(U, V, Z, fig):\n",
        "  \"\"\" Plot a 3D loss surface given meshed inputs U, V and values Z\n",
        "  \"\"\"\n",
        "  ax = fig.add_subplot(1, 2, 2, projection='3d')\n",
        "  ax.view_init(45, -130)\n",
        "\n",
        "  surf = ax.plot_surface(U, V, Z, cmap=plt.cm.coolwarm,\n",
        "                      linewidth=0, antialiased=True, alpha=0.5)\n",
        "\n",
        "  # Select certain level contours to plot\n",
        "  # levels = Z.min() * np.array([1.005, 1.1, 1.3, 1.5, 2.])\n",
        "  # plt.contour(U, V, Z)# levels=levels, alpha=0.5)\n",
        "\n",
        "  ax.set_xlabel('Weight')\n",
        "  ax.set_ylabel('Bias')\n",
        "  ax.set_zlabel('Loss', rotation=90)\n",
        "\n",
        "  return ax\n",
        "\n",
        "\n",
        "def plot_param_distance(best_u, best_v, trajs, fig, styles, labels,\n",
        "                        use_log=False, y_min_v=-12.0, y_max_v=1.5):\n",
        "  \"\"\" Plot the distance to each of the two parameters for a collection of 'trajectories'\n",
        "  \"\"\"\n",
        "  ax = fig.add_subplot(1, 1, 1)\n",
        "\n",
        "  for traj, style, label in zip(trajs, styles, labels):\n",
        "    d0 = np.array([np.abs(_[0] - best_u) for _ in traj])\n",
        "    d1 = np.array([np.abs(_[1] - best_v) for _ in traj])\n",
        "    if use_log:\n",
        "      d0 = np.log(1e-16 + d0)\n",
        "      d1 = np.log(1e-16 + d1)\n",
        "    ax.plot(range(len(traj)), d0, style, label='weight - ' + label)\n",
        "    ax.plot(range(len(traj)), d1, style, label='bias - ' + label)\n",
        "  ax.set_xlabel('Iteration')\n",
        "  if use_log:\n",
        "    ax.set_ylabel('Log distance to optimum (per dimension)')\n",
        "    ax.set_ylim(y_min_v, y_max_v)\n",
        "  else:\n",
        "    ax.set_ylabel('Abs distance to optimum (per dimension)')\n",
        "  ax.legend(loc='right', bbox_to_anchor=(1.5, 0.5),\n",
        "            fancybox=False, shadow=False, ncol=1)\n",
        "\n",
        "  return ax\n",
        "\n",
        "\n",
        "def run_optimizer(inits, eval_fn, update_fn, max_steps=500,\n",
        "                  optim_kwargs={'lr':1e-2}, log_traj=True):\n",
        "  \"\"\"Runs an optimizer on a given objective and logs parameter trajectory\n",
        "\n",
        "  Args:\n",
        "      inits list(scalar): initialization of parameters\n",
        "      eval_fn (callable): function computing the objective to be minimized\n",
        "      update_fn (callable): function executing parameter update\n",
        "      max_steps (int): number of iterations to run\n",
        "      optim_kwargs (dict): customize optimizer hyperparameters\n",
        "\n",
        "  Returns:\n",
        "      list[list]: trajectory information [*params, loss] for each optimization step\n",
        "  \"\"\"\n",
        "\n",
        "  # Initialize parameters and optimizer\n",
        "  params = [nn.Parameter(torch.tensor(_)) for _ in inits]\n",
        "  # Methods like momentum and rmsprop keep and auxiliary vector of parameters\n",
        "  aux_tensors = [torch.zeros_like(_) for _ in params]\n",
        "  if log_traj:\n",
        "    traj = np.zeros((max_steps, len(params)+1))\n",
        "  for _ in range(max_steps):\n",
        "    # Evaluate loss\n",
        "    loss = eval_fn(*params)\n",
        "    # Store 'trajectory' information\n",
        "    if log_traj:\n",
        "      traj[_, :] = [_.item() for _ in params] + [loss.item()]\n",
        "    # Perform update\n",
        "    if update_fn == gradient_update:\n",
        "      gradient_update(loss, params, **optim_kwargs)\n",
        "    else:\n",
        "      update_fn(loss, params, aux_tensors, **optim_kwargs)\n",
        "  if log_traj:\n",
        "    return traj\n",
        "\n",
        "\n",
        "L = 4.\n",
        "xs = np.linspace(-L, L, 30)\n",
        "ys = np.linspace(-L, L, 30)\n",
        "U, V = np.meshgrid(xs, ys)"
      ],
      "execution_count": 24,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "NaLCanLab81Q"
      },
      "source": [
        "## Coding Exercise 4: Implement momentum\n",
        "\n",
        "In this exercise you will implement the momentum update given by:\n",
        "\n",
        "\\begin{equation}\n",
        "w_{t+1} = w_t - \\eta \\nabla J(w_t) + \\beta (w_t - w_{t-1})\n",
        "\\end{equation}\n",
        "\n",
        "It is convenient to re-express this update rule in terms of a recursion. For that, we define 'velocity' as the quantity:\n",
        "\\begin{equation}\n",
        "v_{t-1} := w_{t} - w_{t-1}\n",
        "\\end{equation}\n",
        "\n",
        "which leads to the two-step update rule:\n",
        "\n",
        "\\begin{equation}\n",
        "v_t = - \\eta \\nabla J(w_t) + \\beta (\\underbrace{w_t - w_{t-1}}_{v_{t-1}})\n",
        "\\end{equation}\n",
        "\n",
        "\\begin{equation}\n",
        "w_{t+1} \\leftarrow w_t + v_{t}\n",
        "\\end{equation}\n",
        "\n",
        "Pay attention to the positive sign of the update in the last equation, given the definition of $v_t$, above. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "Zu2jNgoWb81Q",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3134beb0-e383-4d2d-e6fa-77981fa97bc0"
      },
      "source": [
        "def momentum_update(loss, params, grad_vel, lr=1e-3, beta=0.8):\n",
        "  \"\"\"Perform a momentum update over a collection of parameters given a loss and 'velocities'\n",
        "\n",
        "  Args:\n",
        "    loss (tensor): A scalar tensor containing the loss whose gradient will be computed\n",
        "    params (iterable): Collection of parameters with respect to which we compute gradients\n",
        "    grad_vel (iterable): Collection containing the 'velocity' v_t for each parameter\n",
        "    lr (float): Scalar specifying the learning rate or step-size for the update\n",
        "    beta (float): Scalar 'momentum' parameter\n",
        "  \"\"\"\n",
        "  # Clear up gradients as Pytorch automatically accumulates gradients from\n",
        "  # successive backward calls\n",
        "  zero_grad(params)\n",
        "  # Compute gradients on given objective\n",
        "  loss.backward()\n",
        "\n",
        "  with torch.no_grad():\n",
        "    for (par, vel) in zip(params, grad_vel):\n",
        "      #################################################\n",
        "      ## TODO for students: update the value of the parameter ##\n",
        "      raise NotImplementedError(\"Student exercise: implement momentum update\")\n",
        "      #################################################\n",
        "      # Update 'velocity'\n",
        "      vel.data = ...\n",
        "      # Update parameters\n",
        "      par.data += ...\n",
        "\n",
        "set_seed(seed=SEED)\n",
        "model2 = MLP(in_dim=784, out_dim=10, hidden_dims=[])\n",
        "print('\\n The model2 parameters before the update are: \\n')\n",
        "print_params(model2)\n",
        "loss = loss_fn(model2(X), y)\n",
        "initial_vel = [torch.randn_like(p) for p in model2.parameters()]\n",
        "\n",
        "## Uncomment below to test your function\n",
        "# momentum_update(loss, list(model2.parameters()), grad_vel=initial_vel, lr=1e-1, beta=0.9)\n",
        "# print('\\n The model2 parameters after the update are: \\n')\n",
        "# print_params(model2)"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Random seed 2021 has been set.\n",
            "\n",
            " The model2 parameters before the update are: \n",
            "\n",
            "main.0.weight tensor([[-0.0264,  0.0010,  0.0173,  ...,  0.0297,  0.0278, -0.0221],\n",
            "        [-0.0040, -0.0295, -0.0086,  ..., -0.0070,  0.0254, -0.0233],\n",
            "        [ 0.0240, -0.0231,  0.0342,  ...,  0.0124,  0.0270, -0.0180],\n",
            "        ...,\n",
            "        [-0.0005,  0.0157,  0.0111,  ...,  0.0144, -0.0301, -0.0144],\n",
            "        [ 0.0181,  0.0303,  0.0255,  ..., -0.0110, -0.0175,  0.0205],\n",
            "        [ 0.0208, -0.0353, -0.0183,  ..., -0.0271,  0.0099,  0.0003]])\n",
            "main.0.bias tensor([-0.0290, -0.0033,  0.0100, -0.0320,  0.0022,  0.0221,  0.0307,  0.0243,\n",
            "         0.0159, -0.0064])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "CV8XLrFpb81Q"
      },
      "source": [
        "```\n",
        " The model2 parameters after the update are: \n",
        "\n",
        "main.0.weight tensor([[ 1.5898,  0.0116, -2.0239,  ..., -1.0871,  0.4030, -0.9577],\n",
        "        [ 0.4653,  0.6022, -0.7363,  ...,  0.5485, -0.2747, -0.6539],\n",
        "        [-1.4117, -1.1045,  0.6492,  ..., -1.0201,  0.6503,  0.1310],\n",
        "        ...,\n",
        "        [-0.5098,  0.5075, -0.0718,  ...,  1.1192,  0.2900, -0.9657],\n",
        "        [-0.4405, -0.1174,  0.7542,  ...,  0.0792, -0.1857,  0.3537],\n",
        "        [-1.0824,  1.0080, -0.4254,  ..., -0.3760, -1.7491,  0.6025]])\n",
        "main.0.bias tensor([ 0.4147, -1.0440,  0.8720, -1.6201, -0.9632,  0.9430, -0.5180,  1.3417,\n",
        "         0.6574,  0.3677])\n",
        "```"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "-3jkFoUvb81Q"
      },
      "source": [
        "## Interactive Demo 4: Momentum vs. GD\n",
        "\n",
        "The plots below show the distance to the optimum for both variables across the two methods, as well as the parameter trajectory over the loss surface."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "execution": {},
        "id": "2Uf0PtC7b81Q",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 194
        },
        "outputId": "7c2b3881-3f3c-445e-f1d2-e4e0f39692c9"
      },
      "source": [
        "# @markdown Run this cell to enable the widget!\n",
        "from matplotlib.lines import Line2D\n",
        "\n",
        "# Find the optimum of this 2D problem using Newton's method\n",
        "def run_newton(func, init_list=[0., 0.], max_iter=200):\n",
        "\n",
        "  par_tensor = torch.tensor(init_list, requires_grad=True)\n",
        "  t_g = lambda par_tensor: func(par_tensor[0], par_tensor[1])\n",
        "\n",
        "  for _ in tqdm(range(max_iter)):\n",
        "    eval_loss = t_g(par_tensor)\n",
        "    eval_grad = torch.autograd.grad(eval_loss, [par_tensor])[0]\n",
        "    eval_hess = torch.autograd.functional.hessian(t_g, par_tensor)\n",
        "    # Newton's update is:  - inverse(Hessian) x gradient\n",
        "    par_tensor.data -= torch.inverse(eval_hess) @ eval_grad\n",
        "\n",
        "  return par_tensor.data.numpy()\n",
        "\n",
        "\n",
        "set_seed(2021)\n",
        "model = MLP(in_dim=784, out_dim=10, hidden_dims=[])\n",
        "# Define 2d loss objectives and surface values\n",
        "g = lambda u, v: loss_2d(copy.deepcopy(model), u, v)\n",
        "Z = np.fromiter(map(g, U.ravel(), V.ravel()), U.dtype).reshape(V.shape)\n",
        "\n",
        "best_u, best_v  = run_newton(func=g)\n",
        "\n",
        "# Initialization of the variables\n",
        "INITS = [2.5, 3.7]\n",
        "\n",
        "# Used for plotting\n",
        "LABELS = ['GD', 'Momentum']\n",
        "COLORS = ['black', 'red']\n",
        "LSTYLES = ['-', '--']\n",
        "\n",
        "\n",
        "@widgets.interact_manual\n",
        "def momentum_experiment(max_steps=widgets.IntSlider(300, 50, 500, 5),\n",
        "                        lr=widgets.FloatLogSlider(value=1e-1, min=-3, max=0.7, step=0.1),\n",
        "                        beta=widgets.FloatSlider(value=9e-1, min=0, max=1., step=0.01)\n",
        "                        ):\n",
        "\n",
        "  # Execute both optimizers\n",
        "  sgd_traj = run_optimizer(INITS, eval_fn=g, update_fn=gradient_update,\n",
        "                           max_steps=max_steps, optim_kwargs={'lr': lr})\n",
        "  mom_traj = run_optimizer(INITS, eval_fn=g, update_fn=momentum_update,\n",
        "                           max_steps=max_steps, optim_kwargs={'lr': lr, 'beta':beta})\n",
        "\n",
        "  TRAJS = [sgd_traj, mom_traj]\n",
        "\n",
        "  # Plot distances\n",
        "  fig = plt.figure(figsize=(9,4))\n",
        "  plot_param_distance(best_u, best_v, TRAJS, fig,\n",
        "                      LSTYLES, LABELS, use_log=True, y_min_v=-12.0, y_max_v=1.5)\n",
        "\n",
        "  # # Plot trajectories\n",
        "  fig = plt.figure(figsize=(12, 5))\n",
        "  ax = plot_surface(U, V, Z, fig)\n",
        "  for traj, c, label in zip(TRAJS, COLORS, LABELS):\n",
        "    ax.plot3D(*traj.T, c, linewidth=0.3, label=label)\n",
        "    ax.scatter3D(*traj.T, '.-', s=1, c=c)\n",
        "\n",
        "  # Plot optimum point\n",
        "  ax.scatter(best_u, best_v, Z.min(), marker='*', s=80, c='lime', label='Opt.');\n",
        "  lines = [Line2D([0], [0],\n",
        "                  color=c,\n",
        "                  linewidth=3,\n",
        "                  linestyle='--') for c in COLORS]\n",
        "  lines.append(Line2D([0], [0], color='lime', linewidth=0, marker='*'))\n",
        "  ax.legend(lines, LABELS + ['Optimum'], loc='right',\n",
        "            bbox_to_anchor=(.8, -0.1), ncol=len(LABELS) + 1)"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Random seed 2021 has been set.\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "134e077f2b104fe5833bda8577f82873",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "  0%|          | 0/200 [00:00<?, ?it/s]"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "abb719c41c09417d95dc13b284e06c15",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "interactive(children=(IntSlider(value=300, description='max_steps', max=500, min=50, step=5), FloatLogSlider(v…"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "Nee92eWNb81R"
      },
      "source": [
        "## Think! 4: Momentum and oscillations\n",
        "\n",
        "- Discuss how this specific example illustrates the issue of poor conditioning in optimization? How does momentum help resolve these difficulties?\n",
        "\n",
        "- Do you see oscillations for any of these methods? Why does this happen?\n",
        "\n",
        "- Finally, tune the learning rate and momentum parameters to achieve a loss below $10^{-6}$ (for both dimensions) within 100 iterations."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "6cUNE3gxb81R"
      },
      "source": [
        "---\n",
        "# Section 5: Non-convexity"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "GdeDDITIb81R"
      },
      "source": [
        "The introduction of even just 1 hidden layer in the neural network transforms the previous convex optimization problem into a non-convex one. And with great non-convexity, comes great responsibility... (Sorry, we couldn't help it!)\n",
        "\n",
        "**Note:** From this section onwards we will be dealing with non-convex optimization problems for the remaining of the tutorial. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "0JrmLNC1b81R",
        "cellView": "form"
      },
      "source": [
        "# @title Video 5: Overparametrization\n",
        "from ipywidgets import widgets\n",
        "\n",
        "out2 = widgets.Output()\n",
        "with out2:\n",
        "  from IPython.display import IFrame\n",
        "  class BiliVideo(IFrame):\n",
        "    def __init__(self, id, page=1, width=400, height=300, **kwargs):\n",
        "      self.id=id\n",
        "      src = \"https://player.bilibili.com/player.html?bvid={0}&page={1}\".format(id, page)\n",
        "      super(BiliVideo, self).__init__(src, width, height, **kwargs)\n",
        "\n",
        "  video = BiliVideo(id=f\"BV16h41167Jr\", width=854, height=480, fs=1)\n",
        "  print(\"Video available at https://www.bilibili.com/video/{0}\".format(video.id))\n",
        "  display(video)\n",
        "\n",
        "out1 = widgets.Output()\n",
        "with out1:\n",
        "  from IPython.display import YouTubeVideo\n",
        "  video = YouTubeVideo(id=f\"7vUpUEKKl5o\", width=854, height=480, fs=1, rel=0)\n",
        "  print(\"Video available at https://youtube.com/watch?v=\" + video.id)\n",
        "  display(video)\n",
        "\n",
        "out = widgets.Tab([out1, out2])\n",
        "out.set_title(0, 'Youtube')\n",
        "out.set_title(1, 'Bilibili')"
      ],
      "execution_count": 29,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "3v4uHb-db81R"
      },
      "source": [
        "Take a couple of minutes to play with a more complex 3D visualization of the loss landscape of a neural network on a non-convex problem. Visit https://losslandscape.com/explorer.\n",
        "\n",
        "1. Explore the features on the bottom left corner. You can see an explanation for each icon by clicking on the [i] button located on the top right corner.\n",
        "2. Use the 'gradient descent' feature to perform a thought experiment:\n",
        "    -   Choose an initialization\n",
        "    -   Choose the learning rate\n",
        "    -   Mentally formulate your hypothesis about what kind of trajectory you expect to observe \n",
        "3. Run the experiment and contrast your intuition with the observed behavior.\n",
        "4. Repeat this experiment a handful of times for several initialization/learning rate configurations\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "-OjucqR4b81R"
      },
      "source": [
        "## Interactive Demo 5: Overparametrization to the rescue!\n",
        "\n",
        "As you may have seen, the non-convex nature of the surface can lead the optimization process to get stuck in undesirable local-optima. There is ample empirical evidence supporting the claim that 'overparameterized' models are easier to train.\n",
        "\n",
        "We will explore this assertion in the context of our MLP training. For this, we initialize a fixed model and construct several models by small random perturbations to the original initialized weights. Now, we train each of these perturbed models and see how the loss evolves. If we were in the convex setting, we should reach very similar objective values upon convergence since all these models were very close at the beginning of training, and in convex problems, every local optimum is also a global optimum.\n",
        "\n",
        "Use the interactive plot below to visualize the loss progression for these perturbed models:\n",
        "\n",
        "1. Select different settings from the `hidden_dims` drop-down menu.\n",
        "2. Explore the effect of the number of steps and learning rate."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "execution": {},
        "id": "RU-jeyoob81R",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 177,
          "referenced_widgets": [
            "77c22384ed4545c9ae1d42b3a5316bbc",
            "25947d10cdd94e1285ae3125b0f42728",
            "6156c49e4e40435bac70bb84aec85f99",
            "e096980b5cf641a5aba9ecfcef12c9b5",
            "70ffda072cad4120be16fe41659dbc5d",
            "21dc77a1d77c4b47824391c9fb4cc927",
            "334a3037609f491d86967f83bdc7aa61",
            "1b8863c4e5e44ef1a216c41590ace1fe",
            "0d1e29d49f4547429ae9c5f468eccc0a",
            "6184fe25e14840df8bf23396d8586fd8",
            "883a372fcb4c4d9aad2cf5af0e495796",
            "249c5d62e0d647e4a94d03e3b5fc162f",
            "3f9162fa9c484ddeba30065a9baac748",
            "c1c8d96085494405be77985a192d36f0",
            "5d257bf63ee345a3a28d9d5648efae51",
            "1ce3d9e98a46463089e42d285c18a92b",
            "8e86fc0dd37f41cab0c4f9359d8326a4",
            "c104629c835e416187b25b1d835a7443",
            "444ad07c2cac45f8938a1c2e3b537989"
          ]
        },
        "outputId": "7ca1f257-dc5e-45f8-e45a-b4437f562aa1"
      },
      "source": [
        "# @markdown Execute this cell to enable the widget!\n",
        "\n",
        "@widgets.interact_manual\n",
        "def overparam(max_steps=widgets.IntSlider(150, 50, 500, 5),\n",
        "              hidden_dims=widgets.Dropdown(options=[\"10\", \"20, 20\", \"100, 100\"],\n",
        "                                           value=\"10\"),\n",
        "              lr=widgets.FloatLogSlider(value=5e-2, min=-3, max=0, step=0.1),\n",
        "              num_inits=widgets.IntSlider(7, 5, 10, 1)):\n",
        "\n",
        "    X, y = train_set.data[subset_index, :], train_set.targets[subset_index]\n",
        "\n",
        "    hdims = [int(s) for s in hidden_dims.split(',')]\n",
        "    base_model = MLP(in_dim=784, out_dim=10, hidden_dims=hdims)\n",
        "\n",
        "    fig, axs = plt.subplots(1, 1, figsize=(5, 4))\n",
        "\n",
        "    for _ in tqdm(range(num_inits)):\n",
        "      model = copy.deepcopy(base_model)\n",
        "      random_update(model, noise_scale=2e-1)\n",
        "\n",
        "      loss_hist = np.zeros((max_steps, 2))\n",
        "      for step in range(max_steps):\n",
        "        loss = loss_fn(model(X), y)\n",
        "        gradient_update(loss, list(model.parameters()), lr=lr)\n",
        "        loss_hist[step] = np.array([step, loss.item()])\n",
        "\n",
        "      plt.plot(loss_hist[:, 0], loss_hist[:, 1])\n",
        "\n",
        "    plt.xlabel('Iteration')\n",
        "    plt.ylabel('Loss')\n",
        "    plt.ylim(0, 3)\n",
        "    plt.show()\n",
        "\n",
        "    num_params = sum([np.prod(_.shape) for _ in model.parameters()])\n",
        "    print('Number of paramaters in model:  ' + str(num_params))"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "77c22384ed4545c9ae1d42b3a5316bbc",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "interactive(children=(IntSlider(value=150, description='max_steps', max=500, min=50, step=5), Dropdown(descrip…"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "KBDslu6Vb81S"
      },
      "source": [
        "### Think! 5.1: Width and depth of the network\n",
        "\n",
        "- We see that as we increase the width/depth of the network, training becomes faster and more consistent across different initializations. What might be the reasons for this behavior? \n",
        "\n",
        "- What are some potential downsides of this approach to dealing with non-convexity? \n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "vXSA4tj5b81S"
      },
      "source": [
        "---\n",
        "# Section 6: Full gradients are expensive"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "pHU7ucipb81S"
      },
      "source": [
        "So far we have used only a small (fixed) subset of 500 training examples to perform the updates on the model parameters in our quest to minimize the loss. But what if we decided to use the training set? Do our current approach scale to datasets with tens of thousands, or millions of datapoints?\n",
        "\n",
        "In this section we explore an efficient alternative to avoid having to perform computations on all the training examples before performing a parameter update."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "jpreoO61b81S",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 79
        },
        "cellView": "form",
        "outputId": "06704aef-1ce7-483d-cef6-120869153010"
      },
      "source": [
        "# @title Video 6: Mini-batches\n",
        "from ipywidgets import widgets\n",
        "\n",
        "out2 = widgets.Output()\n",
        "with out2:\n",
        "  from IPython.display import IFrame\n",
        "  class BiliVideo(IFrame):\n",
        "    def __init__(self, id, page=1, width=400, height=300, **kwargs):\n",
        "      self.id=id\n",
        "      src = \"https://player.bilibili.com/player.html?bvid={0}&page={1}\".format(id, page)\n",
        "      super(BiliVideo, self).__init__(src, width, height, **kwargs)\n",
        "\n",
        "  video = BiliVideo(id=f\"BV1ty4y1T7Uh\", width=854, height=480, fs=1)\n",
        "  print(\"Video available at https://www.bilibili.com/video/{0}\".format(video.id))\n",
        "  display(video)\n",
        "\n",
        "out1 = widgets.Output()\n",
        "with out1:\n",
        "  from IPython.display import YouTubeVideo\n",
        "  video = YouTubeVideo(id=f\"hbqUxpNBUGk\", width=854, height=480, fs=1, rel=0)\n",
        "  print(\"Video available at https://youtube.com/watch?v=\" + video.id)\n",
        "  display(video)\n",
        "\n",
        "out = widgets.Tab([out1, out2])\n",
        "out.set_title(0, 'Youtube')\n",
        "out.set_title(1, 'Bilibili')\n",
        "\n",
        "\n",
        "display(out)"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "83178402c1e641c7a35a980ce42dd003",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "Tab(children=(Output(), Output()), _titles={'0': 'Youtube', '1': 'Bilibili'})"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "oHkFpH9fb81S"
      },
      "source": [
        "## Interactive Demo 6.1: Cost of computation\n",
        "\n",
        "Evaluating a neural network is a relatively fast process. However, when repeated millions of times, the computational cost of performing forward and backward passes through the network starts to become significant.\n",
        "\n",
        "In the visualization below, we show the time (averaged over 5 runs) of computing a forward and backward pass with a changing number of input examples. Choose from the different options in the drop-down box and note how the vertical scale changes depending on the size of the network. \n",
        "\n",
        "**Remarks:** Note that the computational cost of a forward pass shows a clear linear relationship with the number of input examples, and the cost of the corresponding backward pass exhibits a similar computational complexity."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "execution": {},
        "id": "QwAUkKMlb81S",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 406,
          "referenced_widgets": [
            "52e30b369ed142038d1670f1b4dc0986",
            "c1f2aceb36994e1c94b748f7a7abf095",
            "893ec04995d6485aa33449d05aef5511",
            "94e6bd1e2c7943a391ff908514e60ca6",
            "550fe8ee6c6c4f05979d8cd55472f03b",
            "168ec17e096145e587f31a63e2b7748b",
            "8b65f82758954ca989a51c6ad3ec3a32"
          ]
        },
        "outputId": "488cb760-e00d-4274-b529-43c58e21aed8"
      },
      "source": [
        "# @markdown Execute this cell to enable the widget!\n",
        "\n",
        "def measure_update_time(model, num_points):\n",
        "  X, y = train_set.data[:num_points], train_set.targets[:num_points]\n",
        "  start_time = time.time()\n",
        "  loss = loss_fn(model(X), y)\n",
        "  loss_time = time.time()\n",
        "  gradient_update(loss, list(model.parameters()), lr=0)\n",
        "  gradient_time = time.time()\n",
        "  return loss_time - start_time, gradient_time - loss_time\n",
        "\n",
        "\n",
        "@widgets.interact\n",
        "def computation_time(hidden_dims=widgets.Dropdown(options=[\"1\", \"100\", \"50, 50\"],\n",
        "                                                  value=\"100\")):\n",
        "\n",
        "  hdims = [int(s) for s in hidden_dims.split(',')]\n",
        "  model = MLP(in_dim=784, out_dim=10, hidden_dims=hdims)\n",
        "\n",
        "  NUM_POINTS = [1, 5, 10, 100, 200, 500, 1000, 5000, 10000, 20000, 30000, 50000]\n",
        "  times_list = []\n",
        "  for _ in range(5):\n",
        "    times_list.append(np.array([measure_update_time(model, _) for _ in NUM_POINTS]))\n",
        "\n",
        "  times = np.array(times_list).mean(axis=0)\n",
        "\n",
        "  fig, axs = plt.subplots(1, 1, figsize=(5,4))\n",
        "  plt.plot(NUM_POINTS, times[:, 0], label='Forward')\n",
        "  plt.plot(NUM_POINTS, times[:, 1], label='Backward')\n",
        "  plt.xlabel('Number of data points')\n",
        "  plt.ylabel('Seconds')\n",
        "  plt.legend()"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "52e30b369ed142038d1670f1b4dc0986",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "interactive(children=(Dropdown(description='hidden_dims', index=1, options=('1', '100', '50, 50'), value='100'…"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "Caf186Ltb81T"
      },
      "source": [
        "## Coding Exercise 6: Implement minibatch sampling\n",
        "\n",
        "Complete the code in `sample_minibatch` so as to produce IID subsets of the training set of the desired size. (This is _not_ a trick question.) "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "oEvPZBmVb81T"
      },
      "source": [
        "def sample_minibatch(input_data, target_data, num_points=100):\n",
        "  \"\"\"Sample a minibatch of size num_point from the provided input-target data\n",
        "\n",
        "  Args:\n",
        "    input_data (tensor): Multi-dimensional tensor containing the input data\n",
        "    target_data (tensor): 1D tensor containing the class labels\n",
        "    num_points (int): Number of elements to be included in minibatch\n",
        "\n",
        "  Returns:\n",
        "    batch_inputs (tensor): Minibatch inputs\n",
        "    batch_targets (tensor): Minibatch targets\n",
        "  \"\"\"\n",
        "  #################################################\n",
        "  ## TODO for students: sample minibatch of data ##\n",
        "  raise NotImplementedError(\"Student exercise: implement gradient update\")\n",
        "  #################################################\n",
        "  # Sample a collection of IID indices from the existing data\n",
        "  batch_indices = ...\n",
        "  # Use batch_indices to extract entries from the input and target data tensors\n",
        "  batch_inputs = input_data[...]\n",
        "  batch_targets = target_data[...]\n",
        "\n",
        "  return batch_inputs, batch_targets\n",
        "\n",
        "\n",
        "## Uncomment to test your function\n",
        "# x_batch, y_batch = sample_minibatch(X, y, num_points=100)\n",
        "# print(f\"The input shape is {x_batch.shape} and the target shape is: {y_batch.shape}\")"
      ],
      "execution_count": 35,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "j_mSYeW3b81T",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a22191d8-e78e-4c7a-d51f-3463c8cebd6c"
      },
      "source": [
        "# to_remove solution\n",
        "def sample_minibatch(input_data, target_data, num_points=100):\n",
        "  \"\"\"Sample a minibatch of size num_point from the provided input-target data\n",
        "\n",
        "  Args:\n",
        "    input_data (tensor): Multi-dimensional tensor containing the input data\n",
        "    target_data (tensor): 1D tensor containing the class labels\n",
        "    num_points (int): Number of elements to be included in minibatch\n",
        "\n",
        "  Returns:\n",
        "    batch_inputs (tensor): Minibatch inputs\n",
        "    batch_targets (tensor): Minibatch targets\n",
        "  \"\"\"\n",
        "  # Sample a collection of IID indices from the existing data\n",
        "  batch_indices = np.random.choice(len(input_data), num_points)\n",
        "  # Use batch_indices to extract entries from the input and target data tensors\n",
        "  batch_inputs = input_data[batch_indices, :]\n",
        "  batch_targets = target_data[batch_indices]\n",
        "\n",
        "  return batch_inputs, batch_targets\n",
        "\n",
        "\n",
        "\n",
        "## Uncomment to test your function\n",
        "x_batch, y_batch = sample_minibatch(X, y, num_points=100)\n",
        "print(f\"The input shape is {x_batch.shape} and the target shape is: {y_batch.shape}\")"
      ],
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The input shape is torch.Size([100, 28, 28]) and the target shape is: torch.Size([100])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "_ANGCUkGb81T"
      },
      "source": [
        "```\n",
        "The input shape is torch.Size([100, 28, 28]) and the target shape is: torch.Size([100])\n",
        "```"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "SGAyn9yCb81T"
      },
      "source": [
        "## Interactive Demo 6.2: *Compare* different minibatch sizes\n",
        "\n",
        "What are the trade-offs induced by the choice of minibatch size? The interactive plot below shows the training evolution of a 2-hidden layer MLP with 100 hidden units in each hidden layer. Different plots correspond to a different choice of minibatch size. We have a fixed time budget for all the cases, reflected in the horizontal axes of these plots."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "execution": {},
        "id": "18xLvGzZb81T",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 145
        },
        "outputId": "3f54aa72-f636-4847-a4f7-a7f321269c43"
      },
      "source": [
        "# @markdown Execute this cell to enable the widget!\n",
        "\n",
        "@widgets.interact_manual\n",
        "def minibatch_experiment(batch_sizes='20, 250, 1000',\n",
        "                         lrs='5e-3, 5e-3, 5e-3',\n",
        "                         time_budget=widgets.Dropdown(options=[\"2.5\", \"5\", \"10\"],\n",
        "                                                      value=\"2.5\")):\n",
        "\n",
        "  batch_sizes = [int(s) for s in batch_sizes.split(',')]\n",
        "  lrs = [float(s) for s in lrs.split(',')]\n",
        "\n",
        "  LOSS_HIST = {_:[] for _ in batch_sizes}\n",
        "\n",
        "  X, y = train_set.data, train_set.targets\n",
        "  base_model = MLP(in_dim=784, out_dim=10, hidden_dims=[100, 100])\n",
        "\n",
        "  for id, batch_size in enumerate(tqdm(batch_sizes)):\n",
        "    start_time = time.time()\n",
        "    # Create a new copy of the model for each batch size\n",
        "    model = copy.deepcopy(base_model)\n",
        "    params = list(model.parameters())\n",
        "    lr = lrs[id]\n",
        "    # Fixed budget per choice of batch size\n",
        "    while (time.time() - start_time) < float(time_budget):\n",
        "      data, labels = sample_minibatch(X, y, batch_size)\n",
        "      loss = loss_fn(model(data), labels)\n",
        "      gradient_update(loss, params, lr=lr)\n",
        "      LOSS_HIST[batch_size].append([time.time() - start_time,\n",
        "                                    loss.item()])\n",
        "\n",
        "  fig, axs = plt.subplots(1, len(batch_sizes), figsize=(10, 3))\n",
        "  for ax, batch_size in zip(axs, batch_sizes):\n",
        "    plot_data = np.array(LOSS_HIST[batch_size])\n",
        "    ax.plot(plot_data[:, 0], plot_data[:, 1], label=batch_size,\n",
        "            alpha=0.8)\n",
        "    ax.set_title('Batch size: ' + str(batch_size))\n",
        "    ax.set_xlabel('Seconds')\n",
        "    ax.set_ylabel('Loss')\n",
        "  plt.show()"
      ],
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "88f81d1bce364a789b6cff56d8f6946f",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "interactive(children=(Text(value='20, 250, 1000', description='batch_sizes'), Text(value='5e-3, 5e-3, 5e-3', d…"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "RbFspwT0b81T"
      },
      "source": [
        "**Remarks:** SGD works! We have an algorithm that can be applied (with the due precautions) to learn datasets of arbitrary size. \n",
        "\n",
        "However, **note the diference in the vertical scale** across the plots above. When using a larger minibatch, we can perform fewer parameter updates as the forward and backward passes are more expensive.\n",
        "\n",
        "This highlights the interplay between the minibatch size and the learning rate: when our minibatch is larger, we have a more confident estimator of the direction to move, and thus can afford a larger learning rate. On the other hand, extremely small minibatches are very fast computationally but are not representative of the data distribution and yield estimations of the gradient with high variance.\n",
        "\n",
        "We encourage you to tune the value of the learning rate for each of the minibatch sizes in the previous demo, to achieve a training loss steadily below 0.5 within 5 seconds."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "TuIRLOYzb81T"
      },
      "source": [
        "---\n",
        "# Section 7: Adaptive methods"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "x6LSmv6ib81T"
      },
      "source": [
        "As of now, you should be aware that there are many knobs to turn when working on a machine learning problem. Some of these relate to the optimization algorithm, to the choice of model, or to the objective to minimize. Here are some prototypical examples:\n",
        "\n",
        "- Problem: loss function, regularization coefficients (Day 5)\n",
        "- Model: architecture, activations function\n",
        "- Optimizer: learning rate, batch size, momentum coefficient\n",
        "\n",
        "We concentrate on the choices that are directly related with optimization. In particular, we will explore some _automatic_ methods for setting the learning rate, in a way that fixes the poor-conditioning problem and is robust across different problems."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "H8M_nKzub81U",
        "cellView": "form"
      },
      "source": [
        "# @title Video 7: Adaptive Methods\n",
        "from ipywidgets import widgets\n",
        "\n",
        "out2 = widgets.Output()\n",
        "with out2:\n",
        "  from IPython.display import IFrame\n",
        "  class BiliVideo(IFrame):\n",
        "    def __init__(self, id, page=1, width=400, height=300, **kwargs):\n",
        "      self.id=id\n",
        "      src = \"https://player.bilibili.com/player.html?bvid={0}&page={1}\".format(id, page)\n",
        "      super(BiliVideo, self).__init__(src, width, height, **kwargs)\n",
        "\n",
        "  video = BiliVideo(id=f\"BV1eq4y1W7JG\", width=854, height=480, fs=1)\n",
        "  print(\"Video available at https://www.bilibili.com/video/{0}\".format(video.id))\n",
        "  display(video)\n",
        "\n",
        "out1 = widgets.Output()\n",
        "with out1:\n",
        "  from IPython.display import YouTubeVideo\n",
        "  video = YouTubeVideo(id=f\"Zr6r2kfmQUM\", width=854, height=480, fs=1, rel=0)\n",
        "  print(\"Video available at https://youtube.com/watch?v=\" + video.id)\n",
        "  display(video)\n",
        "\n",
        "out = widgets.Tab([out1, out2])\n",
        "out.set_title(0, 'Youtube')\n",
        "out.set_title(1, 'Bilibili')"
      ],
      "execution_count": 39,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "OQZc_LyLb81U"
      },
      "source": [
        "## Coding Exercise 7: Implement RMSprop\n",
        "\n",
        "In this exercise you will implement the update of the RMSprop optimizer:\n",
        "\n",
        "\\begin{align}\n",
        "v_{t} &= \\alpha v_{t-1} + (1 - \\alpha) \\nabla J(w_t)^2 \\\\ \\\\\n",
        "w_{t+1} &= w_t - \\eta \\frac{\\nabla J(w_t)}{\\sqrt{v_t + \\epsilon}}\n",
        "\\end{align}\n",
        "\n",
        "where the non-standard operations (division of two vectors, squaring a vector, etc) are to be interpreted as element-wise operations, i.e., the operation is applied to each (pair of) entry[ies] of the vector(s) considered as real number(s).\n",
        "\n",
        "Here, the $\\epsilon$ hyperparameter provides numerical estability to the algorithm, by preventing the learning rate to become too big when $v_t$ is small. Typically, we set $\\epsilon$ to a default small value, like $10^{-8}$.  "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "-nwYNXrEb81U",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "65037dad-c645-4f65-a9de-2ae21b12090f"
      },
      "source": [
        "def rmsprop_update(loss, params, grad_sq, lr=1e-3, alpha=0.8, epsilon=1e-8):\n",
        "  \"\"\"Perform an RMSprop update on a collection of parameters\n",
        "\n",
        "  Args:\n",
        "    loss (tensor): A scalar tensor containing the loss whose gradient will be computed\n",
        "    params (iterable): Collection of parameters with respect to which we compute gradients\n",
        "    grad_sq (iterable): Moving average of squared gradients\n",
        "    lr (float): Scalar specifying the learning rate or step-size for the update\n",
        "    alpha (float): Moving average parameter\n",
        "    epsilon (float): for numerical estability\n",
        "  \"\"\"\n",
        "  # Clear up gradients as Pytorch automatically accumulates gradients from\n",
        "  # successive backward calls\n",
        "  zero_grad(params)\n",
        "  # Compute gradients on given objective\n",
        "  loss.backward()\n",
        "\n",
        "  with torch.no_grad():\n",
        "    for (par, gsq) in zip(params, grad_sq):\n",
        "      #################################################\n",
        "      ## TODO for students: update the value of the parameter ##\n",
        "      # Use gsq.data and par.grad\n",
        "      raise NotImplementedError(\"Student exercise: implement gradient update\")\n",
        "      #################################################\n",
        "      # Update estimate of gradient variance\n",
        "      gsq.data = ...\n",
        "      # Update parameters\n",
        "      par.data -=  ...\n",
        "\n",
        "\n",
        "set_seed(seed=SEED)\n",
        "model3 = MLP(in_dim=784, out_dim=10, hidden_dims=[])\n",
        "print('\\n The model3 parameters before the update are: \\n')\n",
        "print_params(model3)\n",
        "loss = loss_fn(model3(X), y)\n",
        "# Intialize the moving average of squared gradients\n",
        "grad_sq = [1e-6*i for i in list(model3.parameters())]\n",
        "\n",
        "\n",
        "\n",
        "## Uncomment below to test your function\n",
        "# rmsprop_update(loss, list(model3.parameters()), grad_sq=grad_sq, lr=1e-3)\n",
        "# print('\\n The model3 parameters after the update are: \\n')\n",
        "# print_params(model3)"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Random seed 2021 has been set.\n",
            "\n",
            " The model3 parameters before the update are: \n",
            "\n",
            "main.0.weight tensor([[-0.0264,  0.0010,  0.0173,  ...,  0.0297,  0.0278, -0.0221],\n",
            "        [-0.0040, -0.0295, -0.0086,  ..., -0.0070,  0.0254, -0.0233],\n",
            "        [ 0.0240, -0.0231,  0.0342,  ...,  0.0124,  0.0270, -0.0180],\n",
            "        ...,\n",
            "        [-0.0005,  0.0157,  0.0111,  ...,  0.0144, -0.0301, -0.0144],\n",
            "        [ 0.0181,  0.0303,  0.0255,  ..., -0.0110, -0.0175,  0.0205],\n",
            "        [ 0.0208, -0.0353, -0.0183,  ..., -0.0271,  0.0099,  0.0003]])\n",
            "main.0.bias tensor([-0.0290, -0.0033,  0.0100, -0.0320,  0.0022,  0.0221,  0.0307,  0.0243,\n",
            "         0.0159, -0.0064])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "uHMyheoqb81U"
      },
      "source": [
        "```\n",
        " The model3 parameters after the update are: \n",
        "\n",
        "main.0.weight tensor([[-0.0240,  0.0031,  0.0193,  ...,  0.0316,  0.0297, -0.0198],\n",
        "        [-0.0063, -0.0318, -0.0109,  ..., -0.0093,  0.0232, -0.0255],\n",
        "        [ 0.0218, -0.0253,  0.0320,  ...,  0.0102,  0.0248, -0.0203],\n",
        "        ...,\n",
        "        [-0.0027,  0.0136,  0.0089,  ...,  0.0123, -0.0324, -0.0166],\n",
        "        [ 0.0159,  0.0281,  0.0233,  ..., -0.0133, -0.0197,  0.0182],\n",
        "        [ 0.0186, -0.0376, -0.0205,  ..., -0.0293,  0.0077, -0.0019]])\n",
        "main.0.bias tensor([-0.0313, -0.0011,  0.0122, -0.0342,  0.0045,  0.0199,  0.0329,  0.0265,\n",
        "         0.0182, -0.0041])\n",
        "```"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "sYrNeUL0b81U"
      },
      "source": [
        "## Interactive Demo 7: Compare optimizers\n",
        "\n",
        "Below, we compare your implementations of SGD, momentum and RMSprop. If you have successfully coded all the exercises so far: congrats! You are now *in the know* of some of the most commonly used and powerful tools of optimization for deep learning. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "execution": {},
        "id": "o1oDo1Rwb81U",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 145,
          "referenced_widgets": [
            "a9fe87ddab07402fadf4bf2583c7b562",
            "658e05ff33eb4a8f829b186533fcddda",
            "78e870b127574ba3bbc9de2edb97629d",
            "ef5df5a9c5ef440b8437b3dfee5ceb31",
            "b2a4055823804bc1a1f8a2bfee5a1d16",
            "99cf734b07f8411ca15cb306d0cba902",
            "1be391bd178b4822964cd3e6cc436fc6",
            "fdda01706e4247f99d26139998251364",
            "621234194ebc4033b984eb1e36964959",
            "c61ed06d0c4040ba8775934678bb2fc3",
            "0f88eb6ae1f64ba4b8543b3fee17fd9c",
            "1ee37614d4904ac692f1eaa5b20b96a7",
            "a822f97653424cae933634c6ad931bd4",
            "bf75999018314a5da90c045f09c1ee7f",
            "1c0529b726674511bb578c3f6a147e95",
            "e497c4296c2f471ab2163b0fa750fd17"
          ]
        },
        "outputId": "88993825-5a0e-46a0-ff7b-93f5b90e5d20"
      },
      "source": [
        "# @markdown Execute this cell to enable the widget!\n",
        "X, y = train_set.data, train_set.targets\n",
        "\n",
        "@widgets.interact_manual\n",
        "def compare_optimizers(\n",
        "    batch_size=(25, 250, 5),\n",
        "    lr=widgets.FloatLogSlider(value=2e-3, min=-5, max=0),\n",
        "    max_steps=(50, 500, 5)):\n",
        "\n",
        "  SGD_DICT = [gradient_update, 'SGD', 'black', '-', {'lr': lr}]\n",
        "  MOM_DICT = [momentum_update, 'Momentum', 'red', '--', {'lr': lr, 'beta': 0.9}]\n",
        "  RMS_DICT = [rmsprop_update, 'RMSprop', 'fuchsia', '-', {'lr': lr, 'alpha': 0.8}]\n",
        "\n",
        "  ALL_DICTS = [SGD_DICT, MOM_DICT, RMS_DICT]\n",
        "\n",
        "  base_model = MLP(in_dim=784, out_dim=10, hidden_dims=[100, 100])\n",
        "\n",
        "  LOSS_HIST = {}\n",
        "\n",
        "  for opt_dict in tqdm(ALL_DICTS):\n",
        "    update_fn, opt_name, color, lstyle, kwargs = opt_dict\n",
        "    LOSS_HIST[opt_name] = []\n",
        "\n",
        "    model = copy.deepcopy(base_model)\n",
        "    params = list(model.parameters())\n",
        "\n",
        "    if opt_name != 'SGD':\n",
        "      aux_tensors = [torch.zeros_like(_) for _ in params]\n",
        "\n",
        "    for step in range(max_steps):\n",
        "      data, labels = sample_minibatch(X, y, batch_size)\n",
        "      loss = loss_fn(model(data), labels)\n",
        "      if opt_name == 'SGD':\n",
        "        update_fn(loss, params, **kwargs)\n",
        "      else:\n",
        "        update_fn(loss, params, aux_tensors, **kwargs)\n",
        "      LOSS_HIST[opt_name].append(loss.item())\n",
        "\n",
        "  fig, axs = plt.subplots(1, len(ALL_DICTS), figsize=(9, 3))\n",
        "  for ax, optim_dict in zip(axs, ALL_DICTS):\n",
        "    opt_name = optim_dict[1]\n",
        "    ax.plot(range(max_steps), LOSS_HIST[opt_name], alpha=0.8)\n",
        "    ax.set_title(opt_name)\n",
        "    ax.set_xlabel('Iteration')\n",
        "    ax.set_ylabel('Loss')\n",
        "    ax.set_ylim(0, 2.5)\n",
        "  plt.show()"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "a9fe87ddab07402fadf4bf2583c7b562",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "interactive(children=(IntSlider(value=135, description='batch_size', max=250, min=25, step=5), FloatLogSlider(…"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "4XgsNJMtb81U"
      },
      "source": [
        "### **Discussion**\n",
        "\n",
        "Tune the 3 methods above in order to make each individually excel and discuss your findings. How do the methods compare in terms of robustness to small changes of the hyperparameters? How easy was it to find a good hyperparameter configuration? "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "aXi2nGW2b81U"
      },
      "source": [
        "\n",
        "**Remarks:** Note that RMSprop is allowing us to use a 'per-dimension' learning rate _without having to tune one learning rate for each dimension **ourselves**_. The method uses information collected about the variance of the gradients throughout training to **adapt** the step size for each of the parameters automatically. The savings in tuning efforts of RMSprop over SGD or 'plain' momentum are undisputed on this task. \n",
        "\n",
        "Moreover, adaptive optimization methods are currently a highly active research domain, with many related algorithms like Adam, AMSgrad, Adagrad being used in practical application and theoretically investigated. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "AJuF0l9Fb81V"
      },
      "source": [
        "### Locality of Gradients\n",
        "As we've seen throught this tutorial, poor conditioning can be a significant burden on convergence to an optimum while using gradient based optimization. Of the methods we've seen to deal with this issue, notice how both momentum and adaptive learning rates incorperate past gradient values into their update schemes. Why do we use past values of our loss function's gradient while updating our current MLP weights?\n",
        "\n",
        "Recall from W1D2 that the gradient of a function, $\\nabla f(w_t)$, is a **local** property and computes the direction of maximum change of $f(w_t)$ at the point $w_t$. However, when we train our MLP model we are hoping to find the __global__ optimum for our training loss. By incorperating past values of our function's gradient into our optimization schemes, we use more information about the overall shape of our function than just a single gradient alone can provide. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "UdhCn5pPb81V"
      },
      "source": [
        "## Think! 7: Loss function and optimization\n",
        "\n",
        "Can you think of other ways we can incorperate more information about our loss function into our optimization schemes?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "tQfkBRjsb81V"
      },
      "source": [
        "---\n",
        "# Summary\n",
        "\n",
        "* Optimization is necessary to create Deep Learning models that are guaranteed to converge \n",
        "* Stochastic Gradient Descent and Momentum are two commonly used optimization techniques\n",
        "* RMSProp is a way of adaptive hyper parameter tuning which utilises a per-dimension learning rate\n",
        "* Poor choice of optimization objectives can lead to unforeseen, undesirable consequences \n",
        "\n",
        "If you have time left, you can read the Bonus material, were we put all together and we compare our model with a benchmark model."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "odbL6PSob81W"
      },
      "source": [
        "---\n",
        "# Bonus: Putting it all together\n",
        "\n",
        "*Time estimate: ~40 mins*"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "JayUafwtb81W"
      },
      "source": [
        "We have progressively built a sophisticated optimization algorithm which is able to deal with a non-convex, poor-conditioned problem concerning tens of thousands of training examples. Now we present _you_ with a small challenge: beat us! :P\n",
        "\n",
        "Your mission is to train an MLP model that can compete with a benchmark model which we have pre-trained for you. In this section you will be able to use the full Pytorch power: loading the data, defining the model, sampling minibatches as well as Pytorch's **optimizer implementations**. \n",
        "\n",
        "There is a big engineering component behind the design of optimizers and their implementation can sometimes become tricky. So unless you are directly doing research in optimization, it's recommended to use an implementation provided by a widely reviewed open-source library."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "8dmFOQLub81X"
      },
      "source": [
        "# @title Video 9: Putting it all together\n",
        "from ipywidgets import widgets\n",
        "\n",
        "out2 = widgets.Output()\n",
        "with out2:\n",
        "  from IPython.display import IFrame\n",
        "  class BiliVideo(IFrame):\n",
        "    def __init__(self, id, page=1, width=400, height=300, **kwargs):\n",
        "      self.id=id\n",
        "      src = \"https://player.bilibili.com/player.html?bvid={0}&page={1}\".format(id, page)\n",
        "      super(BiliVideo, self).__init__(src, width, height, **kwargs)\n",
        "\n",
        "  video = BiliVideo(id=f\"BV1MK4y1u7u2\", width=854, height=480, fs=1)\n",
        "  print(\"Video available at https://www.bilibili.com/video/{0}\".format(video.id))\n",
        "  display(video)\n",
        "\n",
        "out1 = widgets.Output()\n",
        "with out1:\n",
        "  from IPython.display import YouTubeVideo\n",
        "  video = YouTubeVideo(id=f\"DP9c13vLiOM\", width=854, height=480, fs=1, rel=0)\n",
        "  print(\"Video available at https://youtube.com/watch?v=\" + video.id)\n",
        "  display(video)\n",
        "\n",
        "out = widgets.Tab([out1, out2])\n",
        "out.set_title(0, 'Youtube')\n",
        "out.set_title(1, 'Bilibili')"
      ],
      "execution_count": 52,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "execution": {},
        "id": "ri7CvOiSb81X",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "95ccaee5-ae9e-4037-db52-2289bf742732"
      },
      "source": [
        "# @title Download parameters of the benchmark model\n",
        "import requests\n",
        "\n",
        "fname = 'benchmark_model.pt'\n",
        "url = \"https://osf.io/sj4e8/download\"\n",
        "r = requests.get(url, allow_redirects=True)\n",
        "with open(fname, 'wb') as fh:\n",
        "  fh.write(r.content)\n",
        "\n",
        "# Load the benchmark model's parameters\n",
        "DEVICE = set_device()\n",
        "if DEVICE == \"cuda\":\n",
        "  benchmark_state_dict = torch.load(fname)\n",
        "else:\n",
        "  benchmark_state_dict = torch.load(fname, map_location=torch.device('cpu'))"
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "GPU is enabled in this notebook.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "Sn2fehIkb81X"
      },
      "source": [
        "# Create MLP object and update weights with those of saved model\n",
        "benchmark_model = MLP(in_dim=784, out_dim=10,\n",
        "                      hidden_dims=[200, 100, 50]).to(DEVICE)\n",
        "benchmark_model.load_state_dict(benchmark_state_dict)\n",
        "\n",
        "\n",
        "# Define helper function to evaluate models\n",
        "def eval_model(model, data_loader, num_batches=np.inf, device='cpu'):\n",
        "\n",
        "  loss_log, acc_log = [], []\n",
        "  model.to(device=device)\n",
        "\n",
        "  # We are just evaluating the model, no need to compute gradients\n",
        "  with torch.no_grad():\n",
        "    for batch_id, batch in enumerate(data_loader):\n",
        "      # If we only evaluate a number of batches, stop after we reach that number\n",
        "      if batch_id > num_batches:\n",
        "        break\n",
        "      # Extract minibatch data\n",
        "      data, labels = batch[0].to(device), batch[1].to(device)\n",
        "      # Evaluate model and loss on minibatch\n",
        "      preds = model(data)\n",
        "      loss_log.append(loss_fn(preds, labels).item())\n",
        "      acc_log.append(torch.mean(1. * (preds.argmax(dim=1) == labels)).item())\n",
        "\n",
        "  return np.mean(loss_log), np.mean(acc_log)"
      ],
      "execution_count": 46,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "sjteVziIb81X"
      },
      "source": [
        "We define an optimizer in the following steps:\n",
        "\n",
        "1. Load  the corresponding class that implements the parameter updates and other internal management activities, including:\n",
        "    - create auxiliary variables,\n",
        "    - update moving averages,\n",
        "    - adjust learning rate.\n",
        "2. Pass the parameters of the Pytorch model that the optimizer has control over. Note that different parameter groups can potentially be controlled by different optimizers.\n",
        "3. Specify hyperparameters, including learning rate, momentum, moving average factors, etc.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "nV9WFSAvb81X"
      },
      "source": [
        "## Exercise Bonus: Train your own model\n",
        "\n",
        "Now, train the model with your preferred optimizer and find a good combination of hyperparameter settings."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "zHV3o1lsb81X"
      },
      "source": [
        "#################################################\n",
        "## TODO for students: adjust training settings ##\n",
        "\n",
        "# The three parameters below are in your full control\n",
        "MAX_EPOCHS = 2  # select number of epochs to train\n",
        "LR = 1e-5  # choose the step size\n",
        "BATCH_SIZE = 64  # number of examples per minibatch\n",
        "\n",
        "# Define the model and associated optimizer -- you may change its architecture!\n",
        "model = MLP(in_dim=784, out_dim=10, hidden_dims=[200, 100, 50]).to(DEVICE)\n",
        "\n",
        "# You can take your pick from many different optimizers\n",
        "# Check the optimizer documentation and hyperparameter meaning before using!\n",
        "# More details on Pytorch optimizers: https://pytorch.org/docs/stable/optim.html\n",
        "# optimizer = torch.optim.SGD(model.parameters(), lr=LR, momentum=0.9)\n",
        "# optimizer = torch.optim.RMSprop(model.parameters(), lr=LR, alpha=0.99)\n",
        "# optimizer = torch.optim.Adagrad(model.parameters(), lr=LR)\n",
        "optimizer = torch.optim.Adam(model.parameters(), lr=LR)\n",
        "#################################################"
      ],
      "execution_count": 47,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "_b0izi9rb81X",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 270
        },
        "outputId": "539bdf15-eabb-4d4d-b602-afaf12ea7af1"
      },
      "source": [
        "set_seed(seed=SEED)\n",
        "# Print trainig stats every LOG_FREQ minibatches\n",
        "LOG_FREQ = 200\n",
        "# Frequency for evaluating the validation metrics\n",
        "VAL_FREQ = 200\n",
        "# Load data using a Pytorch Dataset\n",
        "train_set_orig, test_set_orig = load_mnist_data(change_tensors=False)\n",
        "\n",
        "# We separate 10,000 training samples to create a validation set\n",
        "train_set_orig, val_set_orig = torch.utils.data.random_split(train_set_orig, [50000, 10000])\n",
        "\n",
        "# Create the corresponding DataLoaders for training and test\n",
        "g_seed = torch.Generator()\n",
        "g_seed.manual_seed(SEED)\n",
        "\n",
        "train_loader = torch.utils.data.DataLoader(train_set_orig,\n",
        "                                           shuffle=True,\n",
        "                                           batch_size=BATCH_SIZE,\n",
        "                                           num_workers=2,\n",
        "                                           worker_init_fn=seed_worker,\n",
        "                                           generator=g_seed)\n",
        "val_loader = torch.utils.data.DataLoader(val_set_orig,\n",
        "                                         shuffle=True,\n",
        "                                         batch_size=256,\n",
        "                                         num_workers=2,\n",
        "                                         worker_init_fn=seed_worker,\n",
        "                                         generator=g_seed)\n",
        "test_loader = torch.utils.data.DataLoader(test_set_orig,\n",
        "                                          batch_size=256,\n",
        "                                          num_workers=2,\n",
        "                                          worker_init_fn=seed_worker,\n",
        "                                          generator=g_seed)\n",
        "\n",
        "# Run training\n",
        "metrics = {'train_loss':[],\n",
        "           'train_acc':[],\n",
        "           'val_loss':[],\n",
        "           'val_acc':[],\n",
        "           'val_idx':[]}\n",
        "\n",
        "step_idx = 0\n",
        "for epoch in tqdm(range(MAX_EPOCHS)):\n",
        "\n",
        "  running_loss, running_acc = 0., 0.\n",
        "\n",
        "  for batch_id, batch in enumerate(train_loader):\n",
        "    step_idx += 1\n",
        "    # Extract minibatch data and labels\n",
        "    data, labels = batch[0].to(DEVICE), batch[1].to(DEVICE)\n",
        "    # Just like before, refresh gradient accumulators.\n",
        "    # Note that this is now a method of the optimizer.\n",
        "    optimizer.zero_grad()\n",
        "    # Evaluate model and loss on minibatch\n",
        "    preds = model(data)\n",
        "    loss = loss_fn(preds, labels)\n",
        "    acc = torch.mean(1.0 * (preds.argmax(dim=1) == labels))\n",
        "    # Compute gradients\n",
        "    loss.backward()\n",
        "    # Update parameters\n",
        "    # Note how all the magic in the update of the parameters is encapsulated by\n",
        "    # the optimizer class.\n",
        "    optimizer.step()\n",
        "    # Log metrics for plotting\n",
        "    metrics['train_loss'].append(loss.cpu().item())\n",
        "    metrics['train_acc'].append(acc.cpu().item())\n",
        "\n",
        "    if batch_id % VAL_FREQ == (VAL_FREQ - 1):\n",
        "      # Get an estimate of the validation accuracy with 100 batches\n",
        "      val_loss, val_acc = eval_model(model, val_loader,\n",
        "                                     num_batches=100,\n",
        "                                     device=DEVICE)\n",
        "      metrics['val_idx'].append(step_idx)\n",
        "      metrics['val_loss'].append(val_loss)\n",
        "      metrics['val_acc'].append(val_acc)\n",
        "\n",
        "      print(f\"[VALID] Epoch {epoch + 1} - Batch {batch_id + 1} - \"\n",
        "            f\"Loss: {val_loss:.3f} - Acc: {100*val_acc:.3f}%\")\n",
        "\n",
        "    # print statistics\n",
        "    running_loss += loss.cpu().item()\n",
        "    running_acc += acc.cpu().item()\n",
        "    # Print every LOG_FREQ minibatches\n",
        "    if batch_id % LOG_FREQ == (LOG_FREQ-1):\n",
        "      print(f\"[TRAIN] Epoch {epoch + 1} - Batch {batch_id + 1} - \"\n",
        "            f\"Loss: {running_loss / LOG_FREQ:.3f} - \"\n",
        "            f\"Acc: {100 * running_acc / LOG_FREQ:.3f}%\")\n",
        "\n",
        "      running_loss, running_acc = 0., 0."
      ],
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Random seed 2021 has been set.\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "30c57a8fed62476496ab3cc7a312d56b",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "  0%|          | 0/2 [00:00<?, ?it/s]"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[VALID] Epoch 1 - Batch 200 - Loss: 2.235 - Acc: 38.174%\n",
            "[TRAIN] Epoch 1 - Batch 200 - Loss: 2.274 - Acc: 30.945%\n",
            "[VALID] Epoch 1 - Batch 400 - Loss: 2.067 - Acc: 52.773%\n",
            "[TRAIN] Epoch 1 - Batch 400 - Loss: 2.166 - Acc: 44.289%\n",
            "[VALID] Epoch 1 - Batch 600 - Loss: 1.789 - Acc: 56.826%\n",
            "[TRAIN] Epoch 1 - Batch 600 - Loss: 1.935 - Acc: 55.352%\n",
            "[VALID] Epoch 2 - Batch 200 - Loss: 1.265 - Acc: 69.561%\n",
            "[TRAIN] Epoch 2 - Batch 200 - Loss: 1.373 - Acc: 66.117%\n",
            "[VALID] Epoch 2 - Batch 400 - Loss: 1.072 - Acc: 77.607%\n",
            "[TRAIN] Epoch 2 - Batch 400 - Loss: 1.168 - Acc: 74.141%\n",
            "[VALID] Epoch 2 - Batch 600 - Loss: 0.928 - Acc: 80.967%\n",
            "[TRAIN] Epoch 2 - Batch 600 - Loss: 0.997 - Acc: 79.094%\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "6Ad-0ATjb81Y",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "outputId": "7798c3a2-fe86-43ce-8584-30a1f91125da"
      },
      "source": [
        "fig, ax = plt.subplots(1, 2, figsize=(10, 4))\n",
        "\n",
        "ax[0].plot(range(len(metrics['train_loss'])), metrics['train_loss'],\n",
        "           alpha=0.8, label='Train')\n",
        "ax[0].plot(metrics['val_idx'], metrics['val_loss'], label='Valid')\n",
        "ax[0].set_xlabel('Iteration')\n",
        "ax[0].set_ylabel('Loss')\n",
        "ax[0].legend()\n",
        "\n",
        "ax[1].plot(range(len(metrics['train_acc'])), metrics['train_acc'],\n",
        "           alpha=0.8, label='Train')\n",
        "ax[1].plot(metrics['val_idx'], metrics['val_acc'], label='Valid')\n",
        "ax[1].set_xlabel('Iteration')\n",
        "ax[1].set_ylabel('Accuracy')\n",
        "ax[1].legend()\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "width": 701,
              "height": 269
            },
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "_vKC4r8db81Y"
      },
      "source": [
        "## Think! Bonus: Metrics\n",
        "\n",
        "Which metric did you optimize when searching for the right configuration? The training set loss? Accuracy? Validation/test set metrics? Why? Discuss!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "VaM61c0yb81Z"
      },
      "source": [
        "### Evaluation\n",
        "\n",
        "We _finally_ can evaluate and compare the performance of the models on previously unseen examples. \n",
        "\n",
        "Which model would you keep? (\\*drum roll*)    "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {},
        "id": "hxnj2Y6yb81Z",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7fbd1198-5c50-438d-cf7c-c280c3b6f7d9"
      },
      "source": [
        "print('Your model...')\n",
        "train_loss, train_accuracy = eval_model(my_model, train_loader, device=DEVICE)\n",
        "test_loss, test_accuracy = eval_model(my_model, test_loader, device=DEVICE)\n",
        "print(f'Train Loss {train_loss:.3f} / Test Loss {test_loss:.3f}')\n",
        "print(f'Train Accuracy {100*train_accuracy:.3f}% / Test Accuracy {100*test_accuracy:.3f}%')\n",
        "\n",
        "print('\\nBenchmark model')\n",
        "train_loss, train_accuracy = eval_model(benchmark_model, train_loader, device=DEVICE)\n",
        "test_loss, test_accuracy = eval_model(benchmark_model, test_loader, device=DEVICE)\n",
        "print(f'Train Loss {train_loss:.3f} / Test Loss {test_loss:.3f}')\n",
        "print(f'Train Accuracy {100*train_accuracy:.3f}% / Test Accuracy {100*test_accuracy:.3f}%')"
      ],
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Your model...\n",
            "Train Loss 2.470 / Test Loss 2.475\n",
            "Train Accuracy 10.340% / Test Accuracy 10.996%\n",
            "\n",
            "Benchmark model\n",
            "Train Loss 0.011 / Test Loss 0.025\n",
            "Train Accuracy 99.784% / Test Accuracy 99.316%\n"
          ]
        }
      ]
    }
  ]
}