CV_Module_5_1__Neural_Networks_Basics_1.ipynb

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        "<a href=\"https://colab.research.google.com/github/SudeepSarkar/sarkar-computer-vision-lectures/blob/main/CV_Module_5_1__Neural_Networks_Basics_1.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "cell_type": "markdown",
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        "id": "ZbAPDWw3MDwb"
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      "source": [
        "# Neural Network Basics 1\n",
        "## (Dive into Deep Learning https://d2l.ai/chapter_linear-networks/index.html)\n",
        "\n",
        "* The material for this notebook is mainly from the Open Source book -- Dive into Deep Learning. I have adapted a few things for the Computer Vision course at the University of South Florida, Tampa.\n",
        "\n",
        "* Some figures are from Richard Szeliski's vision textbook for this course."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5Uz-P8fBbtDD"
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      "source": [
        "# Topics covered\n",
        "\n",
        "* You will get introduced to the essential components that go into constructing and training neural networks\n",
        "\n",
        "* You will be introduced to the linear regression problem and how it can be solved using stochastic gradient descent.\n",
        "\n",
        "* You will learn how to construct the most straightforward classification neural network using softmax operation (activation function). You will also learn about the cross-entropy loss function\n",
        "\n",
        "**Concepts Learned:** linear regression, model, train, mini-batches, *stochastic* gradient search, epochs, hyperparamters, softmax, activation function, cross-entropy loss function, squared loss function, fully connected layer, classification accuracy, python data iterator."
      ]
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      "source": [
        "## Code: setup"
      ]
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        "outputId": "9c9a3b45-d5e3-4620-fb92-e8bfc8ac85ec"
      },
      "source": [
        "!pip install d2l==0.16.2"
      ],
      "execution_count": 1,
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        {
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          "name": "stdout",
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    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 2,
        "tab": [
          "pytorch"
        ],
        "id": "iL0wRD35MDwo"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import torch\n",
        "import torchvision\n",
        "from torch import nn\n",
        "from torch.nn import functional as F\n"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FR3moTlMllHM"
      },
      "source": [
        "# Linear Regression\n",
        "\n",
        "* *Regression* refers to a set of methods for modeling the relationship between one or more **independent** variables and a **dependent** variable or the **predicted** variable.\n",
        "\n",
        "* Examples: local images features (e.g., color values) to label objects in images;  video to label action type;  face image to label emotions\n",
        "\n",
        "\n",
        "* We will implement the entire method from scratch, including\n",
        "\n",
        "    1. the data pipeline,\n",
        "    2. the model,\n",
        "    3. the loss function, and\n",
        "    4. the minibatch stochastic gradient descent optimizer.\n",
        "\n",
        "* For now, we will rely only on tensors and auto differentiation. Afterward, we will introduce a more straightforward implementation, taking advantage of the bells and whistles of deep learning frameworks.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6ZheEvSMrJsV"
      },
      "source": [
        "## Generating the Dataset\n",
        "\n",
        "* We construct an artificial dataset according to a linear model with additive noise.\n",
        "\n",
        "* Our task will be to recover this model's parameters using the finite set of examples in our dataset.\n",
        "\n",
        "* In the following code snippet, we generate a dataset, $\\mathbf{X}$, containing 1000 examples, each consisting of 2 features sampled from a standard normal distribution. Thus our synthetic dataset will be a $1000 \\times 2$ matrix.\n",
        "\n",
        "* This input data is transformed linearly using\n",
        "\n",
        "\\begin{equation}\n",
        "\\mathbf{y}= \\mathbf{X} \\mathbf{w} + b + \\mathbf\\epsilon\n",
        "\\end{equation}\n",
        "\n",
        "* $\\mathbf{w} = [2, -3.4]^\\top$ and $b = 4.2$,\n",
        "and $\\epsilon$ captures potential measurement errors on the features and labels.\n",
        "\n",
        "* We will assume that the standard assumptions hold and thus\n",
        "that $\\epsilon$ obeys a normal distribution with a mean of 0.\n",
        "    * To make our problem easy, we will set its standard deviation to 0.01.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3crxqNpQ4enq"
      },
      "source": [
        "###Code: `generate_synthetic_data`"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DXeMz5634duL"
      },
      "source": [
        "def generate_synthetic_data (w, b, num_examples):\n",
        "    \"\"\"Generate y = Xw + b + noise.\"\"\"\n",
        "    X = torch.normal(0, 1, (num_examples, len(w)))\n",
        "    y = torch.matmul(X, w) + b\n",
        "    y += torch.normal(0, 0.01, y.shape)\n",
        "    return X, y.reshape((-1, 1))\n",
        "\n",
        "true_w = torch.tensor([2, -3.4])\n",
        "true_b = 4.2\n",
        "features, labels = generate_synthetic_data (true_w, true_b, 1000)"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "features.size()"
      ],
      "metadata": {
        "id": "VGgJmrpzAe0F",
        "outputId": "0505c54c-2060-4da2-a982-a101cb95bf12",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([1000, 2])"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 8,
        "id": "k9pAKYylleRa"
      },
      "source": [
        "* **Note that each row in `features` consists of a 2-dimensional data example and that each row in `labels` consists of a 1-dimensional label value (a scalar).**\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 9,
        "tab": [
          "pytorch"
        ],
        "id": "DotgEvroleRc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "34c769ee-9083-4a27-8f63-ebcb0d8fd5f2"
      },
      "source": [
        "print('First 10 features:\\n', features[1:10,:], '\\nFirst 10 labels:\\n', labels[1:10])"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "First 10 features:\n",
            " tensor([[ 1.2221,  0.5372],\n",
            "        [ 1.4228,  0.4576],\n",
            "        [-0.6984, -0.5055],\n",
            "        [ 0.2280,  0.6175],\n",
            "        [ 1.7191, -0.7174],\n",
            "        [-1.6621,  0.5776],\n",
            "        [ 1.5501,  0.3772],\n",
            "        [-0.0956,  0.1393],\n",
            "        [-0.9308, -0.6321]]) \n",
            "First 10 labels:\n",
            " tensor([[ 4.8310],\n",
            "        [ 5.5026],\n",
            "        [ 4.5068],\n",
            "        [ 2.5506],\n",
            "        [10.0801],\n",
            "        [-1.0856],\n",
            "        [ 6.0176],\n",
            "        [ 3.5284],\n",
            "        [ 4.4928]])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 10,
        "id": "UK0wmpQkleRd"
      },
      "source": [
        "* **Observe the linear correlation between the input and the output.**\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 11,
        "tab": [
          "pytorch"
        ],
        "id": "rrAF-IArleRe",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 465
        },
        "outputId": "a682778e-e90c-4377-cdfc-a72383e9b331"
      },
      "source": [
        "fig, ax = plt.subplots(nrows=1, ncols=2)\n",
        "fig.set_size_inches (10, 5)\n",
        "\n",
        "ax[0].scatter(features[:, 0].detach().numpy(),\n",
        "                labels.detach().numpy(), c='b')\n",
        "ax[0].set_xlabel('Dimension 0 of input')\n",
        "ax[0].set_ylabel('Output label')\n",
        "\n",
        "ax[1].scatter(features[:, 1].detach().numpy(),\n",
        "                labels.detach().numpy(), c='r')\n",
        "ax[1].set_xlabel('Dimension 1 of input')\n",
        "ax[1].set_ylabel('Output label');"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 2 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 12,
        "id": "vQSl67GWleRf"
      },
      "source": [
        "## Reading the Dataset\n",
        "\n",
        "* Estimating the linear model parameters from the training data involve iterations over the dataset.\n",
        "\n",
        "* Recall how **gradient descent** or Newton's method (with Hessian) worked for 2D perspective transformation (homography) estimation.\n",
        "\n",
        "    * At each iteration, we computed a gradient value based on the **entire** dataset.\n",
        "\n",
        "* Here, we adopt **stochastic** gradient descent, which works well in practice.\n",
        "\n",
        "    * Instead of considering the entire dataset at each iteration, we\n",
        "form many subsets of the data and use the subsets to update our model, one at a time.\n",
        "\n",
        "* We break the dataset into **mini-batches**, each consisting of **batch size** number of data samples. Each minibatch consists of a tuple of input features and labels.\n",
        "\n",
        "    * At each iteration, we compute the gradient based on one minibatch at a time.\n",
        "\n",
        "    * Updates from the different subsets of the data are randomly varying, which gives its name *stochastic*.\n",
        "\n",
        "    *  Minibatches sizes depend on available GPU hardware. We can also compute the gradient of the loss function for each example in parallel; GPUs allow us to process hundreds of inputs in scarcely more time than it might take to process just a single sample.\n",
        "\n",
        "* Since this process is so fundamental to training machine learning algorithms,\n",
        "it is worth defining a utility function to shuffle the dataset and access it in mini-batches.\n",
        "\n",
        "    * In the following code, we define the **`data_iter` function** to demonstrate one possible implementation of this functionality. The function takes a **batch size, a matrix of features, and a vector of labels, yielding mini-batches of the size `batch_size.`**\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "m4M0m4ONFjIE"
      },
      "source": [
        "### Code: Some python background about iterators, generators\n",
        "\n",
        "* An iterator in Python is an object that contains a finite number of elements that can be iterated upon, i.e. go through the ordered collection  one element at a time.\n",
        "\n",
        "* A generator is a special type of function which returns an iterator object.  *It can be run only once*."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "U7AHd6rgF4lC",
        "outputId": "f2ed293b-6b9c-465b-f78e-732e510b46ea"
      },
      "source": [
        "'''\n",
        "Some python background about iterators, generators, and yield that we will use.\n",
        "Example taken from https://stackoverflow.com/questions/231767/what-does-the-yield-keyword-do\n",
        "'''\n",
        "mylist = [1, 2, 3]\n",
        "for i in mylist:\n",
        "    print(i)"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1\n",
            "2\n",
            "3\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "itZOWPXvElME",
        "outputId": "79dfcc94-519f-41d0-fd6e-38baf567daac"
      },
      "source": [
        "# --------Iterator object--------------------\n",
        "# An iterator in Python is an object that contains a finite number of\n",
        "# elements that can be iterated upon, i.e. go through the ordered collection\n",
        "# one element at a time.\n",
        "\n",
        "print('Iterator output (first run):')\n",
        "mylist = [x*x for x in range(3)]\n",
        "for i in mylist:\n",
        "    print(i)\n",
        "\n",
        "print('Iterator output (second run):')\n",
        "for i in mylist:\n",
        "    print(i)\n"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iterator output (first run):\n",
            "0\n",
            "1\n",
            "4\n",
            "Iterator output (second run):\n",
            "0\n",
            "1\n",
            "4\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YN9mgDLwEr3U",
        "outputId": "2e7db4b9-352e-41ed-c4e1-f640288f75c6"
      },
      "source": [
        "# ---------Generator object--------------------\n",
        "# A generator is a special type of function which returns an iterator object.\n",
        "# Can be run only once.\n",
        "\n",
        "mygenerator = (x*x for x in range(3))\n",
        "\"note the use of parenthesis instead of brackets\"\n",
        "print('Mygenerator created using yield is:', mygenerator) # mygenerator is an object!\n",
        "\n",
        "print('Generator output (first run):')\n",
        "for i in mygenerator:\n",
        "    print(i)\n",
        "\n",
        "print('Generator output (second run):')\n",
        "for i in mygenerator:\n",
        "    print(i)"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mygenerator created using yield is: <generator object <genexpr> at 0x78189e342c00>\n",
            "Generator output (first run):\n",
            "0\n",
            "1\n",
            "4\n",
            "Generator output (second run):\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jxNVbCg6Eu_G",
        "outputId": "a2dc94fd-57a7-4307-df88-563af43b4475"
      },
      "source": [
        "#-----------Yield returns generator object--------\n",
        "# In a generator function, a \"yield\" statement is used rather than a \"return\" statement.\n",
        "# You use generators to create your own iterators.\n",
        "# Can be run only once.\n",
        "\n",
        "def create_generator():\n",
        "    mylist = range(3)\n",
        "    for i in mylist:\n",
        "        yield i*i\n",
        "\n",
        "mygenerator = create_generator() # create a generator\n",
        "print('Mygenerator created using yield is:', mygenerator) # mygenerator is an object!\n",
        "for i in mygenerator:\n",
        "    print(i)\n",
        "\n",
        "print('Mygenerator created using yield is (second run):', mygenerator) # mygenerator is an object!\n",
        "for i in mygenerator:\n",
        "    print(i)\n"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mygenerator created using yield is: <generator object create_generator at 0x78189bdc77d0>\n",
            "0\n",
            "1\n",
            "4\n",
            "Mygenerator created using yield is (second run): <generator object create_generator at 0x78189bdc77d0>\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-o9v1HNoBCd3"
      },
      "source": [
        "### Code: `data_iter` over randomized minibatches"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 13,
        "tab": [
          "pytorch"
        ],
        "id": "0wdEZkZ1leRg",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "bce62553-9a1e-4bdf-d391-163429cc535f"
      },
      "source": [
        "import numpy as np\n",
        "\n",
        "# Generator function over the data\n",
        "def data_iter (batch_size, features, labels):\n",
        "    num_examples = features.shape[0]\n",
        "    # We randomly shuffle the data in the beginning so breakup any bias induced due to order of data\n",
        "    indices = np.random.permutation (num_examples)\n",
        "    for i in range(0, num_examples, batch_size):\n",
        "        batch_indices = torch.tensor(indices[i:min(i + batch_size, num_examples)])\n",
        "        yield features[batch_indices], labels[batch_indices]\n",
        "\" notice yield above\""
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "' notice yield above'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 15,
        "id": "-Pnl_waBleRi"
      },
      "source": [
        "* To build some intuition, let us read and print\n",
        "the first small batch of data examples.\n",
        "The shape of the features in each minibatch tells us\n",
        "both the minibatch size and the number of input features.\n",
        "Likewise, our minibatch of labels will have a shape given by `batch_size`.\n",
        "\n",
        "\n",
        "* As we run the iteration, we obtain distinct mini-batches\n",
        "successively until the entire dataset has been exhausted (try this).\n",
        "\n",
        "\n",
        "* This method works but is inefficient, requiring that we load all the data in memory and perform lots of random memory access. **The built-in iterators implemented in a deep learning framework are considerably more efficient and can deal with data stored in files and data fed via data streams.** We will get introduced to them later.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 16,
        "tab": [
          "pytorch"
        ],
        "id": "EPfwb4-LleRj",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "57ebe14c-cc31-49f1-a5ba-25a85278b90c"
      },
      "source": [
        "batch_size = 11\n",
        "# print first batch and then exit.\n",
        "i = 1\n",
        "for X, y in data_iter(batch_size, features, labels):\n",
        "    print(i, X.size())\n",
        "    i = i+1\n"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1 torch.Size([11, 2])\n",
            "2 torch.Size([11, 2])\n",
            "3 torch.Size([11, 2])\n",
            "4 torch.Size([11, 2])\n",
            "5 torch.Size([11, 2])\n",
            "6 torch.Size([11, 2])\n",
            "7 torch.Size([11, 2])\n",
            "8 torch.Size([11, 2])\n",
            "9 torch.Size([11, 2])\n",
            "10 torch.Size([11, 2])\n",
            "11 torch.Size([11, 2])\n",
            "12 torch.Size([11, 2])\n",
            "13 torch.Size([11, 2])\n",
            "14 torch.Size([11, 2])\n",
            "15 torch.Size([11, 2])\n",
            "16 torch.Size([11, 2])\n",
            "17 torch.Size([11, 2])\n",
            "18 torch.Size([11, 2])\n",
            "19 torch.Size([11, 2])\n",
            "20 torch.Size([11, 2])\n",
            "21 torch.Size([11, 2])\n",
            "22 torch.Size([11, 2])\n",
            "23 torch.Size([11, 2])\n",
            "24 torch.Size([11, 2])\n",
            "25 torch.Size([11, 2])\n",
            "26 torch.Size([11, 2])\n",
            "27 torch.Size([11, 2])\n",
            "28 torch.Size([11, 2])\n",
            "29 torch.Size([11, 2])\n",
            "30 torch.Size([11, 2])\n",
            "31 torch.Size([11, 2])\n",
            "32 torch.Size([11, 2])\n",
            "33 torch.Size([11, 2])\n",
            "34 torch.Size([11, 2])\n",
            "35 torch.Size([11, 2])\n",
            "36 torch.Size([11, 2])\n",
            "37 torch.Size([11, 2])\n",
            "38 torch.Size([11, 2])\n",
            "39 torch.Size([11, 2])\n",
            "40 torch.Size([11, 2])\n",
            "41 torch.Size([11, 2])\n",
            "42 torch.Size([11, 2])\n",
            "43 torch.Size([11, 2])\n",
            "44 torch.Size([11, 2])\n",
            "45 torch.Size([11, 2])\n",
            "46 torch.Size([11, 2])\n",
            "47 torch.Size([11, 2])\n",
            "48 torch.Size([11, 2])\n",
            "49 torch.Size([11, 2])\n",
            "50 torch.Size([11, 2])\n",
            "51 torch.Size([11, 2])\n",
            "52 torch.Size([11, 2])\n",
            "53 torch.Size([11, 2])\n",
            "54 torch.Size([11, 2])\n",
            "55 torch.Size([11, 2])\n",
            "56 torch.Size([11, 2])\n",
            "57 torch.Size([11, 2])\n",
            "58 torch.Size([11, 2])\n",
            "59 torch.Size([11, 2])\n",
            "60 torch.Size([11, 2])\n",
            "61 torch.Size([11, 2])\n",
            "62 torch.Size([11, 2])\n",
            "63 torch.Size([11, 2])\n",
            "64 torch.Size([11, 2])\n",
            "65 torch.Size([11, 2])\n",
            "66 torch.Size([11, 2])\n",
            "67 torch.Size([11, 2])\n",
            "68 torch.Size([11, 2])\n",
            "69 torch.Size([11, 2])\n",
            "70 torch.Size([11, 2])\n",
            "71 torch.Size([11, 2])\n",
            "72 torch.Size([11, 2])\n",
            "73 torch.Size([11, 2])\n",
            "74 torch.Size([11, 2])\n",
            "75 torch.Size([11, 2])\n",
            "76 torch.Size([11, 2])\n",
            "77 torch.Size([11, 2])\n",
            "78 torch.Size([11, 2])\n",
            "79 torch.Size([11, 2])\n",
            "80 torch.Size([11, 2])\n",
            "81 torch.Size([11, 2])\n",
            "82 torch.Size([11, 2])\n",
            "83 torch.Size([11, 2])\n",
            "84 torch.Size([11, 2])\n",
            "85 torch.Size([11, 2])\n",
            "86 torch.Size([11, 2])\n",
            "87 torch.Size([11, 2])\n",
            "88 torch.Size([11, 2])\n",
            "89 torch.Size([11, 2])\n",
            "90 torch.Size([11, 2])\n",
            "91 torch.Size([10, 2])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 17,
        "id": "lptGUv1yleRk"
      },
      "source": [
        "## Initializing model parameters\n",
        "\n",
        "**Before we can begin optimizing our model's parameters** by minibatch stochastic gradient descent, (**we need to have some parameters in the first place.**). In the following code, we initialize weights by sampling random numbers from a normal distribution with a mean of 0 and a standard deviation of 0.01 and setting the bias to 0.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8sWckmB9hFrY"
      },
      "source": [
        "### Code: Initialize parameters (`w, b`)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 19,
        "tab": [
          "pytorch"
        ],
        "id": "vQBOJlKSleRl",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7745a45a-63ca-4e28-94bf-cc18a12e3bb9"
      },
      "source": [
        "w = torch.normal(0, 0.01, size=(2, 1), requires_grad=True)\n",
        "b = torch.zeros(1, requires_grad=True)\n",
        "print('weights:\\n', w, '\\nb=\\n', b)"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "weights:\n",
            " tensor([[ 0.0086],\n",
            "        [-0.0072]], requires_grad=True) \n",
            "b=\n",
            " tensor([0.], requires_grad=True)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ggL2jabTTldk"
      },
      "source": [
        "* After initializing our parameters, our next task is to update them until they fit our data sufficiently well.\n",
        "\n",
        "* Each update requires taking the gradient of our loss function with respect to the parameters.\n",
        "\n",
        "* To compute gradients explicitly, we use automatic differentiation to compute the gradient.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 21,
        "id": "c469aNSjleRl"
      },
      "source": [
        "## Defining the Model\n",
        "\n",
        "* Next, we must **define our model, relating its inputs and parameters to its outputs.**\n",
        "\n",
        "* To calculate the output of the linear model, we take the matrix-vector dot product of the input features $\\mathbf{X}$ and the model weights $\\mathbf{w}$, and add the offset $b$ to each example.\n",
        "\n",
        "* The product $\\mathbf{Xw}$  is a vector, and $b$ is a scalar.\n",
        "    * We will use the *broadcasting* feature to add the scalar.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bYSVVLHK9aQG"
      },
      "source": [
        "![image.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zkJDTKFhUthw"
      },
      "source": [
        "### Code: `linreg`: The linear regression model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 22,
        "tab": [
          "pytorch"
        ],
        "id": "sujiqus-leRl"
      },
      "source": [
        "def linreg(X, w, b):\n",
        "    \"\"\"The linear regression model.\"\"\"\n",
        "    # X is N by d, where N is the number of data elements, d is the dimension of the data\n",
        "    # w is a d by 1 vector of parameters\n",
        "    return torch.matmul(X, w) + b"
      ],
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 23,
        "id": "Y7qEJAEaleRm"
      },
      "source": [
        "## Defining the Loss Function\n",
        "\n",
        "* Since updating our model requires taking the gradient of our loss function, we ought to (**define the loss function next**)\n",
        "\n",
        "* We will use the **squared loss** function (**squared residuals**)\n",
        "\n",
        "* Note that we do **not** sum the residuals yet. The function returns the residuals for **each** data point of the input.\n",
        "\n",
        "* Some python implementation issue: although both `y` and `y_hat` are just a vector of numbers, they might be represented as 1D ($[n]$ sized) or as 2D ($[n,1]$ sized) arrays. We have to reshape one to fit the other.\n",
        "\n",
        "* The result returned by the following function will also have the same shape as `y_hat`.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "g_da04EUhU7P"
      },
      "source": [
        "### Code: `squared_loss` function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 24,
        "tab": [
          "pytorch"
        ],
        "id": "2I_CFWlZleRn"
      },
      "source": [
        "def squared_loss(y_hat, y):\n",
        "    \"\"\"Squared loss.\"\"\"\n",
        "    # although both y and y_hat are just a vector of numbers,\n",
        "    # they might be represented as [n] or as [n,1] arrays.\n",
        "    # that is what we have to reshape one to fit the other.\n",
        "    # Another option would have been to squeeze out the \"1\" dimension\n",
        "    return (y_hat - y.reshape(y_hat.shape))**2 / 2"
      ],
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 25,
        "id": "iwxYBKOdleRn"
      },
      "source": [
        "## Stochastic gradient descent -- the optimization algorithm\n",
        "\n",
        "* For each minibatch of `batch_size`,\n",
        "\n",
        "    1. Estimate the gradient of the loss with respect to our parameters.\n",
        "    2. Update the parameters (`params`) in the direction that may reduce the loss based on a learning rate (`lr`). Because we calculate our loss as a sum over the minibatch of examples, we normalize our step size by the batch size (`batch_size`), so that the magnitude of a typical step size\n",
        "does not depend heavily on our choice of the batch size."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cubF2iRnhcbd"
      },
      "source": [
        "###Code: `stochastic_gradient_descent` function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 27,
        "tab": [
          "pytorch"
        ],
        "id": "DIpuIjQileRn"
      },
      "source": [
        "def stochastic_gradient_descent (params, lr, batch_size):\n",
        "    \"\"\"Minibatch stochastic gradient descent.\"\"\"\n",
        "    with torch.no_grad():\n",
        "        for param in params:\n",
        "            param -= lr * param.grad / batch_size\n",
        "            param.grad.zero_()"
      ],
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 29,
        "id": "bDM_pedOleRo"
      },
      "source": [
        "## Training\n",
        "\n",
        "* Now that we have all the parts in place, we are ready **to implement the main training loop**.\n",
        "\n",
        "* It is crucial that you understand this code because you will see nearly identical training loops repeatedly throughout your career in deep learning.\n",
        "\n",
        "* Initialize parameters $(\\mathbf{w}, b)$\n",
        "* At each iteration over the mini-batches of the *entire* dataset\n",
        "    1. We will grab a minibatch of training examples,\n",
        "    2. Pass minibatch through the model to obtain a set of predictions.\n",
        "    3. Calculate the loss,\n",
        "    3. Compute gradient $\\mathbf{g} \\leftarrow \\partial_{(\\mathbf{w},b)} \\frac{1}{|\\mathcal{B}|} \\sum_{i \\in \\mathcal{B}} l(\\mathbf{x}^{(i)}, y^{(i)}, \\mathbf{w}, b)$\n",
        "        * Initiate the backward pass through the network, computing and storing the gradients with respect to each parameter.\n",
        "    5. Call `stochastic_gradient_descent` to update the model parameters.\n",
        "        * Update parameters $(\\mathbf{w}, b) \\leftarrow (\\mathbf{w}, b) - \\eta \\mathbf{g}$\n",
        "\n",
        "* Each pass (using the `data_iter` function) through the dataset is called one **epoch**. To optimize, we need **multiple epochs**\n",
        "\n",
        "* The number of epochs `num_epochs` and the learning rate `lr` are both **hyperparameters**, which we set here to 3 and 0.03, respectively.\n",
        "\n",
        "* Unfortunately, setting hyperparameters is tricky.\n",
        "Moreover, it requires some adjustment by trial and error.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8yLvIxWmfPrc"
      },
      "source": [
        "###Code: Training"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 30,
        "tab": [
          "pytorch"
        ],
        "id": "XlUvPlhcleRo",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "167652af-132e-49d7-a642-0a5b0c665240"
      },
      "source": [
        "lr = 0.03 # learning rate\n",
        "num_epochs = 10 # number of passes through the entire dataset\n",
        "batch_size = 10\n",
        "net = linreg\n",
        "loss = squared_loss\n",
        "print('Initial w=\\n', w, '\\nInitial b=\\n', b)\n",
        "print('True w=\\n', true_w, '\\nTrue b=\\n', true_b)\n"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Initial w=\n",
            " tensor([[ 0.0086],\n",
            "        [-0.0072]], requires_grad=True) \n",
            "Initial b=\n",
            " tensor([0.], requires_grad=True)\n",
            "True w=\n",
            " tensor([ 2.0000, -3.4000]) \n",
            "True b=\n",
            " 4.2\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 32,
        "tab": [
          "pytorch"
        ],
        "id": "8aGqIgDwleRp",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a8911e02-c9a6-45b8-d55b-b7e6d9ee55e1"
      },
      "source": [
        "for epoch in range(num_epochs):\n",
        "    for X, y in data_iter(batch_size, features, labels):\n",
        "        l = loss(net(X, w, b), y)  # Minibatch loss in `X` and `y`\n",
        "        # Compute gradient on `l` with respect to [`w`, `b`]\n",
        "\n",
        "        l.sum().backward()\n",
        "\n",
        "        stochastic_gradient_descent([w, b], lr, batch_size)  # Update parameters using their gradient\n",
        "\n",
        "    with torch.no_grad():\n",
        "        train_l = loss(net(features, w, b), labels)\n",
        "        #print('\\nw=\\n', w, '\\nb=\\n', b)\n",
        "        print(f'epoch {epoch + 1}, w= {w.numpy().transpose()}, b= {b.numpy()}, loss {float(train_l.mean()):f}',)\n"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "epoch 1, w= [[ 1.9586987 -3.242708 ]], b= [4.0188565], loss 0.030404\n",
            "epoch 2, w= [[ 2.0002077 -3.3929346]], b= [4.1918755], loss 0.000110\n",
            "epoch 3, w= [[ 2.0006409 -3.4000928]], b= [4.199799], loss 0.000049\n",
            "epoch 4, w= [[ 2.0002313 -3.4003437]], b= [4.199756], loss 0.000048\n",
            "epoch 5, w= [[ 2.0003974 -3.4005167]], b= [4.2002077], loss 0.000048\n",
            "epoch 6, w= [[ 2.0004327 -3.4002538]], b= [4.1999335], loss 0.000048\n",
            "epoch 7, w= [[ 2.0003245 -3.4005017]], b= [4.199876], loss 0.000048\n",
            "epoch 8, w= [[ 2.0003724 -3.4001908]], b= [4.1999693], loss 0.000048\n",
            "epoch 9, w= [[ 2.0004184 -3.4002445]], b= [4.199811], loss 0.000048\n",
            "epoch 10, w= [[ 2.0000982 -3.4003506]], b= [4.1999736], loss 0.000048\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 34,
        "id": "3cP_8-7QleRq"
      },
      "source": [
        "In this case, because we synthesized the dataset ourselves, we precisely know the true parameters. Thus, we can **evaluate our success in training by comparing the true parameters with those that we learned** through our training loop. Indeed they turn out to be very close to each other.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 35,
        "tab": [
          "pytorch"
        ],
        "id": "OXw7O_sdleRq",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "05f5a9dd-19f3-4563-a656-2086593087d1"
      },
      "source": [
        "print(f'error in estimating w: {true_w - w.reshape(true_w.shape)}')\n",
        "print(f'error in estimating b: {true_b - b}')"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "error in estimating w: tensor([-9.8228e-05,  3.5048e-04], grad_fn=<SubBackward0>)\n",
            "error in estimating b: tensor([2.6226e-05], grad_fn=<RsubBackward1>)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 36,
        "id": "beQUGGAHleRr"
      },
      "source": [
        "* Note that we should not take it for granted that we can recover the parameters perfectly. However, in machine learning, we are typically less concerned with recovering true underlying parameters and more concerned with parameters that lead to highly accurate predictions. Fortunately, even on complex optimization problems, stochastic gradient descent can often find remarkably good solutions, owing partly to the fact that, for deep networks, there exist many configurations of the parameters that lead to highly accurate predictions.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3SPENOIgiNbF"
      },
      "source": [
        "## Summary\n",
        "\n",
        "* We saw how a deep network could be implemented and optimized from scratch, using just tensors and auto differentiation.\n",
        "\n",
        "* This section only scratches the surface of what is possible. In the following sections, we will describe additional models based on the concepts we have just introduced and learn how to implement them more concisely.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4nueC0ADiPoQ"
      },
      "source": [
        "# Assignment\n",
        "\n",
        "1. Why is the `reshape` function needed in the `squared_loss` function? Try removing the `reshape` function and see.\n",
        "2. What would happen if we were to initialize the weights to zero. Would the algorithm still work? Report the results with zero-initialization and compare with random.\n",
        "3. Experiment with 3 different learning rates to find out how fast the loss function value drops.\n",
        "4. If the number of examples cannot be divided by the batch size, what happens to the `data_iter` function's behavior?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cGWjARwa8_Yd"
      },
      "source": [
        "![image.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vtTj5t4mgtBy"
      },
      "source": [
        "# Fully connected, single-layer, softmax network for classification\n",
        "\n",
        "* Consider the **classification problem**: given the feature of dimension  $d$, we have to label each data item with one of 3 labels.\n",
        "    * For example, given a $N \\times N$ image, i.e. input dimension $d = N^2$, figure out the state of the light, red, green, or orange.\n",
        "\n",
        "* The output layer has multiple outputs, one per class.\n",
        "\n",
        "* Each output is connected to all the inputs. Hence, we have a **fully connected layer**.\n",
        "\n",
        "\\begin{eqnarray}\n",
        "o_1 &= & x_1 w_{11} + \\cdots + x_d w_{1d} + b_1\\\\\n",
        "o_2 &= & x_1 w_{21} + \\cdots + x_d w_{2d} + b_2\\\\\n",
        "\\vdots & = &  \\vdots \\\\\n",
        "o_k &= & x_1 w_{k1} + \\cdots + x_d w_{kd} + b_k\n",
        "\\end{eqnarray}\n",
        "\n",
        "\n",
        "* More compactly, we can use linear algebra notation.\n",
        "\n",
        "\\begin{equation}\n",
        "\\mathbf{o} = \\mathbf{W} \\mathbf{x} + \\mathbf{b}\n",
        "\\end{equation}\n",
        "\n",
        ">* A matrix-vector product of the weights by the input features plus our **biases** $\\mathbf{b}$ results in the output.\n",
        ">* What is the total number of unknown parameters for a fully connected layer with an input of dimension $d$ and $k$ outputs?\n",
        ">* Also referred to as **logits**\n",
        "\n",
        "* Note that is an **affine transformation** of the inputs."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AHCOMYrLYhXw"
      },
      "source": [
        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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VHmqdlvRkQgO"
      },
      "source": [
        "## Softmax operation\n",
        "\n",
        "* Nothing constrains the output from summing to 1. The outputs can take on negative values too.\n",
        "\n",
        "* We would like each output to be a probability, i.e., a number between 0 and 1, that denotes the probability of the corresponding label for any given input.\n",
        "Ideally, only one of the outputs will be near 1, and the rest will be near 0.\n",
        "\n",
        "* We need to transform this output layer into a final output that is guaranteed (even on new data) to be nonnegative and sum to 1.\n",
        "\n",
        "* We also need a loss function that encourages the model to estimate probabilities faithfully. Of all instances when a classifier outputs 0.5, we hope that half of those examples will belong to the predicted class.\n",
        "This is a property called **calibration**.\n",
        "\n",
        "* The **softmax function**, invented in 1959 by the social scientist R. Duncan Luce in the context of *choice models*, does precisely this.\n",
        "\n",
        "\\begin{equation}\n",
        "\\hat{\\mathbf{y}} = \\mathrm{softmax}(\\mathbf{o})\\quad \\text{where}\\quad \\hat{y}_j = \\frac{\\exp(o_j)}{\\sum_k \\exp(o_k)}\n",
        "\\end{equation}\n",
        "\n",
        "* It is easy to see $\\hat{y}_1 + \\hat{y}_2 + \\hat{y}_3 = 1$\n",
        "with $0 \\leq \\hat{y}_j \\leq 1$ for all $j$.\n",
        "Thus, $\\hat{\\mathbf{y}}$ behaves like a probabilities.\n",
        "\n",
        "* Note that the softmax operation does not change the ordering among the logits $\\mathbf{o}$,\n",
        "which are simply the pre-softmax values\n",
        "that determine the probabilities assigned to each class.\n",
        "Therefore, during prediction, we can still pick out the most likely class by\n",
        "\n",
        "$$\n",
        "\\operatorname*{argmax}_j \\hat y_j = \\operatorname*{argmax}_j o_j.\n",
        "$$\n",
        "\n",
        "* Although softmax is a nonlinear function, the outputs of softmax regression are still *determined* by an affine transformation of input features;\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2oewb9NFmogO"
      },
      "source": [
        "## Vectorization for mini-batch\n",
        "\n",
        "* To improve computational efficiency and take advantage of GPUs, we typically carry out vector calculations for mini-batches of data.\n",
        "\n",
        "* Let  $\\mathbf{X}$ be $n \\times d$ matrix representing a minibatch of examples with feature dimensionality (number of inputs) $d$ and batch size $n$.\n",
        "\n",
        "* Then, weights $\\mathbf{W}$ is a ${d \\times q}$ matrix\n",
        "and the bias is a ${1\\times q}$ vector $\\mathbf{b}$.\n",
        "\n",
        "* The fully connected layer with softmax can compute outputs for **all** inputs in a minibatch **simultaneously** using matrix multiply. No for-loops needed.\n",
        "\n",
        "\\begin{equation}\n",
        "\\begin{aligned} \\mathbf{O}^{n \\times q} &= \\mathbf{X}^{n \\times d} \\mathbf{W}^{d \\times q} + \\mathbf{b}^{1\\times q}, \\\\\n",
        "\\hat{\\mathbf{Y}} & = \\mathrm{softmax}(\\mathbf{O}). \\end{aligned}\n",
        "\\end{equation}\n",
        "\n",
        "* [Broadcasting](https://numpy.org/doc/stable/user/basics.broadcasting.html) is triggered during the summation $\\mathbf{X} \\mathbf{W} + \\mathbf{b}$, both the minibatch $\\mathbf{O}$ and output probabilities $\\hat{\\mathbf{Y}}$ are $n \\times q$ matrices.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "okUEMTI6nRMP"
      },
      "source": [
        "## Loss Function -- Cross entropy\n",
        "\n",
        "\n",
        "* Squared difference error is not the appropriate error/residual/loss function to optimize. We use an error function that is appropriate for probability distributions -- **cross-entropy**.\n",
        "\n",
        "* The softmax function gives us a vector $\\hat{\\mathbf{y}}$, which we can interpret as estimated probabilities of each class given any input $\\mathbf{x}$, e.g., $\\hat{y}_1$ = $P(y=\\text{cat} \\mid \\mathbf{x})$.\n",
        "\n",
        "* Suppose that the entire dataset $\\{\\mathbf{X}, \\mathbf{Y}\\}$ has $n$ examples,\n",
        "where the example indexed by $i$ consists of a feature vector $\\mathbf{x}^{(i)}$ and a **one-hot label vector** $\\mathbf{y}^{(i)}$, i.e., an all-zero vector with one entry equal to 1 corresponding to the position denoting the label.\n",
        "\n",
        "* We can compare the estimates with labels by checking how probable the actual classes are according to our model, given the features:\n",
        "\n",
        "\\begin{equation}\n",
        "P(\\mathbf{Y} \\mid \\mathbf{X}) = \\prod_{i=1}^n P(\\mathbf{y}^{(i)} \\mid \\mathbf{x}^{(i)})\n",
        "\\end{equation}\n",
        "\n",
        "* According to maximum likelihood estimation,\n",
        "we maximize $P(\\mathbf{Y} \\mid \\mathbf{X})$,\n",
        "which is\n",
        "equivalent to minimizing the negative log-likelihood:\n",
        "\n",
        "$$\n",
        "-\\log P(\\mathbf{Y} \\mid \\mathbf{X}) = \\sum_{i=1}^n -\\log P(\\mathbf{y}^{(i)} \\mid \\mathbf{x}^{(i)})\n",
        "= \\sum_{i=1}^n l(\\mathbf{y}^{(i)}, \\hat{\\mathbf{y}}^{(i)}),\n",
        "$$\n",
        "\n",
        "> where for any pair of label $\\mathbf{y}$ and model prediction $\\hat{\\mathbf{y}}$ over $q$ classes,\n",
        "the loss function $l$ is\n",
        "\n",
        "\\begin{equation}\n",
        "l(\\mathbf{y}, \\hat{\\mathbf{y}}) = - \\sum_{j=1}^q y_j \\log \\hat{y}_j\n",
        "\\end{equation}\n",
        "\n",
        "\n",
        "* This loss function is commonly called the **cross-entropy loss**.\n",
        "\n",
        "* $\\mathbf{y}$ is a **one-hot vector** of length $q$\n",
        "    * so, the sum over all its coordinates $j$ vanishes for all but one term.\n",
        "\n",
        "* Since all $\\hat{y}_j$ are predicted probabilities, their logarithm is never larger than $0$.\n",
        "\n",
        "* Consequently, the loss function cannot be minimized any further\n",
        "if we correctly predict the actual label with *certainty*,\n",
        "i.e., if the predicted probability $P(\\mathbf{y} \\mid \\mathbf{x}) = 1$ for the actual label $\\mathbf{y}$.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "m_dWgaVYYvVL"
      },
      "source": [
        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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N8Yxppe-P8QA"
      },
      "source": [
        "## Summary of Model\n",
        "\n",
        "* Let  $\\mathbf{X}$ be $n \\times d$ matrix representing a minibatch of examples with feature dimensionality (number of inputs) $d$ and batch size $n$.\n",
        "\n",
        "* Then, weights $\\mathbf{W}$ is a ${d \\times q}$ matrix\n",
        "and the bias is a ${1\\times q}$ vector $\\mathbf{b}$.\n",
        "\n",
        "* The fully connected layer with softmax can compute outputs for **all** inputs in a minibatch **simultaneously** using matrix multiply. No for-loops needed.\n",
        "\n",
        "\\begin{equation}\n",
        "\\begin{aligned} \\mathbf{O} &= \\mathbf{X} \\mathbf{W} + \\mathbf{b}, \\\\ \\hat{\\mathbf{Y}} & = \\mathrm{softmax}(\\mathbf{O}). \\end{aligned}\n",
        "\\end{equation}\n",
        "\n",
        "* This loss function is commonly called the **cross-entropy loss**.\n",
        "\n",
        "\n",
        "\\begin{equation}\n",
        "l(\\mathbf{y}, \\hat{\\mathbf{y}}) = - \\sum_{j=1}^q y_j \\log \\hat{y}_j\n",
        "\\end{equation}\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 0,
        "id": "MIWrDTsdqWqy"
      },
      "source": [
        "## Implementation of softmax regression\n",
        "\n",
        "* Just as we implemented linear regression from scratch, we believe that softmax regression is similarly fundamental, and you ought to know the gory details of softmax regression and how to implement it yourself.\n",
        "\n",
        "* We will work with the [Fashion-MNIST dataset](https://github.com/zalandoresearch/fashion-mnist), setting up a data iterator with batch size 256.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2Xqqn9s1oCB8"
      },
      "source": [
        "###Code: ReadFashion MSNIST data (`train_iter, test_iter`)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 2,
        "tab": [
          "pytorch"
        ],
        "id": "NZZ6kp1tqWq3"
      },
      "source": [
        "import torch\n",
        "from IPython import display\n",
        "from d2l import torch as d2l"
      ],
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 4,
        "tab": [
          "pytorch"
        ],
        "id": "DPzYcAwOqWq7",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a21daf76-2d94-4305-f4d9-c6d0b5c740b1"
      },
      "source": [
        "batch_size = 256\n",
        "train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)\n",
        "\n",
        "for X, y in train_iter:\n",
        "    print('Each element of train_iter has: X=',  X.shape, 'y=', y.shape)\n",
        "    break\n",
        "\n",
        "for X, y in test_iter:\n",
        "    print('Each element of test_iter  has: X=', X.shape, 'y=', y.shape)\n",
        "\n",
        "    print(' We will reshape X before use into =', X.reshape((-1, 784)).shape)\n",
        "    break\n"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/train-images-idx3-ubyte.gz\n",
            "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/train-images-idx3-ubyte.gz to ../data/FashionMNIST/raw/train-images-idx3-ubyte.gz\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 26421880/26421880 [00:00<00:00, 110604059.99it/s]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Extracting ../data/FashionMNIST/raw/train-images-idx3-ubyte.gz to ../data/FashionMNIST/raw\n",
            "\n",
            "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/train-labels-idx1-ubyte.gz\n",
            "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/train-labels-idx1-ubyte.gz to ../data/FashionMNIST/raw/train-labels-idx1-ubyte.gz\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 29515/29515 [00:00<00:00, 5924050.46it/s]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Extracting ../data/FashionMNIST/raw/train-labels-idx1-ubyte.gz to ../data/FashionMNIST/raw\n",
            "\n",
            "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/t10k-images-idx3-ubyte.gz\n",
            "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/t10k-images-idx3-ubyte.gz to ../data/FashionMNIST/raw/t10k-images-idx3-ubyte.gz\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 4422102/4422102 [00:00<00:00, 65461181.02it/s]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Extracting ../data/FashionMNIST/raw/t10k-images-idx3-ubyte.gz to ../data/FashionMNIST/raw\n",
            "\n",
            "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/t10k-labels-idx1-ubyte.gz\n",
            "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/t10k-labels-idx1-ubyte.gz to ../data/FashionMNIST/raw/t10k-labels-idx1-ubyte.gz\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 5148/5148 [00:00<00:00, 5630319.95it/s]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Extracting ../data/FashionMNIST/raw/t10k-labels-idx1-ubyte.gz to ../data/FashionMNIST/raw\n",
            "\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/dist-packages/torch/utils/data/dataloader.py:560: UserWarning: This DataLoader will create 4 worker processes in total. Our suggested max number of worker in current system is 2, which is smaller than what this DataLoader is going to create. Please be aware that excessive worker creation might get DataLoader running slow or even freeze, lower the worker number to avoid potential slowness/freeze if necessary.\n",
            "  warnings.warn(_create_warning_msg(\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Each element of train_iter has: X= torch.Size([256, 1, 28, 28]) y= torch.Size([256])\n",
            "Each element of test_iter  has: X= torch.Size([256, 1, 28, 28]) y= torch.Size([256])\n",
            " We will reshape X before use into = torch.Size([256, 784])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 5,
        "id": "V8v_wSlPqWq8"
      },
      "source": [
        "## Defining the fully connected (FC) layer\n",
        "\n",
        "* As in our linear regression example, each example here will be represented by a fixed-length vector. Each example in the raw dataset is a $28 \\times 28$ image. In this section, **we will flatten each image, treating them as vectors of length 784.** In the future, we will talk about more sophisticated strategies for exploiting the spatial structure in images, but for now, we treat each pixel location as just another feature.\n",
        "\n",
        "* Recall that in softmax regression, we have as many outputs as there are classes. **Because our dataset has 10 classes, our network will have an output dimension of 10.** Consequently, our weights will constitute a $784 \\times 10$ matrix and the biases will constitute a $1 \\times 10$ row vector. As with linear regression, we will initialize our weights `W` with Gaussian noise and our biases to take the initial value 0.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oCC3yB0ppC3X"
      },
      "source": [
        "### Code: Fully connected (FC) layer (`W, b`)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 7,
        "tab": [
          "pytorch"
        ],
        "id": "EnUQmAOMqWq8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "35cfcf27-8e3f-4380-b985-5844fb402657"
      },
      "source": [
        "num_inputs = 784\n",
        "num_outputs = 10\n",
        "\n",
        "W = torch.normal(0, 0.01, size=(num_inputs, num_outputs), requires_grad=True)\n",
        "b = torch.zeros(num_outputs, requires_grad=True)\n",
        "\n",
        "print('W shape is', W.shape, '\\nW=', W)\n",
        "print('\\nb shape is', b.shape, '\\nb=', b)"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "W shape is torch.Size([784, 10]) \n",
            "W= tensor([[ 0.0142,  0.0061,  0.0040,  ..., -0.0048, -0.0061, -0.0059],\n",
            "        [-0.0120,  0.0036, -0.0058,  ..., -0.0127,  0.0062,  0.0005],\n",
            "        [ 0.0032,  0.0016,  0.0045,  ..., -0.0012, -0.0083, -0.0050],\n",
            "        ...,\n",
            "        [-0.0231,  0.0144,  0.0002,  ..., -0.0095, -0.0113, -0.0113],\n",
            "        [ 0.0088, -0.0180,  0.0105,  ..., -0.0032, -0.0049,  0.0055],\n",
            "        [ 0.0162, -0.0069, -0.0055,  ..., -0.0003, -0.0231, -0.0063]],\n",
            "       requires_grad=True)\n",
            "\n",
            "b shape is torch.Size([10]) \n",
            "b= tensor([0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], requires_grad=True)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 9,
        "id": "ME8rTnvPqWq9"
      },
      "source": [
        "## Defining the softmax operation\n",
        "\n",
        "* Before implementing the softmax regression model, let us briefly review how the sum operator works along specific dimensions in a tensor. **Given a matrix `X`, we can sum over all elements (by default) or only over elements in the same axis,**, i.e., the same column (axis 0) or the same row (axis 1).\n",
        "\n",
        "* When invoking the sum operator, we can specify to keep the number of axes in the original tensor rather than collapsing out the dimension that we summed over. The result is a two-dimensional tensor with shape (1, 3).\n",
        "\n",
        "* Note that if `X` is a tensor with shape (2, 3) and we sum over the columns, the result will be a vector with shape (3,).\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 10,
        "tab": [
          "pytorch"
        ],
        "id": "eWUGmp36qWq-",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "bced8afd-cfb5-4ed5-8e11-2fc74258e821"
      },
      "source": [
        "X = torch.tensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])\n",
        "print('X, sum over dim 0\\n', X.sum(0, keepdim=False))\n",
        "print('\\nX, sum over dim 1\\n', X.sum(0, keepdim=True))"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "X, sum over dim 0\n",
            " tensor([5., 7., 9.])\n",
            "\n",
            "X, sum over dim 1\n",
            " tensor([[5., 7., 9.]])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 12,
        "id": "l3J_3JHxqWrA"
      },
      "source": [
        "* We are now ready to **implement the softmax operation**. Recall that softmax consists of three steps:\n",
        "    1. We exponentiate each term (using `exp`)\n",
        "    2. we sum over each row (we have one row per example in the batch) to get the normalization constant for each example\n",
        "    3. We divide each row by its normalization constant, ensuring that the result sums it to 1.\n",
        "\n",
        "* Before looking at the code, let us recall how this looks expressed as an equation. We are processing one minibatch at a time, so $\\mathbf{O}_{ij}$ is `batch_size` $\\times$ `output_dim` matrix, whose rows store the output vector for the corresponding training sample in the minibatch.\n",
        "\n",
        "\\begin{equation}\n",
        "\\mathrm{softmax}(\\mathbf{O})_{ij} = \\frac{\\exp(\\mathbf{O}_{ij})}{\\sum_k \\exp(\\mathbf{O}_{ik})}\n",
        "\\end{equation}\n",
        "\n",
        "* (Advanced Material:) The denominator, or normalization constant, is sometimes called the **partition function** (its logarithm is called the log-partition function). The origins of that name are in [statistical physics](https://en.wikipedia.org/wiki/Partition_function_(statistical_mechanics)), where a related equation models the distribution over an ensemble of particles.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KIFvcud6n9LR"
      },
      "source": [
        "### Code: Softmax layer (`softmax`)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 14,
        "tab": [
          "pytorch"
        ],
        "id": "PjF75KVfqWrB"
      },
      "source": [
        "def softmax(Oh):\n",
        "    Oh_exp = torch.exp(Oh)\n",
        "    partition = Oh_exp.sum(1, keepdim=True)\n",
        "    return Oh_exp / partition  # The broadcasting mechanism is applied here"
      ],
      "execution_count": 25,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 15,
        "id": "XtKo29Y1qWrC"
      },
      "source": [
        "As you can see, for any random input, we turn each element into a non-negative number. Moreover, each row sums up to 1, as is required for a probability measure.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 16,
        "tab": [
          "pytorch"
        ],
        "id": "6dyJcO3VqWrC",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ce3b5cb4-5792-475e-855b-2edc7f140d34"
      },
      "source": [
        "Oh = torch.normal(0, 1, (2, 5))\n",
        "Y_prob = softmax(Oh)\n",
        "print('Oh =\\n', Oh)\n",
        "print('Y_prob =\\n', Y_prob, '\\nSum=', Y_prob.sum(1))"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Oh =\n",
            " tensor([[ 1.3479,  0.5485, -2.4009,  0.4688,  0.1085],\n",
            "        [-0.9598, -0.7806,  0.3442, -1.1599, -0.0571]])\n",
            "Y_prob =\n",
            " tensor([[0.4592, 0.2064, 0.0108, 0.1906, 0.1330],\n",
            "        [0.1091, 0.1305, 0.4020, 0.0893, 0.2691]]) \n",
            "Sum= tensor([1., 1.])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 18,
        "id": "Fka3HSaPqWrD"
      },
      "source": [
        "## Putting together the Model\n",
        "\n",
        "Now that we have defined the softmax operation, we can **implement the softmax regression model.** The below code implements how the input is mapped to the output through the network. Note that we flatten each original image in the batch into a vector using the `reshape` function before passing the data through our model.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6ZmgEm-JphJO"
      },
      "source": [
        "###Code: Model (`net`)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 19,
        "tab": [
          "pytorch"
        ],
        "id": "Jsu1747VqWrD"
      },
      "source": [
        "def net(X):\n",
        "    # X dimension is [256, 1, 28, 28] which we reshape into [256, 784]\n",
        "    # size of W is [784 10]\n",
        "    return softmax(torch.matmul(X.reshape((-1, W.shape[0])), W) + b)\n"
      ],
      "execution_count": 27,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 20,
        "id": "NLsxa4yEqWrE"
      },
      "source": [
        "## Defining the cross-entropy loss function\n",
        "\n",
        "* Recall that cross-entropy takes the negative log-likelihood of the predicted probability assigned to the true label. We can pick all elements by a single operator rather than iterating over the predictions with a Python for-loop (which tends to be inefficient).\n",
        "\n",
        "* Below, we **create sample data `y_hat` with 2 examples of predicted probabilities over 3 classes and their corresponding labels `y`.**\n",
        "\n",
        "* With `y`, we know that in the first example, the first class is the correct prediction, and in the second example, the third class is the ground truth.\n",
        "**Using `y` as the indices of the probabilities in `y_hat`,** we pick the probability of the first class in the first example and the probability of the third class in the second example.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 21,
        "tab": [
          "pytorch"
        ],
        "id": "dr6KM3nXqWrE",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "cdf5200a-108d-4df3-815d-179fe0d38056"
      },
      "source": [
        "y = torch.tensor([0, 2])\n",
        "y_hat = torch.tensor([[0.1, 0.3, 0.6],\n",
        "                      [0.3, 0.2, 0.5]])\n",
        "y_hat[[0, 1], y]"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([0.1000, 0.5000])"
            ]
          },
          "metadata": {},
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 23,
        "id": "Ji6tziV0qWrF"
      },
      "source": [
        "Now we can **implement the cross-entropy loss function** efficiently with just one line of code.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iSgRzJ46pqFx"
      },
      "source": [
        "### Code: `cross_entropy_loss`"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 24,
        "tab": [
          "pytorch"
        ],
        "id": "bzmEvB4xqWrF",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "63c03f9e-faaa-4b68-b7ed-903a65a5691b"
      },
      "source": [
        "def cross_entropy_loss (y_hat, y):\n",
        "\n",
        "    return -torch.log(y_hat[range(len(y_hat)), y])\n",
        "    #range(len(y_hat)) creates indices 0,1,2,len-1\n",
        "\n",
        "cross_entropy_loss (y_hat, y)\n"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([2.3026, 0.6931])"
            ]
          },
          "metadata": {},
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 26,
        "id": "YAEnFgttqWrH"
      },
      "source": [
        "## Classification Accuracy\n",
        "\n",
        "* Given the predicted probability distribution `y_hat`, we typically choose the class with the highest predicted probability whenever we must output a hard prediction.\n",
        "\n",
        "    * Gmail must categorize an email into \"Primary\", \"Social\", \"Updates\", or \"Forums\". It might estimate probabilities internally, but it has to choose one among the classes at the end of the day.\n",
        "\n",
        "* The classification accuracy is the fraction of all correct predictions. Although it can be challenging to optimize accuracy directly (it is not differentiable), it is often the performance measure we care most about, and we will nearly always report it when training classifiers.\n",
        "\n",
        "* To compute accuracy, we do the following.\n",
        "    1. If `y_hat` is a matrix, we assume that the second dimension stores prediction scores for each class. We use `argmax` to obtain the predicted class by the index for the largest entry in each row.\n",
        "    2. We **compare the predicted class with the ground-truth `y` elementwise.** Since the equality operator `==` is sensitive to data types, we convert `y_hat`'s data type to match that of `y`. The result is a tensor containing 0 (false) and 1 (true) entries. Taking the sum yields the number of correct predictions.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 27,
        "tab": [
          "pytorch"
        ],
        "id": "6VUb9lxrqWrI"
      },
      "source": [
        "def accuracy(y_hat, y):\n",
        "    \"\"\"Compute the number of correct predictions.\"\"\"\n",
        "    if len(y_hat.shape) > 1 and y_hat.shape[1] > 1: #The output is a vector -- not just a scalar\n",
        "        y_hat = y_hat.argmax(axis=1)\n",
        "    cmp = y_hat.type(y.dtype) == y\n",
        "    return float(cmp.type(y.dtype).sum())"
      ],
      "execution_count": 31,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 28,
        "id": "bYxWeexwqWrI"
      },
      "source": [
        "We will continue to use the variables `y_hat` and `y`\n",
        "defined before\n",
        "as the predicted probability distributions and labels, respectively.\n",
        "We can see that the first example's prediction class is 2\n",
        "(the largest element of the row is 0.6 with the index 2),\n",
        "which is inconsistent with the actual label, 0.\n",
        "The second example's prediction class is 2\n",
        "(the largest element of the row is 0.5 with the index of 2),\n",
        "which is consistent with the actual label, 2.\n",
        "Therefore, the classification accuracy rate for these two examples is 0.5.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 29,
        "tab": [
          "pytorch"
        ],
        "id": "k29F8SZ8qWrJ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ad791ce6-8346-4b68-d978-3483e4dfc3cc"
      },
      "source": [
        "accuracy(y_hat, y) / len(y)"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.5"
            ]
          },
          "metadata": {},
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 30,
        "id": "_aNMVUXCqWrJ"
      },
      "source": [
        "**Similarly, we can evaluate the accuracy for any model `net` on a dataset** that is accessed via the data iterator `data_iter`.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wz6FJlPNp0yx"
      },
      "source": [
        "###Code: `evaluate_accuracy`"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 32,
        "tab": [
          "pytorch"
        ],
        "id": "97qoPEBhqWrK"
      },
      "source": [
        "def evaluate_accuracy(net, data_iter):\n",
        "    \"\"\"Compute the accuracy for a model on a dataset.\"\"\"\n",
        "    if isinstance(net, torch.nn.Module):\n",
        "        net.eval()  # Set the model to evaluation mode\n",
        "    metric = Accumulator(2)  # No. of correct predictions, no. of predictions\n",
        "\n",
        "    with torch.no_grad():\n",
        "        for X, y in data_iter: # iterate over the minibatches\n",
        "            metric.add(accuracy(net(X), y), y.numel())\n",
        "    return metric[0] / metric[1]"
      ],
      "execution_count": 33,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 33,
        "id": "t1cwLD_JqWrK"
      },
      "source": [
        "* Here `Accumulator` is a utility class to accumulate sums over multiple variables.\n",
        "\n",
        "* In the above `evaluate_accuracy` function, we create 2 variables in the `Accumulator` instance to store the number of correct predictions and the number of predictions, respectively.\n",
        "\n",
        "* We  will accumulate both over time as we iterate over the dataset.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MOtWGowymC07",
        "outputId": "b0edecae-098f-4f5e-9a5e-e894d33fc760"
      },
      "source": [
        "[0.0] * 4"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0.0, 0.0, 0.0, 0.0]"
            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 34,
        "tab": [
          "pytorch"
        ],
        "id": "qGBAw6b9qWrL"
      },
      "source": [
        "class Accumulator:\n",
        "    \"\"\"For accumulating sums over `n` variables.\"\"\"\n",
        "    def __init__(self, n):\n",
        "        self.data = [0.0] * n # creates [0.0, 0.0, ....n-times]\n",
        "\n",
        "    def add(self, *args):\n",
        "        self.data = [a + float(b) for a, b in zip(self.data, args)]\n",
        "        # Example: let self.data = [10, 15] and args be [3, 4]\n",
        "        # zip(self.data, args) will produce the paired iterable [(10, 3), (15, 4)]\n",
        "        # the for loop with go over these paired entries adding them up to result in [13, 19]\n",
        "\n",
        "    def reset(self):\n",
        "        self.data = [0.0] * len(self.data) # creates [0.0, 0.0, ....n-times]\n",
        "\n",
        "    def __getitem__(self, idx):\n",
        "        return self.data[idx]"
      ],
      "execution_count": 35,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 35,
        "id": "jR9a7y2ZqWrL"
      },
      "source": [
        "**Because we initialized the `net` model with random weights, the accuracy of this model should be close to random guessing,** i.e., 0.1 for 10 classes.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 36,
        "tab": [
          "pytorch"
        ],
        "id": "busgI2vnqWrM",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7d507ff6-4b55-4675-d953-2d89f83e794e"
      },
      "source": [
        "evaluate_accuracy(net, test_iter)"
      ],
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.078"
            ]
          },
          "metadata": {},
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 37,
        "id": "TSkjhpp3qWrM"
      },
      "source": [
        "## Training\n",
        "\n",
        "* The training loop for softmax regression should look strikingly familiar to the implementation of linear regression.\n",
        "\n",
        "* Here, we refactor the implementation to make it reusable. First, we define a function to train for one epoch. Note that `updater` is a general function to update the model parameters, which accepts the batch size as an argument.\n",
        "It can be either a wrapper of the `d2l.sgd` function or a framework's built-in optimization function.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cCMTBmqBqx6U"
      },
      "source": [
        "### Code: `train_one_epoch`"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 46,
        "tab": [
          "pytorch"
        ],
        "id": "2Vzs3N1hqWrP"
      },
      "source": [
        "def my_updater (batch_size):\n",
        "    return stochastic_gradient_descent([W, b], lr, batch_size)\n",
        "\n",
        "# we use the minibatch stochastic gradient descent we wrote earlier to\n",
        "# optimize the loss function of the model"
      ],
      "execution_count": 37,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 39,
        "tab": [
          "pytorch"
        ],
        "id": "jaZ8RmpoqWrM"
      },
      "source": [
        "def train_one_epoch (net, train_iter, loss, updater):\n",
        "\n",
        "    metric = Accumulator(3) # Sum of training loss, sum of training accuracy, no. of examples\n",
        "    for X, y in train_iter:\n",
        "        # Compute gradients and update parameters\n",
        "        y_hat = net(X)\n",
        "        l = loss(y_hat, y)\n",
        "        l.sum().backward()\n",
        "        updater(X.shape[0])\n",
        "        metric.add(float(l.sum()), accuracy(y_hat, y), y.numel())\n",
        "    # Return training loss and training accuracy\n",
        "    return metric[0] / metric[2], metric[1] / metric[2]"
      ],
      "execution_count": 38,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 41,
        "id": "zJMZqGc_qWrN"
      },
      "source": [
        "Before showing the implementation of the training function,\n",
        "we define **a utility class that plot data in animation.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k1pO3HuOtCle"
      },
      "source": [
        "###Code: `Animator` class"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 42,
        "tab": [
          "pytorch"
        ],
        "id": "zHA0oIHdqWrN"
      },
      "source": [
        "class Animator:\n",
        "    \"\"\"For plotting data in animation.\"\"\"\n",
        "    def __init__(self, xlabel=None, ylabel=None, legend=None, xlim=None,\n",
        "                 ylim=None, xscale='linear', yscale='linear',\n",
        "                 fmts=('-', 'm--', 'g-.', 'r:'), nrows=1, ncols=1,\n",
        "                 figsize=(5, 5)):\n",
        "        # Incrementally plot multiple lines\n",
        "        if legend is None:\n",
        "            legend = []\n",
        "        d2l.use_svg_display()\n",
        "        self.fig, self.axes = d2l.plt.subplots(nrows, ncols, figsize=figsize)\n",
        "        if nrows * ncols == 1:\n",
        "            self.axes = [self.axes,]\n",
        "        # Use a lambda function to capture arguments\n",
        "        self.config_axes = lambda: d2l.set_axes(self.axes[\n",
        "            0], xlabel, ylabel, xlim, ylim, xscale, yscale, legend)\n",
        "        self.X, self.Y, self.fmts = None, None, fmts\n",
        "\n",
        "    def add(self, x, y):\n",
        "        # Add multiple data points into the figure\n",
        "        if not hasattr(y, \"__len__\"):\n",
        "            y = [y]\n",
        "        n = len(y)\n",
        "        if not hasattr(x, \"__len__\"):\n",
        "            x = [x] * n\n",
        "        if not self.X:\n",
        "            self.X = [[] for _ in range(n)]\n",
        "        if not self.Y:\n",
        "            self.Y = [[] for _ in range(n)]\n",
        "        for i, (a, b) in enumerate(zip(x, y)):\n",
        "            if a is not None and b is not None:\n",
        "                self.X[i].append(a)\n",
        "                self.Y[i].append(b)\n",
        "        self.axes[0].cla()\n",
        "        for x, y, fmt in zip(self.X, self.Y, self.fmts):\n",
        "            self.axes[0].plot(x, y, fmt)\n",
        "        self.config_axes()\n",
        "        display.display(self.fig)\n",
        "        display.clear_output(wait=True)"
      ],
      "execution_count": 39,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 43,
        "id": "5z4l9GYcqWrO"
      },
      "source": [
        "* The following function trains a model `net` on a training dataset accessed via `train_iter` for multiple epochs, which is specified by `num_epochs`.\n",
        "\n",
        "* At the end of each epoch, the model is evaluated on a test dataset accessed via `test_iter`.\n",
        "\n",
        "* We will leverage the `Animator` class to visualize the training progress.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JdBt3dgltJXv"
      },
      "source": [
        "###Code: `train_full`"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 44,
        "tab": [
          "pytorch"
        ],
        "id": "JR0B2c_GqWrO"
      },
      "source": [
        "def train_full (net, train_iter, test_iter, loss, num_epochs, updater):\n",
        "    \"\"\"Train a model (defined in Chapter 3).\"\"\"\n",
        "    animator = Animator(xlabel='epoch', xlim=[1, num_epochs], ylim=[0.3, 0.9],\n",
        "                        legend=['train loss', 'train acc', 'test acc'])\n",
        "    for epoch in range(num_epochs):\n",
        "        train_metrics = train_one_epoch (net, train_iter, loss, updater)\n",
        "        test_acc = evaluate_accuracy(net, test_iter)\n",
        "        animator.add(epoch + 1, train_metrics + (test_acc,))\n",
        "    train_loss, train_acc = train_metrics\n",
        "    return (train_loss, train_acc, test_acc)"
      ],
      "execution_count": 40,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 48,
        "id": "Fk0vMWOuqWrP"
      },
      "source": [
        "Now we **train the model with 10 epochs.** Note that both the number of epochs (`num_epochs`), and learning rate (`lr`) are adjustable hyperparameters. By changing their values, we may be able to increase the classification accuracy of the model.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "u8DnU0HjuXNX"
      },
      "source": [
        "### Code: Run train"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 49,
        "tab": [
          "pytorch"
        ],
        "id": "lyvwxlpvqWrP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "outputId": "c4e857c6-88ef-44a2-d7aa-2df3c0c0bb54"
      },
      "source": [
        "num_epochs = 10\n",
        "lr = 0.1\n",
        "train_full (net, train_iter, test_iter, cross_entropy_loss, num_epochs, my_updater)"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(0.447199605178833, 0.8479333333333333, 0.8327)"
            ]
          },
          "metadata": {},
          "execution_count": 41
        },
        {
          "output_type": "display_data",
          "data": {
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          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "origin_pos": 50,
        "id": "7DWpPZjqqWrQ"
      },
      "source": [
        "## Prediction\n",
        "\n",
        "Now that training is complete, our model is ready to **classify some images.**\n",
        "Given a series of images, we will compare their actual labels (first line of text output) and the predictions from the model (second line of text output).\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IieOngQhx1Ll"
      },
      "source": [
        "### Code: `predict`"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "origin_pos": 51,
        "tab": [
          "pytorch"
        ],
        "id": "N_vlMgT-qWrQ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 174
        },
        "outputId": "84bfde9a-36a5-449d-b1dc-d95bcb5fb5c3"
      },
      "source": [
        "def predict (net, test_iter, n=6):\n",
        "    \"\"\"Predict labels (defined in Chapter 3).\"\"\"\n",
        "    for X, y in test_iter:\n",
        "        break\n",
        "    trues = d2l.get_fashion_mnist_labels(y)\n",
        "    preds = d2l.get_fashion_mnist_labels(net(X).argmax(axis=1)) ## This is how you invoke the model\n",
        "    titles = [true + '\\n' + pred for true, pred in zip(trues, preds)]\n",
        "    d2l.show_images(X[0:n].reshape((n, 28, 28)), 1, n, titles=titles[0:n])\n",
        "\n",
        "predict (net, test_iter)"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 900x150 with 6 Axes>"
            ],
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        "## Summary\n",
        "\n",
        "* With softmax regression, we can train models for multiclass classification.\n",
        "* The training loop of softmax regression is very similar to that in linear regression: retrieve and read data, define models and loss functions, then train models using optimization algorithms. As you will soon find out, most common deep learning models have similar training procedures.\n"
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        "\n",
        "# Assignment\n",
        "\n",
        "1. In this section, we directly implemented the softmax function based on the mathematical definition of the softmax operation. What problems might this cause? Hint: Try calculating the size of $\\exp(50)$.\n",
        "1. The function `cross_entropy` in this section was implemented according to the definition of the cross-entropy loss function. What could be the problem with this implementation? Hint: consider the domain of the logarithm.\n",
        "1. What solutions can you consider to fix the two problems above?\n",
        "1. Is it always a good idea to return the most likely label? For example, would you do this for medical diagnosis?\n",
        "1. Assume that we want to use softmax regression to predict the next word based on some features. What are some problems that might arise from a large vocabulary?\n"
      ]
    }
  ]
}