intro_to_ml.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "gpuType": "T4",
      "authorship_tag": "ABX9TyNPytLuhwDhj1nBkTLiAY4P",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/csce585-mlsystems/tutorials/blob/main/intro_to_ml.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "id": "4boGA9rYdt9l"
      },
      "outputs": [],
      "source": [
        "## Install and import anything required. Capture hides the output from the cell.\n",
        "# @title Install and import required packages. (Run Cell)\n",
        "!pip install -q clu\n",
        "\n",
        "import jax\n",
        "import jax.numpy as jnp\n",
        "import flax\n",
        "import flax.linen as nn\n",
        "from typing import NamedTuple, Any, Dict\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "from clu import parameter_overview\n",
        "\n",
        "from sklearn.datasets import fetch_openml\n",
        "\n",
        "from IPython.display import HTML, Math"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Load the MNIST digits dataset\n",
        "mnist = fetch_openml(name='mnist_784', version=1, as_frame=False, parser='auto')\n",
        "# Extract the data and labels\n",
        "images, labels = mnist.data, mnist.target\n",
        "\n",
        "# Convert labels to integers (they are originally stored as strings)\n",
        "labels = labels.astype(int)\n",
        "\n",
        "# Print shapes of the data\n",
        "print(f\"Images have shape: {images.shape}, and labels have shape: {labels.shape}\")\n",
        "\n",
        "# Verify that we have 10 classes\n",
        "print(f\"Number of classes is: {len(np.unique(labels))}\")\n",
        "\n",
        "# Print the min and max values of the images\n",
        "print(f\"Minimum value in images is: {np.min(images)}\")\n",
        "print(f\"Maximum value in images is: {np.max(images)}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "d5z2gWTi5cGS",
        "outputId": "73cc8887-40b3-4e4d-e682-8f7821e06fb1"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Images have shape: (70000, 784), and labels have shape: (70000,)\n",
            "Number of classes is: 10\n",
            "Minimum value in images is: 0\n",
            "Maximum value in images is: 255\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 746
        },
        "id": "-qXlDhYWH_mW",
        "outputId": "05ebe615-a36a-414b-9998-aa5191a22df0"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x800 with 24 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# @title Plot images\n",
        "def plot_images(images, labels):\n",
        "  rows = 4\n",
        "  cols = 6\n",
        "  num_images = images.shape[0]\n",
        "\n",
        "  fig, axes = plt.subplots(rows, cols, figsize=(8, 8))\n",
        "\n",
        "  for ir in range(rows):\n",
        "    for ic in range(cols):\n",
        "      sample = np.random.randint(0, num_images)\n",
        "      image = images[sample].reshape(28, 28)\n",
        "      axes[ir, ic].imshow(image, cmap='gray')\n",
        "      axes[ir, ic].axis('off')\n",
        "      axes[ir, ic].set_title(f\"Digit {labels[sample]}\")\n",
        "\n",
        "  plt.tight_layout()\n",
        "  plt.show()\n",
        "\n",
        "plot_images(images, labels)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Helper code to plot a Sine curve\n",
        "amplitude = 3\n",
        "x = np.linspace(0, 2*np.pi, 1000)\n",
        "y = amplitude*np.sin(x) + np.random.randn(1000)*0.1   # Calculate y values using the sine function\n",
        "yfit = amplitude*np.sin(x)\n",
        "\n",
        "plt.figure(figsize=(8, 6))\n",
        "plt.scatter(x, y, label=\"data\", color='red')\n",
        "plt.plot(x, yfit, label=f'Sine Curve with Amplitude = {amplitude}', color='black')\n",
        "plt.title('Sine Curve')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.legend()\n",
        "# plt.grid()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "BFhRN01052n0",
        "outputId": "2cb666ff-9f8d-4769-8f62-242c3fe9be0e"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "id": "sBe3ytk5WyvD"
      },
      "outputs": [],
      "source": [
        "# Example implementation of a linear function computation.\n",
        "x.shape[0]\n",
        "\n",
        "x_key = jax.random.PRNGKey(0)\n",
        "dim = 10\n",
        "x = jax.random.uniform(x_key, (dim,))\n",
        "\n",
        "w_key = jax.random.PRNGKey(1)\n",
        "w = jax.random.uniform(w_key, (dim,))\n",
        "\n",
        "b_key = jax.random.PRNGKey(2)\n",
        "b = jax.random.uniform(b_key, (1,))\n",
        "\n",
        "y = jnp.dot(w,x) + b  # can also be achieved using: y = x @ w + b"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "w.shape[0]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MmgbUiXHIocc",
        "outputId": "6982c392-3f10-46a9-e973-7b9c3384d887"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "10"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Run this to generate the data\n",
        "# store the parameters in a dictionary\n",
        "params = dict(w=w, b=b)\n",
        "\n",
        "batch_size = 5\n",
        "X = jax.random.uniform(x_key, (batch_size, dim))\n",
        "data = jax.random.uniform(x_key, (batch_size,))"
      ],
      "metadata": {
        "id": "vnbxIW7i7Oic"
      },
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def linear_model(params: Any, X: jnp.ndarray) -> jnp.ndarray:\n",
        "  # complete this code\n",
        "  w = params['w']\n",
        "  b = params['b']\n",
        "\n",
        "  # compute m = f(x) here using w,b and X\n",
        "  m = X @ w + b\n",
        "\n",
        "  return m\n"
      ],
      "metadata": {
        "id": "snjNEmlV8DZW"
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def test_linear_model():\n",
        "  assert (linear_model(params, X) == X @ w + b).all()\n",
        "  print(\"Nice! Your answer looks correct.\")\n",
        "\n",
        "test_linear_model()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uxcCQPC88e56",
        "outputId": "cebf6e72-e098-43c1-bd07-e88490e9f49f"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Nice! Your answer looks correct.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "w.shape[0]"
      ],
      "metadata": {
        "id": "_9EmkjDX9LeN",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "891eff40-8598-44c7-ff98-3aeac354aead"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "10"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Helper code to plot errors\n",
        "\n",
        "# Set random seed for reproducibility\n",
        "np.random.seed(42)\n",
        "\n",
        "# Number of points to generate\n",
        "num_points = 20\n",
        "\n",
        "# Generate random points and lines\n",
        "points_x = np.random.rand(num_points)\n",
        "slope_random_line = np.random.rand()\n",
        "intercept_random_line = np.random.rand()\n",
        "\n",
        "points_y = slope_random_line*points_x + intercept_random_line + np.random.normal(0, 1, num_points)*0.15\n",
        "\n",
        "# Function to calculate distance from point (x, y) to the line y = mx + b\n",
        "def distance_to_line(x, y, m, b):\n",
        "    return abs(y - m * x - b) / np.sqrt(1 + m**2)\n",
        "\n",
        "# Calculate distances from each point to the random line\n",
        "distances = distance_to_line(points_x, points_y, slope_random_line, intercept_random_line)\n",
        "\n",
        "# Create the scatter plot\n",
        "plt.figure(figsize=(10, 6))\n",
        "\n",
        "# Plot the random line\n",
        "plt.plot(np.sort(points_x), slope_random_line * np.sort(points_x) + intercept_random_line, c='blue', label='Model')\n",
        "\n",
        "# Plot the points\n",
        "plt.scatter(points_x, points_y, c='red', label='Data', marker='o', s=50)\n",
        "\n",
        "# Plot lines from each point to the random line (in different colors)\n",
        "for i in range(num_points):\n",
        "    plt.plot([points_x[i], points_x[i]], [points_y[i], slope_random_line * points_x[i] + intercept_random_line],\n",
        "             c='green', alpha=0.7)\n",
        "\n",
        "plt.xlabel('X')\n",
        "plt.ylabel('Y')\n",
        "plt.title(\"Errors for each data point\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "V4yTGcGV7E3L",
        "outputId": "0bf7b9c3-6a14-4b17-ccf1-e5c0ef441ccf"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Consider the figure above with data points in red. If the blue line is our model, then vertical green lines represent the errors we make on each data point. The loss function tries to capture the total error we make for every data point. One loss function we can use in this case is the <font color='red'>mean square error</font> between the predicted and the true values. This is equivalent to summing up all the distances in green. This can be written mathematically as follows:\n",
        "$ \\mathcal{L}(\\mathbb{θ}) \\, = \\, \\frac{1}{m}∑_{i}({y_i - \\hat{y}_i})^2,$\n",
        "where $\\mathbb{θ} = [\\mathbf{w}, b]$,  $\\mathcal{L}$ denotes the loss function, $\\hat{y}$ represents the predicited value by the model and $m$ is the total number of datapoints.\n",
        "\n",
        "Inserting the formula for a linear model, we obtain the following equation:\n",
        "\n",
        "$\\mathcal{L}(\\mathbb{θ}) \\, = \\, \\frac{1}{m}∑_{i}(y_i - \\mathbf{w}^T\\mathbf{x}_i - b)^2. $\n",
        "\n",
        "<font color='red'>Note: they are different loss functions we could use in this case. You can see some other common loss functions [here](https://www.geeksforgeeks.org/ml-common-loss-functions/).</font>"
      ],
      "metadata": {
        "id": "KtiTFJUT08Rl"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def loss_fn(params: Dict[str, jnp.array], X: jnp.array, y: jnp.array):\n",
        "  # complete this code\n",
        "\n",
        "  pred = linear_model(params, X)\n",
        "\n",
        "  loss = jnp.mean((pred-y)**2)\n",
        "\n",
        "  return loss"
      ],
      "metadata": {
        "id": "CzhA2_Gc8Q8P"
      },
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "🎯 **What is optimization?**\n",
        "\n",
        "Optimization as the name entails is the process of finding the optimal parameters of the model, i.e. the set of parameters that gives the minimum loss possible. Mathematically this is represented as follows\n",
        "\n",
        "$$\\hat{\\theta} \\,= \\, \\underset{\\mathbf{\\theta}}{\\operatorname{argmin}} \\frac{1}{m}∑_{i}(y_i - \\mathbf{w}^T\\mathbf{x}_i - b)^2.$$"
      ],
      "metadata": {
        "id": "B8YkwEx-3tIy"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "<font color='red'> How do we optimise </font>: The figure below is an example plot of the loss at different values of $\\mathbf{w}$ and $b$ for a straight line. The minimum value is indicated with the star. Our goal in optimization is to identify this point.   "
      ],
      "metadata": {
        "id": "V42gum1k3y91"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Helper code (to visualise loss landscape)\n",
        "# Define the loss function (Mean Squared Error)\n",
        "from matplotlib.colors import LogNorm\n",
        "\n",
        "def loss_function(y_true, y_pred):\n",
        "    return np.mean((y_true - y_pred) ** 2)\n",
        "\n",
        "# Create a grid of weight (slope) and bias (intercept) values\n",
        "weight_values = np.linspace(-10, 10, 200)\n",
        "bias_values = np.linspace(-10, 10, 200)\n",
        "weight_grid, bias_grid = np.meshgrid(weight_values, bias_values)\n",
        "\n",
        "# Generate random data points for demonstration\n",
        "np.random.seed(0)\n",
        "x = np.linspace(0, 20, 200)\n",
        "y_true = 3 * x + 5 + 0.1 * np.random.normal(0, 1, 200)\n",
        "y_min = 3*x + 5\n",
        "minima = np.array([5, 3])\n",
        "loss_min = loss_function(y_true, y_min)\n",
        "\n",
        "# Compute the loss for each combination of weight and bias values\n",
        "loss_grid = np.zeros_like(weight_grid)\n",
        "for i in range(len(weight_values)):\n",
        "    for j in range(len(bias_values)):\n",
        "        y_pred = weight_values[i] * x + bias_values[j]\n",
        "        loss_grid[i, j] = loss_function(y_true, y_pred)\n",
        "\n",
        "fig = plt.figure(figsize=(8, 5))\n",
        "ax = plt.axes(projection='3d', elev=50, azim=-50)\n",
        "\n",
        "surf = ax.plot_surface(weight_grid, bias_grid, loss_grid, norm=LogNorm(), rstride=1, cstride=1,\n",
        "                edgecolor='none', alpha=.8, cmap=plt.cm.jet)\n",
        "ax.plot(*minima, loss_min, 'r*', markersize=10)\n",
        "\n",
        "ax.set_xlabel('$w$')\n",
        "ax.set_ylabel('$b$')\n",
        "# Remove z-axis ticks and labels\n",
        "ax.set_zticks([])\n",
        "ax.set_zticklabels([])\n",
        "\n",
        "# Add color bar for reference\n",
        "cbar = plt.colorbar(surf, shrink=0.5, aspect=10)\n",
        "cbar.ax.set_ylabel('Loss')\n",
        "\n",
        "# ax.set_xlim((xmin, xmax))\n",
        "# ax.set_ylim((ymin, ymax))\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 448
        },
        "id": "Iod_K6w49rtm",
        "outputId": "1403763e-81e9-4336-bb8e-a85c03183d82"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x500 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "A **brute force** approach will be to compute the loss function for a large range of possible parameter values and select the parameters with the minimum loss value. While such an approach can work for simple models with 1 or 2 parameters, this is a very tedious approach and the number of possible values to evaluate for large models makes such an approach impractical."
      ],
      "metadata": {
        "id": "jT8YkVu4352p"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Gradient based optimization**\n",
        "\n",
        "The right approach is to use calculus. The derivative of a function is known to be 0 at every turning point (maximum and minimum turning points). Hence to find $\\theta$, which minimises the loss, we need to solve the equation\n",
        "$$\\frac{\\partial \\mathcal{L}}{\\partial \\theta} \\,=\\, 0.$$\n",
        "\n",
        "**Exercise 2:** [OPTIONAL] Can you work out the following expressions for the derivatives of the loss function?\n",
        "\n",
        "$$\\frac{∂ \\mathcal{L}}{\\partial \\mathbf{w}} = \\frac{2}{m}∑_{i}\\mathbf{x}_i(\\mathbf{w}^T\\mathbf{x}_i + b - y_i),$$\n",
        "\n",
        "$$\\frac{∂ \\mathcal{L}}{\\partial b} = \\frac{2}{m}∑_{i}(\\mathbf{w}^T\\mathbf{x}_i + b - y_i).$$\n",
        "\n",
        "Solution here in the [Appendix](#scrollTo=kh_8f4gKyufu)."
      ],
      "metadata": {
        "id": "zFXzcFku37yS"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Fortunately, we do not need to compute these analytical expressions or implement them ourselves from scratch. Machine learning frameworks like Jax, [Pytorch](https://pytorch.org/tutorials/) and [Tensorflow](https://www.tensorflow.org/) have highly optimised tools that will compute these for us. In the case of Jax, we can use the function `jax.grad` to compute the derivative of a function with respect to its parameters."
      ],
      "metadata": {
        "id": "QkSDXhqu4JUK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Computing derivatives with jax.grad\n",
        "# Computing derviatives with jax\n",
        "\n",
        "def quadratic_fn(x):\n",
        "  return x**2\n",
        "\n",
        "\n",
        "# Compute the derivative of quadratic_fn when x = 1\n",
        "grad_fx =  jax.grad(quadratic_fn)(1.0)\n",
        "assert grad_fx == 2.0\n",
        "print(f\"Gradient of the function x**2 at x = 1 is {grad_fx} as expected.\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "oD6aBrTH-Qa3",
        "outputId": "29f1c99b-4244-45d5-a0e8-19899a776bc1"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Gradient of the function x**2 at x = 1 is 2.0 as expected.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Importantly Jax computes the derivative in the same way even if our parameters are passed in a different data type, such as a dictionary. For example, we can compute the gradient of our loss function above as follows."
      ],
      "metadata": {
        "id": "K8CV6KG7yuXM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Compute derivatives of the loss_fn with respect to params\n",
        "\n",
        "grads = jax.grad(loss_fn)(params, X, data)\n",
        "print(f\"gradients: {grads}\")"
      ],
      "metadata": {
        "id": "KgDq6AbR_BZE",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7cf7b573-c802-480f-a1c8-fcb20cbcb054"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "gradients: {'b': Array([4.6627536], dtype=float32), 'w': Array([2.091345 , 1.9300239, 2.740008 , 2.705566 , 1.4073546, 1.8641709,\n",
            "       1.5042092, 3.331741 , 2.4481251, 2.5431075], dtype=float32)}\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "data"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "N6gymC-vyvP7",
        "outputId": "5c5336e3-75c3-418e-f52a-511ff0083239"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Array([0.57450044, 0.09968603, 0.39316022, 0.8941783 , 0.59656656],      dtype=float32)"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "X"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9bheAF-Zzdp9",
        "outputId": "3ecb2704-775b-4a21-c68c-0946c1609e7e"
      },
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Array([[0.42271078, 0.10988367, 0.17936432, 0.557727  , 0.5007241 ,\n",
              "        0.22675169, 0.2110933 , 0.54872036, 0.4301901 , 0.8549892 ],\n",
              "       [0.40325677, 0.21874166, 0.65812516, 0.7035849 , 0.08702171,\n",
              "        0.0146271 , 0.39282465, 0.9139857 , 0.6217127 , 0.63578844],\n",
              "       [0.35615385, 0.60827816, 0.8881558 , 0.3827777 , 0.03948212,\n",
              "        0.94029844, 0.2988342 , 0.5517082 , 0.09887683, 0.08440983],\n",
              "       [0.7204071 , 0.67677045, 0.51662374, 0.47618616, 0.62078416,\n",
              "        0.5653542 , 0.4790753 , 0.8785478 , 0.9574187 , 0.6435374 ],\n",
              "       [0.17340672, 0.45538437, 0.7655853 , 0.8188056 , 0.16407394,\n",
              "        0.37448525, 0.07771182, 0.45887375, 0.1897943 , 0.34695685]],      dtype=float32)"
            ]
          },
          "metadata": {},
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Another similar function in Jax is `jax.value_and_grad` which returns both the value of the function and the gradient."
      ],
      "metadata": {
        "id": "mthj51_i0N63"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Compute derivatives of the loss_fn with respect to params\n",
        "\n",
        "loss, grads = jax.value_and_grad(loss_fn)(params, X, data)\n",
        "print(f\"loss: {loss}\")\n",
        "print(f\"gradients: {grads}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "obacy5pTzr37",
        "outputId": "e170905b-dc53-44ca-900d-a21c91ba0903"
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "loss: 5.745656490325928\n",
            "gradients: {'b': Array([4.6627536], dtype=float32), 'w': Array([2.091345 , 1.9300239, 2.740008 , 2.705566 , 1.4073546, 1.8641709,\n",
            "       1.5042092, 3.331741 , 2.4481251, 2.5431075], dtype=float32)}\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Training the model using Jax"
      ],
      "metadata": {
        "id": "wFCJEQ-f0U7i"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Gradient descent:**\n",
        "\n",
        "Now we have all the basic pieces required to train a machine learning model. Recall the goal is to find the parameters that will make the loss as small as possible. This can be achieved by following the gradient in the direction that reduces the loss. One popular algorithm for this in machine learning is the use of <font color='red'>gradient descent algorithm</font>. The algorithm works as follows:\n",
        "\n",
        "1.   Initialise the parameters with random values.\n",
        "2.   Loop for a number of iterations and during each iteration update the parameters using the following formula.\n",
        "\n",
        "$$ \\mathbf{\\theta} = \\mathbf{\\theta} - η\\frac{∂\\mathcal{L}}{∂\\theta},$$\n",
        "$\\eta$ is called the learning rate. It is a hyperparameter of the gradient descent algorithm meaning we have to choose it beforehand.\n",
        "\n",
        "Intuitively, if the current parameters are the optimal parameters then the gradients, $\\frac{\\partial \\mathcal{L}}{\\partial \\theta}$ will be zero and the parameters will stop changing. Hence one stopping criterion which we can use during training is checking when the parameters stop changing also known as convergence. When a single data point is used at every iteration to compute the gradient the algorithm is called <font color='red'>stochastic gradient descent</font>. When the entire training data is used the algorithm is called <font color='red'>batch gradient descent</font>. Traditionally the best approach is to use small chunks of the data at each step. This approach is called the <font color='red'>mini-batch gradient descent</font>. Most often in practice, people use the term stochastic gradient descent but they actually mean mini-batch gradient descent.\n",
        "\n",
        "Thus during training, we will loop through the datasets for each iteration. When we loop through the entire dataset we called that an epoch. Hence another familiar hyperparameter is the epoch.\n",
        "\n"
      ],
      "metadata": {
        "id": "BeawjM2q0X7h"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Code demonstration: Batch gradient descent implementation\n",
        "def batch_gradient_descent(loss_fn, params, training_data, val_data, learning_rate=0.01, num_epochs=20, batch_size=10):\n",
        "  \"\"\"Batch gradient descent basic jax implementation.\n",
        "\n",
        "  Args:\n",
        "    loss_fn\n",
        "      the loss function for our model.\n",
        "    params:\n",
        "      the initial parameters of the model.\n",
        "    training_data\n",
        "      a tuple with the features and targets for training.\n",
        "    val_data\n",
        "      a tuple with the features and targets for validation.\n",
        "    learning_rate\n",
        "      learning rate\n",
        "    num_epochs\n",
        "      number of epochs\n",
        "    batch_size:\n",
        "      size of every mini batch\n",
        "  \"\"\"\n",
        "\n",
        "  X_train, y_train = training_data\n",
        "  X_val, y_val = val_data\n",
        "\n",
        "  num_samples, num_features = X_train.shape\n",
        "\n",
        "  # Create empty list to store the training and validation loss.\n",
        "  loss_train = [] # training loss\n",
        "  loss_val  = [] # valisation loss\n",
        "\n",
        "  # Define a function that computes loss and gradients\n",
        "  loss_and_grad = jax.value_and_grad(loss_fn)\n",
        "\n",
        "  n_iter = 0 # number iterations\n",
        "  for epoch in range(num_epochs):\n",
        "    # Shuffle the data before every epoch\n",
        "    shuffled_indices = np.arange(num_samples)\n",
        "    np.random.shuffle(shuffled_indices)\n",
        "\n",
        "    for start_idx in range(0, num_samples, batch_size):\n",
        "      end_idx = start_idx + batch_size\n",
        "      if end_idx > num_samples:\n",
        "        end_idx = num_samples\n",
        "\n",
        "      batch_indices = shuffled_indices[start_idx:end_idx]\n",
        "      X_batch = X_train[batch_indices]\n",
        "      y_batch = y_train[batch_indices]\n",
        "\n",
        "      # Compute loss and gradients using value_and_grad\n",
        "      loss, grads = loss_and_grad(params, X_batch, y_batch)\n",
        "      loss_train.append(loss)\n",
        "\n",
        "      # Compute the validation loss\n",
        "      loss_v = loss_fn(params, X_val, y_val)\n",
        "      loss_val.append(loss_v)\n",
        "\n",
        "      # Update the parameters\n",
        "      params = jax.tree_map(lambda p, g: p -learning_rate*g, params, grads)\n",
        "\n",
        "      # Update the iter count\n",
        "      n_iter += 1\n",
        "\n",
        "\n",
        "  # Plot training and validation loss\n",
        "  iters = range(1, n_iter+1)\n",
        "  plt.plot(iters, loss_train, label='Training Loss')\n",
        "  plt.plot(iters, loss_val, label='Validation Loss')\n",
        "  plt.xlabel('Iteration')\n",
        "  plt.ylabel('Loss')\n",
        "  plt.title('Training and Validation Loss')\n",
        "  plt.legend()\n",
        "\n",
        "  # Display the plot\n",
        "  plt.show()\n",
        "\n",
        "  return params"
      ],
      "metadata": {
        "id": "O4X8izr20Gdc"
      },
      "execution_count": 25,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Let's create some dummy data to test the code\n",
        "def create_dummy_data_linear_regression():\n",
        "  \"\"\"We will generate some random data using our linear function above to test the gradient decent implementation\"\"\"\n",
        "\n",
        "  num_samples = 200\n",
        "  num_features = 1  # Modify this to have more features\n",
        "\n",
        "  # Generate random X values in the range [0, 10] for each feature\n",
        "  key = jax.random.PRNGKey(0)\n",
        "  X = jax.random.uniform(key, (num_samples, num_features), minval=0, maxval=10)\n",
        "\n",
        "  # Generate y values based on a linear relationship with some noise\n",
        "  w = jnp.array([3.0]*num_features)  # True coefficients for each feature\n",
        "  b = jnp.array([5.0])\n",
        "\n",
        "  params = dict(w=w, b=b)\n",
        "  y = linear_model(params, X)\n",
        "\n",
        "  # Add some noise\n",
        "  noise = jax.random.normal(key, shape=(num_samples,))*0.30\n",
        "  y = y + noise\n",
        "\n",
        "  # Step 2: Split the data into training and validation sets\n",
        "  train_fraction = 0.8\n",
        "  num_train_samples = int(train_fraction * num_samples)\n",
        "\n",
        "  # Shuffle the indices to randomly split the data\n",
        "  key, subkey = jax.random.split(key)\n",
        "  shuffled_indices = jax.random.permutation(subkey, jnp.arange(num_samples))\n",
        "\n",
        "  # Split the indices into training and validation sets\n",
        "  train_indices = shuffled_indices[:num_train_samples]\n",
        "  val_indices = shuffled_indices[num_train_samples:]\n",
        "\n",
        "  # Get the corresponding data points for training and validation sets\n",
        "  X_train, y_train = X[train_indices], y[train_indices]\n",
        "  X_val, y_val = X[val_indices], y[val_indices]\n",
        "\n",
        "  train_data = (X_train, y_train)\n",
        "  val_data = (X_val, y_val)\n",
        "\n",
        "  # create some random initial params\n",
        "  w_init = jax.random.normal(key, shape=(num_features,))\n",
        "  b_init = 0.0\n",
        "  initial_params = dict(w=w_init, b=b_init)\n",
        "\n",
        "  return train_data, val_data, initial_params\n",
        "\n",
        "\n",
        "def plot_linear_fit(params, X, y):\n",
        "  \"\"\"Overlay the data and fitted model\"\"\"\n",
        "\n",
        "  y_pred = linear_model(params, X).squeeze()\n",
        "  xval = X[:,0]\n",
        "\n",
        "  plt.figure(figsize=(8, 6))\n",
        "  plt.scatter(xval, y, label='Data', color='blue')\n",
        "  plt.plot(xval, y_pred, label='Fit', color='red')\n",
        "  plt.xlabel('X')\n",
        "  plt.ylabel('Y')\n",
        "  plt.legend()\n",
        "  plt.title('Scatter Points and Fitted Curve')\n",
        "  plt.show()"
      ],
      "metadata": {
        "id": "E16RqTIB4eF5"
      },
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "train_data, val_data, initial_params = create_dummy_data_linear_regression()"
      ],
      "metadata": {
        "id": "iRMZJSw-4vhg"
      },
      "execution_count": 27,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "params = batch_gradient_descent(loss_fn, initial_params, train_data, val_data, learning_rate=0.01, num_epochs=2, batch_size=10)\n",
        "\n",
        "# plot the results on validation data\n",
        "Xval, yval = val_data\n",
        "plot_linear_fit(params, Xval, yval)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "CSHAGeK8473S",
        "outputId": "e5d5611b-adad-408a-e009-f623ff7e683a"
      },
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Our model seems to be **underfitting** that data because the fitted line is going through very few of the points.\n",
        "\n",
        "**Exercise:** Discuss with your neighbour how we can improve our model.\n",
        "\n",
        "**Code task:** Modify the learning rate, batch_size and the number of epochs and observe their effects on the results.\n",
        "\n",
        "**Tips:**\n",
        "- In practice, people usually choose learning rates in the range of 0.01 and 1e-5.\n",
        "- Small batch sizes can introduce too much noise in the gradients and this may affect the speed of convergence.\n",
        "- On the other hand, large batch sizes may take longer to converge because parameters are not updated very frequently.\n",
        "- Not that using a very high number of epochs will make the training take long because we did not include any stopping criterion."
      ],
      "metadata": {
        "id": "nu1_VrKj56Hq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Your code here\n",
        "learning_rate = 3e-4 #@param {type:\"slider\", min:1e-5, max:1e-2, step:1e-4}\n",
        "batch_size = 71 #@param {type:\"slider\", min:1, max:5000, step:10}\n",
        "num_epochs = 100 #@param {type:\"slider\", min:2, max:500, step:20}\n",
        "\n",
        "params = batch_gradient_descent(loss_fn, initial_params, train_data, val_data, learning_rate=learning_rate, num_epochs=num_epochs, batch_size=batch_size)\n",
        "\n",
        "# plot the results on validation data\n",
        "Xval, yval = val_data\n",
        "plot_linear_fit(params, Xval, yval)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "cDpSWAdZ5Dip",
        "outputId": "d58cced2-b8cc-499d-a8cd-60c238659ff5"
      },
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "2.2 Non linear regression and neural networks"
      ],
      "metadata": {
        "id": "9ezjBwai6WP8"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Helper code to plot non-linear data\n",
        "def plot_nonlinear_data():\n",
        "\n",
        "  x = np.linspace(-5, 5, 100)\n",
        "  y = np.cos(x)*x + x**2 + np.exp(-x/7)*3 + 0.3*x*np.sin(x)**4\n",
        "\n",
        "  plt.scatter(x, y)\n",
        "  plt.title(\"Example of non linear data\")\n",
        "  plt.show\n",
        "\n",
        "plot_nonlinear_data()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 452
        },
        "id": "RggRZE276WuD",
        "outputId": "e93773bd-7fd0-4505-fea1-1239ab5ee1f9"
      },
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Linear regression is a simple and powerful data inference method; however, it has limitations in capturing non-linear relationships. To model such complexities, we require more powerful models. For example, no single line will perfectly fit the data in the above figure. Nonlinear models, such as polynomials, exponentials, and trigonometric functions, offer solutions to this problem.\n",
        "\n",
        "Before the explosion of deep learning techniques, fitting pre-defined functions to datasets was the go-to machine learning approach. Examples of classical algorithms using this approach include <font color='red'>support vector machines, and naive Bayes</font>, among others.\n",
        "\n",
        "In this section, we will introduce <font color='red'>neural networks</font> which are at the heart of deep learning techniques and recent successes of machine learning."
      ],
      "metadata": {
        "id": "jRtU5KE06uAP"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Model representation\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "JVaxiQYr6yka"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "<center>\n",
        "<img src=\"https://www.tibco.com/sites/tibco/files/media_entity/2021-05/neutral-network-diagram.svg\" width=\"80%\" />\n",
        "</center>\n",
        "\n",
        "      Image of a neural network with 3 hidden layers. Credit: https://www.tibco.com/reference-center/what-is-a-neural-network\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "ite6agWV61hV"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Neural networks are a powerful class of machine learning models inspired by how the human brain functions. Unlike linear regression, which applies a single transformation to the data, neural networks process input data through a series of transformations before reaching the final predictive layer. The term <font color='red'>Deep Learning</font> arises from the numerous transformations applied to the input data.\n",
        "\n",
        "In the image above, the circles represent nodes, and the links connecting them represent the model's parameters."
      ],
      "metadata": {
        "id": "IGYffL4j677o"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Activation functions\n",
        "\n",
        "Activation functions are essential in neural networks. The input to every node is a linear function of all the nodes from the previous layer. Without applying an activation function, also called a non-linearity, the entire neural network, no matter how many layers it has, reduces to a simple linear model. Thus, activation functions are used to break the linearity and ensure that we build a complex non-linear function.\n",
        "\n",
        "The equation for node \\(i\\) in layer \\(j\\) of a neural network can be expressed as follows:\n",
        "\n",
        "$$ \\text{Output}_{ij} = \\text{Activation Function} \\left( \\sum_{k=1}^{n} \\text{Weight}_{ijk} \\times \\text{Output}_{(j-1)k} + \\text{Bias}_{ij} \\right)$$\n",
        "\n",
        "Where:\n",
        "- $\\text{Output}_{ij}$ is the output of node $i$ in layer $j$.\n",
        "- $\\text{Weight}_{ijk}$ is the weight connecting node $i$ in layer $j$ to node $k$ in layer $j-1$.\n",
        "- $\\text{Output}_{(j-1)k}$ is the output of node $k$ in layer $j-1$.\n",
        "- $\\text{Bias}_{ij}$ is the bias term for node $i$ in layer $j$.\n",
        "- $\\text{Activation Function}$ is the chosen activation function that introduces nonlinearity to the output of the neuron.\n"
      ],
      "metadata": {
        "id": "QgJmb4687Bcy"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Some popular activation functions include:\n",
        "\n",
        "- $\\text{ReLU}(x) \\, = \\, \\text{max}(0, x)$\n",
        "\n",
        "    The Rectified Linear Unit (ReLU) is the most popular activation function. It maps it input to range $[0, ∞]$ mapping all negativie values to 0. Both the function and its derivitate are monotonic. However this activation function has the problem it turns all negative inputs to 0 and their descreases the ability of the model to fit data properly.\n",
        "\n",
        "- $\\text{Sigmoid}(x) \\, =\\, \\frac{1}{1+e^{-x}}$\n",
        "\n",
        "    The sigmoid activation maps input the range $[0, 1]$. This is ideal for predicting probabilities. The function is differentiable and monotonic but its derivative is not monotonic. Because its derivative is not monotonic it is not ideal to use this activation in hidden layers as it blocks information transfer between layers. Hence most often activation is applied only to output layers.\n",
        "\n",
        "- $\\text{tanh}(x)\\, = \\, \\frac{e^x - x^{-x}}{e^x + e^{-x}},$\n",
        "  \n",
        "     The $tanh$ activation is similar to the sigmoid activation but it maps inputs to range $[-1, 1]$. This wider range allows for a much better spread when predicting probabilities. Similarly to the sigmoid activation, the $tanh$ is most often applied to the output layers of neural networks.\n",
        "\n",
        "\n",
        "\n",
        "Let's implement the popular [ReLU](https://arxiv.org/https://arxiv.org/abs/1803.08375abs/1803.08375) activation function."
      ],
      "metadata": {
        "id": "jwiNmCO57HSL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Implementation of relu using simple python.\n",
        "\n",
        "def relu(x):\n",
        "  if x > 0 :\n",
        "    return x\n",
        "  else:\n",
        "    return 0\n",
        "\n",
        "def plot_activation(act_fn, label=\"act_fn\"):\n",
        "    max_int = 5\n",
        "    # Generete 100 evenly spaced points from -max_int to max_int\n",
        "    x = np.linspace(-max_int, max_int, 1000)\n",
        "    y = np.array([act_fn(xi) for xi in x])\n",
        "    plt.plot(x, y, label=label)\n",
        "    plt.legend(loc=\"upper left\")\n",
        "    plt.xticks(np.arange(min(x), max(x) + 1, 1))\n",
        "    plt.show()\n",
        "\n",
        "plot_activation(relu, label='ReLU')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "Cue9Ht2B6akR",
        "outputId": "91edfc13-8651-49b7-873c-6143ac0471f6"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Code Task:** Implement and plot another activation function of your choice."
      ],
      "metadata": {
        "id": "vB8dhBBV7XaS"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Your code here\n",
        "def act_fn(x):\n",
        "    # type your code here\n",
        "\n",
        "    y = ...#\n",
        "    return y\n",
        "\n",
        "# Call the plotting function\n",
        "plot_activation(act_fn, label=....) # update this"
      ],
      "metadata": {
        "id": "zZPSYvUh6uXC"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Building a simple neural network model with Jax\n",
        "\n",
        "Fortunately, they are different high-level modules that can be used to develop deep neural networks and we don't have to implement everything from scratch. For example, for Jax based model we can use [haiku]( https://dm-haiku.readthedocs.io/en/latest/) and [flax](https://flax.readthedocs.io/en/latest/getting_started.html). Moreover, advanced optimisation techniques can be implemented using [optax](https://optax.readthedocs.io/en/latest/). In this section, we will use flax to implement a simple 4 layer neural network."
      ],
      "metadata": {
        "id": "8fl7E19b7iMi"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Code demonstration: building a simple neural network with flax\n",
        "# Code for a 4-layer neural network using haiku.\n",
        "# Here assume all the hidden layers have the same number of nodes.\n",
        "# We will use the same activation relu for all the layers except the last layer.\n",
        "\n",
        "class Network(nn.Module):\n",
        "  hidden_size: int\n",
        "  output_size: int\n",
        "\n",
        "  @nn.compact\n",
        "  def __call__(self, x):\n",
        "    # First layer with ReLU activation\n",
        "    x = nn.Dense(self.hidden_size)(x)\n",
        "    x = jax.nn.relu(x)\n",
        "\n",
        "    # Second layer\n",
        "    x = nn.Dense(self.hidden_size)(x)\n",
        "    x = jax.nn.relu(x)\n",
        "\n",
        "    # Third (output) layer with no activation applied\n",
        "    x = nn.Dense(self.output_size)(x)\n",
        "\n",
        "    return x"
      ],
      "metadata": {
        "id": "fPFVwoLM7aid"
      },
      "execution_count": 36,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "The cell above is a basic example of how we can define a neural network using flax. Each linear transformation is implemented using the `nn.Dense` function, and we use `jax.nn.relu` to apply non-linearities to the output of each layer."
      ],
      "metadata": {
        "id": "_DZX7C6a8QAm"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Code demonstration: intialising the model\n",
        "seed = 32\n",
        "input_size = 4\n",
        "hidden_size = 5\n",
        "output_size = 1\n",
        "\n",
        "# Calling the build_neural_network function and applying the required transformations\n",
        "model = Network(hidden_size, output_size)\n",
        "\n",
        "key = jax.random.PRNGKey(seed)\n",
        "dummy = jnp.zeros((1, input_size), dtype=float)\n",
        "initial_params = model.init(key, dummy)\n",
        "\n",
        "# Let's use the CLU: https://github.com/google/CommonLoopUtils to examine the shape of the parameters\n",
        "print(parameter_overview.get_parameter_overview(initial_params, include_stats=False))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2shldtpu7oCv",
        "outputId": "931b4cc6-129b-4e0c-e85c-485f20c273bf"
      },
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "+-----------------------+--------+------+\n",
            "| Name                  | Shape  | Size |\n",
            "+-----------------------+--------+------+\n",
            "| params/Dense_0/bias   | (5,)   | 5    |\n",
            "| params/Dense_0/kernel | (4, 5) | 20   |\n",
            "| params/Dense_1/bias   | (5,)   | 5    |\n",
            "| params/Dense_1/kernel | (5, 5) | 25   |\n",
            "| params/Dense_2/bias   | (1,)   | 1    |\n",
            "| params/Dense_2/kernel | (5, 1) | 5    |\n",
            "+-----------------------+--------+------+\n",
            "Total: 61\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Exercise:** Do you understand the shape of the different parameters?"
      ],
      "metadata": {
        "id": "47-5RQFC8cly"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The above cell demonstrates how to create an instance of the model and get initial parameters. After creating an instance of the model using the `Network` class we call the `init` function with a `jax.random.PRNGKey` and some dummy inputs from which the shape of the parameters will be inferred.  "
      ],
      "metadata": {
        "id": "f2MvngMj8e9r"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "To apply the model to some data we need to call `model.apply` with the current parameters and the input data."
      ],
      "metadata": {
        "id": "IyVz3OFc8h0v"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "z = model.apply(initial_params, dummy)\n",
        "print(f\"Model ouput shape: {z.shape}, Input shape: {dummy.shape}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ECxQfw5p8T-v",
        "outputId": "c0fb1e4f-4619-4c2b-df80-5c54df9dd99c"
      },
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model ouput shape: (1, 1), Input shape: (1, 4)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Classification**\n",
        "Now that we are familiar with the fundamentals of model fitting and we know how to build neural networks, we will now focus on our original objective and build our mnist digit classifier."
      ],
      "metadata": {
        "id": "FVZ5nbvO8oLe"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### 3.1 Logistic regression\n",
        "\n",
        "Linear regression aims to find a function $f$ that maps our **inputs $x$**, where $x \\in \\mathbb{R}^d$ to the corresponding **output/target - $y$**, where $y \\in \\mathbb{R}^n$ (output values are continous). Contrary to regression, the **output/target -$y$** can only take on certain values in logistic regression. When the **target** can only take on one of two values, the algorithm is called **Binary Classification**. When we have more than two categories, it is called a **Multi-class Classification**.\n",
        "\n",
        "Hence the aim of Logistic regression (in the Binary classification case) is to map **inputs $x$**, where $x \\in \\mathbb{R}^d$ to $y$, where $y \\in \\{0,1\\}$.\n",
        "\n",
        "For example, if we are building an image classifier for cats and dogs, 1 may be used to represent the target values for cats and 0 for dogs."
      ],
      "metadata": {
        "id": "B7XK0nt49vOz"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Logits and sigmoid activation function\n",
        "The target values for logistic regression problems are discrete. It is not straightforward how to define a model function that outputs discrete values. Hence we design the model to output probabilities instead. Recall that probabilities only lie in the range of values $[0,1]$, thus we need a function that maps the output to probabilities. As mentioned earlier a good activation function we can use in this case is the **Sigmoid** activation function.\n",
        "<br>\n",
        "<center>\n",
        " $$\\sigma(x) = \\frac{1}{1+e^{-x}}$$\n",
        "\n",
        " ![sigmoid.png](data:image/png;base64,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)\n",
        "</center>\n",
        "<br>\n",
        "<br>\n"
      ],
      "metadata": {
        "id": "ES6G_b0e9zco"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Cross entropy loss function**\n",
        "\n",
        "In binary classification, we can only have one of two values for the targets. Using the mean square error as before generally doesn't perform well in logistic regression. The most common loss function that works best for logistic regression problems is the <font color='red'>cross entropy loss function</font> defined as follows:\n",
        "<br>\n",
        "<center>\n",
        " $$ -y_i \\log(p_i) - (1-y_i) \\log (1-p_i),$$\n",
        "</center>\n",
        "where $p_i = \\sigma (z)$ with $z$ being the output of our model function.\n",
        "<br>\n",
        "\n",
        "**Code task**:\n",
        "1. Implement the sigmoid activation function.\n",
        "2. Implement the cross entropy loss function.\n"
      ],
      "metadata": {
        "id": "7jVIph_x-DMZ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def sigmoid(x):\n",
        "    \"\"\"sigmoid function 1/1+e^-x\"\"\"\n",
        "\n",
        "    prob = ... # update me\n",
        "\n",
        "    return prob"
      ],
      "metadata": {
        "id": "LLi1Ft7_8kvT"
      },
      "execution_count": 39,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Run me to test your code\n",
        "def test_sigmoid_fn():\n",
        "  x  = np.array([0.7, 0.3, 0.8, 0.2])\n",
        "  assert jnp.allclose(sigmoid(x), jax.nn.sigmoid(x)), \"Test failed!\"\n",
        "  print(\"Nice! Your answer looks correct!\")\n",
        "\n",
        "  return"
      ],
      "metadata": {
        "id": "tb8_2tmr-Jnr"
      },
      "execution_count": 40,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# @title sigmoid solution (Try not to peek until you've given it a good try!')\n",
        "def sigmoid(x):\n",
        "  prob = 1/(1+jnp.exp(-x))\n",
        "\n",
        "  return prob"
      ],
      "metadata": {
        "id": "yyPAXqdo-MBg"
      },
      "execution_count": 41,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def cross_entropy_loss(predictions, targets):\n",
        "    # you need to make sure we never have log of 0\n",
        "\n",
        "    # use sigmoid to compute the probs from the predicitions\n",
        "    probs = ... # update me\n",
        "\n",
        "    # your code here\n",
        "    loss = ... # update me\n",
        "\n",
        "    return loss"
      ],
      "metadata": {
        "id": "EkLcakz9-ZKw"
      },
      "execution_count": 42,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "  # @title Run me to test your code\n",
        "  def test_cross_entropy_loss():\n",
        "    predictions = np.array([0.7, 0.3, 0.8, 0.2])\n",
        "    targets = np.array([1, 0, 1, 0])\n",
        "\n",
        "    # Expected cross-entropy loss for the test data\n",
        "    expected_loss = 0.60669523\n",
        "\n",
        "    # Calculate the cross-entropy loss using the implemented function\n",
        "    computed_loss = cross_entropy_loss(predictions, targets)\n",
        "\n",
        "    assert jnp.isclose(computed_loss, expected_loss), \"Test failed!\"\n",
        "\n",
        "    # If the assert statement does not raise an exception, the test is passed.\n",
        "    print(\"Nice! Your anwser looks correct\")\n",
        "\n",
        "    return\n",
        "\n",
        "  test_cross_entropy_loss()"
      ],
      "metadata": {
        "id": "giKI_Y2n-cxH"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Cross entropy loss solution (Try not to peek until you've given it a good try!')\n",
        "def cross_entropy_loss(preds, targets):\n",
        "    eps = 1e-15\n",
        "    probs = sigmoid(preds)\n",
        "\n",
        "    loss = -targets*jnp.log(probs+eps) - (1-targets)*jnp.log(1-probs+eps)\n",
        "\n",
        "    return jnp.mean(loss)"
      ],
      "metadata": {
        "id": "KJqSeqE2-nhG"
      },
      "execution_count": 44,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Extending to Multi-class classification"
      ],
      "metadata": {
        "id": "VTZC_SPR-9Zv"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In multi-class classification, the machine learning model is designed to handle more than two classes, where each class represents a different category or label. For example, in the case of a single-digit classifier, there are 10 classes, each corresponding to a digit from 0 to 9.\n",
        "\n",
        "The model's output is typically a probability distribution over all possible classes, with each class having an associated probability. The dimensions of the output vector match the number of classes, so for a classifier with 3 different classes, the output vector will have a dimension of 3.\n",
        "\n",
        "To make a prediction, the model selects the class with the highest probability as the predicted class for the input data point."
      ],
      "metadata": {
        "id": "510YZz9a-_IF"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**One-hot encoding**\n",
        "\n",
        "One-hot encoding is a common technique used to represent categorical variables, such as class labels, as binary vectors. In the case of multi-class classification with 3 classes, the targets are transformed into one-hot encoded vectors as follows:\n",
        "\n",
        "Class 1: [1, 0, 0]: This means the data point belongs to class 1, and the first element in the vector is set to 1, while the other elements are set to 0.\n",
        "\n",
        "Class 2: [0, 1, 0]: This means the data point belongs to class 2, and the second element in the vector is set to 1, while the other elements are set to 0.\n",
        "\n",
        "Class 3: [0, 0, 1]: This means the data point belongs to class 3, and the third element in the vector is set to 1, while the other elements are set to 0.\n",
        "\n",
        "We can use `jax.nn.one_hot` function to one-hot encode our data.\n"
      ],
      "metadata": {
        "id": "uQPWxWGX_BYF"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# An example using one hot encoding\n",
        "num_classes =  3\n",
        "targets = jnp.array([2, 0, 1])\n",
        "one_hot_targets = jax.nn.one_hot(targets, num_classes)\n",
        "print(f\"Example of One hot encordings: {one_hot_targets}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "E7RnH9ww-we5",
        "outputId": "aed209d9-9f7d-4a48-fbe9-1eef5c08331e"
      },
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Example of One hot encordings: [[0. 0. 1.]\n",
            " [1. 0. 0.]\n",
            " [0. 1. 0.]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Exercise**: Discuss with your neighbour how we should define the loss function in the case of multi-class classification."
      ],
      "metadata": {
        "id": "yzIJVz_E_Ou2"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Solution**: The loss function for a multi-classification is computed similarly to that of a binary classifier. However in this case we define the loss as the sum of the loss for each of the individual classes.\n",
        "<br>\n",
        "<center>\n",
        " $$ \\sum_c -y^c_i \\log(p^c_i),$$\n",
        "</center>\n",
        "where $p^c_i = \\text{softmax}(z) = \\frac{e^{z^c_i}}{\\sum_c e^{z^c_i}}$ with $z$ being the output of our model function.\n",
        "<br>\n",
        "The main difference here is that we use a $\\text{softmax}$ activation function instead of $\\text{sigmoid}$ as for the binary case.\n",
        "\n",
        "**Exercise 3 [OPTIONAL]**: Do your get the initution why this formula is similar to that for the binary case?\n",
        "\n",
        "**Solution**: Scroll to the [Appendix](#scrollTo=fRYbQvz01Zlm)."
      ],
      "metadata": {
        "id": "pWfU8E4G_UZS"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Code task**:\n",
        "  1. Implement the softmax activation function\n",
        "  2. Implement a cross entropy loss function for multiclass classification using softmax and one hot encoding."
      ],
      "metadata": {
        "id": "U-tXCopx_l_Y"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def softmax(logits):\n",
        "  \"\"\"Compute softmax: `exp(x)/sum(exp(x))`\n",
        "\n",
        "  Args:\n",
        "    logits: array of shape (num_samples, num_classes)\n",
        "\n",
        "  Return:\n",
        "    probs: array of shape (num_samples, num_classes)\n",
        "  \"\"\"\n",
        "\n",
        "  # your code here\n",
        "  # make sure you sum across the right axis\n",
        "\n",
        "  probs = ... # update me\n",
        "\n",
        "  return probs"
      ],
      "metadata": {
        "id": "y7l0lwSg_Ldc"
      },
      "execution_count": 46,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Run me to test your code\n",
        "def test_softmax():\n",
        "  x = jnp.array([[1.0, 0.4, 0.3], [10.0, 4.6, 8.9]])\n",
        "  assert jnp.allclose(softmax(x), jax.nn.softmax(x, axis=-1))\n",
        "  print(\"Nice! Your answer looks correct.\")\n",
        "\n",
        "test_softmax()"
      ],
      "metadata": {
        "id": "0eKSJDJz_o7m"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# @title softmax solution (Try not to peek until you've given it a good try!')\n",
        "def softmax(logits):\n",
        "  exp_logits = jnp.exp(logits)\n",
        "  return exp_logits / jnp.sum(exp_logits, axis=-1, keepdims=True)"
      ],
      "metadata": {
        "id": "FvJNYNaK_qcP"
      },
      "execution_count": 48,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def cross_entropy_softmax_loss(predictions, targets):\n",
        "    \"\"\"Compute the cross entropy softmax loss function\n",
        "\n",
        "      Args:\n",
        "        predictions: (num_samples, num_classes)\n",
        "        targets: (num_samples)\n",
        "    \"\"\"\n",
        "\n",
        "    # Compute the softmax probabilities\n",
        "    probs = ... # update me\n",
        "\n",
        "    num_classes = ... # update me\n",
        "\n",
        "    # One-hot encode the targets\n",
        "    targets_one_hot = ... # update me\n",
        "\n",
        "    # Compute the cross-entropy loss\n",
        "    eps = 1e-15\n",
        "    probs += eps # to avoid calling log with 0 values\n",
        "\n",
        "    loss = ... # update me\n",
        "\n",
        "    return loss"
      ],
      "metadata": {
        "id": "2Cqu0Vuq_t-j"
      },
      "execution_count": 49,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Run me to test your code\n",
        "def test_cross_entropy_softmax_loss():\n",
        "  # Fixed predictions (logits) for each class\n",
        "  predictions = jnp.array([[1.5, 0.3, 2.7],\n",
        "        [0.8, 1.2, 3.1], [2.3, 1.7, 0.5],\n",
        "        [3.0, 0.5, 1.2], [0.2, 2.8, 1.0]])\n",
        "\n",
        "  # Fixed true class labels\n",
        "  targets = jnp.array([2, 1, 0, 0, 2])\n",
        "\n",
        "  # Expected loss computed manually\n",
        "  expected_loss = 1.0456787\n",
        "\n",
        "  # Compute the cross-entropy softmax loss using your implementation\n",
        "  loss = cross_entropy_softmax_loss(predictions, targets)\n",
        "\n",
        "  # Check if the computed loss matches the JAX built-in loss\n",
        "  assert jnp.allclose(loss, expected_loss), \"Loss value do not match!\"\n",
        "\n",
        "  print(\"Nice! Your answer looks correct.\")\n",
        "\n",
        "test_cross_entropy_softmax_loss()"
      ],
      "metadata": {
        "id": "5s8745pS_v5L"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Cross entropy softmax solution (Try not to peek until you've given it a good try!')\n",
        "def cross_entropy_softmax_loss(predictions, targets):\n",
        "    \"\"\"Compute the cross entropy softmax loss function\n",
        "\n",
        "      Args:\n",
        "        predictions: (num_samples, num_classes)\n",
        "        targets: (num_samples)\n",
        "    \"\"\"\n",
        "\n",
        "    # Compute the softmax probabilities\n",
        "    probs = softmax(predictions) # update me\n",
        "\n",
        "    num_classes = predictions.shape[-1]\n",
        "\n",
        "    # One-hot encode the targets\n",
        "    targets_one_hot = jax.nn.one_hot(targets, num_classes) # update me\n",
        "\n",
        "    # Compute the cross-entropy loss\n",
        "    eps = 1e-15\n",
        "    probs += eps # to avoid calling log with 0 values\n",
        "\n",
        "    loss_i = jnp.sum(-targets_one_hot*jnp.log(probs), axis=-1) # update me\n",
        "\n",
        "    return jnp.mean(loss_i)"
      ],
      "metadata": {
        "id": "TrU_21TS_zvl"
      },
      "execution_count": 50,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Building a simple neural network for classification\n",
        "\n",
        "In this section, we will assemble all the pieces and train a deep neural network for classification. Let's recall all the tools we mentioned initially that are necessary to train a machine learning model.\n",
        "\n",
        "1. Dataset: we need to have a dataset which we will split into training and validation sets in the ratio 80:20.\n",
        "2. A model function.\n",
        "3. A loss function.\n",
        "4. An optimisation algorithm.\n",
        "\n",
        "We will load the data using [sklearn](https://scikit-learn.org/stable/datasets/toy_dataset.html). We have not discussed data preprocessing but in practice, we usually have to preprocess our datasets before using them for training. Such steps may include for example visualising the data to have intuition, identifying outliers, transforming and even dropping some features."
      ],
      "metadata": {
        "id": "jKP2yadw_7IO"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn import datasets\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.preprocessing import MinMaxScaler\n",
        "\n",
        "import jax\n",
        "import jax.numpy as jnp\n",
        "from typing import NamedTuple, Any\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "# Let re-adapt our batch gradient descent function\n",
        "def batch_gradient_descent(loss_fn, params, training_data, val_data, learning_rate=0.01, num_epochs=20, batch_size=10):\n",
        "  \"\"\"Batch gradient descent basic jax implementation.\n",
        "\n",
        "  Args:\n",
        "    loss_fn\n",
        "      the loss function for our model.\n",
        "    params:\n",
        "      the initial parameters of the model.\n",
        "    training_data\n",
        "      a tuple with the features and targets for training.\n",
        "    val_data\n",
        "      a tuple with the features and targets for validation.\n",
        "    learning_rate\n",
        "      learning rate\n",
        "    num_epochs\n",
        "      number of epochs\n",
        "    batch_size:\n",
        "      size of every mini batch\n",
        "  \"\"\"\n",
        "\n",
        "  X_train, y_train = training_data\n",
        "  X_val, y_val = val_data\n",
        "\n",
        "  num_samples, num_features = X_train.shape\n",
        "\n",
        "  # Create empty list to store the training and validation loss.\n",
        "  loss_train = [] # training loss\n",
        "  loss_val  = [] # valisation loss\n",
        "\n",
        "  # Define a function that computes loss and gradients\n",
        "  loss_and_grad = jax.value_and_grad(loss_fn)\n",
        "\n",
        "  for epoch in range(num_epochs):\n",
        "    # Shuffle the data before every epoch\n",
        "    shuffled_indices = np.arange(num_samples)\n",
        "    np.random.shuffle(shuffled_indices)\n",
        "\n",
        "    loss_train_epoch = []\n",
        "\n",
        "    for start_idx in range(0, num_samples, batch_size):\n",
        "      end_idx = start_idx + batch_size\n",
        "      if end_idx > num_samples:\n",
        "        end_idx = num_samples\n",
        "\n",
        "      batch_indices = shuffled_indices[start_idx:end_idx]\n",
        "      X_batch = X_train[batch_indices]\n",
        "      y_batch = y_train[batch_indices]\n",
        "      # Compute loss and gradients using value_and_grad\n",
        "      loss, grads = loss_and_grad(params, X_batch, y_batch)\n",
        "      loss_train_epoch.append(loss)\n",
        "\n",
        "      # Update the parameters\n",
        "      params = jax.tree_map(lambda p, g: p -learning_rate*g, params, grads)\n",
        "\n",
        "    # We need to turn the list in to an array before applying jnp.mean\n",
        "    mean_loss = jnp.mean(jnp.array(loss_train_epoch))\n",
        "    loss_train.append(mean_loss)\n",
        "\n",
        "    # Compute the validation loss at the end of the epoch\n",
        "    loss_v = loss_fn(params, X_val, y_val)\n",
        "    loss_val.append(loss_v)\n",
        "\n",
        "  # Plot training and validation loss\n",
        "  epochs = range(1, num_epochs+1)\n",
        "  plt.plot(epochs, loss_train, label='Training Loss')\n",
        "  plt.plot(epochs, loss_val, label='Validation Loss')\n",
        "  plt.xlabel('Epoch')\n",
        "  plt.ylabel('Loss')\n",
        "  plt.title('Training and Validation Loss')\n",
        "  plt.legend()\n",
        "\n",
        "  # Display the plot\n",
        "  plt.show()\n",
        "\n",
        "  return params\n",
        "\n",
        "# Load the mnist dataset\n",
        "def load_dataset(seed):\n",
        "  mnist = fetch_openml(name='mnist_784', version=1, as_frame=False, parser='auto')\n",
        "  # Extract the data and labels\n",
        "  images, labels = mnist.data, mnist.target\n",
        "\n",
        "  # These images consist of integer values from 0 to 255.0\n",
        "  # We scale the images to min and max of 1\n",
        "  x_max = 255.0\n",
        "  x_min = 0.0\n",
        "\n",
        "  images = (images - x_min)/(x_max - x_min)\n",
        "  images = images.astype(jnp.float32)\n",
        "  labels = labels.astype(jnp.float32)\n",
        "\n",
        "  # These are images of shape 28x28 which have been flatten to shape 784\n",
        "  X_train, X_test, y_train, y_test = train_test_split(\n",
        "      images, labels, test_size=0.2, train_size=0.8, random_state=seed\n",
        "  )\n",
        "\n",
        "  train_dataset = (X_train, y_train)\n",
        "  test_dataset = (X_test, y_test)\n",
        "\n",
        "  return train_dataset, test_dataset\n",
        "\n",
        "training_data, val_data = load_dataset(32)"
      ],
      "metadata": {
        "id": "cpxpQ-Fp_4l3"
      },
      "execution_count": 52,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Code task:**\n",
        "1. Build a neural network that outputs logits for each of the 10 classes.\n",
        "2. Initialise your model with some dummy input.\n",
        "3. Define your softmax cross entropy function."
      ],
      "metadata": {
        "id": "nK-ShLYFAKj_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Your code here\n",
        "class Network(nn.Module):\n",
        "  hidden_size: int\n",
        "  output_size: int\n",
        "\n",
        "  @nn.compact\n",
        "  def __call__(self, x):\n",
        "    # First layer with ReLU activation\n",
        "    x = nn.Dense(self.hidden_size)(x)\n",
        "    x = jax.nn.relu(x)\n",
        "\n",
        "    # Second layer\n",
        "    x = ...  # update me\n",
        "    x = ...  # update me\n",
        "\n",
        "    # Third (output) layer with no activation applied\n",
        "    x = nn.Dense(self.output_size)(x)\n",
        "\n",
        "    return x\n",
        "\n",
        "# transform and intialiase the model.\n",
        "seed = 32\n",
        "input_size = 784 # remember our features are images of shape 28x28 flatten\n",
        "hidden_size = ... # update me\n",
        "output_size = ... # update me (hint: number classes)\n",
        "\n",
        "# instantiate the model\n",
        "model = Network... # update me\n",
        "\n",
        "key = jax.random.PRNGKey(seed)\n",
        "dummy = jnp.zeros((1, input_size), dtype=float)\n",
        "initial_params = model.init(key, dummy)\n",
        "\n",
        "def softmax(logits):\n",
        "  exp_logits = jnp.exp(logits)\n",
        "  return exp_logits / jnp.sum(exp_logits, axis=-1, keepdims=True)\n",
        "\n",
        "\n",
        "def cross_entropy_softmax_loss(params, X, targets):\n",
        "    \"\"\"Compute the cross entropy softmax loss function\n",
        "\n",
        "      Args:\n",
        "        params: model parameters\n",
        "        X: features arrary (num_samples, num_features)\n",
        "        targets: (num_samples)\n",
        "    \"\"\"\n",
        "\n",
        "    # use the model to compute the predictions\n",
        "    preds = model.apply(params, X)\n",
        "\n",
        "    # Compute the softmax probabilities\n",
        "    probs = softmax(preds)\n",
        "\n",
        "    num_classes = preds.shape[-1]\n",
        "\n",
        "    # One-hot encode the targets\n",
        "    targets_one_hot = jax.nn.one_hot(targets, num_classes)\n",
        "\n",
        "    # Compute the cross-entropy loss\n",
        "    eps = 1e-15\n",
        "    probs += eps # to avoid calling log with 0 values\n",
        "\n",
        "    loss_i = jnp.sum(-targets_one_hot*jnp.log(probs), axis=-1)\n",
        "\n",
        "    return jnp.mean(loss_i)\n"
      ],
      "metadata": {
        "id": "x8rxg153_9q4"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Sample solution (Try not to peek until you've given it a good try!')\n",
        "class Network(nn.Module):\n",
        "  hidden_size: int\n",
        "  output_size: int\n",
        "\n",
        "  @nn.compact\n",
        "  def __call__(self, x):\n",
        "    # First layer with ReLU activation\n",
        "    x = nn.Dense(self.hidden_size)(x)\n",
        "    x = jax.nn.relu(x)\n",
        "\n",
        "    # Second layer\n",
        "    x = nn.Dense(self.hidden_size)(x)\n",
        "    x = jax.nn.relu(x)\n",
        "\n",
        "    # Third (output) layer with no activation applied\n",
        "    x = nn.Dense(self.output_size)(x)\n",
        "\n",
        "    return x\n",
        "\n",
        "# transform and intialiase the model.\n",
        "seed = 67\n",
        "input_size = 784\n",
        "hidden_size = 100\n",
        "output_size = 10\n",
        "\n",
        "# Instantiate the model\n",
        "model = Network(hidden_size, output_size)\n",
        "\n",
        "key = jax.random.PRNGKey(seed)\n",
        "dummy = jnp.zeros((1, input_size), dtype=float)\n",
        "initial_params = model.init(key, dummy)\n",
        "\n",
        "def softmax(logits):\n",
        "  exp_logits = jnp.exp(logits)\n",
        "  return exp_logits / jnp.sum(exp_logits, axis=-1, keepdims=True)\n",
        "\n",
        "def cross_entropy_softmax_loss(params, X, targets):\n",
        "    \"\"\"Compute the cross entropy softmax loss function\n",
        "\n",
        "      Args:\n",
        "        params: model params\n",
        "        X: (num_features, num_classes)\n",
        "        targets: (num_samples)\n",
        "    \"\"\"\n",
        "\n",
        "    preds = model.apply(params, X)\n",
        "\n",
        "    # Compute the softmax probabilities\n",
        "    probs = softmax(preds)\n",
        "\n",
        "    num_classes = preds.shape[-1]\n",
        "\n",
        "    # One-hot encode the targets\n",
        "    targets_one_hot = jax.nn.one_hot(targets, num_classes)\n",
        "\n",
        "    # Compute the cross-entropy loss\n",
        "    eps = 1e-15\n",
        "    probs += eps # to avoid calling log with 0 values\n",
        "\n",
        "    loss_i = jnp.sum(-targets_one_hot*jnp.log(probs), axis=-1)\n",
        "\n",
        "    return jnp.mean(loss_i)\n"
      ],
      "metadata": {
        "id": "F8wly5vsAMWs"
      },
      "execution_count": 54,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Training the model\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "0XkvYMyzASvK"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Code task:**\n",
        "  1. Call the `batch_gradient_descent` function to train the model.\n",
        "  2. Vary the `learning_rate` and the `batch_size` and observe the behaviour of the loss function."
      ],
      "metadata": {
        "id": "nsxgIhuVAVD3"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "params = batch_gradient_descent ... # update me"
      ],
      "metadata": {
        "id": "ESMhTdejAQM9"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Sample solution (Try not to peek until you've given it a good try!')\n",
        "params = batch_gradient_descent(cross_entropy_softmax_loss, initial_params, training_data, val_data, learning_rate=0.01, num_epochs=10, batch_size=1000)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "M_Zuy0SzAX-G",
        "outputId": "84f1e1cf-8e57-4b77-8dcd-95df3bae8db1"
      },
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Evaluating the model\n",
        "So far the only metric we have used to evaluate the performance of our model has been the loss function. However, when training a machine learning model, several other metrics can be used to assess the performance of the model. Furthermore, hyper-parameters are generally selected (fine-tuned) based on the most important metric we want to optimise. Below are some metrics that can be used for classification tasks.\n",
        "*   **Accuracy**: This is the most common metric generally used in classification. It is a measure of the proportion of instances classified correctly. $$ \\text{Accuracy} = \\frac{\\text{Number of correct predictions}}{\\text{Total number of predictions}}$$\n",
        "\n",
        "* **Precision**: This is a measure of the number of positive predictions. For example, if our model predicts 100 data points to belong to class 1, the precision is the percentage of these 100 data points that effectively belong to class 1. High precision is maybe necessary for example in medical diagnosis, where we don't want to make a wrong diagnosis on patients that leads to unnecessary treatment.\n",
        "\n",
        "* **Recall**: This is a measure of the model's ability to efficiently identify all positive instances. For example, if the dataset has 100 data points belonging to class 1, how many are effectively classified to belong to class 1? The recall is crucial in cases where we don't want to miss any positive instance. For example, if we have a security company, we don't want to wrongly classify the signal from a user as being safe while he is actually in danger."
      ],
      "metadata": {
        "id": "TT2OPDYfAetk"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Let's use accuracy to evaluate the performance of our trained classifier.**\n",
        "\n",
        "Firstly let's define a prediction function that transforms the model output to class. Recall the output of the classifier is logits which correspond to unnormalised probabilities belonging to each class. Thus the predicted class is the one with the highest probability    \n",
        "\n",
        "**Code Task**\n",
        "  1. Implement a function `model_predict` that selects the appropriate class from the output of the model."
      ],
      "metadata": {
        "id": "_5IkX8ymAhqG"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Your code here\n",
        "def model_predict(params, X):\n",
        "    \"\"\"Use the model for predicition\n",
        "\n",
        "      args:\n",
        "        params: model parameters\n",
        "        X: features array (num_samples, num_features)\n",
        "\n",
        "      return\n",
        "        pred: predicted class (num_samples, 1)\n",
        "    \"\"\"\n",
        "\n",
        "    # call the model to compute the logits\n",
        "    logits = model... # update me\n",
        "    preds = ... # update me: hint use jnp.argmax\n",
        "\n",
        "    return preds"
      ],
      "metadata": {
        "id": "iRHTMiJcAbTY"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Run to test your code\n",
        "def test_model_predict():\n",
        "    features = val_data[0][0:10]\n",
        "    preds = model_predict(params, features)\n",
        "    expected = jnp.argmax(model.apply(params, features), axis=-1)\n",
        "    assert jnp.array_equal(preds, expected), \"Failed! try again\"\n",
        "    print(\"Nice! Your answer looks correct.\")\n",
        "\n",
        "test_model_predict()"
      ],
      "metadata": {
        "id": "er_Jbn-8AkG_"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Solution model predict (Try not to peek until you've given it a good try!')\n",
        "def model_predict(params, X):\n",
        "    \"\"\"Use the model for predicition\n",
        "\n",
        "      args:\n",
        "        params: model parameters\n",
        "        X: features array (num_samples, num_features)\n",
        "\n",
        "      return\n",
        "        pred: predicted class (num_samples, 1)\n",
        "    \"\"\"\n",
        "\n",
        "    # call the model to compute the logits\n",
        "    logits = model.apply(params, X)\n",
        "    preds = jnp.argmax(logits, axis=-1)\n",
        "\n",
        "    return preds"
      ],
      "metadata": {
        "id": "UMvrkUCvApeI"
      },
      "execution_count": 59,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Compute the accuray of your model\n",
        "def compute_accuracy(data):\n",
        "  \"\"\"Compute the accuracy of the model\"\"\"\n",
        "\n",
        "  X, y_true = data\n",
        "  y_pred = model_predict(params, X).squeeze()\n",
        "\n",
        "  acc = sum(y_pred==y_true)/len(y_true)\n",
        "\n",
        "  return acc\n",
        "\n",
        "train_acc = compute_accuracy(training_data)\n",
        "val_acc = compute_accuracy(val_data)\n",
        "print(f\"The training accuracy is {train_acc} while the validation accuracy is {val_acc}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uQHwV0h2BZj1",
        "outputId": "96547a26-aadd-4454-aefd-225dc30a3068"
      },
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The training accuracy is 0.8274464011192322 while the validation accuracy is 0.8309999704360962\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Congratulations, we've just trained a machine learning model for classification using the popular mnist digit dataset.\n",
        "\n",
        "**Take home challenge**:\n",
        "- Are you satisfied with the accuracy of your model?\n",
        "- What can you do to improve the accuracy of the model?"
      ],
      "metadata": {
        "id": "maqj9SyqBjdi"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Conclusion\n",
        "**Summary:**\n",
        "\n",
        "- Machine learning is the science of using data to build intelligent systems.\n",
        "- Deep learning is the subset of machine learning methods that uses neural networks.\n",
        "- Optimisation is the process of finding the parameters that make the loss of a function as small as possible.\n",
        "- JAX is a new popular framework that can be used to compute derivatives and train machine learning models.  \n",
        "\n",
        "\n",
        "**References:**\n",
        "\n",
        "1. https://d2l.ai/chapter_linear-networks/linear-regression.html\n",
        "2. https://www.simplilearn.com/tutorials/artificial-intelligence-tutorial/ai-vs-machine-learning-vs-deep-learning\n",
        "3. https://www.javatpoint.com/machine-learning"
      ],
      "metadata": {
        "id": "Mokn_O0qBq7K"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Appendix\n",
        "\n",
        "### Basis of JAX [OPTIONAL]\n",
        "Jax is very similar to numpy but they are some important minor differences we need to be aware of."
      ],
      "metadata": {
        "id": "vT2yl6O6BziR"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Similarities between JAX and Numpy"
      ],
      "metadata": {
        "id": "OZmj8YVpB1Z4"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Create NumPy arrays\n",
        "np_array1 = np.array([1, 2, 3])\n",
        "np_array2 = np.array([4, 5, 6])\n",
        "\n",
        "# Create JAX arrays\n",
        "jax_array1 = jnp.array([1, 2, 3])\n",
        "jax_array2 = jnp.array([4, 5, 6])\n",
        "\n",
        "# Element-wise addition using NumPy\n",
        "np_result = np_array1 + np_array2\n",
        "print(\"NumPy result:\", np_result)\n",
        "\n",
        "# Element-wise addition using JAX\n",
        "jax_result = jax_array1 + jax_array2\n",
        "print(\"JAX result:\", jax_result)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XKdpyikoBkBo",
        "outputId": "3fbb3e8b-04a4-4a5f-8c5d-ea2889efc7d9"
      },
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "NumPy result: [5 7 9]\n",
            "JAX result: [5 7 9]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Array concatenation using NumPy\n",
        "np_array1 = np.array([1, 2, 3])\n",
        "np_array2 = np.array([4, 5, 6])\n",
        "np_concatenated = np.concatenate([np_array1, np_array2])\n",
        "\n",
        "# Array concatenation using JAX\n",
        "jax_array1 = jnp.array([1, 2, 3])\n",
        "jax_array2 = jnp.array([4, 5, 6])\n",
        "jax_concatenated = jnp.concatenate([jax_array1, jax_array2])"
      ],
      "metadata": {
        "id": "ai33BS8TB4eM"
      },
      "execution_count": 62,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Element-wise functions using NumPy\n",
        "np_array = np.array([0, np.pi/2, np.pi])\n",
        "np_sin = np.sin(np_array)\n",
        "\n",
        "# Element-wise functions using JAX\n",
        "jax_array = jnp.array([0, jnp.pi/2, jnp.pi])\n",
        "jax_sin = jnp.sin(jax_array)"
      ],
      "metadata": {
        "id": "dmBiHlsbB6N-"
      },
      "execution_count": 63,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Reduction operations using NumPy\n",
        "np_array = np.array([1, 2, 3])\n",
        "np_sum = np.sum(np_array)\n",
        "np_mean = np.mean(np_array)\n",
        "\n",
        "# Reduction operations using JAX\n",
        "jax_array = jnp.array([1, 2, 3])\n",
        "jax_sum = jnp.sum(jax_array)\n",
        "jax_mean = jnp.mean(jax_array)"
      ],
      "metadata": {
        "id": "juu49e93B7tl"
      },
      "execution_count": 64,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "JAX and NumPy - Differences ❌\n",
        "\n",
        "Although JAX and NumPy have some similarities, they do have some important differences:\n",
        "- Jax arrays are **immutable** (they can't be modified after they are created).\n",
        "- The way they handle **randomness** -- JAX handles randomness explicitly.\n",
        "\n"
      ],
      "metadata": {
        "id": "ncCweXUoCAWJ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "JAX arrays are immutable, while NumPy arrays are not.\n",
        "\n",
        "JAX and NumPy arrays are often interchangeable, **but** Jax arrays are **immutable** (they can't be modified after they are created). Allowing mutations makes transforms difficult and violates conditions for [pure functions](https://en.wikipedia.org/wiki/Pure_function)."
      ],
      "metadata": {
        "id": "kvw_D4cpCCmA"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's see this in practice by changing the number at the beginning of an array."
      ],
      "metadata": {
        "id": "DNZ6Zq5_CE8y"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# NumPy: mutable arrays\n",
        "x = np.arange(10)\n",
        "x[0] = 10\n",
        "print(x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ofWR36c1B-Fv",
        "outputId": "dcca0526-388a-4e05-bf4b-de36f25c31dd"
      },
      "execution_count": 65,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[10  1  2  3  4  5  6  7  8  9]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's try this in JAX."
      ],
      "metadata": {
        "id": "knds_oIkCIy7"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# JAX: immutable arrays\n",
        "# Should raise an error.\n",
        "try:\n",
        "    x = jnp.arange(10)\n",
        "    x[0] = 10\n",
        "except Exception as e:\n",
        "    print(\"Exception {}\".format(e))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6JabbUggCGzO",
        "outputId": "5589e684-d2ef-4189-dd02-32d59ef32c50"
      },
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Exception '<class 'jaxlib.xla_extension.ArrayImpl'>' object does not support item assignment. JAX arrays are immutable. Instead of ``x[idx] = y``, use ``x = x.at[idx].set(y)`` or another .at[] method: https://jax.readthedocs.io/en/latest/_autosummary/jax.numpy.ndarray.at.html\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "So it fails! We can't mutate a JAX array once it has been created. To update JAX arrays, we need to use [helper functions](https://jax.readthedocs.io/en/latest/_autosummary/jax.numpy.ndarray.at.html) that return an updated copy of the JAX array.\n",
        "\n",
        "Instead of doing this `x[idx] = y`, we need to do this `x = x.at[idx].set(y)`."
      ],
      "metadata": {
        "id": "Vp0W487PCMfK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x = jnp.arange(10)\n",
        "new_x = x.at[0].set(10)\n",
        "print(f\" new_x: {new_x} original x: {x}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FpJEsf2fCKNt",
        "outputId": "7178e771-472a-44de-ccb1-e1c6c9120434"
      },
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            " new_x: [10  1  2  3  4  5  6  7  8  9] original x: [0 1 2 3 4 5 6 7 8 9]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Note here that `new_x` is a copy and that the original `x` is unchanged."
      ],
      "metadata": {
        "id": "woAv2J37CRCC"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Randomness in NumPy vs JAX\n",
        "\n",
        "JAX is more explicit in Pseudo Random Number Generation (PRNG) than NumPy and other libraries (such as TensorFlow or PyTorch). [PRNG](https://en.wikipedia.org/wiki/Pseudorandom_number_generator) is the process of algorithmically generating a sequence of numbers, which *approximate* the properties of a sequence of random numbers.  \n",
        "\n",
        "Let's see the differences in how JAX and NumPy generate random numbers."
      ],
      "metadata": {
        "id": "AF5qFLehCTH7"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In Numpy, PRNG is based on a global `state`\n",
        "\n",
        "Let's set the initial seed."
      ],
      "metadata": {
        "id": "f1bSaA-GCVQb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Set random seed\n",
        "np.random.seed(42)\n",
        "prng_state = np.random.get_state()"
      ],
      "metadata": {
        "id": "Te45PK3PCOKf"
      },
      "execution_count": 68,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Helper function to compare prng keys (Run Cell)\n",
        "def is_prng_state_the_same(prng_1, prng_2):\n",
        "    \"\"\"Helper function to compare two prng keys.\"\"\"\n",
        "    # concat all elements in prng tuple\n",
        "    list_prng_data_equal = [(a == b) for a, b in zip(prng_1, prng_2)]\n",
        "    # stack all elements together\n",
        "    list_prng_data_equal = np.hstack(list_prng_data_equal)\n",
        "    # check if all elements are the same\n",
        "    is_prng_equal = all(list_prng_data_equal)\n",
        "    return is_prng_equal"
      ],
      "metadata": {
        "id": "rYfQIHwlCXFO"
      },
      "execution_count": 69,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's take a few samples from a Gaussian (normal) Distribution and check if PRNG keys/global state change."
      ],
      "metadata": {
        "id": "1KACf7f2CZ50"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(\n",
        "    f\"sample 1 = {np.random.normal()} Did prng state change: {not is_prng_state_the_same(prng_state,np.random.get_state())}\"\n",
        ")\n",
        "prng_state = np.random.get_state()\n",
        "print(\n",
        "    f\"sample 2 = {np.random.normal()} Did prng state change: {not is_prng_state_the_same(prng_state,np.random.get_state())}\"\n",
        ")\n",
        "prng_state = np.random.get_state()\n",
        "print(\n",
        "    f\"sample 3 = {np.random.normal()} Did prng state change: {not is_prng_state_the_same(prng_state,np.random.get_state())}\"\n",
        ")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uh58ENZiCYUd",
        "outputId": "d1c85482-6d70-4671-f408-a424c9c794ac"
      },
      "execution_count": 70,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "sample 1 = 0.4967141530112327 Did prng state change: True\n",
            "sample 2 = -0.13826430117118466 Did prng state change: True\n",
            "sample 3 = 0.6476885381006925 Did prng state change: True\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Numpy's global random state is updated every time a random number is generated, so *sample 1 != sample 2 != sample 3*.\n",
        "\n",
        "Having the state automatically updated, makes it difficult to handle randomness in a **reproducible** way across different threads, processes and devices."
      ],
      "metadata": {
        "id": "zOl1ZTjRCfe-"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In JAX, PRNG is explicit.\n",
        "\n",
        "In JAX, for each random number generation, you need to explicitly pass in a random key/state.\n",
        "\n",
        "Passing the same state/key results in the same number being generated. This is generally undesirable."
      ],
      "metadata": {
        "id": "rbIGvqvACh-8"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from jax import random\n",
        "\n",
        "key = random.PRNGKey(42)\n",
        "print(f\"sample 1 = {random.normal(key)}\")\n",
        "print(f\"sample 2 = {random.normal(key)}\")\n",
        "print(f\"sample 3 = {random.normal(key)}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Ldo9XuNMCbY5",
        "outputId": "08187eef-adc2-45f3-ae84-c40586e10d5e"
      },
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "sample 1 = -0.1847117692232132\n",
            "sample 2 = -0.1847117692232132\n",
            "sample 3 = -0.1847117692232132\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "To generate different and independent samples, you need to manually split the keys."
      ],
      "metadata": {
        "id": "ziWAVZoTCnS0"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from jax import random\n",
        "\n",
        "key = random.PRNGKey(42)\n",
        "print(f\"sample 1 = {random.normal(key)}\")\n",
        "\n",
        "# We split the key -> new key and subkey\n",
        "new_key, subkey = random.split(key)\n",
        "\n",
        "# We use the subkey immediately and keep the new key for future splits.\n",
        "# It doesn't really matter which key we keep and which one we use immediately.\n",
        "print(f\"sample 2 = {random.normal(subkey)}\")\n",
        "\n",
        "# We split the new key -> new key2 and subkey\n",
        "new_key2, subkey = random.split(new_key)\n",
        "print(f\"sample 3 = {random.normal(subkey)}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "E2okfjjhCls4",
        "outputId": "bf27efda-dd01-4336-c0d6-a62b5d1340f5"
      },
      "execution_count": 72,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "sample 1 = -0.1847117692232132\n",
            "sample 2 = 1.369469404220581\n",
            "sample 3 = -0.19947023689746857\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "By using JAX, we can more easily reproduce random number generation in parallel across threads, processes, or even devices by explicitly passing and keeping track of the prng key (without relying on a global state that automatically gets updated)."
      ],
      "metadata": {
        "id": "99BI3TvoCqi4"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Derivation of partial derivatives for exercise 2 [OPTIONAL]\n",
        "Derive $\\frac{\\partial \\mathcal{L}}{\\partial \\mathbf{w}}$:\n",
        "\\begin{aligned}\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial \\mathbf{w}} & = \\frac{ \\partial}{\\partial \\mathbf{w}} (\\frac{1}{m} \\sum_{i=1}^m (y_i - (\\mathbf{w}^T \\mathbf{x}_i + b))^2) \\quad \\text{: Definition of $\\mathcal{L}$} \\\\\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial \\mathbf{w}} & = \\frac{1}{m} \\frac{ \\partial }{\\partial \\mathbf{w}} ( \\sum_{i=1}^m (y_i - (\\mathbf{w}^T \\mathbf{x}_i + b))^2) \\quad \\text{: Constant multiple rule} \\\\\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial \\mathbf{w}} & = \\frac{1}{m} \\sum_{i=1}^m \\frac{ \\partial }{\\partial \\mathbf{w}} (y_i - (\\mathbf{w}^T \\mathbf{x}_i + b))^2 \\quad \\text{: Sum Rule - derivative of sum is sum of derivatives.} \\\\\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial \\mathbf{w}} & = \\frac{1}{m} \\sum_{i=1}^m 2 (y_i - (\\mathbf{w}^T \\mathbf{x}_i + b)) \\frac{ \\partial }{\\partial \\mathbf{w}}(y_i -(\\mathbf{w}^T \\mathbf{x}_i + b))  \\quad \\text{: Power Rule + Chain Rule.} \\\\\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial \\mathbf{w}} & = \\frac{1}{m} \\sum_{i=1}^m 2 (y_i - (\\mathbf{w}^T \\mathbf{x}_i + b)) (-\\mathbf{x}_i)  \\quad \\text{: Compute derative.} \\\\\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial \\mathbf{w}} & = \\frac{2}{m} \\sum_{i=1}^m (y_i - (\\mathbf{w}^T \\mathbf{x}_i + b)) (-\\mathbf{x}_i)  \\quad \\text{: Factor constant out of summation.} \\\\\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial \\mathbf{w}} & = \\frac{2}{m} \\sum_{i=1}^m \\mathbf{x}_i((\\mathbf{w}^T \\mathbf{x}_i + b) -y_i ) \\quad \\text{: Rearrange.} \\\\  \n",
        "\\end{aligned}\n",
        "\n",
        "Derive $\\frac{\\partial \\mathcal{L}}{\\partial b}$:\n",
        "\\begin{aligned}\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial b} & = \\frac{ \\partial}{\\partial b} (\\frac{1}{m} \\sum_{i=1}^m (y_i - (\\mathbf{w}^T \\mathbf{x}_i + b))^2) \\quad \\text{: Definition of $\\mathcal{L}$} \\\\\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial b} & = \\frac{1}{m} \\frac{ \\partial }{\\partial b} ( \\sum_{i=1}^m (y_i - (\\mathbf{w}^T \\mathbf{x}_i + b))^2) \\quad \\text{: Constant multiple rule} \\\\\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial b} & = \\frac{1}{m} \\sum_{i=1}^m \\frac{ \\partial }{\\partial b} (y_i - (\\mathbf{w}^T \\mathbf{x}_i + b))^2 \\quad \\text{: Sum Rule - derivative of sum is sum of derivatives.} \\\\\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial b} & = \\frac{1}{m} \\sum_{i=1}^m 2 (y_i - (\\mathbf{w}^T \\mathbf{x}_i + b)) \\frac{ \\partial }{\\partial b}(y_i -(\\mathbf{w}^T \\mathbf{x}_i + b))  \\quad \\text{: Power Rule + Chain Rule.} \\\\\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial b} & = \\frac{1}{m} \\sum_{i=1}^m 2 (y_i - (\\mathbf{w}^T \\mathbf{x}_i + b)) (-1)  \\quad \\text{: Compute derative.} \\\\\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial b} & = \\frac{2}{m} \\sum_{i=1}^m (y_i - (\\mathbf{w}^T \\mathbf{x}_i + b)) (-1)  \\quad \\text{: Factor constant out of summation.} \\\\\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial b} & = \\frac{2}{m} \\sum_{i=1}^m ((\\mathbf{w}^T \\mathbf{x}_i + b) -y_i ) \\quad \\text{: Rearrange.} \\\\  \n",
        "\\end{aligned}"
      ],
      "metadata": {
        "id": "Z_3W_pjbCs6b"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Intuition for multi-class CE loss: exercise 3 [OPTIONAL]\n",
        "\n",
        "For binary classifies we use the following formula for the cross entropy loss\n",
        " $$ -y_i \\log(p_i) - (1-y_i) \\log (1-p_i).$$\n",
        "\n",
        "Recall in binary classier we have one class, so the output of our model is the probability, $p$ of belonging to that class. Instead, we can treat our binary classifier as two classes defined as follows\n",
        "  - Class 1: Belonging to the class in question.\n",
        "  - Class 2: Not belonging to the class.\n",
        "\n",
        "Then if the probability for the data point $y$_i of belonging to Class 1 is $p$_i, this means its probability of not belonging to Class 1 which is equivalent to belonging to Class 2 is $(1-p_i)$. Anagoulsy since target values are one hot encoded for a multi-class classification if $y_i$ is the label that it indicates if the data point belongs to Class 1 or not the corresponding label for belonging to Class 2 will be $(1 - y_i)$. Hence we can rewrite our cross entropy loss in compact form as follows\n",
        "$$ \\sum_c -y^c_i \\log(p^c_i).$$"
      ],
      "metadata": {
        "id": "djfrvgtxCvsU"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "dTov8Q8bCo5m"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}