{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "96d04eef",
   "metadata": {},
   "source": [
    "# Lab 1: Gradient descent\n",
    "_Samuel Vaiter_ (<samuel.vaiter@cnrs.fr>)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "afa37198",
   "metadata": {},
   "source": [
    "In this practical, we are going to study the **gradient descent** algorithm, and several variations of it, through the lenses of three examples:\n",
    "1. Two simple 2D functions to optimize, easy to visualize thanks to `matplotlib.pyplot.contour`\n",
    "2. The ordinary least square problem\n",
    "3. Digits classification with multinomial logistic regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "252a382a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a6bd7d6",
   "metadata": {},
   "source": [
    "## Toy example in 2D"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a84d3d23",
   "metadata": {},
   "source": [
    "We are going to test first our methods on two functions, one convex (potentially strongly convex), the other not.\n",
    "\n",
    "The convex function is going to be a simple quadratic form on $\\mathbb{R}^2$ defined by\n",
    "$$ f(x) = (x_0 - x_1 - 1)^2 + \\frac{\\mu}{2} x_0^2 , $$\n",
    "for some $\\mu \\in \\mathbb{R}$.\n",
    "\n",
    "**Q1**. Does the function $f$ is convex? When is it strongly convex?\n",
    "\n",
    "**Q2**. Determine its unique minimizer when $\\mu > 0$.\n",
    "\n",
    "**Q3**. Implement it as a function `f2D_convex(x, mu=1.0)` taking as arguments the 2D vector `x` and the strong-convexity parameter `mu`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e41623c5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f2D_convex(x, mu=1.0):\n",
    "    pass"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8aa85540",
   "metadata": {},
   "source": [
    "**Q4**. Display the levelsets of the function `f2D_convex` around $(0,0)$. Modify the value of $\\mu$ and see how the geometry change. _Hint_: You should look at the help of `np.meshgrid`, `plt.contourf` and eventually `np.vectorize`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ec8ef3f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.contour.QuadContourSet at 0x137bef0a0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display the level sets of `f2D_convex`\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e472ae23",
   "metadata": {},
   "source": [
    "**Q5**. Observe what happens when $\\mu = 0$. Can you explain it?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "81357b54",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(2,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5313be4",
   "metadata": {},
   "source": [
    "We now turn to another function, \n",
    "$$ f(x) = \\cos(x_0) + \\sin(x_1) . $$\n",
    "\n",
    "**Q6**. Is it a convex function? Describe the minima of $f$.\n",
    "\n",
    "**Q7**. Implement it as a function `f2D_nonconvex(x)` taking as arguments the 2D vector `x`. Display its levelsets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ef4664bc",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f2D_nonconvex(x):\n",
    "    pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e26c6eb6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.contour.QuadContourSet at 0x137ed00d0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display the level sets of `f2D_convex`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b3e844d",
   "metadata": {},
   "source": [
    "## Gradient descent procedure\n",
    "\n",
    "We recall that a gradient step takes the form\n",
    "$$ x^{(t+1)} = x^{(t)} - \\eta^{(t)} \\nabla f(x^{(t)}) $$\n",
    "with some initialization $x^{(0)}$ and $\\eta^{(t)}$ a learning rate policy.\n",
    "\n",
    "**Q1**. Implement a function `gradient_descent_tmp` taking as argument `grad_f`, `eta`, `x0` and `max_iter`. `grad_f` will take as input an optimization variable `x`, `eta` is the learning policy taking as arguments `x` and `t` the current iteration, `x0` is the initialization and `max_iter` a maximal number of iterations. As an example, a constant learning rate policy can defined as\n",
    "```python\n",
    "def constant_eta(x, t):\n",
    "    return 0.01\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "725a609f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent_tmp(grad_f, eta, x0, max_iter):\n",
    "    x = x0\n",
    "    for t in range(max_iter):\n",
    "        continue \n",
    "    return x"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec8db654",
   "metadata": {},
   "source": [
    "**Q2**. Implement a function `grad_f2D_convex` returning the gradient of the convex function defined in Section 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "50f1b164",
   "metadata": {},
   "outputs": [],
   "source": [
    "def grad_f2D_convex(x, mu=1.0):\n",
    "    return None"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e412fbb3",
   "metadata": {},
   "source": [
    "**Q3**. Compute the Lipschitz constant of $\\nabla f(x)$ and deduce a learning rate policy `lr_policy_f2D-convex(x,t)`. Discuss the difference between $\\mu = 0$ and $\\mu \\neq 0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9a233f1d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def hessian_f2D_convex(x, mu=1.0):\n",
    "    return None \n",
    "\n",
    "\n",
    "def lr_policy_f2D_convex(x, t):\n",
    "    return None"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "acd8e23d",
   "metadata": {},
   "source": [
    "**Q4**. Test these functions, and observe the impact of `max_iter`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "465b94f7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.1765725 , -0.77385011])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gradient_descent_tmp(grad_f2D_convex, lr_policy_f2D_convex, np.zeros(2), 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf18ff9d",
   "metadata": {},
   "source": [
    "**Q5**. Implement a function `gradient_descent` taking as arguments `grad_f`, `eta`, `x0`, `max_iter` (defined as in *2.Q1*), `return_all` a boolean indicating if we keep in memory all iterates and `callback` a callable that is called at each iteration if not `None`. If `return_all` and `callback` are `None`, it should behave like `gradient_descent_tmp`. Otherwise, it should return a `dict` containing the final iterate, and eventually all the iterates and outputs of the callback. The function may look like the following stub\n",
    "```python\n",
    "def gradient_descent(grad_f, eta, x0, max_iter, return_all=False, callback=None):\n",
    "    x = x0\n",
    "    fxs = []\n",
    "    xs = []\n",
    "    # Do something\n",
    "    if not callback and not return_all:\n",
    "        return x\n",
    "    else:\n",
    "        return {\n",
    "            'res': x,\n",
    "            'callbacks': fxs,\n",
    "            'iterates': xs,\n",
    "        }\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "193ab301",
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent(grad_f, eta, x0, max_iter, return_all=False, callback=None):\n",
    "    pass"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f333a059",
   "metadata": {},
   "source": [
    "**Q6**. Display the gradient descent on `f2D_convex` by plotting the function value both in linear scale, and loglog scale. Look at the documentation of `matplotlib.pyplot.loglog`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3acbf3c2",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "923b1848",
   "metadata": {},
   "source": [
    "**Q7**. Visualize the gradient steps on a contour plot. Try several initializations. Try several step-sizes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6e788d25",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1475eca30>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x900 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-1,1,50)\n",
    "y = np.linspace(-1.5,0.5,50)\n",
    "X,Y = np.meshgrid(x,y)\n",
    "Z = np.vectorize(lambda x,y: f2D_convex(np.array([x,y])))(X,Y)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(9, 9))\n",
    "ax.contourf(X, Y, Z, 20)\n",
    "ax.contour(X,Y,Z, 20, colors='k')\n",
    "\n",
    "# Display the iterates\n",
    "xs = res['iterates']\n",
    "# BEGIN STUDENT CODE\n",
    "\n",
    "# END STUDENT CODE\n",
    "solution = np.array([0,-1])\n",
    "ax.plot(solution[0],solution[1],marker='x', color ='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "451e1e72",
   "metadata": {},
   "source": [
    "## Let's go to higher dimension.\n",
    "\n",
    "For a matrix $A \\in \\mathbb{R}^{n \\times p}$ and a vector $b \\in \\mathbb{R}^{n}$, the least-square objective reads\n",
    "$$ f(x) = \\frac{1}{2n} \\| A x - b \\|_2^2 . $$\n",
    "\n",
    "**Q1**. Generate a matrix `A` of size 100 by 200 with i.i.d. normal entries and `b` also i.i.d. normal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0b127465",
   "metadata": {},
   "outputs": [],
   "source": [
    "n, p = 5, 5\n",
    "rng = np.random.default_rng()\n",
    "# BEGIN STUDENT CODE\n",
    "\n",
    "# END STUDENT CODE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "776e11a1",
   "metadata": {},
   "source": [
    "**Q2**. Implement `least_square` and its gradient `grad_least_square` with respect to `x`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f435e6b1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def least_square(x):\n",
    "    pass\n",
    "\n",
    "def grad_least_square(x):\n",
    "    pass"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aab9d3c1",
   "metadata": {},
   "source": [
    "**Q3**. Compute the Lipschitz constant $L$ of $\\nabla f$ and write a learning rate policy `lr_policy_least_square` _independant_ from the strong-convexity constant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "70a60dbb",
   "metadata": {},
   "outputs": [],
   "source": [
    "L = np.linalg.norm(1/n * A.T @ A, 2) # DONT FORGET THE 2 !!!!!!!\n",
    "def lr_policy_least_square(x, t):\n",
    "    pass"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d57e551",
   "metadata": {},
   "source": [
    "**Q4**. Run the gradient descent with the obtained policy, and plot in semilogy scale the evolution of the objective function. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cc1cb82",
   "metadata": {},
   "source": [
    "**Q5**. Perform the same experiment with `A` of size 100 x 100. Does the numerics confirm the theory studied in the lecture? If not, how to explain this behavior? If yes, explain."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e18f184e",
   "metadata": {},
   "source": [
    "## Digits classification\n",
    "\n",
    "We now turn our attention to a classification problem.\n",
    "For the sake of simplicity, we will use the digits UCI ML dataset contained in `scikit-learn`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "f266424f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load digits dataset, note that the first time you run this, it will download the dataset (could take a while)\n",
    "from sklearn.datasets import load_digits"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3a3acb2",
   "metadata": {},
   "source": [
    "This dataset is composed of 1797 samples, each of theme of size $8 \\times 8 = 64$ in gray level (coded on [0,255]).\n",
    "This is a low resolution dataset that will be easy to treat as a \"batch\".\n",
    "We can access the data as vectors in `digits.data` and as images in `digits.images`.\n",
    "The labels are contained in `digits.target`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "837587a3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset dimensions: (1797, 64)\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 800x800 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "digits = load_digits()\n",
    "(n_samples, n_features) = digits.data.shape\n",
    "print(f\"Dataset dimensions: {(n_samples, n_features)}\")\n",
    "\n",
    "# Display a few digits\n",
    "fig, axs = plt.subplots(2, 2, figsize=(8, 8))\n",
    "idx = [0, 42, 345, 826]\n",
    "for i, ax in enumerate(axs.ravel()):\n",
    "    ax.imshow(digits.images[idx[i]], cmap='gray')\n",
    "    ax.set_title(f\"Label {digits.target[idx[i]]}\")\n",
    "    ax.axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54150977",
   "metadata": {},
   "source": [
    "**Q1**. Using `sklearn.model_selection.train_test_split`, split the dataset into a training and a test sets.\n",
    "Center the training and the test set relative to the mean image of the training set.\n",
    "Add a column of ones to take into account the potential bias term"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "61ee1b56",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Split the dataset into train and test with a 80/20 ratio\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    digits.data, digits.target, test_size=0.2, random_state=42\n",
    ")\n",
    "\n",
    "# Center the data\n",
    "X_train = (X_train - X_train.mean(axis=0))\n",
    "X_test = (X_test - X_train.mean(axis=0))\n",
    "\n",
    "# Add a column of ones to the data to account for the bias\n",
    "X_train = np.hstack([X_train, np.ones((X_train.shape[0], 1))])\n",
    "X_test = np.hstack([X_test, np.ones((X_test.shape[0], 1))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "4e95efa1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x147ec2610>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(X_train.mean(axis=0)[:-1].reshape((8,8)), cmap=\"Greys\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a724482",
   "metadata": {},
   "source": [
    "To perform our classification task, we will turn to the multinomial logistic regression, or softmax classification.\n",
    "The objective function here will be seek a weight matrix $W \\in \\mathbb{R}^{K \\times p}$\n",
    "\n",
    "$$ f(W) = {\\color{red}-\\frac{1}{n}} \\sum_{i=1}^n \\sum_{k=0}^{K-1} [y_i = k] \\log(\\hat p(y_i = k | X_i)) + \\lambda \\| W \\|_{Fro}^2, $$\n",
    "where\n",
    "$$ \\hat p(y_i = k | X_i) = \\frac{\\exp(X_i^\\top W_k)}{\\sum_{l=0}^{K-1}\\exp(X_i^\\top W_l)} . $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c570c3e1",
   "metadata": {},
   "source": [
    "**Numerical stability of the softmax**. When computing the softmax of a vector, one has to be careful of the potential numerical errors due to the large values of $\\exp$ when the argument is above 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "dde8bcad",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/8t/5m3w4y0s2jd1lbgfyj_h3_280000gn/T/ipykernel_79230/1233423015.py:1: RuntimeWarning: overflow encountered in exp\n",
      "  np.exp(1000.0)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "inf"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(1000.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "3af9d3cd",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/8t/5m3w4y0s2jd1lbgfyj_h3_280000gn/T/ipykernel_79230/25557391.py:2: RuntimeWarning: overflow encountered in exp\n",
      "  proba = np.exp(scores) / np.sum(np.exp(scores))\n",
      "/var/folders/8t/5m3w4y0s2jd1lbgfyj_h3_280000gn/T/ipykernel_79230/25557391.py:2: RuntimeWarning: invalid value encountered in divide\n",
      "  proba = np.exp(scores) / np.sum(np.exp(scores))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0., nan])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores = np.array([433, 23, 766])\n",
    "proba = np.exp(scores) / np.sum(np.exp(scores))\n",
    "proba"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d87db96e",
   "metadata": {},
   "source": [
    "Clearly here, we would expect to obtain `[0., 0., 1.]`.\n",
    "Remark that for any $c > 0$,\n",
    "$$\n",
    "\\sigma(z)_i\n",
    "=\n",
    "\\frac{\\exp(z_i)}{\\sum_{i=1}^p \\exp{(z_j)}}\n",
    "=\n",
    "\\frac{c\\exp(z_i)}{c\\sum_{i=1}^p \\exp{(z_j)}}\n",
    "=\n",
    "\\frac{\\exp(z_i + \\log c)}{\\sum_{i=1}^p \\exp{(z_j + \\log c)}}\n",
    "$$\n",
    "A typical choice of $c$ is given by the solution of $\\log c = - \\max_j z_j$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "61455c3e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.39848787e-145, 1.97626258e-323, 1.00000000e+000])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores = np.array([433, 23, 766])\n",
    "scores -= np.max(scores)\n",
    "proba = np.exp(scores) / np.sum(np.exp(scores))\n",
    "proba"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dcc3b932",
   "metadata": {},
   "source": [
    "**Q2**. Implement the `softmax_loss` function below. Take care to the potential numerical errors thanks to the trick above. _Hint_: remember that `numpy.arange(n)` build a ndarray containing all integer from 0 to `n` (included)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "755f0ffa",
   "metadata": {},
   "outputs": [],
   "source": [
    "def softmax_loss(W, X, y, reg):\n",
    "    \"\"\"\n",
    "    Softmax loss function\n",
    "\n",
    "    Inputs:\n",
    "    - W: ndarray (n_features, K) containing weights.\n",
    "    - X: ndarray (n, n_features) containing data.\n",
    "    - y: ndarray (n,) containing training labels\n",
    "    - reg: (float) regularization\n",
    "\n",
    "    Returns the softmax loss (with regularization)\n",
    "    \"\"\"\n",
    "    return None"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35171b04",
   "metadata": {},
   "source": [
    "To debug it, run the following cell. You should obtain a value close to $-\\log(1/10)$.\n",
    "\n",
    "**Q3**: Why should we obtain something close to this value?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "fadc3c76",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loss: 2.3008829569560394, expected: 2.3025850929940455\n"
     ]
    }
   ],
   "source": [
    "# Generate a random softmax weight matrix\n",
    "W = np.random.randn(64+1, 10) * 0.001\n",
    "# Compute the softmax loss\n",
    "loss = softmax_loss(W, X_train, y_train, 0.0)\n",
    "\n",
    "# As a rough sanity check, our loss should be something more or less close to -log(0.1).\n",
    "print(f\"Loss: {loss}, expected: {-np.log(0.1)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5a284fc",
   "metadata": {},
   "source": [
    "**Q4**. Compute the gradient of the loss $\\nabla f(W)$ with respect to weight matrix."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ef51224",
   "metadata": {},
   "source": [
    "**Q5**. Implement the gradient of the softmax loss as a `softmax_grad` function below. _Hint_: This function will be _very_ close to `softmax_loss`. Note that it would be more adequate to write a unique function returning _both_ the loss and the gradient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "61c97e63",
   "metadata": {},
   "outputs": [],
   "source": [
    "def softmax_grad(W, X, y, reg):\n",
    "    return pass"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "675e72f8",
   "metadata": {},
   "source": [
    "**Q6**. Run the gradient descent on the loss function defined by the training set. You should use a constant step size policy. _Hint_: define `softmax_grad_train` and `softmax_loss_train` taking only `W` as input."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "61da860c",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$f(x^{(t)}) - f(x^\\\\star)$')"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "reg = 0.001\n",
    "n_iter = 1000\n",
    "\n",
    "# BEGIN STUDENT CODE\n",
    "\n",
    "# END STUDENT CODE\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.semilogy(res['callbacks'][:int(0.9*n_iter)] - res['callbacks'][-1])\n",
    "ax.set_xlabel('iterate $t$')\n",
    "ax.set_ylabel('$f(x^{(t)}) - f(x^\\star)$')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e17a770",
   "metadata": {},
   "source": [
    "**Q7**. Display the training and test accuracies. Comment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c62c787e",
   "metadata": {
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training set accuracy: 0.9909533750869868\n",
      "Test set accuracy: 0.8583333333333333\n"
     ]
    }
   ],
   "source": [
    "# BEGIN STUDENT CODE\n",
    "\n",
    "# END STUDENT CODE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36bb7b3f",
   "metadata": {},
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  },
  "vscode": {
   "interpreter": {
    "hash": "6c32173c3c9387216480b2d6fa4b8cb6520c491e98c28fd9af26a916640dbc8f"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
