talks/neural_networks_training.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Training neural networks to predict turbulence\n",
    "\n",
    "Preamble: Run the cells below to import the necessary Python packages\n",
    "\n",
    "*This notebook created by William Gilpin. Consult the [course website](https://www.wgilpin.com/cphy) for all content and [GitHub repository](https://github.com/williamgilpin/cphy) for raw files and runnable online code.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Preamble / required packages\n",
    "import numpy as np\n",
    "np.random.seed(0)\n",
    "\n",
    "## Import local plotting functions and in-notebook display functions\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import Image, display\n",
    "%matplotlib inline\n",
    "\n",
    "import warnings\n",
    "## Comment this out to activate warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "\n",
    "# plt.style.use(\"dark_background\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training a model\n",
    "\n",
    "+ Given a model $f(\\boldsymbol{x}; \\boldsymbol{\\theta})$ and a dataset $\\{(\\boldsymbol{x}_i, y_i)\\}$, we want to find the parameters $\\boldsymbol{\\theta}$ that best describe the data.\n",
    "\n",
    "+ Linear regression had an analytic equation for the weight matrix $\\boldsymbol{\\theta}$, turns out to minimize the least-squares cost function $J(\\boldsymbol{\\theta}) = \\frac{1}{2} \\sum_i (y_i - f(\\boldsymbol{x}_i; \\boldsymbol{\\theta}))^2$.\n",
    "\n",
    "+ Usually we aren't so lucky as to have an exactly solvable convex optimization problem\n",
    "\n",
    "+ The next best thing is to have an optimization problem (possibly non-convex) where the loss is a smooth, differentiable function of the weights. In this case, we can use gradient descent and its variants\n",
    "\n",
    "#### An aside: What if our problem is non-differentiable?\n",
    "\n",
    "+ Brute force (try random parameters or grid search and see what gives the best result).\n",
    "\n",
    "+ Genetic algorithms, reinforcement learning\n",
    "\n",
    "+ Can attempt to use gradient descent, if we can construct a differentiable surrogate function for the true loss\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Revisiting predicting the Reynolds number of a turbulent flow\n",
    "\n",
    "+ Our dataset consists of snapshots of the velocity field of a turbulent flow, labelled the corresponding Reynolds number.\n",
    "\n",
    "+ Recall that the Reynolds number is a dimensionless number that characterizes the flow regime of a fluid. The higher the Reynolds number, the more turbulent the flow.\n",
    "\n",
    "+ Because we are going to use fully-connected nets, we need to downsample the dataset substantially to have a reasonable training time\n",
    "\n",
    "+ We will implement a data loader that will fetch the dataset, and perform standardization and downsampling.\n",
    "\n",
    "+ We will also perform a train/test split in the data loader"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset size: X_train: (1920, 4096), y_train: (1920,)\n",
      "Dataset size: X_test: (480, 4096), y_test: (480,)\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1200x300 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Load the Reynold number regression dataset\n",
    "\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler, MinMaxScaler\n",
    "\n",
    "class ReynoldsDataset:\n",
    "    \"\"\"\n",
    "    Class to load the Reynolds number classification dataset\n",
    "    \n",
    "    Parameters:\n",
    "        downsample (int): Factor by which to downsample the dataset\n",
    "        split (float): Fraction of data to use for testing\n",
    "        random_state (int): Random seed for reproducibility\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, downsample=1, split=0.2, random_state=None):\n",
    "        \n",
    "        self.random_state = random_state\n",
    "\n",
    "        all_vorticity_fields = list()\n",
    "        all_reynolds_numbers = list()\n",
    "\n",
    "        # Load simulations for different Reynolds numbers\n",
    "        re_vals = [300, 600, 900, 1200]\n",
    "        for re_val in re_vals:\n",
    "\n",
    "            # Load the two-dimensional velocity field data. Data is stored in a 4D numpy array,\n",
    "            # where the first dimension is the time index, the second and third dimensions are the\n",
    "            # x and y coordinates, and the fourth dimension is the velocity components (ux or uv).\n",
    "            vfield = np.load(\n",
    "                f\"../resources/von_karman_street/vortex_street_velocities_Re_{re_val}_largefile.npz\", \n",
    "                allow_pickle=True\n",
    "            )\n",
    "\n",
    "            # Calculate the vorticity, which is the curl of the velocity field\n",
    "            vort_field = np.diff(vfield, axis=1)[..., :-1, 1] + np.diff(vfield, axis=2)[:, :-1, :, 0]\n",
    "\n",
    "            # Crop to wake field only\n",
    "            vort_field = vort_field[::5, -127:, :][:, 32:96, 32:96]\n",
    "\n",
    "            # downsample the dataset\n",
    "            vort_field = vort_field[:, ::downsample, ::downsample]\n",
    "\n",
    "            all_vorticity_fields.append(vort_field)\n",
    "            all_reynolds_numbers.extend(re_val * np.ones(vort_field.shape[0]))\n",
    "\n",
    "        self.data_shape = vort_field[0].shape\n",
    "\n",
    "        all_vorticity_fields = np.vstack(all_vorticity_fields)\n",
    "        all_reynolds_numbers = np.array(all_reynolds_numbers)\n",
    "\n",
    "        X = np.reshape(all_vorticity_fields, (all_vorticity_fields.shape[0], -1))\n",
    "        y = all_reynolds_numbers\n",
    "\n",
    "        X_train, X_test, y_train, y_test = train_test_split(X, y, \n",
    "                                                            test_size=split, \n",
    "                                                            random_state=self.random_state\n",
    "                                                            )\n",
    "\n",
    "        self.X_train = X_train\n",
    "        self.X_test = X_test\n",
    "        self.y_train = y_train\n",
    "        self.y_test = y_test\n",
    "        self.X = np.vstack([X_train, X_test])\n",
    "        self.y = np.hstack([y_train, y_test])\n",
    "\n",
    "    def reshape(self, X):\n",
    "        if len(X.shape) == 1:\n",
    "            return X.reshape(self.data_shape)\n",
    "        elif len(X.shape) == 2:\n",
    "            return np.reshape(X, (X.shape[0], *self.data_shape))\n",
    "        else:\n",
    "            raise ValueError(\"X must be a 1D or 2D array\")\n",
    "    \n",
    "    def __len__(self):\n",
    "        return len(self.y)\n",
    "\n",
    "    def __getitem__(self, idx):\n",
    "        return self.X[idx], self.y[idx]\n",
    "\n",
    "\n",
    "dataset = ReynoldsDataset()\n",
    "\n",
    "print(f\"Dataset size: X_train: {dataset.X_train.shape}, y_train: {dataset.y_train.shape}\")\n",
    "print(f\"Dataset size: X_test: {dataset.X_test.shape}, y_test: {dataset.y_test.shape}\")\n",
    "\n",
    "## plot examples of the dataset\n",
    "fig, ax = plt.subplots(1, 4, figsize=(12, 3))\n",
    "for i, re in enumerate([300, 600, 900, 1200]):\n",
    "    ax[i].imshow(dataset.reshape(dataset.X[dataset.y == re][0]), cmap='coolwarm', vmin=-.005, vmax=.005)\n",
    "    ax[i].set_title(f\"Re = {re}\")\n",
    "    ax[i].axis(\"off\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x300 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 4, figsize=(12, 3))\n",
    "for i, re in enumerate([300, 600, 900, 1200]):\n",
    "    ax[i].imshow(dataset.reshape(dataset.X[dataset.y == re][0]), cmap='coolwarm', vmin=-.005, vmax=.005)\n",
    "    ax[i].set_title(f\"Re = {re}\")\n",
    "    ax[i].axis(\"off\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Before fitting a model, check the data\n",
    "\n",
    "We first perform an unsupervised embedding, and color the points by the true Reynolds number. \n",
    "\n",
    "+ We see that the data is not linearly separable, so this is likely a non-trivial learning problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'PCA Component 2')"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "## Perform PCA on the dataset\n",
    "pca = PCA(n_components=2)\n",
    "pca.fit(dataset.X_train)\n",
    "\n",
    "## Plot the PCA components\n",
    "fig, ax = plt.subplots(figsize=(6, 6))\n",
    "ax.scatter(dataset.X_train[:, 0], dataset.X_train[:, 1], c=dataset.y_train, cmap='rainbow')\n",
    "ax.set_xlabel(\"PCA Component 1\")\n",
    "ax.set_ylabel(\"PCA Component 2\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Are the classes balanced?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fraction of class 1200: 0.261\n",
      "Fraction of class 1200: 0.244\n",
      "Fraction of class 1200: 0.251\n",
      "Fraction of class 1200: 0.244\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Number of Samples in Training Set')"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Are the classes balanced?\n",
    "class_ids = np.unique(dataset.y_train)\n",
    "counts = list()\n",
    "for id in class_ids:\n",
    "    print(f\"Fraction of class {re}: {np.mean(dataset.y_train == id):.3f}\")\n",
    "    counts.append(np.sum(dataset.y_train == id))\n",
    "\n",
    "plt.figure(figsize=(6, 4))\n",
    "plt.bar(class_ids, counts, width=100)\n",
    "plt.xticks(class_ids)\n",
    "plt.xlabel(\"Reynolds Number\")\n",
    "plt.ylabel(\"Number of Samples in Training Set\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate baseline predictions\n",
    "\n",
    "+ Since this is a regression problem, we will generate baseline predictions using a linear regression model\n",
    "\n",
    "+ We will use the `sklearn` implementation of ridge regression\n",
    "\n",
    "+ Instead of manually tuning the regularization parameter, we will use cross-validation to find the best value. `sklearn` has a built-in model that will perform this automatically, `RidgeCV`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test set R^2: 0.205\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import RidgeCV\n",
    "\n",
    "## Train a linear model to predict the Reynolds number\n",
    "model = RidgeCV()\n",
    "model.fit(dataset.X_train, dataset.y_train)\n",
    "y_pred = model.predict(dataset.X_test)\n",
    "\n",
    "## Evaluate the model on the test set\n",
    "print(f\"Test set R^2: {model.score(dataset.X_test, dataset.y_test):.3f}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Let's try a neural network"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "+ Recall that a two-layer multilayer perceptron has the form\n",
    "\n",
    "  $$\n",
    "  \\hat{\\mathbf{y}} = \\sigma(\\boldsymbol{\\theta}_2 \\sigma(\\boldsymbol{\\theta}_1 \\mathbf{x}))\n",
    "  $$\n",
    "\n",
    "  where $\\sigma$ is an elementwise function (such as the logistic function), and $\\boldsymbol{\\theta}_1$ and $\\boldsymbol{\\theta}_2$ are trainable weight matrices.\n",
    "\n",
    "+ For our problem, $\\mathbf{x}$ is the flattened velocity field, and $\\hat{\\mathbf{y}}$ is the predicted Reynolds number. While the output is a scalar here, this isn't a requirement of the model.\n",
    "\n",
    "+ We will use `scikit-learn`'s own implementation of a multi-layer perceptron (MLP) \n",
    "\n",
    "+ This implements a few architectural features and hyperparameters that would be difficult for us to implement ourselves: \n",
    "    + The \"Adam\" optimizer is a variant of gradient descent that uses adaptive learning rates and momentum\n",
    "    + The \"relu\" activation function is a non-linear function that is more robust to vanishing gradients than the logistic function\n",
    "    + The \"batch size\" is the number of samples used to compute the gradient at each step. This is a compromise between using the full dataset (which is slow) and using a single sample (which is noisy). \n",
    "    + The \"epoch\" is the number of times the entire dataset is used to compute the gradient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2 score: 0.982845\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Predicted Reynolds number')"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.neural_network import MLPRegressor\n",
    "mlp = MLPRegressor(\n",
    "    hidden_layer_sizes=(10, 10), \n",
    "    activation='relu', \n",
    "    solver='adam', \n",
    "    learning_rate='constant',\n",
    "    learning_rate_init=0.001, \n",
    "    max_iter=1000, \n",
    "    random_state=0, \n",
    "    batch_size=32\n",
    ")\n",
    "\n",
    "# Fit the model to the data.\n",
    "mlp.fit(dataset.X_train, dataset.y_train)\n",
    "\n",
    "# Generate predictions on the test set.\n",
    "y_test_pred = mlp.predict(dataset.X_test)\n",
    "\n",
    "## Score using R^2\n",
    "print(\"R^2 score: %f\" % mlp.score(dataset.X_test, dataset.y_test))\n",
    "\n",
    "plt.figure(figsize=(6, 6))\n",
    "plt.plot(dataset.y_test, y_test_pred, '.', alpha=0.1)\n",
    "plt.xlabel(\"True Reynolds number\")\n",
    "plt.ylabel(\"Predicted Reynolds number\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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  },
  {
   "cell_type": "code",
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   "cell_type": "markdown",
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   "source": [
    "# How do we train a multilayer perceptron? Iterative optimization\n",
    "\n",
    "\n",
    "\n",
    "Given a model \n",
    "$$\n",
    "\\hat{\\mathbf{y}} = \\sigma(\\boldsymbol{\\theta}_2 \\sigma(\\boldsymbol{\\theta}_1 \\mathbf{x}))\n",
    "$$\n",
    "\n",
    "with known true labels $y$ for every $\\mathbf{x}$, we can update the weights with gradient descent:\n",
    "\n",
    "$$\\theta_{i+1} = \\theta_i - \\eta \\frac{\\partial \\mathcal{L}}{\\partial \\theta_i}$$\n",
    "\n",
    "where $\\eta$ is the learning rate. Given a training set with $N$ examples, we usually take the average of the gradient computed over the $N$ examples.\n",
    "\n",
    "\n",
    "### Linear model\n",
    "\n",
    "We saw that linear regression and ridge regression have an analytic solution for the optimal weights. This is not the case for neural networks. Instead, we need to use gradient descent. It turns out that we can also frame linear regression as a neural network, and use the same gradient descent algorithm to train it. This is useful for large datasets, where pseudo-inverse methods are too slow.\n",
    "\n",
    "A linear model is given by\n",
    "\n",
    "$$\\hat{y} = \\theta_0 + \\theta_1 x_1 + \\theta_2 x_2 + \\cdots + \\theta_n x_M$$\n",
    "\n",
    "For linear regression, we typically use the mean-squared loss function,\n",
    "\n",
    "$$\\mathcal{L} = \\frac{1}{2} \\sum_{i=1}^N (\\hat{y}_i - y_i)^2$$\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\mathcal{L}}{\\partial \\theta_j} = \\sum_{i=1}^N (\\hat{y}_j - y_j) x_{ij}\n",
    "$$\n",
    "\n",
    "where $i$ indexes the data points and $j$ indexes the features.\n",
    "\n",
    "### Logistic model:\n",
    "\n",
    "The model is\n",
    "\n",
    "$$\\hat{y} = \\frac{1}{1 + e^{-\\theta_0 - \\theta_1 x_1 - \\theta_2 x_2 - \\cdots - \\theta_n x_M}}$$\n",
    "\n",
    "Instead of mean-squared error, logistic models are often trained using cross-entropy loss:\n",
    "\n",
    "$$\\mathcal{L} = - \\sum_{i=1}^N y_i \\log \\hat{y}_i + (1 - y_i) \\log (1 - \\hat{y}_i)$$\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\mathcal{L}}{\\partial \\theta_j} = -\\sum_{i=1}^N \\dfrac{1}{4} x_{ij} \\log(2 y_i - 1) \\text{sech}^2\\left(\\dfrac{\\theta_j x_{ij}}{2}\\right)\n",
    "$$\n",
    "\n",
    "where $i$ indexes the data points and $j = 1, 2, ..., M$ indexes the features. $\\frac{\\partial \\mathcal{L}}{\\partial \\theta_j} \\in \\mathbb{R}^M$ is the gradient of the loss with respect to the weights.\n",
    "\n",
    "\n",
    "\n",
    "### Multivariate Linear model\n",
    "\n",
    "The model is\n",
    "\n",
    "$$\\hat{\\mathbf{y}} = \\boldsymbol{\\theta} \\mathbf{X}$$\n",
    "\n",
    "where $\\mathbf{x}$ is a $1 \\times D$ matrix with $N$ data points and $D$ features, the weight matrix $\\boldsymbol{\\theta} \\in \\mathbb{R}^{M \\times D}$ , and the prediction vector is $\\hat{\\mathbf{y}} \\in \\mathbb{R}^M$. Usually, we work with the data matrix $X = \\{ \\mathbf{x}_i \\} \\in \\mathbb{R}^{N \\times D}$.\n",
    "\n",
    "The mean-squared loss function is\n",
    "\n",
    "$$\\mathcal{L} = \\frac{1}{2} \\sum_{i=1}^N (\\hat{\\mathbf{y}}_i - \\mathbf{y}_i)^T(\\hat{\\mathbf{y}}_i - \\mathbf{y}_i)$$\n",
    "\n",
    "The gradient is\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\mathcal{L}}{\\partial \\boldsymbol{\\theta}} = \\sum_{i=1}^N (\\hat{\\mathbf{y}}_i - \\mathbf{y}_i) \\mathbf{x}_i^T\n",
    "$$\n",
    "\n",
    "Notice that the gradient is a matrix $\\frac{\\partial \\mathcal{L}}{\\partial \\boldsymbol{\\theta}}  \\in  \\mathbb{R}^{M \\times D}$, where each row is the gradient of the loss with respect to the weights for a single output. This means that we have update values separately for each element of the weight matrix. Also, note that the right hand side is an outer product, while the forward pass is an inner product.\n",
    "\n",
    "<!-- ### Neural network\n",
    "\n",
    "The model is\n",
    "\n",
    "$$\\hat{y} = f(\\theta_0 + \\theta_1 x_1 + \\theta_2 x_2 + \\cdots + \\theta_n x_n)$$\n",
    "\n",
    "where $f$ is a non-linear function. For example, $f$ could be a sigmoid function:\n",
    "\n",
    "$$f(x) = \\frac{1}{1 + e^{-x}}$$ -->\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
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   "metadata": {},
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gradient descent requires us to take gradients of each trainable parameter with respect to the loss\n",
    "\n",
    "+ Let's start by thinking about how we would do this in low dimensions\n",
    "\n",
    "+ Suppose I wanted to take the gradient of the double well potential\n",
    "\n",
    "$$\n",
    "V(x) = x^4 - 2 x^2\n",
    "$$\n",
    "\n",
    "I could find the gradient analytically by taking the derivative\n",
    "\n",
    "The gradient of the potential is\n",
    "$$\n",
    "\\frac{\\partial V}{\\partial x} = 4 x^3 - 4 x\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def double_well(x):\n",
    "    \"\"\"Double well potential function\"\"\"\n",
    "    return x**4 - 2*x**2\n",
    "\n",
    "def double_well_grad(x):\n",
    "    \"\"\"Derivative of double well potential function\"\"\"\n",
    "    return 4*x**3 - 4*x\n",
    "\n",
    "print(double_well(0.12132987))\n",
    "print(double_well_grad(0.12132987))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### But we implicitly performed several subroutines to do this.\n",
    "\n",
    "### Let's write out these functions in terms of basic computational steps\n",
    "\n",
    "\n",
    "\n",
    "Given an $x$, computing $V(x)$ (the forward evaluation, or *forward pass*) can be broken up into\n",
    "\n",
    "$$\n",
    "h_1 = x^4\n",
    "$$\n",
    "$$\n",
    "h_2 = 2 x^2\n",
    "$$\n",
    "$$\n",
    "V = h_1 - h_2\n",
    "$$\n",
    "\n",
    "\n",
    "\n",
    "Now, given $V$, we want to compute $\\frac{\\partial V}{\\partial x}$ (the backward evaluation, or *backward pass*). We can break this up into\n",
    "\n",
    "$$\n",
    "g_1 = 4 x\n",
    "$$\n",
    "$$\n",
    "g_2 = 4 x^3\n",
    "$$\n",
    "$$\n",
    "g_3 = -1\n",
    "$$\n",
    "$$\n",
    "\\frac{\\partial V}{\\partial x} = g_2 + g_3 g_1\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def double_well_primitive(x):\n",
    "    \"\"\"Decompose the double well calculation into primitive operations\"\"\"\n",
    "    h1a = x**4\n",
    "    h1b = 2*x**2\n",
    "    h2 = h1a - h1b\n",
    "    return h2\n",
    "\n",
    "def double_well_primitive_grad(x):\n",
    "    \"\"\"Decompose the double well gradient calculation into primitive operations\"\"\"\n",
    "    dh2dh1a = 1\n",
    "    dh2dh1b = -1\n",
    "    dh1adx = 4*x**3\n",
    "    dh1bdx = 4*x\n",
    "    dh2dx = dh2dh1a * dh1adx + dh2dh1b * dh1bdx\n",
    "    return dh2dx\n",
    "\n",
    "print(double_well_primitive(0.12132987))\n",
    "print(double_well_primitive_grad(0.12132987))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Backpropagation is the chain rule on a computation graph\n",
    "\n",
    "\n",
    "<img src=\"../resources/backprop1.png\" width=\"750\">\n",
    "<img src=\"../resources/backprop2.png\" width=\"750\">\n",
    "\n",
    "*Diagrams from [UW CSE599W lecture notes](https://dlsys.cs.washington.edu/pdf/lecture4.pdf)*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vector-valued functions\n",
    "\n",
    "+ We can see that we were able to simplify the calculation by breaking the forward pass into discrete steps that got combined, and that the backward pass was able to reuse some of the intermediate calculations.\n",
    "\n",
    "+ What if we go to higher dimensions? Recall that our neural network has a forward pass that looks like\n",
    "\n",
    "$$\n",
    "\\hat{\\mathbf{y}} = \\sigma(\\boldsymbol{\\theta}_2 \\sigma(\\boldsymbol{\\theta}_1 \\mathbf{x}))\n",
    "$$\n",
    "\n",
    "where $\\sigma$ is the logistic function. We combine a given prediction on a single datapoint $\\hat{\\mathbf{y}}$ with the true label $\\mathbf{y}$ to compute the mean-squared error loss\n",
    "\n",
    "$$\n",
    "\\mathcal{L} = \\frac{1}{2} (\\hat{\\mathbf{y}} - \\mathbf{y})^T (\\hat{\\mathbf{y}} - \\mathbf{y})\n",
    "$$\n",
    "\n",
    "In order to perform gradient descent, we need to compute the gradient of the loss with respect to the weights $\\boldsymbol{\\theta}_1$ and $\\boldsymbol{\\theta}_2$. While the loss is a scalar, the gradient is a vector."
   ]
  },
  {
   "cell_type": "code",
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  },
  {
   "cell_type": "code",
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   "source": [
    "## Backpropagation through a multilayer perceptron\n",
    "\n",
    "### Forward pass\n",
    "\n",
    "When a trained neural network is given an input $\\mathbf{x}$, it computes an output $\\hat{\\mathbf{y}}$ by passing the input through a series of layers. Each layer is a linear transformation followed by a non-linear function. For example, a two-layer network is given by\n",
    "\n",
    "$$\n",
    "\\hat{\\mathbf{y}} = \\sigma(\\boldsymbol{\\theta}_2 \\sigma(\\boldsymbol{\\theta}_1 \\mathbf{x}))\n",
    "$$\n",
    "for concreteness, we will use the sigmoid nonlinearity $\\sigma(x) = \\frac{1}{1 + e^{-x}}$.\n",
    "\n",
    "We start by breaking this into single steps\n",
    "\n",
    "$$\n",
    "\\mathbf{h}_1^{u} = \\boldsymbol{\\theta}_1 \\mathbf{x}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\mathbf{h}_1 = \\sigma(\\mathbf{h}_1^{u})\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\mathbf{h}_2^{u} = \\boldsymbol{\\theta}_2 \\mathbf{h}_1\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\hat{\\mathbf{y}} = \\sigma(\\mathbf{h}_2^{u})\n",
    "$$\n",
    "\n",
    "\n",
    "### Backward pass\n",
    "\n",
    "Suppose we pass an input $\\mathbf{x} \\in \\mathbb{R}^D$ and get an output $\\hat{\\mathbf{y}} \\in \\mathbb{R}^M$, and we know the true output is $\\mathbf{y}\\in \\mathbb{R}^M$.\n",
    "\n",
    "If we are using the mean-squared error loss function, then for a single training example $\\mathbf{y}$, the loss $\\mathcal{L} \\in \\mathbb{R}$ is\n",
    "\n",
    "$$\n",
    "\\mathcal{L} = \\frac{1}{2} (\\hat{\\mathbf{y}} - \\mathbf{y})^\\top(\\hat{\\mathbf{y}} - \\mathbf{y})\n",
    "$$\n",
    "\n",
    "We want to update all the parameters $\\boldsymbol{\\theta}_1$ and $\\boldsymbol{\\theta}_2$ to minimize this loss.\n",
    "\n",
    "To calculate $\\frac{\\partial \\mathcal{L}}{\\partial \\boldsymbol{\\theta}_2} \\in \\mathbb{R}^{M \\times H_2}$, we need to use the chain rule,\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\mathcal{L}}{\\partial \\boldsymbol{\\theta}_2} = \\frac{\\partial \\mathcal{L}}{\\partial \\hat{\\mathbf{y}}} \\frac{\\partial \\hat{\\mathbf{y}}}{\\partial \\mathbf{h}_2^{u}} \\frac{\\partial \\mathbf{h}_2^{u}}{\\partial \\boldsymbol{\\theta}_2}\n",
    "$$\n",
    "\n",
    "In a *reverse-mode* chain rule evaluation, we can solving this sequence from left-to-right,\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\mathcal{L}}{\\partial \\hat{\\mathbf{y}}} = \\hat{\\mathbf{y}} - \\mathbf{y}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\hat{\\mathbf{y}}}{\\partial \\mathbf{h}_2^{u}} = \\hat{\\mathbf{y}} (1 - \\hat{\\mathbf{y}})\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\mathbf{h}_2^{u}}{\\partial \\boldsymbol{\\theta}_2} = \\mathbf{h}_1^\\top\n",
    "$$\n",
    "\n",
    "Putting this all together,\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\mathcal{L}}{\\partial \\boldsymbol{\\theta}_2} = (\\hat{\\mathbf{y}} - \\mathbf{y}) \\odot \\hat{\\mathbf{y}} (1 - \\hat{\\mathbf{y}}) \\mathbf{h}_1^\\top\n",
    "$$\n",
    "\n",
    "where $\\odot$ is the element-wise product. Notice how we actually traversed the network *backwards*, starting with the gradient of the last evaluation we performed during the forward pass.\n",
    "\n",
    "We can now compute the gradient for the first layer.\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\mathcal{L}}{\\partial \\boldsymbol{\\theta}_1} = \n",
    "\n",
    "\\frac{\\partial \\mathcal{L}}{\\partial \\hat{\\mathbf{y}}} \\frac{\\partial \\hat{\\mathbf{y}}}{\\partial \\mathbf{h}_2^{u}} \n",
    "\n",
    "\n",
    " \\frac{\\partial \\mathbf{h}_2^{u}}{\\partial \\mathbf{h}_1} \\frac{\\partial \\mathbf{h}_1}{\\partial \\mathbf{h}_1^{u}} \\frac{\\partial \\mathbf{h}_1^{u}}{\\partial \\boldsymbol{\\theta}_1}\n",
    "$$\n",
    "\n",
    "We can combine the first two terms, which we already calculated above, and then solve from left to right.\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\mathcal{L}}{\\partial \\mathbf{h}_2^{u}} = (\\hat{\\mathbf{y}} - \\mathbf{y}) \\odot \\hat{\\mathbf{y}} (1 - \\hat{\\mathbf{y}}) \\boldsymbol{\\theta}_2^\\top\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\mathbf{h}_2^{u}}{\\partial \\mathbf{h}_1} = \\mathbf{h}_1 (1 - \\mathbf{h}_1)\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\mathbf{h}_1}{\\partial \\mathbf{h}_1^{u}} = \\mathbf{h}_1^{u} (1 - \\mathbf{h}_1^{u})\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\mathbf{h}_1^{u}}{\\partial \\boldsymbol{\\theta}_1} = \\mathbf{x}^\\top\n",
    "$$\n",
    "\n",
    "Putting this all together,\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\mathcal{L}}{\\partial \\boldsymbol{\\theta}_1} = (\\hat{\\mathbf{y}} - \\mathbf{y}) \\odot \\hat{\\mathbf{y}} (1 - \\hat{\\mathbf{y}}) \\boldsymbol{\\theta}_2^\\top \\odot \\mathbf{h}_1 (1 - \\mathbf{h}_1) \\odot \\mathbf{h}_1^{u} (1 - \\mathbf{h}_1^{u}) \\mathbf{x}^\\top\n",
    "$$\n",
    "\n",
    "\n",
    "\n",
    "### Some things to note\n",
    "\n",
    "+ Several of the \"intermediate\" values we computed during the forward pass re-appear when we perform the backwards pass. If we cached these values, then we don't have to recompute them during the backward pass. \n",
    "\n",
    "+ Notice that when we compute the \"forward\" pass we start with the innermost portion of the function composition, and then work our way out. For the backwards pass, we start with the outermost portion of the function composition, and work our way in. \n",
    "\n",
    "+ Notice that the sigmoid function's derivative is a function of its output. This is a common pattern in autodiff. \n",
    "\n",
    "+ In order to keep track of indicies and transposes, it helps to think about the dimensions of the input/output of each primitive operation.\n",
    "\n",
    "+ It's useful to remember the some [rules for matrix multiplication:](https://www.math.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf)\n",
    "\n",
    "$$\n",
    "\\frac{\\partial\\mathbf{A} \\mathbf{B}}{\\partial \\mathbf{A}} = \\mathbf{B}^\\top, \\qquad\n",
    "\\frac{\\partial\\mathbf{A} \\mathbf{B}}{\\partial \\mathbf{B}} = \\mathbf{A}\n",
    "$$\n",
    "<!-- \n",
    "These left-right rules are also used in the derivation of the linear regression pseudoinverse global solution.\n",
    "\n",
    "Additionally, we should remember the chain rule for derivatives:\n",
    "$$\n",
    "\\frac{\\partial\\mathbf{A}(u) \\mathbf{B}(u)}{\\partial u} = \\frac{\\partial\\mathbf{A}(u)}{\\partial u} \\mathbf{B}(u) + \\mathbf{A}(u) \\frac{\\partial\\mathbf{B}(u)}{\\partial u}\n",
    "$$ -->\n"
   ]
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  {
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   "metadata": {},
   "source": [
    "# A reminder regarding indices...\n",
    "\n",
    "For a single datapoint (vector) $\\mathbf{x} \\in \\mathbb{R}^{d}$, the forward pass of a multilayer perceptron is\n",
    "$$\n",
    "\\hat{\\mathbf{y}} = \\sigma(\\boldsymbol{\\theta}_2 \\sigma(\\boldsymbol{\\theta}_1 \\mathbf{x}))\n",
    "$$\n",
    "\n",
    "We normally aggregate many datapoints into a matrix $\\mathbf{X} \\in \\mathbb{R}^{N \\times d}$, where $N$ is the number of datapoints. In this case, the forward pass returns $\\hat{\\mathbf{Y}} \\in \\mathbb{R}^{N \\times 1}$, where each row is the prediction for a single datapoint. For some regression problems (such as the fluid forecasting problem on the homework), $\\hat{\\mathbf{Y}} \\in \\mathbb{R}^{N \\times M}$\n",
    "\n",
    "The first index, the data or \"batch\" index, is usually vectorized: it passes right through the model, since every data point has an output. The first index usually recieves special treatment in high-level packages like PyTorch and TensorFlow, since it is often used to aggregate gradients from multiple datapoints.\n",
    "\n",
    "The loss function is usually a function of the entire dataset, including the batch index. For example, the mean squared loss is\n",
    "$$\n",
    "\\mathcal{L}(X, \\mathbf{y}, \\boldsymbol{\\theta}) = \\frac{1}{N} \\sum_{i=1}^N \\frac{1}{2} (\\hat{y}_i - y_i)^2\n",
    "$$\n",
    "\n",
    "For a multivariate prediction problem, the loss function is\n",
    "\n",
    "$$\n",
    "\\mathcal{L}(X, Y, \\boldsymbol{\\theta}) = \\frac{1}{N} \\sum_{i=1}^N \\frac{1}{2} \\|\\hat{\\mathbf{y}}_i - \\mathbf{y}_i\\|^2\n",
    "$$\n",
    "\n",
    "where $\\hat{\\mathbf{y}}_i \\in \\mathbb{R}^{M}$ and $\\mathbf{y}_i \\in \\mathbb{R}^{M}$.\n",
    "\n",
    "\n",
    "Importantly, when we compute gradients of the loss, we treat *the entire dataset* $X$, the true labels $Y$, and even the current predicted labels $\\hat{Y}$ as a fixed set of constant parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
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   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
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  },
  {
   "cell_type": "code",
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  {
   "cell_type": "markdown",
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   "source": [
    "## What does the code actually look like?\n",
    "\n",
    "+ We will put all of these ideas together into a multilayer perceptron class. \n",
    "\n",
    "+ We will use the RELU activation function, and the mean-squared error loss function.\n",
    "\n",
    "**Note: the code below doesn't work very well on this problem**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2 score: nan\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "def relu(x):\n",
    "    return np.maximum(0, x)\n",
    "\n",
    "def relu_derivative(x):\n",
    "    return np.where(x > 0, 1.0, 0.0)\n",
    "\n",
    "class MultiLayerPerceptron:\n",
    "    \"\"\"\n",
    "    An MLP for regression with mean squared loss\n",
    "\n",
    "    Attributes:\n",
    "        hidden_layer_sizes (tuple): Number of neurons in each hidden layer\n",
    "        activation (str): Activation function to use. Options are \"relu\", \"tanh\", and \"identity\"\n",
    "        learning_rate (float): Learning rate for gradient descent\n",
    "        max_iter (int): Maximum number of iterations to train for\n",
    "        batch_size (int): Size of the mini-batches for gradient descent\n",
    "        random_state (int): Random seed for reproducibility\n",
    "        store_history (bool): Whether to store the training history\n",
    "\n",
    "\n",
    "    \"\"\"\n",
    "    def __init__(self, hidden_layer_sizes=(100,), activation='relu', learning_rate=0.001, \n",
    "                 max_iter=1000, batch_size=32, store_history=False, random_state=0):\n",
    "        self.hidden_layer_sizes = hidden_layer_sizes\n",
    "        self.activation = activation\n",
    "        self.learning_rate = learning_rate\n",
    "        self.max_iter = max_iter\n",
    "        self.batch_size = batch_size\n",
    "        self.random_state = random_state\n",
    "        np.random.seed(self.random_state)\n",
    "        \n",
    "        self.weights = []\n",
    "        self.biases = []\n",
    "        self.store_history = store_history\n",
    "        if self.store_history:\n",
    "            self.history = []\n",
    "\n",
    "    def loss(self, y_true, y_pred):\n",
    "        return np.mean((y_true - y_pred)**2)\n",
    "    \n",
    "    def initialize_parameters(self, input_size, output_size):\n",
    "        \"\"\"Initialize all model parameters using random numbers\"\"\"\n",
    "        layer_sizes = [input_size] + list(self.hidden_layer_sizes) + [output_size]\n",
    "        self.weights = [np.random.randn(layer_sizes[i], layer_sizes[i+1]) * 0.01 \n",
    "                        for i in range(len(layer_sizes) - 1)]\n",
    "        self.biases = [np.zeros((1, size)) for size in layer_sizes[1:]]\n",
    "    \n",
    "    def forward_pass(self, X):\n",
    "        \"\"\"Given an input, compute the activations of all layers. The activations of the last layer\n",
    "        are the predictions of the model\"\"\"\n",
    "        activations = [X]\n",
    "        for w, b in zip(self.weights, self.biases):\n",
    "            z = np.dot(activations[-1], w) + b\n",
    "            a = relu(z)\n",
    "            activations.append(a)\n",
    "        return activations\n",
    "    \n",
    "    def backward_pass(self, activations, y):\n",
    "        \"\"\"\n",
    "        Given the activations of all layers and the true labels, compute the gradients of the\n",
    "        loss with respect to the weights and biases of all layers\n",
    "        \"\"\"\n",
    "        deltas = [(activations[-1] - y)]\n",
    "        for i in reversed(range(len(self.weights)-1)):\n",
    "            delta = np.dot(deltas[0], self.weights[i+1].T) * relu_derivative(activations[i+1])\n",
    "            deltas.insert(0, delta)\n",
    "        \n",
    "        grad_w = [np.dot(activations[i].T, deltas[i]) for i in range(len(self.weights))]\n",
    "        grad_b = [np.sum(deltas[i], axis=0, keepdims=True) for i in range(len(self.biases))]\n",
    "        \n",
    "        return grad_w, grad_b\n",
    "    \n",
    "    def update_parameters(self, grad_w, grad_b):\n",
    "        \"\"\"Given the gradients of the loss with respect to the weights and biases, update the\n",
    "        weights and biases using gradient descent\"\"\"\n",
    "        for i in range(len(self.weights)):\n",
    "            self.weights[i] -= self.learning_rate * grad_w[i]\n",
    "            self.biases[i] -= self.learning_rate * grad_b[i]\n",
    "    \n",
    "    def fit(self, X, y):\n",
    "\n",
    "        # Promote y to a 2D array if it is 1D\n",
    "        if y.ndim == 1:\n",
    "            y = y.reshape(-1, 1)\n",
    "        \n",
    "        self.initialize_parameters(X.shape[1], y.shape[1])\n",
    "        for i in range(self.max_iter):\n",
    "            for batch in range(0, X.shape[0], self.batch_size):\n",
    "\n",
    "                # Random subsample a batch from the training set\n",
    "                # This provides the stochastic part of the stochastic gradient descent \n",
    "                # algorithm\n",
    "                X_batch = X[batch:batch+self.batch_size]\n",
    "                y_batch = y[batch:batch+self.batch_size]\n",
    "                \n",
    "                # We cache all activations, not just the predictions\n",
    "                activations = self.forward_pass(X_batch)\n",
    "                grad_w, grad_b = self.backward_pass(activations, y_batch)\n",
    "                self.update_parameters(grad_w, grad_b)\n",
    "            \n",
    "            if self.store_history:\n",
    "                mse = self.loss(y, self.predict(X))\n",
    "                self.history.append(mse)\n",
    "        \n",
    "    def predict(self, X):\n",
    "        activations = self.forward_pass(X)\n",
    "        return activations[-1]\n",
    "\n",
    "mlp = MultiLayerPerceptron(hidden_layer_sizes=(10, 10), learning_rate=0.001, store_history=True)\n",
    "mlp.fit(X_train, y_train)\n",
    "predictions = mlp.predict(X_test)\n",
    "\n",
    "plt.plot(mlp.history)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Harder cases: branching paths, loops, and shared weights\n",
    "\n",
    "+ For more sophisticated architectures, we might have multiple paths through the network. For example, we might have a residual connection, where the output of the first layer is added to the output of the second layer.\n",
    "\n",
    "+ Backpropagation is more complicated, but as long as everything is deterministic and continuous, it should still be possible to implement all gradients at nodes.\n",
    "\n",
    "<img src=\"../resources/inceptionnet.png\" width=\"350\">\n",
    "\n",
    "*Diagram from [Szegedy et al. (2014)](https://arxiv.org/abs/1409.4842)*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Math is hard: Automatic Differentiation\n",
    "\n",
    "+ Computing symbolic gradients of vector functions is exact but laborious\n",
    "\n",
    "+ Finite-difference gradients are approximate, easy, but expensive in high dimensions:\n",
    "\n",
    "+ + If the input to our network is $D$-dimensional, then we need to compute $2\\,M$ gradients. For a 1 Megapixel image, this is a million gradient operations per gradient descent step\n",
    "\n",
    "*Automatic differentiation* is a technique that can compute the *exact* gradient of a function in a computationally-efficient manner.\n",
    "\n",
    "*Backpropagation* is just reverse-mode autodiff applied to train deep neural networks."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let the computer do the work\n",
    "\n",
    "+ Most existing deep learning frameworks are built on top of autodiff\n",
    "\n",
    "+ Tensorflow, PyTorch, JAX, and many others allow you to specify the neural network as a function composition graph, and can compute the gradient automatically as long as everything is differentiable\n",
    "\n",
    "+ Implictly, these networks build a computation \"graph\" that is later traversed backwards to compute the gradient\n",
    "\n",
    "+ Caching forward pass values can speed up the backwards pass, since many derivatives depend on forward pass values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Forward pass value: -0.029225168711847025\n",
      "Analytic calculation backwards pass -0.4781751223381389\n",
      "Jax autodiff backwards pass -0.4781751\n"
     ]
    }
   ],
   "source": [
    "import jax\n",
    "\n",
    "def double_well(x):\n",
    "    \"\"\"Double well potential function\"\"\"\n",
    "    return x**4 - 2*x**2\n",
    "\n",
    "print(\"Forward pass value:\", double_well(0.12132987))\n",
    "print(\"Analytic calculation backwards pass\", double_well_grad(0.12132987))\n",
    "print(\"Jax autodiff backwards pass\", jax.grad(double_well)(0.12132987))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 282,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Forward pass value:\n",
      " 0.5584225\n",
      "\n",
      "Analytic calculation backwards pass:\n",
      " [0.19981267 0.21903262 0.0847854  0.421329   0.42325357]\n",
      "\n",
      "Jax autodiff backwards pass:\n",
      " [0.19981267 0.21903262 0.0847854  0.421329   0.42325357]\n"
     ]
    }
   ],
   "source": [
    "import jax.numpy as jnp\n",
    "\n",
    "a = jnp.array(np.random.random((5, )))\n",
    "x = jnp.array(np.random.random((5, )))\n",
    "\n",
    "def forward_pass(x, a):\n",
    "    \"\"\"Forward pass of a simple neural network\"\"\"\n",
    "    return jnp.tanh(a.T @ x)\n",
    "\n",
    "def backward_pass(x, a):\n",
    "    \"\"\"Backward pass of a simple neural network\"\"\"\n",
    "    return (1 - np.tanh(a.T @ x)**2) * x.T\n",
    "\n",
    "print(\"Forward pass value:\\n\", forward_pass(x, a))\n",
    "\n",
    "print(\"\\nAnalytic calculation backwards pass:\\n\", backward_pass(x, a))\n",
    "\n",
    "print(\"\\nJax autodiff backwards pass:\\n\", jax.grad(forward_pass, argnums=1)(x, a))\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Some optimization tricks\n",
    "\n",
    "+ Instead of \"full batch\" gradient descent, where we compute the average of the gradient $\\nabla_\\theta \\mathcal{L}(\\theta)$ over all training examples $x_i$, we can use *stochastic gradient descent*, where we randomly sample a *subset* of the training data during each gradient descent epoch. Smaller batch sizes are more noisy, while larger batch sizes are more accurate to the global geometry of the loss function.\n",
    "\n",
    "+  Instead of just gradient descent, we can use momentum and many other tricks we saw in optimization:\n",
    "    +  Stochastic\n",
    "    +  Momentum\n",
    "    +  Second-order methods (e.g. Newton's method)\n",
    "    +  Adaptive learning rates\n",
    "    +  Constrained Optimization (e.g. L1/L2 regularization)\n",
    "\n",
    "\n",
    "+ Currently, many practioners use [the Adam optimizer](https://arxiv.org/abs/1412.6980), which is a combination of momentum and weight-based learning rate adjustment. Second-order methods are less commonly used for large problems, due to the expense of finding the full Hessian, but approximates methods based on its eigenvalues are viable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How do different hyperparameters affect training?\n",
    "\n",
    "Two common hyperparameters that we'll encounter when training large networks are the learning rate $\\eta$ and the batch size $B$.\n",
    "\n",
    "+ Batch size $B$: The number of training examples used to compute the gradient. Larger batch sizes are better estimators of the overall gradient of the loss landscape, but more expensive to compute. Smaller batch sizes are more noisy, but can be faster to compute. The stochasticity of small batch sizes can also help the network avoid local minima.\n",
    "\n",
    "+ Learning rate: The size of the step taken in the direction of the gradient. If the learning rate is too small, then the network will take a long time to converge. If the learning rate is too large, then the network will oscillate around the minimum, or even diverge.\n",
    "\n",
    "+ We'll demonstrate these hyperparameters using `scikit-learn`'s own `MLPRegressor` class, which is a multilayer perceptron for regression problems. We'll use the `adam` iterative optimization algorithm, which is a combination of momentum and adaptive learning rates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2 score: 0.999712\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Loss')"
      ]
     },
     "execution_count": 169,
     "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": [
    "from sklearn.neural_network import MLPRegressor\n",
    "\n",
    "\n",
    "\n",
    "mlp = MLPRegressor(hidden_layer_sizes=(100, 100), activation='relu', solver='adam', learning_rate='constant',\n",
    "                     learning_rate_init=0.001, max_iter=1000, random_state=0, batch_size=32)\n",
    "\n",
    "\n",
    "X_train, X_test, y_train, y_test = dataset.X_train, dataset.X_test, dataset.y_train, dataset.y_test\n",
    "\n",
    "mlp.fit(X_train, y_train)\n",
    "\n",
    "## Score\n",
    "print(\"R^2 score: %f\" % mlp.score(X_test, y_test))\n",
    "\n",
    "plt.semilogy(mlp.loss_curve_)\n",
    "plt.xlabel('Epoch')\n",
    "plt.ylabel('Loss')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2cdfc2490>"
      ]
     },
     "execution_count": 170,
     "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": [
    "for batch_size_value in [2, 32, 512]:\n",
    "    mlp = MLPRegressor(hidden_layer_sizes=(100, 100), activation='relu', solver='adam', learning_rate='constant',\n",
    "                     learning_rate_init=0.001, max_iter=1000, random_state=0, batch_size=batch_size_value)\n",
    "\n",
    "    mlp.fit(X_train, y_train)\n",
    "    plt.semilogy(mlp.loss_curve_, label=f\"batch_size={batch_size_value}\")\n",
    "plt.xlabel('Epoch')\n",
    "plt.ylabel('Loss')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Loss')"
      ]
     },
     "execution_count": 216,
     "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": [
    "for lr in [1e0, 1e-1, 1e-3, 1e-5]:\n",
    "    mlp = MLPRegressor(hidden_layer_sizes=(100, 100), \n",
    "                       activation='relu', \n",
    "                       solver='adam', \n",
    "                       learning_rate='constant',\n",
    "                       learning_rate_init=lr, \n",
    "                       max_iter=1000, \n",
    "                       random_state=0,\n",
    "                       batch_size=32)\n",
    "\n",
    "    mlp.fit(X_train, y_train)\n",
    "    plt.semilogy(mlp.loss_curve_, label=f\"learning_rate={lr}\")\n",
    "plt.xlabel('Epoch')\n",
    "plt.ylabel('Loss')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.10.4 ('cphy')",
   "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": "3.11.5"
  },
  "vscode": {
   "interpreter": {
    "hash": "0e972983abb2b5c6293c34082f6ff1f6e60e8afbd2a068e0026ccecbb212fdb6"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}