ExtremalTraining.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Extremal Training"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook walks through the technique detailed in https://arxiv.org/abs/2102.03626"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we import dependencies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import rc\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Instantiate the model. This model has two layers, with 64 neurons in the first and 32 in the second. We will call this network N1. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = tf.keras.Sequential()\n",
    "model.add(tf.keras.layers.Dense(64, activation='relu', kernel_initializer=\"uniform\"))\n",
    "model.add(tf.keras.layers.Dense(32, activation='relu', kernel_initializer=\"uniform\"))\n",
    "model.add(tf.keras.layers.Dense(1, kernel_initializer=\"uniform\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Defining the Input-Optimizing Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the class definition for the input-updating network. This will be used later, once the standard model is trained. It is important to note that this network has the same structure as the network N1. This network will be called N2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "class MLP(tf.keras.Model):\n",
    "    def __init__(self, train_params):\n",
    "        super().__init__()\n",
    "        #The layers of this network match the layers of the standard network N1.\n",
    "        self.L1 = tf.keras.layers.Dense(64, activation='relu', kernel_initializer=\"uniform\")\n",
    "        self.L2 = tf.keras.layers.Dense(32, activation='relu', kernel_initializer=\"uniform\")\n",
    "        self.OutputLayer = tf.keras.layers.Dense(1, kernel_initializer=\"uniform\")\n",
    "        \n",
    "        #Define a tensorflow constant that holds the input of this network.\n",
    "        self.trainInputs = tf.constant(train_params.numpy())\n",
    "    \n",
    "    def updt(self, x, model):\n",
    "        #Tensorflow uses deferrred initialization, so first run the model to create the input shape\n",
    "        self(x)\n",
    "        #Get model weights (which are set as the weights of the dense layers of this new network - this \n",
    "        #is why the model structure needs to match the model structure of the standard network N1)\n",
    "        self.set_weights(model.get_weights())\n",
    "        #Freeze all the weights of the network so that they are not trained during gradient descent\n",
    "        self.L1.trainable = False\n",
    "        self.L2.trainable = False\n",
    "        self.OutputLayer.trainable = False\n",
    "        #Set the trainInputs attribute to trainable - it is not exactly a part of the neural network here,\n",
    "        #but rather just the input\n",
    "        self.trainInputs = tf.Variable(x.numpy(), trainable=True)\n",
    "    \n",
    "    def call(self, x_dummy):\n",
    "        #x_dummy is not used, but it's needed to use the .call(x) method\n",
    "        #Run the model with the trainInputs as the input each time .call(x) is used\n",
    "        x = self.trainInputs\n",
    "        return self.OutputLayer((self.L2(self.L1(x))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generating the data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the function that the network is trained to mimic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generating function\n",
    "def genFunc(x_feats):\n",
    "    y = 1 - tf.abs(x_feats[:, 0]) - tf.square(x_feats[:, 1]) - x_feats[:, 2] - tf.exp(x_feats[:, 3]) + tf.random.normal(mean = 0.0, stddev = 0.05, shape = (x_feats[:, 0].shape))\n",
    "    return y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This code generates the data to be fed into the function we are trying to model (above). A random seed is set to keep the code consistent each time it is run."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generateData():\n",
    "    tf.random.set_seed(10)\n",
    "    x1 = tf.random.uniform(shape=(1000, 1), minval=-1, maxval=1)\n",
    "    x2 = tf.random.uniform(shape=(1000, 1), minval=-1, maxval=1)\n",
    "    x3 = tf.random.uniform(shape=(1000, 1), minval=-1, maxval=1)\n",
    "    x4 = tf.random.uniform(shape=(1000, 1), minval=-1, maxval=1)\n",
    "    x_feats = tf.concat([x1, x2, x3, x4], 1)\n",
    "    \n",
    "    return x_feats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_feats = generateData()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([45., 35., 52., 46., 50., 45., 62., 54., 50., 61., 49., 62., 47.,\n",
       "        60., 53., 44., 45., 50., 47., 43.]),\n",
       " array([-9.9817276e-01, -8.9828891e-01, -7.9840499e-01, -6.9852114e-01,\n",
       "        -5.9863722e-01, -4.9875337e-01, -3.9886948e-01, -2.9898560e-01,\n",
       "        -1.9910173e-01, -9.9217854e-02,  6.6602230e-04,  1.0054990e-01,\n",
       "         2.0043378e-01,  3.0031765e-01,  4.0020153e-01,  5.0008541e-01,\n",
       "         5.9996927e-01,  6.9985318e-01,  7.9973704e-01,  8.9962095e-01,\n",
       "         9.9950480e-01], dtype=float32),\n",
       " <a list of 20 Patch objects>)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(x_feats[:,0], bins=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The output needs to be reshaped so that it can be fed into the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = tf.reshape(genFunc(x_feats), shape=(1000,))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training the model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, the model's learning rate, optimizer and loss function are set. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "learning_rate = 0.001\n",
    "opt = tf.keras.optimizers.Adam(learning_rate=learning_rate)\n",
    "model.compile(optimizer=opt, loss=tf.keras.losses.MSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/80\n",
      "1000/1000 [==============================] - 1s 663us/step - loss: 0.3338\n",
      "Epoch 2/80\n",
      "1000/1000 [==============================] - 1s 662us/step - loss: 0.0391\n",
      "Epoch 3/80\n",
      "1000/1000 [==============================] - 1s 702us/step - loss: 0.0126\n",
      "Epoch 4/80\n",
      "1000/1000 [==============================] - 1s 694us/step - loss: 0.0107\n",
      "Epoch 5/80\n",
      "1000/1000 [==============================] - 1s 656us/step - loss: 0.0104\n",
      "Epoch 6/80\n",
      "1000/1000 [==============================] - 1s 768us/step - loss: 0.0086\n",
      "Epoch 7/80\n",
      "1000/1000 [==============================] - 1s 719us/step - loss: 0.0075\n",
      "Epoch 8/80\n",
      "1000/1000 [==============================] - 1s 722us/step - loss: 0.0075\n",
      "Epoch 9/80\n",
      "1000/1000 [==============================] - 1s 747us/step - loss: 0.0073\n",
      "Epoch 10/80\n",
      "1000/1000 [==============================] - 1s 748us/step - loss: 0.0074\n",
      "Epoch 11/80\n",
      "1000/1000 [==============================] - 1s 704us/step - loss: 0.0073\n",
      "Epoch 12/80\n",
      "1000/1000 [==============================] - 1s 688us/step - loss: 0.0068\n",
      "Epoch 13/80\n",
      "1000/1000 [==============================] - 1s 775us/step - loss: 0.0064\n",
      "Epoch 14/80\n",
      "1000/1000 [==============================] - 1s 718us/step - loss: 0.0062\n",
      "Epoch 15/80\n",
      "1000/1000 [==============================] - 1s 696us/step - loss: 0.0063\n",
      "Epoch 16/80\n",
      "1000/1000 [==============================] - 1s 907us/step - loss: 0.0059\n",
      "Epoch 17/80\n",
      "1000/1000 [==============================] - 1s 646us/step - loss: 0.0063\n",
      "Epoch 18/80\n",
      "1000/1000 [==============================] - 1s 713us/step - loss: 0.0064\n",
      "Epoch 19/80\n",
      "1000/1000 [==============================] - 1s 674us/step - loss: 0.0058\n",
      "Epoch 20/80\n",
      "1000/1000 [==============================] - 1s 716us/step - loss: 0.0065\n",
      "Epoch 21/80\n",
      "1000/1000 [==============================] - 1s 806us/step - loss: 0.0060\n",
      "Epoch 22/80\n",
      "1000/1000 [==============================] - 1s 719us/step - loss: 0.0051\n",
      "Epoch 23/80\n",
      "1000/1000 [==============================] - 1s 655us/step - loss: 0.0064\n",
      "Epoch 24/80\n",
      "1000/1000 [==============================] - 1s 710us/step - loss: 0.0056\n",
      "Epoch 25/80\n",
      "1000/1000 [==============================] - 1s 719us/step - loss: 0.0057\n",
      "Epoch 26/80\n",
      "1000/1000 [==============================] - 1s 744us/step - loss: 0.0058\n",
      "Epoch 27/80\n",
      "1000/1000 [==============================] - 1s 769us/step - loss: 0.0062\n",
      "Epoch 28/80\n",
      "1000/1000 [==============================] - 1s 685us/step - loss: 0.0058\n",
      "Epoch 29/80\n",
      "1000/1000 [==============================] - 1s 753us/step - loss: 0.0055\n",
      "Epoch 30/80\n",
      "1000/1000 [==============================] - 1s 694us/step - loss: 0.0059\n",
      "Epoch 31/80\n",
      "1000/1000 [==============================] - 1s 603us/step - loss: 0.0059\n",
      "Epoch 32/80\n",
      "1000/1000 [==============================] - 1s 592us/step - loss: 0.0055\n",
      "Epoch 33/80\n",
      "1000/1000 [==============================] - 1s 619us/step - loss: 0.0052\n",
      "Epoch 34/80\n",
      "1000/1000 [==============================] - 1s 679us/step - loss: 0.0058\n",
      "Epoch 35/80\n",
      "1000/1000 [==============================] - 1s 632us/step - loss: 0.0053\n",
      "Epoch 36/80\n",
      "1000/1000 [==============================] - 1s 654us/step - loss: 0.0056\n",
      "Epoch 37/80\n",
      "1000/1000 [==============================] - 1s 616us/step - loss: 0.0057\n",
      "Epoch 38/80\n",
      "1000/1000 [==============================] - 1s 665us/step - loss: 0.0060\n",
      "Epoch 39/80\n",
      "1000/1000 [==============================] - 1s 619us/step - loss: 0.0051\n",
      "Epoch 40/80\n",
      "1000/1000 [==============================] - 1s 636us/step - loss: 0.0052\n",
      "Epoch 41/80\n",
      "1000/1000 [==============================] - 1s 769us/step - loss: 0.0050\n",
      "Epoch 42/80\n",
      "1000/1000 [==============================] - 1s 749us/step - loss: 0.0051\n",
      "Epoch 43/80\n",
      "1000/1000 [==============================] - 1s 747us/step - loss: 0.0052\n",
      "Epoch 44/80\n",
      "1000/1000 [==============================] - 1s 862us/step - loss: 0.0046\n",
      "Epoch 45/80\n",
      "1000/1000 [==============================] - 1s 797us/step - loss: 0.0050\n",
      "Epoch 46/80\n",
      "1000/1000 [==============================] - 1s 630us/step - loss: 0.0050\n",
      "Epoch 47/80\n",
      "1000/1000 [==============================] - 1s 626us/step - loss: 0.0052\n",
      "Epoch 48/80\n",
      "1000/1000 [==============================] - 1s 693us/step - loss: 0.0049\n",
      "Epoch 49/80\n",
      "1000/1000 [==============================] - 1s 643us/step - loss: 0.0056\n",
      "Epoch 50/80\n",
      "1000/1000 [==============================] - 1s 571us/step - loss: 0.0050\n",
      "Epoch 51/80\n",
      "1000/1000 [==============================] - 1s 633us/step - loss: 0.0051\n",
      "Epoch 52/80\n",
      "1000/1000 [==============================] - 1s 601us/step - loss: 0.0050\n",
      "Epoch 53/80\n",
      "1000/1000 [==============================] - 1s 604us/step - loss: 0.0048\n",
      "Epoch 54/80\n",
      "1000/1000 [==============================] - 1s 583us/step - loss: 0.0054\n",
      "Epoch 55/80\n",
      "1000/1000 [==============================] - 1s 596us/step - loss: 0.0050\n",
      "Epoch 56/80\n",
      "1000/1000 [==============================] - 1s 639us/step - loss: 0.0045\n",
      "Epoch 57/80\n",
      "1000/1000 [==============================] - 1s 640us/step - loss: 0.0046\n",
      "Epoch 58/80\n",
      "1000/1000 [==============================] - 1s 630us/step - loss: 0.0052\n",
      "Epoch 59/80\n",
      "1000/1000 [==============================] - 1s 626us/step - loss: 0.0047\n",
      "Epoch 60/80\n",
      "1000/1000 [==============================] - 1s 614us/step - loss: 0.0041\n",
      "Epoch 61/80\n",
      "1000/1000 [==============================] - 1s 657us/step - loss: 0.0044\n",
      "Epoch 62/80\n",
      "1000/1000 [==============================] - 1s 585us/step - loss: 0.0049\n",
      "Epoch 63/80\n",
      "1000/1000 [==============================] - 1s 623us/step - loss: 0.0054\n",
      "Epoch 64/80\n",
      "1000/1000 [==============================] - 1s 658us/step - loss: 0.0049\n",
      "Epoch 65/80\n",
      "1000/1000 [==============================] - 1s 606us/step - loss: 0.0046\n",
      "Epoch 66/80\n",
      "1000/1000 [==============================] - 1s 597us/step - loss: 0.0046\n",
      "Epoch 67/80\n",
      "1000/1000 [==============================] - 1s 692us/step - loss: 0.0044\n",
      "Epoch 68/80\n",
      "1000/1000 [==============================] - 1s 623us/step - loss: 0.0045\n",
      "Epoch 69/80\n",
      "1000/1000 [==============================] - 1s 678us/step - loss: 0.0049\n",
      "Epoch 70/80\n",
      "1000/1000 [==============================] - 1s 823us/step - loss: 0.0042\n",
      "Epoch 71/80\n",
      "1000/1000 [==============================] - 1s 637us/step - loss: 0.0044\n",
      "Epoch 72/80\n",
      "1000/1000 [==============================] - 1s 788us/step - loss: 0.0047\n",
      "Epoch 73/80\n",
      "1000/1000 [==============================] - 1s 618us/step - loss: 0.0044\n",
      "Epoch 74/80\n",
      "1000/1000 [==============================] - 1s 582us/step - loss: 0.0047\n",
      "Epoch 75/80\n",
      "1000/1000 [==============================] - 1s 719us/step - loss: 0.0045\n",
      "Epoch 76/80\n",
      "1000/1000 [==============================] - 1s 666us/step - loss: 0.0041\n",
      "Epoch 77/80\n",
      "1000/1000 [==============================] - 1s 667us/step - loss: 0.0045\n",
      "Epoch 78/80\n",
      "1000/1000 [==============================] - 1s 635us/step - loss: 0.0047\n",
      "Epoch 79/80\n",
      "1000/1000 [==============================] - 1s 657us/step - loss: 0.0052\n",
      "Epoch 80/80\n",
      "1000/1000 [==============================] - 1s 646us/step - loss: 0.0045\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<tensorflow.python.keras.callbacks.History at 0x14f91c294a8>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(x_feats, y, epochs = 80, batch_size=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This code allows for a visual check of whether the model is accurately modelling the function we trained it on. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Feature generation\n",
    "rc('font',**{'family':'sans-serif','sans-serif':['Helvetica']})\n",
    "rc('text', usetex=True)\n",
    "\n",
    "def plotComparision(x_feats, model):\n",
    "    inputs = ['Carbohydrate', 'Protein', 'Cake', 'Candy']\n",
    "    numFeats = 4\n",
    "    feats = [x_feats[0], x_feats[1], x_feats[2], x_feats[3]]\n",
    "    for i in range(numFeats):\n",
    "        for j in range(len(feats)):\n",
    "            feats[j] = tf.zeros(shape=(1000,1))\n",
    "        \n",
    "        \n",
    "        #reassign the ith dimension/feature\n",
    "        feats[i] = tf.reshape(tf.range(-1, 1, 0.002), shape=(1000, 1))\n",
    "        x_feats = tf.concat(feats, 1)\n",
    "        \n",
    "        plt.figure(i)\n",
    "        \n",
    "        plt.rc('text', usetex=True)\n",
    "        plt.rc('font', family='serif')\n",
    "        \n",
    "        plt.plot(feats[i], genFunc(x_feats), label='Generated Training Data')\n",
    "        plt.plot(feats[i], model(x_feats), label='Model Prediction')\n",
    "        \n",
    "        plt.xlabel(r'\\textbf{Intake}')\n",
    "        plt.ylabel(r'\\textbf{Health}')\n",
    "        plt.title(  \n",
    "                  r\"Health vs. \" + inputs[i] + \" Intake\",\n",
    "                  fontsize=16, color='black')\n",
    "\n",
    "        plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotComparision(x_feats, model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "dense (Dense)                (None, 64)                320       \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (None, 32)                2080      \n",
      "_________________________________________________________________\n",
      "dense_2 (Dense)              (None, 1)                 33        \n",
      "=================================================================\n",
      "Total params: 2,433\n",
      "Trainable params: 2,433\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optimizing the input"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this section, the an input we give to the optimizing model N2 is going to be optimized. \n",
    "\n",
    "First, the four features of the input are randomly generated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "tf.random.set_seed(42)\n",
    "optimizationModel = MLP(tf.random.normal(shape=(1, 4)))\n",
    "optimizationModel.updt(tf.random.normal(shape=(1, 4)), model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.08422458 -0.86090374  0.37812304 -0.00519627]]\n"
     ]
    }
   ],
   "source": [
    "inputInit = optimizationModel.trainable_variables[0].numpy().copy()\n",
    "print(inputInit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(1, 1), dtype=float32, numpy=array([[-1.2307081]], dtype=float32)>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model(optimizationModel.trainable_variables[0].numpy())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The custom loss functions are defined as found in the paper."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def maximizationLoss(y_dummy, y_pred):\n",
    "       \n",
    "    result = tf.cond(y_pred <= tf.constant([0.0]), lambda : -10*y_pred + 1, lambda : 1/(tf.square(y_pred) + 1))\n",
    "    return result\n",
    "\n",
    "def extrapolationLoss(weights, x):\n",
    "\n",
    "    mean = tf.reshape(tf.reduce_mean(x, axis=0), shape=(1, 4))\n",
    "    x_std_expand = tf.reshape(tf.math.reduce_std(x, axis=0), shape=(1, 4))\n",
    "\n",
    "    #How many std's to allow the extrapolation to be within\n",
    "    num_stds = 2\n",
    "    \n",
    "    #Creates a matrix of zeros with the same shape as the input vector x\n",
    "    zero_mat = tf.zeros(weights[0].shape)\n",
    "    \n",
    "    #At each element, loss_1 is assigned the value of x if the condition is true, else y (which is filled with zeros)\n",
    "    loss_1 = tf.raw_ops.Select(\n",
    "        condition = weights[0] < (means - num_stds*x_std_expand), x = weights[0]-mean+num_stds*x_std_expand, y = zero_mat, name=None\n",
    "    )\n",
    "    \n",
    "    loss_2 = tf.raw_ops.Select(\n",
    "        condition = weights[0] > (means + num_stds*x_std_expand), x = weights[0]-mean-num_stds*x_std_expand, y = zero_mat, name=None\n",
    "    )\n",
    "    \n",
    "    #Return squared loss \n",
    "    return (tf.reduce_sum(tf.square(loss_1)) + tf.reduce_sum(tf.square(loss_1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[0.55495155, 0.5766216 , 0.5774474 , 0.56745553]], dtype=float32),\n",
       " array([[ 0.0068051 , -0.02758399,  0.0049364 ,  0.00633236]],\n",
       "       dtype=float32))"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "means = tf.reshape(tf.reduce_mean(x_feats, axis=0), shape=(1, 4)).numpy()\n",
    "stds = tf.reshape(tf.math.reduce_std(x_feats, axis=0), shape=(1, 4)).numpy()\n",
    "\n",
    "stds, means"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(), dtype=float32, numpy=0.0>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "extrapolationLoss(optimizationModel.trainable_variables, x_feats)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In addition to the optimizer, add the custom losses as follows. A default loss can be added in the *compile* method, and it will automatically receive y_true and y_pred (in that order). A custom loss with custom inputs is added using the *add_loss* method. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "opt = tf.keras.optimizers.Adam(learning_rate=0.0005)\n",
    "optimizationModel.compile(optimizer=opt, loss=maximizationLoss)\n",
    "\n",
    "optimizationModel.add_loss(\n",
    "    lambda : extrapolationLoss(optimizationModel.trainable_variables, x_feats)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/50\n",
      "1000/1000 [==============================] - 1s 593us/step - loss: 5.1919\n",
      "Epoch 2/50\n",
      "1000/1000 [==============================] - 1s 583us/step - loss: 0.9997\n",
      "Epoch 3/50\n",
      "1000/1000 [==============================] - 1s 637us/step - loss: 0.9992\n",
      "Epoch 4/50\n",
      "1000/1000 [==============================] - 1s 632us/step - loss: 0.9939\n",
      "Epoch 5/50\n",
      "1000/1000 [==============================] - 1s 643us/step - loss: 0.9439\n",
      "Epoch 6/50\n",
      "1000/1000 [==============================] - 1s 919us/step - loss: 0.7475\n",
      "Epoch 7/50\n",
      "1000/1000 [==============================] - 1s 606us/step - loss: 0.4902\n",
      "Epoch 8/50\n",
      "1000/1000 [==============================] - 1s 603us/step - loss: 0.3618\n",
      "Epoch 9/50\n",
      "1000/1000 [==============================] - 1s 665us/step - loss: 0.3139\n",
      "Epoch 10/50\n",
      "1000/1000 [==============================] - 1s 755us/step - loss: 0.3115\n",
      "Epoch 11/50\n",
      "1000/1000 [==============================] - 1s 908us/step - loss: 0.3112\n",
      "Epoch 12/50\n",
      "1000/1000 [==============================] - 1s 786us/step - loss: 0.3108\n",
      "Epoch 13/50\n",
      "1000/1000 [==============================] - 1s 834us/step - loss: 0.3108\n",
      "Epoch 14/50\n",
      "1000/1000 [==============================] - 1s 758us/step - loss: 0.3108\n",
      "Epoch 15/50\n",
      "1000/1000 [==============================] - 1s 903us/step - loss: 0.3108\n",
      "Epoch 16/50\n",
      "1000/1000 [==============================] - 1s 861us/step - loss: 0.3108\n",
      "Epoch 17/50\n",
      "1000/1000 [==============================] - 1s 733us/step - loss: 0.3108\n",
      "Epoch 18/50\n",
      "1000/1000 [==============================] - 1s 590us/step - loss: 0.3108\n",
      "Epoch 19/50\n",
      "1000/1000 [==============================] - 1s 590us/step - loss: 0.3108\n",
      "Epoch 20/50\n",
      "1000/1000 [==============================] - 1s 591us/step - loss: 0.3108\n",
      "Epoch 21/50\n",
      "1000/1000 [==============================] - 1s 597us/step - loss: 0.3108\n",
      "Epoch 22/50\n",
      "1000/1000 [==============================] - 1s 641us/step - loss: 0.3108\n",
      "Epoch 23/50\n",
      "1000/1000 [==============================] - 1s 715us/step - loss: 0.3108\n",
      "Epoch 24/50\n",
      "1000/1000 [==============================] - 1s 630us/step - loss: 0.3108\n",
      "Epoch 25/50\n",
      "1000/1000 [==============================] - 1s 580us/step - loss: 0.3108\n",
      "Epoch 26/50\n",
      "1000/1000 [==============================] - 1s 569us/step - loss: 0.3108\n",
      "Epoch 27/50\n",
      "1000/1000 [==============================] - 1s 596us/step - loss: 0.3108\n",
      "Epoch 28/50\n",
      "1000/1000 [==============================] - 1s 583us/step - loss: 0.3108\n",
      "Epoch 29/50\n",
      "1000/1000 [==============================] - 1s 567us/step - loss: 0.3108\n",
      "Epoch 30/50\n",
      "1000/1000 [==============================] - 1s 610us/step - loss: 0.3108\n",
      "Epoch 31/50\n",
      "1000/1000 [==============================] - 1s 563us/step - loss: 0.3108\n",
      "Epoch 32/50\n",
      "1000/1000 [==============================] - 1s 583us/step - loss: 0.3108\n",
      "Epoch 33/50\n",
      "1000/1000 [==============================] - 1s 605us/step - loss: 0.3108\n",
      "Epoch 34/50\n",
      "1000/1000 [==============================] - 1s 590us/step - loss: 0.3108\n",
      "Epoch 35/50\n",
      "1000/1000 [==============================] - 1s 556us/step - loss: 0.3108\n",
      "Epoch 36/50\n",
      "1000/1000 [==============================] - 1s 567us/step - loss: 0.3108\n",
      "Epoch 37/50\n",
      "1000/1000 [==============================] - 1s 572us/step - loss: 0.3108\n",
      "Epoch 38/50\n",
      "1000/1000 [==============================] - 1s 563us/step - loss: 0.3108\n",
      "Epoch 39/50\n",
      "1000/1000 [==============================] - 1s 569us/step - loss: 0.3108\n",
      "Epoch 40/50\n",
      "1000/1000 [==============================] - 1s 569us/step - loss: 0.3108\n",
      "Epoch 41/50\n",
      "1000/1000 [==============================] - 1s 565us/step - loss: 0.3108\n",
      "Epoch 42/50\n",
      "1000/1000 [==============================] - 1s 562us/step - loss: 0.3108\n",
      "Epoch 43/50\n",
      "1000/1000 [==============================] - 1s 558us/step - loss: 0.3108\n",
      "Epoch 44/50\n",
      "1000/1000 [==============================] - 1s 583us/step - loss: 0.3108\n",
      "Epoch 45/50\n",
      "1000/1000 [==============================] - 1s 564us/step - loss: 0.3108\n",
      "Epoch 46/50\n",
      "1000/1000 [==============================] - 1s 624us/step - loss: 0.3108\n",
      "Epoch 47/50\n",
      "1000/1000 [==============================] - 1s 562us/step - loss: 0.3108\n",
      "Epoch 48/50\n",
      "1000/1000 [==============================] - 1s 558us/step - loss: 0.3108\n",
      "Epoch 49/50\n",
      "1000/1000 [==============================] - 1s 627us/step - loss: 0.3108\n",
      "Epoch 50/50\n",
      "1000/1000 [==============================] - 1s 784us/step - loss: 0.3108\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<tensorflow.python.keras.callbacks.History at 0x14f92fd8240>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optimizationModel.fit(x_feats, y, epochs = 50, batch_size=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.10853714,  0.08773184, -1.1939849 , -1.1601902 ]],\n",
       "      dtype=float32)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optimizationModel.trainable_variables[0].numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.08422458, -0.86090374,  0.37812304, -0.00519627]],\n",
       "      dtype=float32)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inputInit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maximum from optimized input is 1.702\n"
     ]
    }
   ],
   "source": [
    "y = 1 - abs(-0.16720928) - (-0.0865911)**2 - (-1.1929115) - np.exp(-1.1527836)\n",
    "print(\"Maximum from optimized input is \" + str(y.round(3)))"
   ]
  }
 ],
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