{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "7b5cfa64-246c-42de-afb3-de4aa8bb6936",
   "metadata": {},
   "source": [
    "<h1>Rectified Linear Unit (ReLU) Activation Function</h1>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "90ddf3b1-54a8-46b5-ac74-887af6360cfe",
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "def relu(z):\n",
    "    return max(0, z)\n",
    "\n",
    "def grad_relu(z):\n",
    "    if z > 0:\n",
    "        return 1\n",
    "    else:\n",
    "        return 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "117eb03a-265a-4073-8c39-922529d5d2c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "z = [t for t in np.arange(-5.0, 5.0, 0.01)]\n",
    "y = [relu(i) for i in z]\n",
    "y_grad = [grad_relu(i) for i in z]\n",
    "\n",
    "plt.plot(z, y, 'g', label='ReLU')\n",
    "plt.plot(z, y_grad, 'r', label='Gradient')\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('z')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5ad16c1-36ec-4c4c-bf96-f96c09f7a08f",
   "metadata": {},
   "source": [
    "<h1>Points to note:</h1>\n",
    "<p> </p>\n",
    "<h3>The ReLU function was introduced in 1975 and has become one of the mst popular activation functions (See research paper by Nair and Hinton - https://www.cs.toronto.edu/~fritz/absps/reluICML.pdf).</h3>\n",
    "<h3>The ReLU function output is unbounded when z is positive (0 to infinity) - No vanishing gradients.</h3>\n",
    "<h4>This means that values are always positive potentially creating slightly biased and unstable training. This potentially means training over more epochs.</h4>\n",
    "<h3>The ReLU function is continuous and monotonic and it is computationally cheap due to its linear nature making it much faster to train.</h3>\n",
    "<h3>The gradient curve is smooth, this helps model convergeance.</h3>\n",
    "<h3>the gradient calculation is also cheap and straight forward (See Perceptron slides).</h3>\n",
    "<p> </p>\n",
    "<h2>Watch out for Exploding Gradients!</h2>\n",
    "<h2>Also look out for Dead ReLU! (netowrk falls into a dead state)</h2>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0e3ca1c0-5c79-4eb9-be3f-0c430d6cc924",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total time taken by scratch implementation is  18.388986587524414  micro-seconds\n",
      "Total time taken by Keras implementation is  46.5395450592041  micro-seconds\n",
      "Total time taken by Tensorflow.NN implementation is  18.00394058227539  micro-seconds\n"
     ]
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "import time\n",
    "\n",
    "z = [t for t in np.arange(-500.0, 500.0, 0.01)]\n",
    "\n",
    "t1 = time.time()\n",
    "y = [relu(i) for i in z]\n",
    "total_time1 = (time.time() - t1)*1000\n",
    "print(\"Total time taken by scratch implementation is \", total_time1, \" micro-seconds\")\n",
    "\n",
    "t2 = time.time()\n",
    "out1 = tf.keras.activations.relu(z)\n",
    "total_time2 = (time.time() - t2)*1000\n",
    "print(\"Total time taken by Keras implementation is \", total_time2, \" micro-seconds\")\n",
    "\n",
    "t3 = time.time()\n",
    "out2 = tf.nn.relu(z)\n",
    "total_time3 = (time.time() - t3)*1000\n",
    "print(\"Total time taken by Tensorflow.NN implementation is \", total_time3, \" micro-seconds\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a96b4771-bd44-4f2a-8dfc-49631e8b396d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result of scratch:  [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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499.18999999909124, 499.19999999909123, 499.2099999990912, 499.2199999990912, 499.2299999990912, 499.2399999990912, 499.2499999990912, 499.2599999990912, 499.26999999909117, 499.27999999909116, 499.28999999909115, 499.29999999909114, 499.30999999909113, 499.3199999990911, 499.3299999990911, 499.3399999990911, 499.3499999990911, 499.3599999990911, 499.3699999990911, 499.37999999909107, 499.38999999909106, 499.39999999909105, 499.40999999909104, 499.41999999909103, 499.429999999091, 499.439999999091, 499.449999999091, 499.459999999091, 499.469999999091, 499.479999999091, 499.48999999909097, 499.49999999909096, 499.50999999909095, 499.51999999909094, 499.52999999909093, 499.5399999990909, 499.5499999990909, 499.5599999990909, 499.5699999990909, 499.5799999990909, 499.5899999990909, 499.59999999909087, 499.60999999909086, 499.61999999909085, 499.62999999909084, 499.63999999909083, 499.6499999990908, 499.6599999990908, 499.6699999990908, 499.6799999990908, 499.6899999990908, 499.6999999990908, 499.70999999909077, 499.71999999909076, 499.72999999909075, 499.73999999909074, 499.74999999909073, 499.7599999990907, 499.7699999990907, 499.7799999990907, 499.7899999990907, 499.7999999990907, 499.8099999990907, 499.81999999909067, 499.82999999909066, 499.83999999909065, 499.84999999909064, 499.85999999909063, 499.8699999990906, 499.8799999990906, 499.8899999990906, 499.8999999990906, 499.9099999990906, 499.9199999990906, 499.92999999909057, 499.93999999909056, 499.94999999909055, 499.95999999909054, 499.96999999909053, 499.9799999990905, 499.9899999990905]\n",
      "\n",
      "result of Keras:  tf.Tensor([  0.     0.     0.   ... 499.97 499.98 499.99], shape=(100000,), dtype=float64)\n",
      "\n",
      "result of Tensorflow.NN:  tf.Tensor([  0.     0.     0.   ... 499.97 499.98 499.99], shape=(100000,), dtype=float64)\n"
     ]
    }
   ],
   "source": [
    "print(\"result of scratch: \", y)\n",
    "print()\n",
    "print(\"result of Keras: \", out1)\n",
    "print()\n",
    "print(\"result of Tensorflow.NN: \", out2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f44b6408-3786-4c52-8526-3a0b0a394f6b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(z, y, 'g', label='ReLU Scratch')\n",
    "# plt.plot(z, y_grad, 'r', label='Gradient')\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('z')\n",
    "\n",
    "plt.show()\n",
    "\n",
    "plt.plot(z, out1, 'g', label='ReLU Keras')\n",
    "# plt.plot(z, y_grad, 'r', label='Gradient')\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('z')\n",
    "\n",
    "plt.show()\n",
    "\n",
    "plt.plot(z, out2, 'g', label='ReLU TF.NN')\n",
    "# plt.plot(z, y_grad, 'r', label='Gradient')\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('z')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "76f55708-314d-4eca-8e88-be2d9aff959e",
   "metadata": {},
   "outputs": [],
   "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": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}