tensorflow2/006-learning-rate-schedules/learning-rate-schedules.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Learning Rate schedules in Practice\n",
    "\n",
    "This is a notebook for the medium article [Learning Rate schedule in Practice](https://medium.com/@bindiatwork/learning-rate-schedule-in-practice-an-example-with-keras-and-tensorflow-2-0-2f48b2888a0c)\n",
    "\n",
    "Please check out article for instructions\n",
    "\n",
    "**License**: [BSD 2-Clause](https://opensource.org/licenses/BSD-2-Clause)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "os.environ['KMP_DUPLICATE_LIB_OK']='True'\n",
    "\n",
    "from tensorflow import keras\n",
    "import tensorflow as tf\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fashion MMIST dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "fashion_mnist = keras.datasets.fashion_mnist\n",
    "(X_train_full, y_train_full), (X_test, y_test) = fashion_mnist.load_data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 28, 28)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train_full.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('uint8')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train_full.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# For faster training, let's use a subset 10,000\n",
    "X_train, y_train = X_train_full[:10000] / 255.0, y_train_full[:10000]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Building a NN model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from tensorflow.keras.models import Sequential\n",
    "from tensorflow.keras.layers import Dense, Flatten\n",
    "\n",
    "def create_model(): \n",
    "    model = Sequential([\n",
    "        Flatten(input_shape=(28, 28)),\n",
    "        Dense(300, activation='relu'),\n",
    "        Dense(100, activation='relu'),\n",
    "        Dense(10, activation='softmax'),\n",
    "    ])\n",
    "    return model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "flatten (Flatten)            (None, 784)               0         \n",
      "_________________________________________________________________\n",
      "dense (Dense)                (None, 300)               235500    \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (None, 100)               30100     \n",
      "_________________________________________________________________\n",
      "dense_2 (Dense)              (None, 10)                1010      \n",
      "=================================================================\n",
      "Total params: 266,610\n",
      "Trainable params: 266,610\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model = create_model()\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Helper functions for plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "\n",
    "def plot_lr(history):\n",
    "    learning_rate = history.history['lr']\n",
    "    epochs = range(1, len(learning_rate) + 1)\n",
    "    plt.plot(epochs, learning_rate)\n",
    "    plt.title('Learning rate')\n",
    "    plt.xlabel('Epochs')\n",
    "    plt.ylabel('Learning rate')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_metric(history, metric):\n",
    "    train_metrics = history.history[metric]\n",
    "    val_metrics = history.history['val_'+metric]\n",
    "    epochs = range(1, len(train_metrics) + 1)\n",
    "    plt.plot(epochs, train_metrics)\n",
    "    plt.plot(epochs, val_metrics)\n",
    "    plt.title('Training and validation '+ metric)\n",
    "    plt.xlabel(\"Epochs\")\n",
    "    plt.ylabel(metric)\n",
    "    plt.legend([\"train_\"+metric, 'val_'+metric])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Constant Learning Rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a new model\n",
    "model = create_model()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 8000 samples, validate on 2000 samples\n",
      "Epoch 1/100\n",
      "8000/8000 [==============================] - 1s 178us/sample - loss: 1.4910 - accuracy: 0.5939 - val_loss: 1.0801 - val_accuracy: 0.6875\n",
      "Epoch 2/100\n",
      "8000/8000 [==============================] - 1s 67us/sample - loss: 0.9260 - accuracy: 0.7188 - val_loss: 0.8577 - val_accuracy: 0.7160\n",
      "Epoch 3/100\n",
      "8000/8000 [==============================] - 1s 68us/sample - loss: 0.7750 - accuracy: 0.7496 - val_loss: 0.7544 - val_accuracy: 0.7560\n",
      "Epoch 4/100\n",
      "8000/8000 [==============================] - 1s 67us/sample - loss: 0.6967 - accuracy: 0.7731 - val_loss: 0.6986 - val_accuracy: 0.7630\n",
      "Epoch 5/100\n",
      "8000/8000 [==============================] - 1s 69us/sample - loss: 0.6464 - accuracy: 0.7908 - val_loss: 0.6592 - val_accuracy: 0.7770\n",
      "Epoch 6/100\n",
      "8000/8000 [==============================] - 1s 69us/sample - loss: 0.6122 - accuracy: 0.7971 - val_loss: 0.6402 - val_accuracy: 0.7785\n",
      "Epoch 7/100\n",
      "8000/8000 [==============================] - 1s 70us/sample - loss: 0.5830 - accuracy: 0.8021 - val_loss: 0.6014 - val_accuracy: 0.8015\n",
      "Epoch 8/100\n",
      "8000/8000 [==============================] - 1s 72us/sample - loss: 0.5612 - accuracy: 0.8116 - val_loss: 0.5878 - val_accuracy: 0.8020\n",
      "Epoch 9/100\n",
      "8000/8000 [==============================] - 1s 74us/sample - loss: 0.5436 - accuracy: 0.8189 - val_loss: 0.5663 - val_accuracy: 0.8080\n",
      "Epoch 10/100\n",
      "8000/8000 [==============================] - 1s 72us/sample - loss: 0.5271 - accuracy: 0.8230 - val_loss: 0.5589 - val_accuracy: 0.8065\n",
      "Epoch 11/100\n",
      "8000/8000 [==============================] - 1s 71us/sample - loss: 0.5108 - accuracy: 0.8300 - val_loss: 0.5611 - val_accuracy: 0.8030\n",
      "Epoch 12/100\n",
      "8000/8000 [==============================] - 1s 72us/sample - loss: 0.5024 - accuracy: 0.8310 - val_loss: 0.5439 - val_accuracy: 0.8115\n",
      "Epoch 13/100\n",
      "8000/8000 [==============================] - 1s 75us/sample - loss: 0.4895 - accuracy: 0.8347 - val_loss: 0.5374 - val_accuracy: 0.8090\n",
      "Epoch 14/100\n",
      "8000/8000 [==============================] - 1s 75us/sample - loss: 0.4818 - accuracy: 0.8355 - val_loss: 0.5217 - val_accuracy: 0.8060\n",
      "Epoch 15/100\n",
      "8000/8000 [==============================] - 1s 76us/sample - loss: 0.4715 - accuracy: 0.8394 - val_loss: 0.5130 - val_accuracy: 0.8175\n",
      "Epoch 16/100\n",
      "8000/8000 [==============================] - 1s 82us/sample - loss: 0.4633 - accuracy: 0.8422 - val_loss: 0.5066 - val_accuracy: 0.8275\n",
      "Epoch 17/100\n",
      "8000/8000 [==============================] - 1s 81us/sample - loss: 0.4561 - accuracy: 0.8466 - val_loss: 0.5126 - val_accuracy: 0.8165\n",
      "Epoch 18/100\n",
      "8000/8000 [==============================] - 1s 79us/sample - loss: 0.4502 - accuracy: 0.8468 - val_loss: 0.4979 - val_accuracy: 0.8325\n",
      "Epoch 19/100\n",
      "8000/8000 [==============================] - 1s 78us/sample - loss: 0.4428 - accuracy: 0.8518 - val_loss: 0.4990 - val_accuracy: 0.8245\n",
      "Epoch 20/100\n",
      "8000/8000 [==============================] - 1s 79us/sample - loss: 0.4376 - accuracy: 0.8504 - val_loss: 0.4881 - val_accuracy: 0.8240\n",
      "Epoch 21/100\n",
      "8000/8000 [==============================] - 1s 76us/sample - loss: 0.4329 - accuracy: 0.8506 - val_loss: 0.4982 - val_accuracy: 0.8150\n",
      "Epoch 22/100\n",
      "8000/8000 [==============================] - 1s 79us/sample - loss: 0.4261 - accuracy: 0.8555 - val_loss: 0.4928 - val_accuracy: 0.8185\n",
      "Epoch 23/100\n",
      "8000/8000 [==============================] - 1s 80us/sample - loss: 0.4203 - accuracy: 0.8566 - val_loss: 0.4839 - val_accuracy: 0.8275\n",
      "Epoch 24/100\n",
      "8000/8000 [==============================] - 1s 78us/sample - loss: 0.4167 - accuracy: 0.8581 - val_loss: 0.4862 - val_accuracy: 0.8295\n",
      "Epoch 25/100\n",
      "8000/8000 [==============================] - 1s 78us/sample - loss: 0.4117 - accuracy: 0.8610 - val_loss: 0.4887 - val_accuracy: 0.8215\n",
      "Epoch 26/100\n",
      "8000/8000 [==============================] - 1s 81us/sample - loss: 0.4093 - accuracy: 0.8602 - val_loss: 0.4687 - val_accuracy: 0.8360\n",
      "Epoch 27/100\n",
      "8000/8000 [==============================] - 1s 78us/sample - loss: 0.4031 - accuracy: 0.8604 - val_loss: 0.4728 - val_accuracy: 0.8315\n",
      "Epoch 28/100\n",
      "8000/8000 [==============================] - 1s 79us/sample - loss: 0.3983 - accuracy: 0.8629 - val_loss: 0.4677 - val_accuracy: 0.8330\n",
      "Epoch 29/100\n",
      "8000/8000 [==============================] - 1s 83us/sample - loss: 0.3961 - accuracy: 0.8633 - val_loss: 0.4559 - val_accuracy: 0.8385\n",
      "Epoch 30/100\n",
      "8000/8000 [==============================] - 1s 80us/sample - loss: 0.3895 - accuracy: 0.8651 - val_loss: 0.4632 - val_accuracy: 0.8395\n",
      "Epoch 31/100\n",
      "8000/8000 [==============================] - 1s 80us/sample - loss: 0.3879 - accuracy: 0.8643 - val_loss: 0.4582 - val_accuracy: 0.8400\n",
      "Epoch 32/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.3814 - accuracy: 0.8681 - val_loss: 0.4567 - val_accuracy: 0.8370\n",
      "Epoch 33/100\n",
      "8000/8000 [==============================] - 1s 82us/sample - loss: 0.3813 - accuracy: 0.8679 - val_loss: 0.4534 - val_accuracy: 0.8440\n",
      "Epoch 34/100\n",
      "8000/8000 [==============================] - 1s 83us/sample - loss: 0.3756 - accuracy: 0.8719 - val_loss: 0.4505 - val_accuracy: 0.8420\n",
      "Epoch 35/100\n",
      "8000/8000 [==============================] - 1s 84us/sample - loss: 0.3732 - accuracy: 0.8692 - val_loss: 0.4647 - val_accuracy: 0.8330\n",
      "Epoch 36/100\n",
      "8000/8000 [==============================] - 1s 81us/sample - loss: 0.3705 - accuracy: 0.8752 - val_loss: 0.4469 - val_accuracy: 0.8425\n",
      "Epoch 37/100\n",
      "8000/8000 [==============================] - 1s 84us/sample - loss: 0.3646 - accuracy: 0.8745 - val_loss: 0.4832 - val_accuracy: 0.8240\n",
      "Epoch 38/100\n",
      "8000/8000 [==============================] - 1s 82us/sample - loss: 0.3624 - accuracy: 0.8754 - val_loss: 0.4455 - val_accuracy: 0.8445\n",
      "Epoch 39/100\n",
      "8000/8000 [==============================] - 1s 80us/sample - loss: 0.3582 - accuracy: 0.8779 - val_loss: 0.4572 - val_accuracy: 0.8365\n",
      "Epoch 40/100\n",
      "8000/8000 [==============================] - 1s 82us/sample - loss: 0.3531 - accuracy: 0.8769 - val_loss: 0.4456 - val_accuracy: 0.8460\n",
      "Epoch 41/100\n",
      "8000/8000 [==============================] - 1s 82us/sample - loss: 0.3550 - accuracy: 0.8749 - val_loss: 0.4473 - val_accuracy: 0.8450\n",
      "Epoch 42/100\n",
      "8000/8000 [==============================] - 1s 84us/sample - loss: 0.3487 - accuracy: 0.8808 - val_loss: 0.4432 - val_accuracy: 0.8460\n",
      "Epoch 43/100\n",
      "8000/8000 [==============================] - 1s 84us/sample - loss: 0.3447 - accuracy: 0.8808 - val_loss: 0.4370 - val_accuracy: 0.8490\n",
      "Epoch 44/100\n",
      "8000/8000 [==============================] - 1s 84us/sample - loss: 0.3434 - accuracy: 0.8809 - val_loss: 0.4396 - val_accuracy: 0.8490\n",
      "Epoch 45/100\n",
      "8000/8000 [==============================] - 1s 83us/sample - loss: 0.3407 - accuracy: 0.8848 - val_loss: 0.4400 - val_accuracy: 0.8465\n",
      "Epoch 46/100\n",
      "8000/8000 [==============================] - 1s 83us/sample - loss: 0.3375 - accuracy: 0.8832 - val_loss: 0.4546 - val_accuracy: 0.8330\n",
      "Epoch 47/100\n",
      "8000/8000 [==============================] - 1s 83us/sample - loss: 0.3331 - accuracy: 0.8859 - val_loss: 0.4368 - val_accuracy: 0.8445\n",
      "Epoch 48/100\n",
      "8000/8000 [==============================] - 1s 81us/sample - loss: 0.3304 - accuracy: 0.8854 - val_loss: 0.4350 - val_accuracy: 0.8490\n",
      "Epoch 49/100\n",
      "8000/8000 [==============================] - 1s 82us/sample - loss: 0.3278 - accuracy: 0.8865 - val_loss: 0.4372 - val_accuracy: 0.8470\n",
      "Epoch 50/100\n",
      "8000/8000 [==============================] - 1s 83us/sample - loss: 0.3261 - accuracy: 0.8881 - val_loss: 0.4320 - val_accuracy: 0.8485\n",
      "Epoch 51/100\n",
      "8000/8000 [==============================] - 1s 83us/sample - loss: 0.3274 - accuracy: 0.8886 - val_loss: 0.4279 - val_accuracy: 0.8495\n",
      "Epoch 52/100\n",
      "8000/8000 [==============================] - 1s 86us/sample - loss: 0.3219 - accuracy: 0.8910 - val_loss: 0.4316 - val_accuracy: 0.8485\n",
      "Epoch 53/100\n",
      "8000/8000 [==============================] - 1s 83us/sample - loss: 0.3220 - accuracy: 0.8884 - val_loss: 0.4321 - val_accuracy: 0.8525\n",
      "Epoch 54/100\n",
      "8000/8000 [==============================] - 1s 86us/sample - loss: 0.3167 - accuracy: 0.8903 - val_loss: 0.4251 - val_accuracy: 0.8515\n",
      "Epoch 55/100\n",
      "8000/8000 [==============================] - 1s 86us/sample - loss: 0.3146 - accuracy: 0.8938 - val_loss: 0.4456 - val_accuracy: 0.8410\n",
      "Epoch 56/100\n",
      "8000/8000 [==============================] - 1s 85us/sample - loss: 0.3128 - accuracy: 0.8929 - val_loss: 0.4340 - val_accuracy: 0.8450\n",
      "Epoch 57/100\n",
      "8000/8000 [==============================] - 1s 84us/sample - loss: 0.3113 - accuracy: 0.8947 - val_loss: 0.4236 - val_accuracy: 0.8510\n",
      "Epoch 58/100\n",
      "8000/8000 [==============================] - 1s 86us/sample - loss: 0.3058 - accuracy: 0.8961 - val_loss: 0.4284 - val_accuracy: 0.8450\n",
      "Epoch 59/100\n",
      "8000/8000 [==============================] - 1s 92us/sample - loss: 0.3047 - accuracy: 0.8964 - val_loss: 0.4317 - val_accuracy: 0.8485\n",
      "Epoch 60/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.3001 - accuracy: 0.8995 - val_loss: 0.4289 - val_accuracy: 0.8475\n",
      "Epoch 61/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.3008 - accuracy: 0.8971 - val_loss: 0.4221 - val_accuracy: 0.8515\n",
      "Epoch 62/100\n",
      "8000/8000 [==============================] - 1s 87us/sample - loss: 0.2979 - accuracy: 0.8976 - val_loss: 0.4290 - val_accuracy: 0.8470\n",
      "Epoch 63/100\n",
      "8000/8000 [==============================] - 1s 86us/sample - loss: 0.2964 - accuracy: 0.8974 - val_loss: 0.4212 - val_accuracy: 0.8540\n",
      "Epoch 64/100\n",
      "8000/8000 [==============================] - 1s 87us/sample - loss: 0.2899 - accuracy: 0.9028 - val_loss: 0.4208 - val_accuracy: 0.8545\n",
      "Epoch 65/100\n",
      "8000/8000 [==============================] - 1s 91us/sample - loss: 0.2909 - accuracy: 0.8997 - val_loss: 0.4249 - val_accuracy: 0.8485\n",
      "Epoch 66/100\n",
      "8000/8000 [==============================] - 1s 87us/sample - loss: 0.2914 - accuracy: 0.9001 - val_loss: 0.4395 - val_accuracy: 0.8440\n",
      "Epoch 67/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.2884 - accuracy: 0.9001 - val_loss: 0.4364 - val_accuracy: 0.8455\n",
      "Epoch 68/100\n",
      "8000/8000 [==============================] - 1s 90us/sample - loss: 0.2832 - accuracy: 0.9020 - val_loss: 0.4321 - val_accuracy: 0.8465\n",
      "Epoch 69/100\n",
      "8000/8000 [==============================] - 1s 92us/sample - loss: 0.2804 - accuracy: 0.9038 - val_loss: 0.4206 - val_accuracy: 0.8515\n",
      "Epoch 70/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.2782 - accuracy: 0.9030 - val_loss: 0.4243 - val_accuracy: 0.8470\n",
      "Epoch 71/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.2734 - accuracy: 0.9072 - val_loss: 0.4239 - val_accuracy: 0.8500\n",
      "Epoch 72/100\n",
      "8000/8000 [==============================] - 1s 90us/sample - loss: 0.2762 - accuracy: 0.9050 - val_loss: 0.4471 - val_accuracy: 0.8380\n",
      "Epoch 73/100\n",
      "8000/8000 [==============================] - 1s 91us/sample - loss: 0.2723 - accuracy: 0.9070 - val_loss: 0.4177 - val_accuracy: 0.8520\n",
      "Epoch 74/100\n",
      "8000/8000 [==============================] - 1s 94us/sample - loss: 0.2721 - accuracy: 0.9085 - val_loss: 0.4629 - val_accuracy: 0.8365\n",
      "Epoch 75/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.2694 - accuracy: 0.9074 - val_loss: 0.4639 - val_accuracy: 0.8390\n",
      "Epoch 76/100\n",
      "8000/8000 [==============================] - 1s 93us/sample - loss: 0.2675 - accuracy: 0.9072 - val_loss: 0.4179 - val_accuracy: 0.8460\n",
      "Epoch 77/100\n",
      "8000/8000 [==============================] - 1s 90us/sample - loss: 0.2663 - accuracy: 0.9082 - val_loss: 0.4238 - val_accuracy: 0.8475\n",
      "Epoch 78/100\n",
      "8000/8000 [==============================] - 1s 90us/sample - loss: 0.2624 - accuracy: 0.9129 - val_loss: 0.4191 - val_accuracy: 0.8510\n",
      "Epoch 79/100\n",
      "8000/8000 [==============================] - 1s 93us/sample - loss: 0.2595 - accuracy: 0.9126 - val_loss: 0.4615 - val_accuracy: 0.8365\n",
      "Epoch 80/100\n",
      "8000/8000 [==============================] - 1s 90us/sample - loss: 0.2591 - accuracy: 0.9107 - val_loss: 0.4168 - val_accuracy: 0.8535\n",
      "Epoch 81/100\n",
      "8000/8000 [==============================] - 1s 91us/sample - loss: 0.2540 - accuracy: 0.9161 - val_loss: 0.4191 - val_accuracy: 0.8535\n",
      "Epoch 82/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.2576 - accuracy: 0.9099 - val_loss: 0.4135 - val_accuracy: 0.8530\n",
      "Epoch 83/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.2541 - accuracy: 0.9158 - val_loss: 0.4233 - val_accuracy: 0.8485\n",
      "Epoch 84/100\n",
      "8000/8000 [==============================] - 1s 90us/sample - loss: 0.2496 - accuracy: 0.9147 - val_loss: 0.4196 - val_accuracy: 0.8520\n",
      "Epoch 85/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.2502 - accuracy: 0.9150 - val_loss: 0.4177 - val_accuracy: 0.8505\n",
      "Epoch 86/100\n",
      "8000/8000 [==============================] - 1s 91us/sample - loss: 0.2474 - accuracy: 0.9185 - val_loss: 0.4127 - val_accuracy: 0.8515\n",
      "Epoch 87/100\n",
      "8000/8000 [==============================] - 1s 90us/sample - loss: 0.2478 - accuracy: 0.9158 - val_loss: 0.4161 - val_accuracy: 0.8525\n",
      "Epoch 88/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.2422 - accuracy: 0.9176 - val_loss: 0.4144 - val_accuracy: 0.8525\n",
      "Epoch 89/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.2370 - accuracy: 0.9189 - val_loss: 0.4131 - val_accuracy: 0.8555\n",
      "Epoch 90/100\n",
      "8000/8000 [==============================] - 1s 90us/sample - loss: 0.2403 - accuracy: 0.9181 - val_loss: 0.4180 - val_accuracy: 0.8500\n",
      "Epoch 91/100\n",
      "8000/8000 [==============================] - 1s 90us/sample - loss: 0.2415 - accuracy: 0.9199 - val_loss: 0.4272 - val_accuracy: 0.8480\n",
      "Epoch 92/100\n",
      "8000/8000 [==============================] - 1s 87us/sample - loss: 0.2379 - accuracy: 0.9180 - val_loss: 0.4121 - val_accuracy: 0.8540\n",
      "Epoch 93/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.2298 - accuracy: 0.9225 - val_loss: 0.4358 - val_accuracy: 0.8430\n",
      "Epoch 94/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.2341 - accuracy: 0.9222 - val_loss: 0.4446 - val_accuracy: 0.8405\n",
      "Epoch 95/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.2278 - accuracy: 0.9230 - val_loss: 0.4163 - val_accuracy: 0.8465\n",
      "Epoch 96/100\n",
      "8000/8000 [==============================] - 1s 90us/sample - loss: 0.2278 - accuracy: 0.9240 - val_loss: 0.4397 - val_accuracy: 0.8475\n",
      "Epoch 97/100\n",
      "8000/8000 [==============================] - 1s 90us/sample - loss: 0.2271 - accuracy: 0.9219 - val_loss: 0.4211 - val_accuracy: 0.8480\n",
      "Epoch 98/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.2252 - accuracy: 0.9244 - val_loss: 0.4097 - val_accuracy: 0.8535\n",
      "Epoch 99/100\n",
      "8000/8000 [==============================] - 1s 87us/sample - loss: 0.2265 - accuracy: 0.9225 - val_loss: 0.4208 - val_accuracy: 0.8495\n",
      "Epoch 100/100\n",
      "8000/8000 [==============================] - 1s 97us/sample - loss: 0.2236 - accuracy: 0.9255 - val_loss: 0.4062 - val_accuracy: 0.8545\n"
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   "source": [
    "# Learning rate defaults to 0.01 according to https://keras.io/api/optimizers/sgd/\n",
    "# To use a custom Learning Rate\n",
    "sgd = tf.keras.optimizers.SGD(learning_rate=0.01)\n",
    "\n",
    "model.compile(\n",
    "    optimizer=sgd, \n",
    "    loss='sparse_categorical_crossentropy', \n",
    "    metrics=['accuracy']\n",
    ")\n",
    "\n",
    "history_constant = model.fit(\n",
    "    X_train, \n",
    "    y_train, \n",
    "    epochs=100, \n",
    "    validation_split=0.2,\n",
    "    batch_size=64\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
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       " <defs>\n",
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       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_metric(history_constant, 'accuracy')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Time-Based Decay"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a new model\n",
    "model = create_model()\n",
    "\n",
    "model.compile(\n",
    "    optimizer='sgd', # Learning rate defaults to 0.01\n",
    "    loss='sparse_categorical_crossentropy', \n",
    "    metrics=['accuracy']\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 8000 samples, validate on 2000 samples\n",
      "\n",
      "Epoch 00001: LearningRateScheduler reducing learning rate to 0.009999999776482582.\n",
      "Epoch 1/100\n",
      "8000/8000 [==============================] - 1s 146us/sample - loss: 1.6332 - accuracy: 0.5425 - val_loss: 1.1615 - val_accuracy: 0.6595\n",
      "\n",
      "Epoch 00002: LearningRateScheduler reducing learning rate to 0.009998999876494932.\n",
      "Epoch 2/100\n",
      "8000/8000 [==============================] - 1s 70us/sample - loss: 0.9720 - accuracy: 0.7063 - val_loss: 0.8714 - val_accuracy: 0.7135\n",
      "\n",
      "Epoch 00003: LearningRateScheduler reducing learning rate to 0.009997000136010244.\n",
      "Epoch 3/100\n",
      "8000/8000 [==============================] - 1s 68us/sample - loss: 0.7963 - accuracy: 0.7459 - val_loss: 0.7679 - val_accuracy: 0.7485\n",
      "\n",
      "Epoch 00004: LearningRateScheduler reducing learning rate to 0.009994001785933966.\n",
      "Epoch 4/100\n",
      "8000/8000 [==============================] - 1s 69us/sample - loss: 0.7131 - accuracy: 0.7686 - val_loss: 0.7078 - val_accuracy: 0.7625\n",
      "\n",
      "Epoch 00005: LearningRateScheduler reducing learning rate to 0.009990006056679388.\n",
      "Epoch 5/100\n",
      "8000/8000 [==============================] - 1s 70us/sample - loss: 0.6599 - accuracy: 0.7880 - val_loss: 0.6682 - val_accuracy: 0.7685\n",
      "\n",
      "Epoch 00006: LearningRateScheduler reducing learning rate to 0.009985013247310728.\n",
      "Epoch 6/100\n",
      "8000/8000 [==============================] - 1s 71us/sample - loss: 0.6224 - accuracy: 0.7980 - val_loss: 0.6379 - val_accuracy: 0.7825\n",
      "\n",
      "Epoch 00007: LearningRateScheduler reducing learning rate to 0.00997902551830089.\n",
      "Epoch 7/100\n",
      "8000/8000 [==============================] - 1s 70us/sample - loss: 0.5925 - accuracy: 0.8060 - val_loss: 0.6170 - val_accuracy: 0.7865\n",
      "\n",
      "Epoch 00008: LearningRateScheduler reducing learning rate to 0.009972045029259186.\n",
      "Epoch 8/100\n",
      "8000/8000 [==============================] - 1s 69us/sample - loss: 0.5681 - accuracy: 0.8115 - val_loss: 0.6054 - val_accuracy: 0.7910\n",
      "\n",
      "Epoch 00009: LearningRateScheduler reducing learning rate to 0.00996407393893178.\n",
      "Epoch 9/100\n",
      "8000/8000 [==============================] - 1s 71us/sample - loss: 0.5469 - accuracy: 0.8204 - val_loss: 0.5733 - val_accuracy: 0.8040\n",
      "\n",
      "Epoch 00010: LearningRateScheduler reducing learning rate to 0.009955114405202109.\n",
      "Epoch 10/100\n",
      "8000/8000 [==============================] - 1s 73us/sample - loss: 0.5329 - accuracy: 0.8227 - val_loss: 0.5580 - val_accuracy: 0.8115\n",
      "\n",
      "Epoch 00011: LearningRateScheduler reducing learning rate to 0.009945169515483507.\n",
      "Epoch 11/100\n",
      "8000/8000 [==============================] - 1s 72us/sample - loss: 0.5175 - accuracy: 0.8290 - val_loss: 0.5474 - val_accuracy: 0.8140\n",
      "\n",
      "Epoch 00012: LearningRateScheduler reducing learning rate to 0.009934241425656447.\n",
      "Epoch 12/100\n",
      "8000/8000 [==============================] - 1s 71us/sample - loss: 0.5048 - accuracy: 0.8326 - val_loss: 0.5425 - val_accuracy: 0.8150\n",
      "\n",
      "Epoch 00013: LearningRateScheduler reducing learning rate to 0.009922335081359075.\n",
      "Epoch 13/100\n",
      "8000/8000 [==============================] - 1s 75us/sample - loss: 0.4950 - accuracy: 0.8347 - val_loss: 0.5313 - val_accuracy: 0.8165\n",
      "\n",
      "Epoch 00014: LearningRateScheduler reducing learning rate to 0.00990945263591356.\n",
      "Epoch 14/100\n",
      "8000/8000 [==============================] - 1s 76us/sample - loss: 0.4848 - accuracy: 0.8372 - val_loss: 0.5199 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00015: LearningRateScheduler reducing learning rate to 0.009895599031843585.\n",
      "Epoch 15/100\n",
      "8000/8000 [==============================] - 1s 74us/sample - loss: 0.4737 - accuracy: 0.8451 - val_loss: 0.5288 - val_accuracy: 0.8090\n",
      "\n",
      "Epoch 00016: LearningRateScheduler reducing learning rate to 0.009880778279771104.\n",
      "Epoch 16/100\n",
      "8000/8000 [==============================] - 1s 77us/sample - loss: 0.4683 - accuracy: 0.8420 - val_loss: 0.5157 - val_accuracy: 0.8200\n",
      "\n",
      "Epoch 00017: LearningRateScheduler reducing learning rate to 0.009864994388716384.\n",
      "Epoch 17/100\n",
      "8000/8000 [==============================] - 1s 77us/sample - loss: 0.4627 - accuracy: 0.8415 - val_loss: 0.5100 - val_accuracy: 0.8215\n",
      "\n",
      "Epoch 00018: LearningRateScheduler reducing learning rate to 0.009848252295840817.\n",
      "Epoch 18/100\n",
      "8000/8000 [==============================] - 1s 75us/sample - loss: 0.4567 - accuracy: 0.8475 - val_loss: 0.4938 - val_accuracy: 0.8240\n",
      "\n",
      "Epoch 00019: LearningRateScheduler reducing learning rate to 0.009830556936334483.\n",
      "Epoch 19/100\n",
      "8000/8000 [==============================] - 1s 78us/sample - loss: 0.4469 - accuracy: 0.8494 - val_loss: 0.4985 - val_accuracy: 0.8195\n",
      "\n",
      "Epoch 00020: LearningRateScheduler reducing learning rate to 0.009811914172973541.\n",
      "Epoch 20/100\n",
      "8000/8000 [==============================] - 1s 77us/sample - loss: 0.4414 - accuracy: 0.8501 - val_loss: 0.5046 - val_accuracy: 0.8130\n",
      "\n",
      "Epoch 00021: LearningRateScheduler reducing learning rate to 0.009792329866193725.\n",
      "Epoch 21/100\n",
      "8000/8000 [==============================] - 1s 78us/sample - loss: 0.4361 - accuracy: 0.8560 - val_loss: 0.4847 - val_accuracy: 0.8260\n",
      "\n",
      "Epoch 00022: LearningRateScheduler reducing learning rate to 0.00977180894472061.\n",
      "Epoch 22/100\n",
      "8000/8000 [==============================] - 1s 80us/sample - loss: 0.4316 - accuracy: 0.8553 - val_loss: 0.4838 - val_accuracy: 0.8255\n",
      "\n",
      "Epoch 00023: LearningRateScheduler reducing learning rate to 0.009750358193868935.\n",
      "Epoch 23/100\n",
      "8000/8000 [==============================] - 1s 79us/sample - loss: 0.4235 - accuracy: 0.8575 - val_loss: 0.4849 - val_accuracy: 0.8270\n",
      "\n",
      "Epoch 00024: LearningRateScheduler reducing learning rate to 0.009727983467060091.\n",
      "Epoch 24/100\n",
      "8000/8000 [==============================] - 1s 79us/sample - loss: 0.4199 - accuracy: 0.8559 - val_loss: 0.4698 - val_accuracy: 0.8310\n",
      "\n",
      "Epoch 00025: LearningRateScheduler reducing learning rate to 0.00970469247356521.\n",
      "Epoch 25/100\n",
      "8000/8000 [==============================] - 1s 79us/sample - loss: 0.4170 - accuracy: 0.8577 - val_loss: 0.4877 - val_accuracy: 0.8280\n",
      "\n",
      "Epoch 00026: LearningRateScheduler reducing learning rate to 0.00968049106157926.\n",
      "Epoch 26/100\n",
      "8000/8000 [==============================] - 1s 78us/sample - loss: 0.4111 - accuracy: 0.8599 - val_loss: 0.4748 - val_accuracy: 0.8280\n",
      "\n",
      "Epoch 00027: LearningRateScheduler reducing learning rate to 0.009655386934778826.\n",
      "Epoch 27/100\n",
      "8000/8000 [==============================] - 1s 80us/sample - loss: 0.4063 - accuracy: 0.8615 - val_loss: 0.4661 - val_accuracy: 0.8350\n",
      "\n",
      "Epoch 00028: LearningRateScheduler reducing learning rate to 0.009629387793767319.\n",
      "Epoch 28/100\n",
      "8000/8000 [==============================] - 1s 78us/sample - loss: 0.4017 - accuracy: 0.8651 - val_loss: 0.4764 - val_accuracy: 0.8320\n",
      "\n",
      "Epoch 00029: LearningRateScheduler reducing learning rate to 0.009602500407354359.\n",
      "Epoch 29/100\n",
      "8000/8000 [==============================] - 1s 79us/sample - loss: 0.3994 - accuracy: 0.8658 - val_loss: 0.4948 - val_accuracy: 0.8135\n",
      "\n",
      "Epoch 00030: LearningRateScheduler reducing learning rate to 0.009574733398908965.\n",
      "Epoch 30/100\n",
      "8000/8000 [==============================] - 1s 80us/sample - loss: 0.3947 - accuracy: 0.8680 - val_loss: 0.4604 - val_accuracy: 0.8345\n",
      "\n",
      "Epoch 00031: LearningRateScheduler reducing learning rate to 0.009546095388361132.\n",
      "Epoch 31/100\n",
      "8000/8000 [==============================] - 1s 82us/sample - loss: 0.3925 - accuracy: 0.8676 - val_loss: 0.4617 - val_accuracy: 0.8325\n",
      "\n",
      "Epoch 00032: LearningRateScheduler reducing learning rate to 0.009516594063759135.\n",
      "Epoch 32/100\n",
      "8000/8000 [==============================] - 1s 80us/sample - loss: 0.3883 - accuracy: 0.8670 - val_loss: 0.4601 - val_accuracy: 0.8370\n",
      "\n",
      "Epoch 00033: LearningRateScheduler reducing learning rate to 0.009486238038437693.\n",
      "Epoch 33/100\n",
      "8000/8000 [==============================] - 1s 81us/sample - loss: 0.3847 - accuracy: 0.8706 - val_loss: 0.4621 - val_accuracy: 0.8340\n",
      "\n",
      "Epoch 00034: LearningRateScheduler reducing learning rate to 0.009455036850556838.\n",
      "Epoch 34/100\n",
      "8000/8000 [==============================] - 1s 85us/sample - loss: 0.3799 - accuracy: 0.8692 - val_loss: 0.4898 - val_accuracy: 0.8175\n",
      "\n",
      "Epoch 00035: LearningRateScheduler reducing learning rate to 0.009422999106307464.\n",
      "Epoch 35/100\n",
      "8000/8000 [==============================] - 1s 83us/sample - loss: 0.3783 - accuracy: 0.8716 - val_loss: 0.4503 - val_accuracy: 0.8355\n",
      "\n",
      "Epoch 00036: LearningRateScheduler reducing learning rate to 0.009390133408449988.\n",
      "Epoch 36/100\n",
      "8000/8000 [==============================] - 1s 82us/sample - loss: 0.3776 - accuracy: 0.8731 - val_loss: 0.4604 - val_accuracy: 0.8300\n",
      "\n",
      "Epoch 00037: LearningRateScheduler reducing learning rate to 0.00935645021227975.\n",
      "Epoch 37/100\n",
      "8000/8000 [==============================] - 1s 81us/sample - loss: 0.3728 - accuracy: 0.8746 - val_loss: 0.4410 - val_accuracy: 0.8420\n",
      "\n",
      "Epoch 00038: LearningRateScheduler reducing learning rate to 0.009321959041036006.\n",
      "Epoch 38/100\n",
      "8000/8000 [==============================] - 1s 82us/sample - loss: 0.3652 - accuracy: 0.8750 - val_loss: 0.4442 - val_accuracy: 0.8435\n",
      "\n",
      "Epoch 00039: LearningRateScheduler reducing learning rate to 0.009286669414163135.\n",
      "Epoch 39/100\n",
      "8000/8000 [==============================] - 1s 83us/sample - loss: 0.3649 - accuracy: 0.8792 - val_loss: 0.4620 - val_accuracy: 0.8330\n",
      "\n",
      "Epoch 00040: LearningRateScheduler reducing learning rate to 0.009250591775017058.\n",
      "Epoch 40/100\n",
      "8000/8000 [==============================] - 1s 83us/sample - loss: 0.3598 - accuracy: 0.8773 - val_loss: 0.4583 - val_accuracy: 0.8360\n",
      "\n",
      "Epoch 00041: LearningRateScheduler reducing learning rate to 0.009213736562792998.\n",
      "Epoch 41/100\n",
      "8000/8000 [==============================] - 1s 83us/sample - loss: 0.3607 - accuracy: 0.8789 - val_loss: 0.4506 - val_accuracy: 0.8455\n",
      "\n",
      "Epoch 00042: LearningRateScheduler reducing learning rate to 0.009176114212527548.\n",
      "Epoch 42/100\n",
      "8000/8000 [==============================] - 1s 86us/sample - loss: 0.3562 - accuracy: 0.8791 - val_loss: 0.4439 - val_accuracy: 0.8375\n",
      "\n",
      "Epoch 00043: LearningRateScheduler reducing learning rate to 0.009137736082528127.\n",
      "Epoch 43/100\n",
      "8000/8000 [==============================] - 1s 84us/sample - loss: 0.3533 - accuracy: 0.8788 - val_loss: 0.4386 - val_accuracy: 0.8440\n",
      "\n",
      "Epoch 00044: LearningRateScheduler reducing learning rate to 0.00909861167190821.\n",
      "Epoch 44/100\n",
      "8000/8000 [==============================] - 1s 86us/sample - loss: 0.3521 - accuracy: 0.8819 - val_loss: 0.4422 - val_accuracy: 0.8445\n",
      "\n",
      "Epoch 00045: LearningRateScheduler reducing learning rate to 0.009058753257726399.\n",
      "Epoch 45/100\n",
      "8000/8000 [==============================] - 1s 86us/sample - loss: 0.3511 - accuracy: 0.8798 - val_loss: 0.4727 - val_accuracy: 0.8295\n",
      "\n",
      "Epoch 00046: LearningRateScheduler reducing learning rate to 0.009018171257851669.\n",
      "Epoch 46/100\n",
      "8000/8000 [==============================] - 1s 86us/sample - loss: 0.3479 - accuracy: 0.8830 - val_loss: 0.4344 - val_accuracy: 0.8435\n",
      "\n",
      "Epoch 00047: LearningRateScheduler reducing learning rate to 0.008976877940121149.\n",
      "Epoch 47/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.3445 - accuracy: 0.8820 - val_loss: 0.4341 - val_accuracy: 0.8455\n",
      "\n",
      "Epoch 00048: LearningRateScheduler reducing learning rate to 0.008934883713556118.\n",
      "Epoch 48/100\n",
      "8000/8000 [==============================] - 1s 85us/sample - loss: 0.3395 - accuracy: 0.8864 - val_loss: 0.4386 - val_accuracy: 0.8460\n",
      "\n",
      "Epoch 00049: LearningRateScheduler reducing learning rate to 0.008892200836781295.\n",
      "Epoch 49/100\n",
      "8000/8000 [==============================] - 1s 84us/sample - loss: 0.3376 - accuracy: 0.8876 - val_loss: 0.4409 - val_accuracy: 0.8430\n",
      "\n",
      "Epoch 00050: LearningRateScheduler reducing learning rate to 0.008848841563541862.\n",
      "Epoch 50/100\n",
      "8000/8000 [==============================] - 1s 87us/sample - loss: 0.3362 - accuracy: 0.8863 - val_loss: 0.4320 - val_accuracy: 0.8455\n",
      "\n",
      "Epoch 00051: LearningRateScheduler reducing learning rate to 0.008804817216016761.\n",
      "Epoch 51/100\n",
      "8000/8000 [==============================] - 1s 86us/sample - loss: 0.3318 - accuracy: 0.8919 - val_loss: 0.4577 - val_accuracy: 0.8345\n",
      "\n",
      "Epoch 00052: LearningRateScheduler reducing learning rate to 0.008760140038475967.\n",
      "Epoch 52/100\n",
      "8000/8000 [==============================] - 1s 85us/sample - loss: 0.3309 - accuracy: 0.8881 - val_loss: 0.4393 - val_accuracy: 0.8420\n",
      "\n",
      "Epoch 00053: LearningRateScheduler reducing learning rate to 0.008714823196821842.\n",
      "Epoch 53/100\n",
      "8000/8000 [==============================] - 1s 86us/sample - loss: 0.3298 - accuracy: 0.8889 - val_loss: 0.4317 - val_accuracy: 0.8500\n",
      "\n",
      "Epoch 00054: LearningRateScheduler reducing learning rate to 0.008668877998892969.\n",
      "Epoch 54/100\n",
      "8000/8000 [==============================] - 1s 87us/sample - loss: 0.3254 - accuracy: 0.8903 - val_loss: 0.4387 - val_accuracy: 0.8435\n",
      "\n",
      "Epoch 00055: LearningRateScheduler reducing learning rate to 0.008622317600669978.\n",
      "Epoch 55/100\n",
      "8000/8000 [==============================] - 1s 90us/sample - loss: 0.3236 - accuracy: 0.8895 - val_loss: 0.4432 - val_accuracy: 0.8435\n",
      "\n",
      "Epoch 00056: LearningRateScheduler reducing learning rate to 0.008575154226671575.\n",
      "Epoch 56/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.3236 - accuracy: 0.8911 - val_loss: 0.4320 - val_accuracy: 0.8470\n",
      "\n",
      "Epoch 00057: LearningRateScheduler reducing learning rate to 0.008527401022690102.\n",
      "Epoch 57/100\n",
      "8000/8000 [==============================] - 1s 90us/sample - loss: 0.3200 - accuracy: 0.8885 - val_loss: 0.4294 - val_accuracy: 0.8475\n",
      "\n",
      "Epoch 00058: LearningRateScheduler reducing learning rate to 0.008479070203245261.\n",
      "Epoch 58/100\n",
      "8000/8000 [==============================] - 1s 91us/sample - loss: 0.3187 - accuracy: 0.8941 - val_loss: 0.4272 - val_accuracy: 0.8445\n",
      "\n",
      "Epoch 00059: LearningRateScheduler reducing learning rate to 0.008430174903951171.\n",
      "Epoch 59/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.3167 - accuracy: 0.8916 - val_loss: 0.4325 - val_accuracy: 0.8485\n",
      "\n",
      "Epoch 00060: LearningRateScheduler reducing learning rate to 0.00838072825519853.\n",
      "Epoch 60/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.3141 - accuracy: 0.8965 - val_loss: 0.4226 - val_accuracy: 0.8550\n",
      "\n",
      "Epoch 00061: LearningRateScheduler reducing learning rate to 0.008330743382157198.\n",
      "Epoch 61/100\n",
      "8000/8000 [==============================] - 1s 90us/sample - loss: 0.3115 - accuracy: 0.8931 - val_loss: 0.4367 - val_accuracy: 0.8415\n",
      "\n",
      "Epoch 00062: LearningRateScheduler reducing learning rate to 0.008280234330454755.\n",
      "Epoch 62/100\n",
      "8000/8000 [==============================] - 1s 90us/sample - loss: 0.3081 - accuracy: 0.8971 - val_loss: 0.4329 - val_accuracy: 0.8460\n",
      "\n",
      "Epoch 00063: LearningRateScheduler reducing learning rate to 0.008229213288967236.\n",
      "Epoch 63/100\n",
      "8000/8000 [==============================] - 1s 94us/sample - loss: 0.3085 - accuracy: 0.8953 - val_loss: 0.4350 - val_accuracy: 0.8450\n",
      "\n",
      "Epoch 00064: LearningRateScheduler reducing learning rate to 0.008177693367217628.\n",
      "Epoch 64/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.3055 - accuracy: 0.8972 - val_loss: 0.4292 - val_accuracy: 0.8505\n",
      "\n",
      "Epoch 00065: LearningRateScheduler reducing learning rate to 0.008125688594918468.\n",
      "Epoch 65/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.3038 - accuracy: 0.8999 - val_loss: 0.4274 - val_accuracy: 0.8510\n",
      "\n",
      "Epoch 00066: LearningRateScheduler reducing learning rate to 0.008073212996206648.\n",
      "Epoch 66/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.3014 - accuracy: 0.8982 - val_loss: 0.4293 - val_accuracy: 0.8505\n",
      "\n",
      "Epoch 00067: LearningRateScheduler reducing learning rate to 0.008020278739213897.\n",
      "Epoch 67/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.3002 - accuracy: 0.8989 - val_loss: 0.4198 - val_accuracy: 0.8520\n",
      "\n",
      "Epoch 00068: LearningRateScheduler reducing learning rate to 0.007966900762609802.\n",
      "Epoch 68/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.2963 - accuracy: 0.9006 - val_loss: 0.4198 - val_accuracy: 0.8585\n",
      "\n",
      "Epoch 00069: LearningRateScheduler reducing learning rate to 0.007913092149064141.\n",
      "Epoch 69/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.2947 - accuracy: 0.8994 - val_loss: 0.4317 - val_accuracy: 0.8440\n",
      "\n",
      "Epoch 00070: LearningRateScheduler reducing learning rate to 0.007858865976049477.\n",
      "Epoch 70/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.2954 - accuracy: 0.8997 - val_loss: 0.4207 - val_accuracy: 0.8565\n",
      "\n",
      "Epoch 00071: LearningRateScheduler reducing learning rate to 0.007804236240692386.\n",
      "Epoch 71/100\n",
      "8000/8000 [==============================] - 1s 91us/sample - loss: 0.2922 - accuracy: 0.9009 - val_loss: 0.4356 - val_accuracy: 0.8425\n",
      "\n",
      "Epoch 00072: LearningRateScheduler reducing learning rate to 0.007749216934560059.\n",
      "Epoch 72/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.2911 - accuracy: 0.9028 - val_loss: 0.4226 - val_accuracy: 0.8515\n",
      "\n",
      "Epoch 00073: LearningRateScheduler reducing learning rate to 0.007693821581330584.\n",
      "Epoch 73/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.2901 - accuracy: 0.9020 - val_loss: 0.4259 - val_accuracy: 0.8480\n",
      "\n",
      "Epoch 00074: LearningRateScheduler reducing learning rate to 0.007638063699311773.\n",
      "Epoch 74/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.2857 - accuracy: 0.9039 - val_loss: 0.4181 - val_accuracy: 0.8515\n",
      "\n",
      "Epoch 00075: LearningRateScheduler reducing learning rate to 0.007581957263684542.\n",
      "Epoch 75/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.2830 - accuracy: 0.9054 - val_loss: 0.4207 - val_accuracy: 0.8535\n",
      "\n",
      "Epoch 00076: LearningRateScheduler reducing learning rate to 0.007525515781886524.\n",
      "Epoch 76/100\n",
      "8000/8000 [==============================] - 1s 90us/sample - loss: 0.2835 - accuracy: 0.9044 - val_loss: 0.4161 - val_accuracy: 0.8565\n",
      "\n",
      "Epoch 00077: LearningRateScheduler reducing learning rate to 0.007468753218142084.\n",
      "Epoch 77/100\n",
      "8000/8000 [==============================] - 1s 92us/sample - loss: 0.2816 - accuracy: 0.9043 - val_loss: 0.4239 - val_accuracy: 0.8500\n",
      "\n",
      "Epoch 00078: LearningRateScheduler reducing learning rate to 0.007411683069029485.\n",
      "Epoch 78/100\n",
      "8000/8000 [==============================] - 1s 91us/sample - loss: 0.2791 - accuracy: 0.9061 - val_loss: 0.4162 - val_accuracy: 0.8590\n",
      "\n",
      "Epoch 00079: LearningRateScheduler reducing learning rate to 0.007354319287827384.\n",
      "Epoch 79/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.2783 - accuracy: 0.9082 - val_loss: 0.4267 - val_accuracy: 0.8520\n",
      "\n",
      "Epoch 00080: LearningRateScheduler reducing learning rate to 0.007296675360265475.\n",
      "Epoch 80/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.2751 - accuracy: 0.9069 - val_loss: 0.4151 - val_accuracy: 0.8560\n",
      "\n",
      "Epoch 00081: LearningRateScheduler reducing learning rate to 0.0072387652286875345.\n",
      "Epoch 81/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.2734 - accuracy: 0.9081 - val_loss: 0.4458 - val_accuracy: 0.8410\n",
      "\n",
      "Epoch 00082: LearningRateScheduler reducing learning rate to 0.007180602367985474.\n",
      "Epoch 82/100\n",
      "8000/8000 [==============================] - 1s 91us/sample - loss: 0.2749 - accuracy: 0.9064 - val_loss: 0.4197 - val_accuracy: 0.8545\n",
      "\n",
      "Epoch 00083: LearningRateScheduler reducing learning rate to 0.0071222002477050895.\n",
      "Epoch 83/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.2721 - accuracy: 0.9091 - val_loss: 0.4247 - val_accuracy: 0.8485\n",
      "\n",
      "Epoch 00084: LearningRateScheduler reducing learning rate to 0.007063572793876819.\n",
      "Epoch 84/100\n",
      "8000/8000 [==============================] - 1s 87us/sample - loss: 0.2698 - accuracy: 0.9099 - val_loss: 0.4244 - val_accuracy: 0.8470\n",
      "\n",
      "Epoch 00085: LearningRateScheduler reducing learning rate to 0.007004733003442461.\n",
      "Epoch 85/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.2669 - accuracy: 0.9106 - val_loss: 0.4366 - val_accuracy: 0.8425\n",
      "\n",
      "Epoch 00086: LearningRateScheduler reducing learning rate to 0.0069456947916619076.\n",
      "Epoch 86/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.2677 - accuracy: 0.9094 - val_loss: 0.4180 - val_accuracy: 0.8545\n",
      "\n",
      "Epoch 00087: LearningRateScheduler reducing learning rate to 0.006886471144894913.\n",
      "Epoch 87/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.2655 - accuracy: 0.9107 - val_loss: 0.4290 - val_accuracy: 0.8460\n",
      "\n",
      "Epoch 00088: LearningRateScheduler reducing learning rate to 0.006827075505996467.\n",
      "Epoch 88/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.2621 - accuracy: 0.9114 - val_loss: 0.4160 - val_accuracy: 0.8575\n",
      "\n",
      "Epoch 00089: LearningRateScheduler reducing learning rate to 0.006767521312491323.\n",
      "Epoch 89/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.2636 - accuracy: 0.9116 - val_loss: 0.4227 - val_accuracy: 0.8490\n",
      "\n",
      "Epoch 00090: LearningRateScheduler reducing learning rate to 0.0067078215350231795.\n",
      "Epoch 90/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.2597 - accuracy: 0.9110 - val_loss: 0.4182 - val_accuracy: 0.8560\n",
      "\n",
      "Epoch 00091: LearningRateScheduler reducing learning rate to 0.006647989600601471.\n",
      "Epoch 91/100\n",
      "8000/8000 [==============================] - 1s 86us/sample - loss: 0.2596 - accuracy: 0.9149 - val_loss: 0.4172 - val_accuracy: 0.8540\n",
      "\n",
      "Epoch 00092: LearningRateScheduler reducing learning rate to 0.006588038469451279.\n",
      "Epoch 92/100\n",
      "8000/8000 [==============================] - 1s 87us/sample - loss: 0.2585 - accuracy: 0.9128 - val_loss: 0.4160 - val_accuracy: 0.8580\n",
      "\n",
      "Epoch 00093: LearningRateScheduler reducing learning rate to 0.0065279810966608585.\n",
      "Epoch 93/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.2543 - accuracy: 0.9162 - val_loss: 0.4205 - val_accuracy: 0.8490\n",
      "\n",
      "Epoch 00094: LearningRateScheduler reducing learning rate to 0.006467830432184172.\n",
      "Epoch 94/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.2540 - accuracy: 0.9158 - val_loss: 0.4175 - val_accuracy: 0.8550\n",
      "\n",
      "Epoch 00095: LearningRateScheduler reducing learning rate to 0.006407598959518607.\n",
      "Epoch 95/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.2538 - accuracy: 0.9140 - val_loss: 0.4163 - val_accuracy: 0.8550\n",
      "\n",
      "Epoch 00096: LearningRateScheduler reducing learning rate to 0.00634729961849428.\n",
      "Epoch 96/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.2508 - accuracy: 0.9165 - val_loss: 0.4221 - val_accuracy: 0.8510\n",
      "\n",
      "Epoch 00097: LearningRateScheduler reducing learning rate to 0.006286944882581143.\n",
      "Epoch 97/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.2508 - accuracy: 0.9164 - val_loss: 0.4147 - val_accuracy: 0.8560\n",
      "\n",
      "Epoch 00098: LearningRateScheduler reducing learning rate to 0.006226547220307694.\n",
      "Epoch 98/100\n",
      "8000/8000 [==============================] - 1s 85us/sample - loss: 0.2485 - accuracy: 0.9189 - val_loss: 0.4121 - val_accuracy: 0.8570\n",
      "\n",
      "Epoch 00099: LearningRateScheduler reducing learning rate to 0.006166119095263422.\n",
      "Epoch 99/100\n",
      "8000/8000 [==============================] - 1s 87us/sample - loss: 0.2468 - accuracy: 0.9176 - val_loss: 0.4489 - val_accuracy: 0.8435\n",
      "\n",
      "Epoch 00100: LearningRateScheduler reducing learning rate to 0.00610567296610125.\n",
      "Epoch 100/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.2458 - accuracy: 0.9191 - val_loss: 0.4199 - val_accuracy: 0.8520\n"
     ]
    }
   ],
   "source": [
    "from tensorflow.keras.callbacks import LearningRateScheduler\n",
    "\n",
    "# Define the learning rate schedule function\n",
    "initial_learning_rate = 0.01\n",
    "epochs = 100\n",
    "decay = initial_learning_rate / epochs\n",
    "\n",
    "def lr_time_based_decay(epoch, lr):\n",
    "    return lr * 1 / (1 + decay * epoch)\n",
    "\n",
    "history_time_based_decay = model.fit(\n",
    "    X_train, \n",
    "    y_train, \n",
    "    epochs=100, \n",
    "    validation_split=0.2,\n",
    "    batch_size=64,\n",
    "    callbacks=[LearningRateScheduler(lr_time_based_decay, verbose=1)],\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
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    "plot_metric(history_time_based_decay, 'accuracy')"
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   "execution_count": 18,
   "metadata": {},
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       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"pb11188b8f8\">\n",
       "   <rect height=\"217.44\" width=\"334.8\" x=\"62.86875\" y=\"22.318125\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_lr(history_time_based_decay)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Step decay"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a new model\n",
    "model = create_model()\n",
    "\n",
    "model.compile(\n",
    "    optimizer='sgd', # Learning rate defaults to 0.01\n",
    "    loss='sparse_categorical_crossentropy', \n",
    "    metrics=['accuracy']\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 8000 samples, validate on 2000 samples\n",
      "\n",
      "Epoch 00001: LearningRateScheduler reducing learning rate to 0.01.\n",
      "Epoch 1/100\n",
      "8000/8000 [==============================] - 1s 145us/sample - loss: 1.5509 - accuracy: 0.5437 - val_loss: 1.1118 - val_accuracy: 0.6640\n",
      "\n",
      "Epoch 00002: LearningRateScheduler reducing learning rate to 0.01.\n",
      "Epoch 2/100\n",
      "8000/8000 [==============================] - 1s 71us/sample - loss: 0.9472 - accuracy: 0.6940 - val_loss: 0.8605 - val_accuracy: 0.7050\n",
      "\n",
      "Epoch 00003: LearningRateScheduler reducing learning rate to 0.01.\n",
      "Epoch 3/100\n",
      "8000/8000 [==============================] - 1s 66us/sample - loss: 0.7901 - accuracy: 0.7385 - val_loss: 0.7603 - val_accuracy: 0.7420\n",
      "\n",
      "Epoch 00004: LearningRateScheduler reducing learning rate to 0.01.\n",
      "Epoch 4/100\n",
      "8000/8000 [==============================] - 1s 67us/sample - loss: 0.7092 - accuracy: 0.7648 - val_loss: 0.7079 - val_accuracy: 0.7495\n",
      "\n",
      "Epoch 00005: LearningRateScheduler reducing learning rate to 0.01.\n",
      "Epoch 5/100\n",
      "8000/8000 [==============================] - 1s 68us/sample - loss: 0.6590 - accuracy: 0.7795 - val_loss: 0.6587 - val_accuracy: 0.7880\n",
      "\n",
      "Epoch 00006: LearningRateScheduler reducing learning rate to 0.01.\n",
      "Epoch 6/100\n",
      "8000/8000 [==============================] - 1s 68us/sample - loss: 0.6172 - accuracy: 0.7951 - val_loss: 0.6414 - val_accuracy: 0.7715\n",
      "\n",
      "Epoch 00007: LearningRateScheduler reducing learning rate to 0.01.\n",
      "Epoch 7/100\n",
      "8000/8000 [==============================] - 1s 69us/sample - loss: 0.5885 - accuracy: 0.8052 - val_loss: 0.6135 - val_accuracy: 0.7910\n",
      "\n",
      "Epoch 00008: LearningRateScheduler reducing learning rate to 0.01.\n",
      "Epoch 8/100\n",
      "8000/8000 [==============================] - 1s 70us/sample - loss: 0.5645 - accuracy: 0.8074 - val_loss: 0.5936 - val_accuracy: 0.7885\n",
      "\n",
      "Epoch 00009: LearningRateScheduler reducing learning rate to 0.01.\n",
      "Epoch 9/100\n",
      "8000/8000 [==============================] - 1s 72us/sample - loss: 0.5423 - accuracy: 0.8186 - val_loss: 0.5923 - val_accuracy: 0.7930\n",
      "\n",
      "Epoch 00010: LearningRateScheduler reducing learning rate to 0.01.\n",
      "Epoch 10/100\n",
      "8000/8000 [==============================] - 1s 71us/sample - loss: 0.5277 - accuracy: 0.8195 - val_loss: 0.5656 - val_accuracy: 0.7990\n",
      "\n",
      "Epoch 00011: LearningRateScheduler reducing learning rate to 0.005.\n",
      "Epoch 11/100\n",
      "8000/8000 [==============================] - 1s 75us/sample - loss: 0.5105 - accuracy: 0.8275 - val_loss: 0.5472 - val_accuracy: 0.8095\n",
      "\n",
      "Epoch 00012: LearningRateScheduler reducing learning rate to 0.005.\n",
      "Epoch 12/100\n",
      "8000/8000 [==============================] - 1s 72us/sample - loss: 0.5015 - accuracy: 0.8304 - val_loss: 0.5388 - val_accuracy: 0.8125\n",
      "\n",
      "Epoch 00013: LearningRateScheduler reducing learning rate to 0.005.\n",
      "Epoch 13/100\n",
      "8000/8000 [==============================] - 1s 72us/sample - loss: 0.4950 - accuracy: 0.8304 - val_loss: 0.5305 - val_accuracy: 0.8190\n",
      "\n",
      "Epoch 00014: LearningRateScheduler reducing learning rate to 0.005.\n",
      "Epoch 14/100\n",
      "8000/8000 [==============================] - 1s 73us/sample - loss: 0.4887 - accuracy: 0.8338 - val_loss: 0.5258 - val_accuracy: 0.8175\n",
      "\n",
      "Epoch 00015: LearningRateScheduler reducing learning rate to 0.005.\n",
      "Epoch 15/100\n",
      "8000/8000 [==============================] - 1s 74us/sample - loss: 0.4841 - accuracy: 0.8366 - val_loss: 0.5248 - val_accuracy: 0.8165\n",
      "\n",
      "Epoch 00016: LearningRateScheduler reducing learning rate to 0.005.\n",
      "Epoch 16/100\n",
      "8000/8000 [==============================] - 1s 77us/sample - loss: 0.4789 - accuracy: 0.8367 - val_loss: 0.5196 - val_accuracy: 0.8175\n",
      "\n",
      "Epoch 00017: LearningRateScheduler reducing learning rate to 0.005.\n",
      "Epoch 17/100\n",
      "8000/8000 [==============================] - 1s 77us/sample - loss: 0.4745 - accuracy: 0.8388 - val_loss: 0.5193 - val_accuracy: 0.8200\n",
      "\n",
      "Epoch 00018: LearningRateScheduler reducing learning rate to 0.005.\n",
      "Epoch 18/100\n",
      "8000/8000 [==============================] - 1s 77us/sample - loss: 0.4693 - accuracy: 0.8400 - val_loss: 0.5098 - val_accuracy: 0.8275\n",
      "\n",
      "Epoch 00019: LearningRateScheduler reducing learning rate to 0.005.\n",
      "Epoch 19/100\n",
      "8000/8000 [==============================] - 1s 74us/sample - loss: 0.4655 - accuracy: 0.8403 - val_loss: 0.5133 - val_accuracy: 0.8170\n",
      "\n",
      "Epoch 00020: LearningRateScheduler reducing learning rate to 0.005.\n",
      "Epoch 20/100\n",
      "8000/8000 [==============================] - 1s 75us/sample - loss: 0.4600 - accuracy: 0.8430 - val_loss: 0.5143 - val_accuracy: 0.8160\n",
      "\n",
      "Epoch 00021: LearningRateScheduler reducing learning rate to 0.0025.\n",
      "Epoch 21/100\n",
      "8000/8000 [==============================] - 1s 77us/sample - loss: 0.4536 - accuracy: 0.8465 - val_loss: 0.5049 - val_accuracy: 0.8245\n",
      "\n",
      "Epoch 00022: LearningRateScheduler reducing learning rate to 0.0025.\n",
      "Epoch 22/100\n",
      "8000/8000 [==============================] - 1s 78us/sample - loss: 0.4521 - accuracy: 0.8465 - val_loss: 0.5025 - val_accuracy: 0.8285\n",
      "\n",
      "Epoch 00023: LearningRateScheduler reducing learning rate to 0.0025.\n",
      "Epoch 23/100\n",
      "8000/8000 [==============================] - 1s 79us/sample - loss: 0.4491 - accuracy: 0.8471 - val_loss: 0.4970 - val_accuracy: 0.8250\n",
      "\n",
      "Epoch 00024: LearningRateScheduler reducing learning rate to 0.0025.\n",
      "Epoch 24/100\n",
      "8000/8000 [==============================] - 1s 80us/sample - loss: 0.4476 - accuracy: 0.8471 - val_loss: 0.4975 - val_accuracy: 0.8275\n",
      "\n",
      "Epoch 00025: LearningRateScheduler reducing learning rate to 0.0025.\n",
      "Epoch 25/100\n",
      "8000/8000 [==============================] - 1s 79us/sample - loss: 0.4455 - accuracy: 0.8478 - val_loss: 0.4955 - val_accuracy: 0.8300\n",
      "\n",
      "Epoch 00026: LearningRateScheduler reducing learning rate to 0.0025.\n",
      "Epoch 26/100\n",
      "8000/8000 [==============================] - 1s 78us/sample - loss: 0.4430 - accuracy: 0.8486 - val_loss: 0.4965 - val_accuracy: 0.8255\n",
      "\n",
      "Epoch 00027: LearningRateScheduler reducing learning rate to 0.0025.\n",
      "Epoch 27/100\n",
      "8000/8000 [==============================] - 1s 78us/sample - loss: 0.4407 - accuracy: 0.8505 - val_loss: 0.4991 - val_accuracy: 0.8290\n",
      "\n",
      "Epoch 00028: LearningRateScheduler reducing learning rate to 0.0025.\n",
      "Epoch 28/100\n",
      "8000/8000 [==============================] - 1s 81us/sample - loss: 0.4405 - accuracy: 0.8499 - val_loss: 0.4917 - val_accuracy: 0.8325\n",
      "\n",
      "Epoch 00029: LearningRateScheduler reducing learning rate to 0.0025.\n",
      "Epoch 29/100\n",
      "8000/8000 [==============================] - 1s 83us/sample - loss: 0.4386 - accuracy: 0.8515 - val_loss: 0.4878 - val_accuracy: 0.8310\n",
      "\n",
      "Epoch 00030: LearningRateScheduler reducing learning rate to 0.0025.\n",
      "Epoch 30/100\n",
      "8000/8000 [==============================] - 1s 81us/sample - loss: 0.4366 - accuracy: 0.8522 - val_loss: 0.4880 - val_accuracy: 0.8310\n",
      "\n",
      "Epoch 00031: LearningRateScheduler reducing learning rate to 0.00125.\n",
      "Epoch 31/100\n",
      "8000/8000 [==============================] - 1s 79us/sample - loss: 0.4336 - accuracy: 0.8524 - val_loss: 0.4881 - val_accuracy: 0.8315\n",
      "\n",
      "Epoch 00032: LearningRateScheduler reducing learning rate to 0.00125.\n",
      "Epoch 32/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.4327 - accuracy: 0.8529 - val_loss: 0.4878 - val_accuracy: 0.8330\n",
      "\n",
      "Epoch 00033: LearningRateScheduler reducing learning rate to 0.00125.\n",
      "Epoch 33/100\n",
      "8000/8000 [==============================] - 1s 86us/sample - loss: 0.4317 - accuracy: 0.8549 - val_loss: 0.4861 - val_accuracy: 0.8325\n",
      "\n",
      "Epoch 00034: LearningRateScheduler reducing learning rate to 0.00125.\n",
      "Epoch 34/100\n",
      "8000/8000 [==============================] - 1s 81us/sample - loss: 0.4313 - accuracy: 0.8541 - val_loss: 0.4854 - val_accuracy: 0.8340\n",
      "\n",
      "Epoch 00035: LearningRateScheduler reducing learning rate to 0.00125.\n",
      "Epoch 35/100\n",
      "8000/8000 [==============================] - 1s 83us/sample - loss: 0.4305 - accuracy: 0.8533 - val_loss: 0.4852 - val_accuracy: 0.8345\n",
      "\n",
      "Epoch 00036: LearningRateScheduler reducing learning rate to 0.00125.\n",
      "Epoch 36/100\n",
      "8000/8000 [==============================] - 1s 82us/sample - loss: 0.4295 - accuracy: 0.8522 - val_loss: 0.4854 - val_accuracy: 0.8335\n",
      "\n",
      "Epoch 00037: LearningRateScheduler reducing learning rate to 0.00125.\n",
      "Epoch 37/100\n",
      "8000/8000 [==============================] - 1s 83us/sample - loss: 0.4282 - accuracy: 0.8549 - val_loss: 0.4866 - val_accuracy: 0.8315\n",
      "\n",
      "Epoch 00038: LearningRateScheduler reducing learning rate to 0.00125.\n",
      "Epoch 38/100\n",
      "8000/8000 [==============================] - 1s 81us/sample - loss: 0.4279 - accuracy: 0.8559 - val_loss: 0.4830 - val_accuracy: 0.8355\n",
      "\n",
      "Epoch 00039: LearningRateScheduler reducing learning rate to 0.00125.\n",
      "Epoch 39/100\n",
      "8000/8000 [==============================] - 1s 81us/sample - loss: 0.4274 - accuracy: 0.8543 - val_loss: 0.4833 - val_accuracy: 0.8335\n",
      "\n",
      "Epoch 00040: LearningRateScheduler reducing learning rate to 0.00125.\n",
      "Epoch 40/100\n",
      "8000/8000 [==============================] - 1s 80us/sample - loss: 0.4260 - accuracy: 0.8547 - val_loss: 0.4826 - val_accuracy: 0.8340\n",
      "\n",
      "Epoch 00041: LearningRateScheduler reducing learning rate to 0.000625.\n",
      "Epoch 41/100\n",
      "8000/8000 [==============================] - 1s 80us/sample - loss: 0.4247 - accuracy: 0.8550 - val_loss: 0.4819 - val_accuracy: 0.8360\n",
      "\n",
      "Epoch 00042: LearningRateScheduler reducing learning rate to 0.000625.\n",
      "Epoch 42/100\n",
      "8000/8000 [==============================] - 1s 81us/sample - loss: 0.4244 - accuracy: 0.8558 - val_loss: 0.4815 - val_accuracy: 0.8350\n",
      "\n",
      "Epoch 00043: LearningRateScheduler reducing learning rate to 0.000625.\n",
      "Epoch 43/100\n",
      "8000/8000 [==============================] - 1s 82us/sample - loss: 0.4239 - accuracy: 0.8555 - val_loss: 0.4811 - val_accuracy: 0.8340\n",
      "\n",
      "Epoch 00044: LearningRateScheduler reducing learning rate to 0.000625.\n",
      "Epoch 44/100\n",
      "8000/8000 [==============================] - 1s 85us/sample - loss: 0.4234 - accuracy: 0.8556 - val_loss: 0.4797 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00045: LearningRateScheduler reducing learning rate to 0.000625.\n",
      "Epoch 45/100\n",
      "8000/8000 [==============================] - 1s 86us/sample - loss: 0.4230 - accuracy: 0.8565 - val_loss: 0.4821 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00046: LearningRateScheduler reducing learning rate to 0.000625.\n",
      "Epoch 46/100\n",
      "8000/8000 [==============================] - 1s 95us/sample - loss: 0.4229 - accuracy: 0.8564 - val_loss: 0.4808 - val_accuracy: 0.8360\n",
      "\n",
      "Epoch 00047: LearningRateScheduler reducing learning rate to 0.000625.\n",
      "Epoch 47/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.4220 - accuracy: 0.8555 - val_loss: 0.4805 - val_accuracy: 0.8355\n",
      "\n",
      "Epoch 00048: LearningRateScheduler reducing learning rate to 0.000625.\n",
      "Epoch 48/100\n",
      "8000/8000 [==============================] - 1s 90us/sample - loss: 0.4220 - accuracy: 0.8559 - val_loss: 0.4799 - val_accuracy: 0.8360\n",
      "\n",
      "Epoch 00049: LearningRateScheduler reducing learning rate to 0.000625.\n",
      "Epoch 49/100\n",
      "8000/8000 [==============================] - 1s 87us/sample - loss: 0.4213 - accuracy: 0.8569 - val_loss: 0.4806 - val_accuracy: 0.8380\n",
      "\n",
      "Epoch 00050: LearningRateScheduler reducing learning rate to 0.000625.\n",
      "Epoch 50/100\n",
      "8000/8000 [==============================] - 1s 87us/sample - loss: 0.4213 - accuracy: 0.8556 - val_loss: 0.4782 - val_accuracy: 0.8370\n",
      "\n",
      "Epoch 00051: LearningRateScheduler reducing learning rate to 0.0003125.\n",
      "Epoch 51/100\n",
      "8000/8000 [==============================] - 1s 86us/sample - loss: 0.4204 - accuracy: 0.8571 - val_loss: 0.4785 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00052: LearningRateScheduler reducing learning rate to 0.0003125.\n",
      "Epoch 52/100\n",
      "8000/8000 [==============================] - 1s 85us/sample - loss: 0.4202 - accuracy: 0.8571 - val_loss: 0.4787 - val_accuracy: 0.8355\n",
      "\n",
      "Epoch 00053: LearningRateScheduler reducing learning rate to 0.0003125.\n",
      "Epoch 53/100\n",
      "8000/8000 [==============================] - 1s 84us/sample - loss: 0.4199 - accuracy: 0.8571 - val_loss: 0.4785 - val_accuracy: 0.8360\n",
      "\n",
      "Epoch 00054: LearningRateScheduler reducing learning rate to 0.0003125.\n",
      "Epoch 54/100\n",
      "8000/8000 [==============================] - 1s 83us/sample - loss: 0.4197 - accuracy: 0.8581 - val_loss: 0.4791 - val_accuracy: 0.8345\n",
      "\n",
      "Epoch 00055: LearningRateScheduler reducing learning rate to 0.0003125.\n",
      "Epoch 55/100\n",
      "8000/8000 [==============================] - 1s 85us/sample - loss: 0.4196 - accuracy: 0.8570 - val_loss: 0.4789 - val_accuracy: 0.8380\n",
      "\n",
      "Epoch 00056: LearningRateScheduler reducing learning rate to 0.0003125.\n",
      "Epoch 56/100\n",
      "8000/8000 [==============================] - 1s 86us/sample - loss: 0.4195 - accuracy: 0.8576 - val_loss: 0.4785 - val_accuracy: 0.8355\n",
      "\n",
      "Epoch 00057: LearningRateScheduler reducing learning rate to 0.0003125.\n",
      "Epoch 57/100\n",
      "8000/8000 [==============================] - 1s 87us/sample - loss: 0.4192 - accuracy: 0.8572 - val_loss: 0.4783 - val_accuracy: 0.8370\n",
      "\n",
      "Epoch 00058: LearningRateScheduler reducing learning rate to 0.0003125.\n",
      "Epoch 58/100\n",
      "8000/8000 [==============================] - 1s 90us/sample - loss: 0.4189 - accuracy: 0.8572 - val_loss: 0.4777 - val_accuracy: 0.8360\n",
      "\n",
      "Epoch 00059: LearningRateScheduler reducing learning rate to 0.0003125.\n",
      "Epoch 59/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.4189 - accuracy: 0.8572 - val_loss: 0.4783 - val_accuracy: 0.8360\n",
      "\n",
      "Epoch 00060: LearningRateScheduler reducing learning rate to 0.0003125.\n",
      "Epoch 60/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.4188 - accuracy: 0.8572 - val_loss: 0.4780 - val_accuracy: 0.8355\n",
      "\n",
      "Epoch 00061: LearningRateScheduler reducing learning rate to 0.00015625.\n",
      "Epoch 61/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.4183 - accuracy: 0.8584 - val_loss: 0.4778 - val_accuracy: 0.8370\n",
      "\n",
      "Epoch 00062: LearningRateScheduler reducing learning rate to 0.00015625.\n",
      "Epoch 62/100\n",
      "8000/8000 [==============================] - 1s 97us/sample - loss: 0.4181 - accuracy: 0.8584 - val_loss: 0.4778 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00063: LearningRateScheduler reducing learning rate to 0.00015625.\n",
      "Epoch 63/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.4180 - accuracy: 0.8580 - val_loss: 0.4777 - val_accuracy: 0.8370\n",
      "\n",
      "Epoch 00064: LearningRateScheduler reducing learning rate to 0.00015625.\n",
      "Epoch 64/100\n",
      "8000/8000 [==============================] - 1s 98us/sample - loss: 0.4180 - accuracy: 0.8581 - val_loss: 0.4775 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00065: LearningRateScheduler reducing learning rate to 0.00015625.\n",
      "Epoch 65/100\n",
      "8000/8000 [==============================] - 1s 90us/sample - loss: 0.4179 - accuracy: 0.8584 - val_loss: 0.4772 - val_accuracy: 0.8360\n",
      "\n",
      "Epoch 00066: LearningRateScheduler reducing learning rate to 0.00015625.\n",
      "Epoch 66/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.4177 - accuracy: 0.8581 - val_loss: 0.4771 - val_accuracy: 0.8370\n",
      "\n",
      "Epoch 00067: LearningRateScheduler reducing learning rate to 0.00015625.\n",
      "Epoch 67/100\n",
      "8000/8000 [==============================] - 1s 91us/sample - loss: 0.4176 - accuracy: 0.8579 - val_loss: 0.4773 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00068: LearningRateScheduler reducing learning rate to 0.00015625.\n",
      "Epoch 68/100\n",
      "8000/8000 [==============================] - 1s 91us/sample - loss: 0.4175 - accuracy: 0.8585 - val_loss: 0.4770 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00069: LearningRateScheduler reducing learning rate to 0.00015625.\n",
      "Epoch 69/100\n",
      "8000/8000 [==============================] - 1s 91us/sample - loss: 0.4175 - accuracy: 0.8587 - val_loss: 0.4770 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00070: LearningRateScheduler reducing learning rate to 0.00015625.\n",
      "Epoch 70/100\n",
      "8000/8000 [==============================] - 1s 96us/sample - loss: 0.4173 - accuracy: 0.8572 - val_loss: 0.4774 - val_accuracy: 0.8370\n",
      "\n",
      "Epoch 00071: LearningRateScheduler reducing learning rate to 7.8125e-05.\n",
      "Epoch 71/100\n",
      "8000/8000 [==============================] - 1s 90us/sample - loss: 0.4172 - accuracy: 0.8587 - val_loss: 0.4772 - val_accuracy: 0.8360\n",
      "\n",
      "Epoch 00072: LearningRateScheduler reducing learning rate to 7.8125e-05.\n",
      "Epoch 72/100\n",
      "8000/8000 [==============================] - 1s 92us/sample - loss: 0.4171 - accuracy: 0.8587 - val_loss: 0.4770 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00073: LearningRateScheduler reducing learning rate to 7.8125e-05.\n",
      "Epoch 73/100\n",
      "8000/8000 [==============================] - 1s 92us/sample - loss: 0.4171 - accuracy: 0.8586 - val_loss: 0.4769 - val_accuracy: 0.8360\n",
      "\n",
      "Epoch 00074: LearningRateScheduler reducing learning rate to 7.8125e-05.\n",
      "Epoch 74/100\n",
      "8000/8000 [==============================] - 1s 99us/sample - loss: 0.4170 - accuracy: 0.8589 - val_loss: 0.4768 - val_accuracy: 0.8360\n",
      "\n",
      "Epoch 00075: LearningRateScheduler reducing learning rate to 7.8125e-05.\n",
      "Epoch 75/100\n",
      "8000/8000 [==============================] - 1s 98us/sample - loss: 0.4170 - accuracy: 0.8584 - val_loss: 0.4769 - val_accuracy: 0.8370\n",
      "\n",
      "Epoch 00076: LearningRateScheduler reducing learning rate to 7.8125e-05.\n",
      "Epoch 76/100\n",
      "8000/8000 [==============================] - 1s 92us/sample - loss: 0.4169 - accuracy: 0.8586 - val_loss: 0.4769 - val_accuracy: 0.8370\n",
      "\n",
      "Epoch 00077: LearningRateScheduler reducing learning rate to 7.8125e-05.\n",
      "Epoch 77/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.4169 - accuracy: 0.8580 - val_loss: 0.4769 - val_accuracy: 0.8370\n",
      "\n",
      "Epoch 00078: LearningRateScheduler reducing learning rate to 7.8125e-05.\n",
      "Epoch 78/100\n",
      "8000/8000 [==============================] - 1s 92us/sample - loss: 0.4168 - accuracy: 0.8589 - val_loss: 0.4768 - val_accuracy: 0.8360\n",
      "\n",
      "Epoch 00079: LearningRateScheduler reducing learning rate to 7.8125e-05.\n",
      "Epoch 79/100\n",
      "8000/8000 [==============================] - 1s 92us/sample - loss: 0.4168 - accuracy: 0.8587 - val_loss: 0.4767 - val_accuracy: 0.8360\n",
      "\n",
      "Epoch 00080: LearningRateScheduler reducing learning rate to 7.8125e-05.\n",
      "Epoch 80/100\n",
      "8000/8000 [==============================] - 1s 96us/sample - loss: 0.4167 - accuracy: 0.8585 - val_loss: 0.4767 - val_accuracy: 0.8360\n",
      "\n",
      "Epoch 00081: LearningRateScheduler reducing learning rate to 3.90625e-05.\n",
      "Epoch 81/100\n",
      "8000/8000 [==============================] - 1s 97us/sample - loss: 0.4166 - accuracy: 0.8587 - val_loss: 0.4767 - val_accuracy: 0.8360\n",
      "\n",
      "Epoch 00082: LearningRateScheduler reducing learning rate to 3.90625e-05.\n",
      "Epoch 82/100\n",
      "8000/8000 [==============================] - 1s 93us/sample - loss: 0.4166 - accuracy: 0.8584 - val_loss: 0.4767 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00083: LearningRateScheduler reducing learning rate to 3.90625e-05.\n",
      "Epoch 83/100\n",
      "8000/8000 [==============================] - 1s 93us/sample - loss: 0.4166 - accuracy: 0.8587 - val_loss: 0.4767 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00084: LearningRateScheduler reducing learning rate to 3.90625e-05.\n",
      "Epoch 84/100\n",
      "8000/8000 [==============================] - 1s 92us/sample - loss: 0.4166 - accuracy: 0.8589 - val_loss: 0.4767 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00085: LearningRateScheduler reducing learning rate to 3.90625e-05.\n",
      "Epoch 85/100\n",
      "8000/8000 [==============================] - 1s 92us/sample - loss: 0.4165 - accuracy: 0.8586 - val_loss: 0.4767 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00086: LearningRateScheduler reducing learning rate to 3.90625e-05.\n",
      "Epoch 86/100\n",
      "8000/8000 [==============================] - 1s 92us/sample - loss: 0.4165 - accuracy: 0.8587 - val_loss: 0.4766 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00087: LearningRateScheduler reducing learning rate to 3.90625e-05.\n",
      "Epoch 87/100\n",
      "8000/8000 [==============================] - 1s 100us/sample - loss: 0.4165 - accuracy: 0.8587 - val_loss: 0.4766 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00088: LearningRateScheduler reducing learning rate to 3.90625e-05.\n",
      "Epoch 88/100\n",
      "8000/8000 [==============================] - 1s 98us/sample - loss: 0.4165 - accuracy: 0.8586 - val_loss: 0.4766 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00089: LearningRateScheduler reducing learning rate to 3.90625e-05.\n",
      "Epoch 89/100\n",
      "8000/8000 [==============================] - 1s 94us/sample - loss: 0.4165 - accuracy: 0.8590 - val_loss: 0.4766 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00090: LearningRateScheduler reducing learning rate to 3.90625e-05.\n",
      "Epoch 90/100\n",
      "8000/8000 [==============================] - 1s 90us/sample - loss: 0.4164 - accuracy: 0.8586 - val_loss: 0.4766 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00091: LearningRateScheduler reducing learning rate to 1.953125e-05.\n",
      "Epoch 91/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.4164 - accuracy: 0.8589 - val_loss: 0.4766 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00092: LearningRateScheduler reducing learning rate to 1.953125e-05.\n",
      "Epoch 92/100\n",
      "8000/8000 [==============================] - 1s 91us/sample - loss: 0.4164 - accuracy: 0.8590 - val_loss: 0.4766 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00093: LearningRateScheduler reducing learning rate to 1.953125e-05.\n",
      "Epoch 93/100\n",
      "8000/8000 [==============================] - 1s 92us/sample - loss: 0.4163 - accuracy: 0.8589 - val_loss: 0.4766 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00094: LearningRateScheduler reducing learning rate to 1.953125e-05.\n",
      "Epoch 94/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.4163 - accuracy: 0.8587 - val_loss: 0.4765 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00095: LearningRateScheduler reducing learning rate to 1.953125e-05.\n",
      "Epoch 95/100\n",
      "8000/8000 [==============================] - 1s 87us/sample - loss: 0.4163 - accuracy: 0.8590 - val_loss: 0.4765 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00096: LearningRateScheduler reducing learning rate to 1.953125e-05.\n",
      "Epoch 96/100\n",
      "8000/8000 [==============================] - 1s 86us/sample - loss: 0.4163 - accuracy: 0.8587 - val_loss: 0.4765 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00097: LearningRateScheduler reducing learning rate to 1.953125e-05.\n",
      "Epoch 97/100\n",
      "8000/8000 [==============================] - 1s 86us/sample - loss: 0.4163 - accuracy: 0.8589 - val_loss: 0.4765 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00098: LearningRateScheduler reducing learning rate to 1.953125e-05.\n",
      "Epoch 98/100\n",
      "8000/8000 [==============================] - 1s 86us/sample - loss: 0.4163 - accuracy: 0.8589 - val_loss: 0.4765 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00099: LearningRateScheduler reducing learning rate to 1.953125e-05.\n",
      "Epoch 99/100\n",
      "8000/8000 [==============================] - 1s 86us/sample - loss: 0.4163 - accuracy: 0.8589 - val_loss: 0.4765 - val_accuracy: 0.8365\n",
      "\n",
      "Epoch 00100: LearningRateScheduler reducing learning rate to 1.953125e-05.\n",
      "Epoch 100/100\n",
      "8000/8000 [==============================] - 1s 85us/sample - loss: 0.4163 - accuracy: 0.8589 - val_loss: 0.4765 - val_accuracy: 0.8365\n"
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   ],
   "source": [
    "# Define the learning rate schedule function\n",
    "initial_learning_rate = 0.01\n",
    "\n",
    "def lr_step_decay(epoch, lr):\n",
    "    drop_rate = 0.5\n",
    "    epochs_drop = 10.0\n",
    "    return initial_learning_rate * math.pow(drop_rate, math.floor(epoch/epochs_drop))\n",
    "\n",
    "# Fit the model to the training data\n",
    "history_step_decay = model.fit(\n",
    "    X_train, \n",
    "    y_train, \n",
    "    epochs=100, \n",
    "    validation_split=0.2,\n",
    "    batch_size=64,\n",
    "    callbacks=[LearningRateScheduler(lr_step_decay, verbose=1)],\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
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   ],
   "source": [
    "plot_lr(history_step_decay)"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Exponential Decay"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a new model\n",
    "model = create_model()\n",
    "\n",
    "model.compile(\n",
    "    optimizer='sgd', # Learning rate defaults to 0.01\n",
    "    loss='sparse_categorical_crossentropy', \n",
    "    metrics=['accuracy']\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
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     "text": [
      "Train on 8000 samples, validate on 2000 samples\n",
      "\n",
      "Epoch 00001: LearningRateScheduler reducing learning rate to 0.01.\n",
      "Epoch 1/100\n",
      "8000/8000 [==============================] - 1s 137us/sample - loss: 1.5663 - accuracy: 0.5537 - val_loss: 1.1171 - val_accuracy: 0.6670\n",
      "\n",
      "Epoch 00002: LearningRateScheduler reducing learning rate to 0.009048374180359595.\n",
      "Epoch 2/100\n",
      "8000/8000 [==============================] - 1s 66us/sample - loss: 0.9513 - accuracy: 0.7153 - val_loss: 0.8652 - val_accuracy: 0.7215\n",
      "\n",
      "Epoch 00003: LearningRateScheduler reducing learning rate to 0.008187307530779819.\n",
      "Epoch 3/100\n",
      "8000/8000 [==============================] - 1s 66us/sample - loss: 0.7915 - accuracy: 0.7530 - val_loss: 0.7659 - val_accuracy: 0.7545\n",
      "\n",
      "Epoch 00004: LearningRateScheduler reducing learning rate to 0.007408182206817179.\n",
      "Epoch 4/100\n",
      "8000/8000 [==============================] - 1s 68us/sample - loss: 0.7177 - accuracy: 0.7678 - val_loss: 0.7187 - val_accuracy: 0.7595\n",
      "\n",
      "Epoch 00005: LearningRateScheduler reducing learning rate to 0.006703200460356393.\n",
      "Epoch 5/100\n",
      "8000/8000 [==============================] - 1s 68us/sample - loss: 0.6717 - accuracy: 0.7828 - val_loss: 0.6825 - val_accuracy: 0.7740\n",
      "\n",
      "Epoch 00006: LearningRateScheduler reducing learning rate to 0.006065306597126334.\n",
      "Epoch 6/100\n",
      "8000/8000 [==============================] - 1s 68us/sample - loss: 0.6399 - accuracy: 0.7920 - val_loss: 0.6520 - val_accuracy: 0.7890\n",
      "\n",
      "Epoch 00007: LearningRateScheduler reducing learning rate to 0.005488116360940264.\n",
      "Epoch 7/100\n",
      "8000/8000 [==============================] - 1s 67us/sample - loss: 0.6161 - accuracy: 0.7971 - val_loss: 0.6367 - val_accuracy: 0.7905\n",
      "\n",
      "Epoch 00008: LearningRateScheduler reducing learning rate to 0.004965853037914095.\n",
      "Epoch 8/100\n",
      "8000/8000 [==============================] - 1s 71us/sample - loss: 0.5972 - accuracy: 0.8076 - val_loss: 0.6208 - val_accuracy: 0.7900\n",
      "\n",
      "Epoch 00009: LearningRateScheduler reducing learning rate to 0.004493289641172216.\n",
      "Epoch 9/100\n",
      "8000/8000 [==============================] - 1s 68us/sample - loss: 0.5826 - accuracy: 0.8111 - val_loss: 0.6069 - val_accuracy: 0.8015\n",
      "\n",
      "Epoch 00010: LearningRateScheduler reducing learning rate to 0.004065696597405992.\n",
      "Epoch 10/100\n",
      "8000/8000 [==============================] - 1s 69us/sample - loss: 0.5696 - accuracy: 0.8125 - val_loss: 0.5995 - val_accuracy: 0.8025\n",
      "\n",
      "Epoch 00011: LearningRateScheduler reducing learning rate to 0.0036787944117144234.\n",
      "Epoch 11/100\n",
      "8000/8000 [==============================] - 1s 71us/sample - loss: 0.5605 - accuracy: 0.8150 - val_loss: 0.5884 - val_accuracy: 0.8065\n",
      "\n",
      "Epoch 00012: LearningRateScheduler reducing learning rate to 0.003328710836980796.\n",
      "Epoch 12/100\n",
      "8000/8000 [==============================] - 1s 69us/sample - loss: 0.5524 - accuracy: 0.8167 - val_loss: 0.5825 - val_accuracy: 0.8065\n",
      "\n",
      "Epoch 00013: LearningRateScheduler reducing learning rate to 0.0030119421191220205.\n",
      "Epoch 13/100\n",
      "8000/8000 [==============================] - 1s 71us/sample - loss: 0.5446 - accuracy: 0.8192 - val_loss: 0.5762 - val_accuracy: 0.8110\n",
      "\n",
      "Epoch 00014: LearningRateScheduler reducing learning rate to 0.002725317930340126.\n",
      "Epoch 14/100\n",
      "8000/8000 [==============================] - 1s 70us/sample - loss: 0.5390 - accuracy: 0.8205 - val_loss: 0.5707 - val_accuracy: 0.8115\n",
      "\n",
      "Epoch 00015: LearningRateScheduler reducing learning rate to 0.0024659696394160645.\n",
      "Epoch 15/100\n",
      "8000/8000 [==============================] - 1s 73us/sample - loss: 0.5330 - accuracy: 0.8232 - val_loss: 0.5688 - val_accuracy: 0.8125\n",
      "\n",
      "Epoch 00016: LearningRateScheduler reducing learning rate to 0.0022313016014842983.\n",
      "Epoch 16/100\n",
      "8000/8000 [==============================] - 1s 70us/sample - loss: 0.5278 - accuracy: 0.8251 - val_loss: 0.5668 - val_accuracy: 0.8145\n",
      "\n",
      "Epoch 00017: LearningRateScheduler reducing learning rate to 0.002018965179946554.\n",
      "Epoch 17/100\n",
      "8000/8000 [==============================] - 1s 72us/sample - loss: 0.5243 - accuracy: 0.8239 - val_loss: 0.5641 - val_accuracy: 0.8160\n",
      "\n",
      "Epoch 00018: LearningRateScheduler reducing learning rate to 0.001826835240527346.\n",
      "Epoch 18/100\n",
      "8000/8000 [==============================] - 1s 71us/sample - loss: 0.5209 - accuracy: 0.8279 - val_loss: 0.5580 - val_accuracy: 0.8145\n",
      "\n",
      "Epoch 00019: LearningRateScheduler reducing learning rate to 0.0016529888822158654.\n",
      "Epoch 19/100\n",
      "8000/8000 [==============================] - 1s 78us/sample - loss: 0.5181 - accuracy: 0.8278 - val_loss: 0.5565 - val_accuracy: 0.8160\n",
      "\n",
      "Epoch 00020: LearningRateScheduler reducing learning rate to 0.0014956861922263505.\n",
      "Epoch 20/100\n",
      "8000/8000 [==============================] - 1s 77us/sample - loss: 0.5152 - accuracy: 0.8280 - val_loss: 0.5525 - val_accuracy: 0.8180\n",
      "\n",
      "Epoch 00021: LearningRateScheduler reducing learning rate to 0.0013533528323661271.\n",
      "Epoch 21/100\n",
      "8000/8000 [==============================] - 1s 74us/sample - loss: 0.5123 - accuracy: 0.8276 - val_loss: 0.5518 - val_accuracy: 0.8160\n",
      "\n",
      "Epoch 00022: LearningRateScheduler reducing learning rate to 0.001224564282529819.\n",
      "Epoch 22/100\n",
      "8000/8000 [==============================] - 1s 75us/sample - loss: 0.5103 - accuracy: 0.8289 - val_loss: 0.5521 - val_accuracy: 0.8125\n",
      "\n",
      "Epoch 00023: LearningRateScheduler reducing learning rate to 0.0011080315836233387.\n",
      "Epoch 23/100\n",
      "8000/8000 [==============================] - 1s 74us/sample - loss: 0.5089 - accuracy: 0.8299 - val_loss: 0.5480 - val_accuracy: 0.8175\n",
      "\n",
      "Epoch 00024: LearningRateScheduler reducing learning rate to 0.001002588437228037.\n",
      "Epoch 24/100\n",
      "8000/8000 [==============================] - 1s 74us/sample - loss: 0.5064 - accuracy: 0.8319 - val_loss: 0.5466 - val_accuracy: 0.8195\n",
      "\n",
      "Epoch 00025: LearningRateScheduler reducing learning rate to 0.0009071795328941247.\n",
      "Epoch 25/100\n",
      "8000/8000 [==============================] - 1s 80us/sample - loss: 0.5053 - accuracy: 0.8322 - val_loss: 0.5458 - val_accuracy: 0.8215\n",
      "\n",
      "Epoch 00026: LearningRateScheduler reducing learning rate to 0.0008208499862389881.\n",
      "Epoch 26/100\n",
      "8000/8000 [==============================] - 1s 78us/sample - loss: 0.5040 - accuracy: 0.8310 - val_loss: 0.5456 - val_accuracy: 0.8195\n",
      "\n",
      "Epoch 00027: LearningRateScheduler reducing learning rate to 0.0007427357821433388.\n",
      "Epoch 27/100\n",
      "8000/8000 [==============================] - 1s 74us/sample - loss: 0.5028 - accuracy: 0.8328 - val_loss: 0.5443 - val_accuracy: 0.8210\n",
      "\n",
      "Epoch 00028: LearningRateScheduler reducing learning rate to 0.0006720551273974976.\n",
      "Epoch 28/100\n",
      "8000/8000 [==============================] - 1s 74us/sample - loss: 0.5018 - accuracy: 0.8332 - val_loss: 0.5436 - val_accuracy: 0.8195\n",
      "\n",
      "Epoch 00029: LearningRateScheduler reducing learning rate to 0.0006081006262521795.\n",
      "Epoch 29/100\n",
      "8000/8000 [==============================] - 1s 75us/sample - loss: 0.5007 - accuracy: 0.8342 - val_loss: 0.5434 - val_accuracy: 0.8210\n",
      "\n",
      "Epoch 00030: LearningRateScheduler reducing learning rate to 0.0005502322005640721.\n",
      "Epoch 30/100\n",
      "8000/8000 [==============================] - 1s 74us/sample - loss: 0.4999 - accuracy: 0.8331 - val_loss: 0.5420 - val_accuracy: 0.8200\n",
      "\n",
      "Epoch 00031: LearningRateScheduler reducing learning rate to 0.0004978706836786395.\n",
      "Epoch 31/100\n",
      "8000/8000 [==============================] - 1s 75us/sample - loss: 0.4990 - accuracy: 0.8339 - val_loss: 0.5414 - val_accuracy: 0.8195\n",
      "\n",
      "Epoch 00032: LearningRateScheduler reducing learning rate to 0.000450492023935578.\n",
      "Epoch 32/100\n",
      "8000/8000 [==============================] - 1s 78us/sample - loss: 0.4980 - accuracy: 0.8330 - val_loss: 0.5406 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00033: LearningRateScheduler reducing learning rate to 0.0004076220397836621.\n",
      "Epoch 33/100\n",
      "8000/8000 [==============================] - 1s 83us/sample - loss: 0.4976 - accuracy: 0.8336 - val_loss: 0.5401 - val_accuracy: 0.8240\n",
      "\n",
      "Epoch 00034: LearningRateScheduler reducing learning rate to 0.00036883167401239995.\n",
      "Epoch 34/100\n",
      "8000/8000 [==============================] - 1s 78us/sample - loss: 0.4971 - accuracy: 0.8335 - val_loss: 0.5398 - val_accuracy: 0.8250\n",
      "\n",
      "Epoch 00035: LearningRateScheduler reducing learning rate to 0.0003337326996032607.\n",
      "Epoch 35/100\n",
      "8000/8000 [==============================] - 1s 78us/sample - loss: 0.4964 - accuracy: 0.8349 - val_loss: 0.5394 - val_accuracy: 0.8230\n",
      "\n",
      "Epoch 00036: LearningRateScheduler reducing learning rate to 0.00030197383422318503.\n",
      "Epoch 36/100\n",
      "8000/8000 [==============================] - 1s 80us/sample - loss: 0.4961 - accuracy: 0.8340 - val_loss: 0.5391 - val_accuracy: 0.8230\n",
      "\n",
      "Epoch 00037: LearningRateScheduler reducing learning rate to 0.0002732372244729256.\n",
      "Epoch 37/100\n",
      "8000/8000 [==============================] - 1s 77us/sample - loss: 0.4956 - accuracy: 0.8339 - val_loss: 0.5391 - val_accuracy: 0.8245\n",
      "\n",
      "Epoch 00038: LearningRateScheduler reducing learning rate to 0.00024723526470339386.\n",
      "Epoch 38/100\n",
      "8000/8000 [==============================] - 1s 78us/sample - loss: 0.4951 - accuracy: 0.8342 - val_loss: 0.5386 - val_accuracy: 0.8205\n",
      "\n",
      "Epoch 00039: LearningRateScheduler reducing learning rate to 0.00022370771856165591.\n",
      "Epoch 39/100\n",
      "8000/8000 [==============================] - 1s 77us/sample - loss: 0.4949 - accuracy: 0.8350 - val_loss: 0.5383 - val_accuracy: 0.8240\n",
      "\n",
      "Epoch 00040: LearningRateScheduler reducing learning rate to 0.0002024191144580438.\n",
      "Epoch 40/100\n",
      "8000/8000 [==============================] - 1s 79us/sample - loss: 0.4945 - accuracy: 0.8344 - val_loss: 0.5379 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00041: LearningRateScheduler reducing learning rate to 0.00018315638888734178.\n",
      "Epoch 41/100\n",
      "8000/8000 [==============================] - 1s 81us/sample - loss: 0.4942 - accuracy: 0.8353 - val_loss: 0.5379 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00042: LearningRateScheduler reducing learning rate to 0.00016572675401761236.\n",
      "Epoch 42/100\n",
      "8000/8000 [==============================] - 1s 80us/sample - loss: 0.4940 - accuracy: 0.8354 - val_loss: 0.5376 - val_accuracy: 0.8245\n",
      "\n",
      "Epoch 00043: LearningRateScheduler reducing learning rate to 0.00014995576820477704.\n",
      "Epoch 43/100\n",
      "8000/8000 [==============================] - 1s 79us/sample - loss: 0.4937 - accuracy: 0.8355 - val_loss: 0.5374 - val_accuracy: 0.8220\n",
      "\n",
      "Epoch 00044: LearningRateScheduler reducing learning rate to 0.00013568559012200934.\n",
      "Epoch 44/100\n",
      "8000/8000 [==============================] - 1s 77us/sample - loss: 0.4935 - accuracy: 0.8356 - val_loss: 0.5373 - val_accuracy: 0.8240\n",
      "\n",
      "Epoch 00045: LearningRateScheduler reducing learning rate to 0.00012277339903068437.\n",
      "Epoch 45/100\n",
      "8000/8000 [==============================] - 1s 77us/sample - loss: 0.4933 - accuracy: 0.8350 - val_loss: 0.5372 - val_accuracy: 0.8240\n",
      "\n",
      "Epoch 00046: LearningRateScheduler reducing learning rate to 0.00011108996538242307.\n",
      "Epoch 46/100\n",
      "8000/8000 [==============================] - 1s 78us/sample - loss: 0.4931 - accuracy: 0.8347 - val_loss: 0.5370 - val_accuracy: 0.8230\n",
      "\n",
      "Epoch 00047: LearningRateScheduler reducing learning rate to 0.00010051835744633576.\n",
      "Epoch 47/100\n",
      "8000/8000 [==============================] - 1s 77us/sample - loss: 0.4930 - accuracy: 0.8353 - val_loss: 0.5369 - val_accuracy: 0.8230\n",
      "\n",
      "Epoch 00048: LearningRateScheduler reducing learning rate to 9.095277101695816e-05.\n",
      "Epoch 48/100\n",
      "8000/8000 [==============================] - 1s 79us/sample - loss: 0.4929 - accuracy: 0.8353 - val_loss: 0.5368 - val_accuracy: 0.8240\n",
      "\n",
      "Epoch 00049: LearningRateScheduler reducing learning rate to 8.229747049020023e-05.\n",
      "Epoch 49/100\n",
      "8000/8000 [==============================] - 1s 80us/sample - loss: 0.4927 - accuracy: 0.8355 - val_loss: 0.5367 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00050: LearningRateScheduler reducing learning rate to 7.446583070924338e-05.\n",
      "Epoch 50/100\n",
      "8000/8000 [==============================] - 1s 78us/sample - loss: 0.4926 - accuracy: 0.8354 - val_loss: 0.5367 - val_accuracy: 0.8240\n",
      "\n",
      "Epoch 00051: LearningRateScheduler reducing learning rate to 6.737946999085467e-05.\n",
      "Epoch 51/100\n",
      "8000/8000 [==============================] - 1s 79us/sample - loss: 0.4925 - accuracy: 0.8351 - val_loss: 0.5366 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00052: LearningRateScheduler reducing learning rate to 6.096746565515633e-05.\n",
      "Epoch 52/100\n",
      "8000/8000 [==============================] - 1s 81us/sample - loss: 0.4924 - accuracy: 0.8356 - val_loss: 0.5365 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00053: LearningRateScheduler reducing learning rate to 5.5165644207607714e-05.\n",
      "Epoch 53/100\n",
      "8000/8000 [==============================] - 1s 79us/sample - loss: 0.4923 - accuracy: 0.8355 - val_loss: 0.5365 - val_accuracy: 0.8240\n",
      "\n",
      "Epoch 00054: LearningRateScheduler reducing learning rate to 4.991593906910213e-05.\n",
      "Epoch 54/100\n",
      "8000/8000 [==============================] - 1s 84us/sample - loss: 0.4923 - accuracy: 0.8354 - val_loss: 0.5364 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00055: LearningRateScheduler reducing learning rate to 4.516580942612666e-05.\n",
      "Epoch 55/100\n",
      "8000/8000 [==============================] - 1s 84us/sample - loss: 0.4922 - accuracy: 0.8355 - val_loss: 0.5364 - val_accuracy: 0.8240\n",
      "\n",
      "Epoch 00056: LearningRateScheduler reducing learning rate to 4.086771438464067e-05.\n",
      "Epoch 56/100\n",
      "8000/8000 [==============================] - 1s 80us/sample - loss: 0.4921 - accuracy: 0.8353 - val_loss: 0.5363 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00057: LearningRateScheduler reducing learning rate to 3.697863716482929e-05.\n",
      "Epoch 57/100\n",
      "8000/8000 [==============================] - 1s 82us/sample - loss: 0.4921 - accuracy: 0.8355 - val_loss: 0.5363 - val_accuracy: 0.8240\n",
      "\n",
      "Epoch 00058: LearningRateScheduler reducing learning rate to 3.3459654574712724e-05.\n",
      "Epoch 58/100\n",
      "8000/8000 [==============================] - 1s 81us/sample - loss: 0.4920 - accuracy: 0.8357 - val_loss: 0.5362 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00059: LearningRateScheduler reducing learning rate to 3.027554745375813e-05.\n",
      "Epoch 59/100\n",
      "8000/8000 [==============================] - 1s 80us/sample - loss: 0.4920 - accuracy: 0.8354 - val_loss: 0.5362 - val_accuracy: 0.8240\n",
      "\n",
      "Epoch 00060: LearningRateScheduler reducing learning rate to 2.7394448187683685e-05.\n",
      "Epoch 60/100\n",
      "8000/8000 [==============================] - 1s 81us/sample - loss: 0.4919 - accuracy: 0.8355 - val_loss: 0.5362 - val_accuracy: 0.8240\n",
      "\n",
      "Epoch 00061: LearningRateScheduler reducing learning rate to 2.4787521766663585e-05.\n",
      "Epoch 61/100\n",
      "8000/8000 [==============================] - 1s 82us/sample - loss: 0.4919 - accuracy: 0.8353 - val_loss: 0.5361 - val_accuracy: 0.8240\n",
      "\n",
      "Epoch 00062: LearningRateScheduler reducing learning rate to 2.2428677194858013e-05.\n",
      "Epoch 62/100\n",
      "8000/8000 [==============================] - 1s 79us/sample - loss: 0.4919 - accuracy: 0.8354 - val_loss: 0.5361 - val_accuracy: 0.8240\n",
      "\n",
      "Epoch 00063: LearningRateScheduler reducing learning rate to 2.029430636295734e-05.\n",
      "Epoch 63/100\n",
      "8000/8000 [==============================] - 1s 81us/sample - loss: 0.4918 - accuracy: 0.8353 - val_loss: 0.5361 - val_accuracy: 0.8240\n",
      "\n",
      "Epoch 00064: LearningRateScheduler reducing learning rate to 1.8363047770289057e-05.\n",
      "Epoch 64/100\n",
      "8000/8000 [==============================] - 1s 85us/sample - loss: 0.4918 - accuracy: 0.8355 - val_loss: 0.5361 - val_accuracy: 0.8240\n",
      "\n",
      "Epoch 00065: LearningRateScheduler reducing learning rate to 1.661557273173934e-05.\n",
      "Epoch 65/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.4918 - accuracy: 0.8355 - val_loss: 0.5361 - val_accuracy: 0.8240\n",
      "\n",
      "Epoch 00066: LearningRateScheduler reducing learning rate to 1.5034391929775723e-05.\n",
      "Epoch 66/100\n",
      "8000/8000 [==============================] - 1s 83us/sample - loss: 0.4918 - accuracy: 0.8354 - val_loss: 0.5360 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00067: LearningRateScheduler reducing learning rate to 1.3603680375478928e-05.\n",
      "Epoch 67/100\n",
      "8000/8000 [==============================] - 1s 87us/sample - loss: 0.4917 - accuracy: 0.8356 - val_loss: 0.5360 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00068: LearningRateScheduler reducing learning rate to 1.230911902673481e-05.\n",
      "Epoch 68/100\n",
      "8000/8000 [==============================] - 1s 83us/sample - loss: 0.4917 - accuracy: 0.8356 - val_loss: 0.5360 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00069: LearningRateScheduler reducing learning rate to 1.1137751478448024e-05.\n",
      "Epoch 69/100\n",
      "8000/8000 [==============================] - 1s 86us/sample - loss: 0.4917 - accuracy: 0.8354 - val_loss: 0.5360 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00070: LearningRateScheduler reducing learning rate to 1.0077854290485104e-05.\n",
      "Epoch 70/100\n",
      "8000/8000 [==============================] - 1s 89us/sample - loss: 0.4917 - accuracy: 0.8355 - val_loss: 0.5360 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00071: LearningRateScheduler reducing learning rate to 9.118819655545163e-06.\n",
      "Epoch 71/100\n",
      "8000/8000 [==============================] - 1s 86us/sample - loss: 0.4917 - accuracy: 0.8355 - val_loss: 0.5360 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00072: LearningRateScheduler reducing learning rate to 8.25104923265904e-06.\n",
      "Epoch 72/100\n",
      "8000/8000 [==============================] - 1s 84us/sample - loss: 0.4916 - accuracy: 0.8356 - val_loss: 0.5360 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00073: LearningRateScheduler reducing learning rate to 7.465858083766792e-06.\n",
      "Epoch 73/100\n",
      "8000/8000 [==============================] - 1s 86us/sample - loss: 0.4916 - accuracy: 0.8355 - val_loss: 0.5360 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00074: LearningRateScheduler reducing learning rate to 6.755387751938438e-06.\n",
      "Epoch 74/100\n",
      "8000/8000 [==============================] - 1s 84us/sample - loss: 0.4916 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00075: LearningRateScheduler reducing learning rate to 6.112527611295723e-06.\n",
      "Epoch 75/100\n",
      "8000/8000 [==============================] - 1s 86us/sample - loss: 0.4916 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00076: LearningRateScheduler reducing learning rate to 5.530843701478336e-06.\n",
      "Epoch 76/100\n",
      "8000/8000 [==============================] - 1s 85us/sample - loss: 0.4916 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00077: LearningRateScheduler reducing learning rate to 5.004514334406104e-06.\n",
      "Epoch 77/100\n",
      "8000/8000 [==============================] - 1s 84us/sample - loss: 0.4916 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00078: LearningRateScheduler reducing learning rate to 4.528271828867969e-06.\n",
      "Epoch 78/100\n",
      "8000/8000 [==============================] - 1s 85us/sample - loss: 0.4916 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00079: LearningRateScheduler reducing learning rate to 4.097349789797864e-06.\n",
      "Epoch 79/100\n",
      "8000/8000 [==============================] - 1s 85us/sample - loss: 0.4916 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00080: LearningRateScheduler reducing learning rate to 3.707435404590882e-06.\n",
      "Epoch 80/100\n",
      "8000/8000 [==============================] - 1s 83us/sample - loss: 0.4916 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00081: LearningRateScheduler reducing learning rate to 3.3546262790251185e-06.\n",
      "Epoch 81/100\n",
      "8000/8000 [==============================] - 1s 84us/sample - loss: 0.4916 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00082: LearningRateScheduler reducing learning rate to 3.035391380788668e-06.\n",
      "Epoch 82/100\n",
      "8000/8000 [==============================] - 1s 87us/sample - loss: 0.4916 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00083: LearningRateScheduler reducing learning rate to 2.7465356997214204e-06.\n",
      "Epoch 83/100\n",
      "8000/8000 [==============================] - 1s 85us/sample - loss: 0.4916 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00084: LearningRateScheduler reducing learning rate to 2.4851682710795183e-06.\n",
      "Epoch 84/100\n",
      "8000/8000 [==============================] - 1s 84us/sample - loss: 0.4916 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00085: LearningRateScheduler reducing learning rate to 2.248673241788482e-06.\n",
      "Epoch 85/100\n",
      "8000/8000 [==============================] - 1s 91us/sample - loss: 0.4916 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00086: LearningRateScheduler reducing learning rate to 2.0346836901064417e-06.\n",
      "Epoch 86/100\n",
      "8000/8000 [==============================] - 1s 87us/sample - loss: 0.4916 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00087: LearningRateScheduler reducing learning rate to 1.841057936675792e-06.\n",
      "Epoch 87/100\n",
      "8000/8000 [==============================] - 1s 83us/sample - loss: 0.4916 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00088: LearningRateScheduler reducing learning rate to 1.6658581098763324e-06.\n",
      "Epoch 88/100\n",
      "8000/8000 [==============================] - 1s 88us/sample - loss: 0.4915 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00089: LearningRateScheduler reducing learning rate to 1.507330750954765e-06.\n",
      "Epoch 89/100\n",
      "8000/8000 [==============================] - 1s 83us/sample - loss: 0.4915 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00090: LearningRateScheduler reducing learning rate to 1.363889264820114e-06.\n",
      "Epoch 90/100\n",
      "8000/8000 [==============================] - 1s 83us/sample - loss: 0.4915 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00091: LearningRateScheduler reducing learning rate to 1.2340980408667956e-06.\n",
      "Epoch 91/100\n",
      "8000/8000 [==============================] - 1s 83us/sample - loss: 0.4915 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00092: LearningRateScheduler reducing learning rate to 1.1166580849011478e-06.\n",
      "Epoch 92/100\n",
      "8000/8000 [==============================] - 1s 87us/sample - loss: 0.4915 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00093: LearningRateScheduler reducing learning rate to 1.0103940183709325e-06.\n",
      "Epoch 93/100\n",
      "8000/8000 [==============================] - 1s 91us/sample - loss: 0.4915 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00094: LearningRateScheduler reducing learning rate to 9.142423147817327e-07.\n",
      "Epoch 94/100\n",
      "8000/8000 [==============================] - 1s 92us/sample - loss: 0.4915 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00095: LearningRateScheduler reducing learning rate to 8.272406555663223e-07.\n",
      "Epoch 95/100\n",
      "8000/8000 [==============================] - 1s 90us/sample - loss: 0.4915 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00096: LearningRateScheduler reducing learning rate to 7.48518298877006e-07.\n",
      "Epoch 96/100\n",
      "8000/8000 [==============================] - 1s 83us/sample - loss: 0.4915 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00097: LearningRateScheduler reducing learning rate to 6.772873649085378e-07.\n",
      "Epoch 97/100\n",
      "8000/8000 [==============================] - 1s 85us/sample - loss: 0.4915 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00098: LearningRateScheduler reducing learning rate to 6.128349505322203e-07.\n",
      "Epoch 98/100\n",
      "8000/8000 [==============================] - 1s 84us/sample - loss: 0.4915 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00099: LearningRateScheduler reducing learning rate to 5.545159943217694e-07.\n",
      "Epoch 99/100\n",
      "8000/8000 [==============================] - 1s 82us/sample - loss: 0.4915 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n",
      "\n",
      "Epoch 00100: LearningRateScheduler reducing learning rate to 5.017468205617528e-07.\n",
      "Epoch 100/100\n",
      "8000/8000 [==============================] - 1s 83us/sample - loss: 0.4915 - accuracy: 0.8355 - val_loss: 0.5359 - val_accuracy: 0.8235\n"
     ]
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   ],
   "source": [
    "initial_learning_rate = 0.01\n",
    "\n",
    "def lr_exp_decay(epoch, lr):\n",
    "    k = 0.1\n",
    "    return initial_learning_rate * math.exp(-k*epoch)\n",
    "\n",
    "# Fit the model to the training data\n",
    "history_exp_decay = model.fit(\n",
    "    X_train, \n",
    "    y_train, \n",
    "    epochs=100, \n",
    "    validation_split=0.2,\n",
    "    batch_size=64,\n",
    "    callbacks=[LearningRateScheduler(lr_exp_decay, verbose=1)],\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
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   "metadata": {},
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   "source": [
    "plot_lr(history_exp_decay)"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compare model accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
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   ],
   "source": [
    "epochs = range(1, 101)\n",
    "plt.plot(epochs,history_constant.history['val_accuracy'],label='Constant')\n",
    "plt.plot(epochs,history_time_based_decay.history['val_accuracy'],label='Time-based')\n",
    "plt.plot(epochs,history_step_decay.history['val_accuracy'],label='Step decay')\n",
    "plt.plot(epochs,history_exp_decay.history['val_accuracy'],label='Exponential decay')\n",
    "plt.legend(loc=0)\n",
    "plt.xlabel('epochs')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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