MNIST simple NN (Keras)(with graphs).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Importing the dataset through Keras"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\h5py\\__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
      "  from ._conv import register_converters as _register_converters\n",
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "from keras.datasets import mnist"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Library imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras.utils import to_categorical\n",
    "import numpy as np\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense,Conv2D,MaxPooling2D,Flatten\n",
    "from matplotlib import pyplot as plt\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\", category=FutureWarning)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading the dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each image has a label associated with it denoting the correct digit that's drawn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "(train_imgs,train_lbls),(test_imgs,test_lbls)=mnist.load_data()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are 10 classes to classify the images into (0-9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classes=np.unique(train_lbls)\n",
    "nClasses=len(classes)\n",
    "nClasses"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Shape of the test and train labels to see how many test and train images we have"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10000\n",
      "60000\n"
     ]
    }
   ],
   "source": [
    "print(len(test_lbls))\n",
    "print(len(train_lbls))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "784"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dimdata=np.prod(train_imgs.shape[1:]) #28*28\n",
    "dimdata"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(28, 28)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_imgs[0].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Number of training images (60,000), and each image has dimensions 28x28"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 28, 28)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_imgs.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Flattening the images (since neural networks cannot take 2D input directly)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_data = train_imgs.reshape(train_imgs.shape[0], dimdata)\n",
    "test_data = test_imgs.reshape(test_imgs.shape[0], dimdata)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 784)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "#converting to float\n",
    "train_data = train_data.astype('float32')\n",
    "test_data = test_data.astype('float32')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Converting values to lie between 0 and 1 (since they are currently digits between 0 and 255, denoting how black each pixel is)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_data /= 255\n",
    "test_data /= 255"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Keras uses one hot encoding\n",
    "\n",
    "Hence changing the labels from integer to categorical data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original label :  4\n",
      "After conversion to categorical ( one-hot ) :  [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n"
     ]
    }
   ],
   "source": [
    "train_labels_one_hot = to_categorical(train_lbls)\n",
    "test_labels_one_hot = to_categorical(test_lbls)\n",
    " \n",
    "#Display the change for category label using one-hot encoding\n",
    "print('Original label : ', train_lbls[2])\n",
    "print('After conversion to categorical ( one-hot ) : ', train_labels_one_hot[2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Making the Keras Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "model=Sequential()\n",
    "model.add(Dense(256,activation='relu',input_shape=(dimdata,)))\n",
    "model.add(Dense(512,activation='relu'))\n",
    "model.add(Dense(nClasses,activation='softmax'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**We add 2 dense layers that are fully interconnected. These perform linear operations**\n",
    "\n",
    "The last Dense layer has 10 units (since we need to classify into 10 classes (0-9))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compiling the model, using RMSProp optimizer, with a categorical crossentropy loss so we can predict into multiple classes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "model.compile(optimizer='rmsprop',loss='categorical_crossentropy',metrics=[\"accuracy\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fitting out data onto the model, with 256 images at a time, for 20 epochs.\n",
    "We use the test data as validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 60000 samples, validate on 10000 samples\n",
      "Epoch 1/20\n",
      "60000/60000 [==============================] - 17s 281us/step - loss: 0.3064 - acc: 0.9069 - val_loss: 0.1601 - val_acc: 0.9502\n",
      "Epoch 2/20\n",
      "60000/60000 [==============================] - 3s 53us/step - loss: 0.1118 - acc: 0.9654 - val_loss: 0.1021 - val_acc: 0.9683\n",
      "Epoch 3/20\n",
      "60000/60000 [==============================] - 3s 53us/step - loss: 0.0727 - acc: 0.9780 - val_loss: 0.0799 - val_acc: 0.9754\n",
      "Epoch 4/20\n",
      "60000/60000 [==============================] - 3s 53us/step - loss: 0.0519 - acc: 0.9837 - val_loss: 0.0862 - val_acc: 0.9721\n",
      "Epoch 5/20\n",
      "60000/60000 [==============================] - 3s 52us/step - loss: 0.0378 - acc: 0.9880 - val_loss: 0.0921 - val_acc: 0.9741\n",
      "Epoch 6/20\n",
      "60000/60000 [==============================] - 3s 54us/step - loss: 0.0284 - acc: 0.9910 - val_loss: 0.0834 - val_acc: 0.9767\n",
      "Epoch 7/20\n",
      "60000/60000 [==============================] - 3s 53us/step - loss: 0.0223 - acc: 0.9925 - val_loss: 0.0856 - val_acc: 0.9789\n",
      "Epoch 8/20\n",
      "60000/60000 [==============================] - 3s 54us/step - loss: 0.0178 - acc: 0.9944 - val_loss: 0.0755 - val_acc: 0.9795\n",
      "Epoch 9/20\n",
      "60000/60000 [==============================] - 3s 56us/step - loss: 0.0138 - acc: 0.9956 - val_loss: 0.0924 - val_acc: 0.9788\n",
      "Epoch 10/20\n",
      "60000/60000 [==============================] - 3s 57us/step - loss: 0.0121 - acc: 0.9962 - val_loss: 0.0966 - val_acc: 0.9794\n",
      "Epoch 11/20\n",
      "60000/60000 [==============================] - 4s 61us/step - loss: 0.0089 - acc: 0.9971 - val_loss: 0.0911 - val_acc: 0.9814\n",
      "Epoch 12/20\n",
      "60000/60000 [==============================] - 3s 52us/step - loss: 0.0087 - acc: 0.9972 - val_loss: 0.1053 - val_acc: 0.9783\n",
      "Epoch 13/20\n",
      "60000/60000 [==============================] - 3s 53us/step - loss: 0.0066 - acc: 0.9980 - val_loss: 0.1055 - val_acc: 0.9799\n",
      "Epoch 14/20\n",
      "60000/60000 [==============================] - 3s 53us/step - loss: 0.0066 - acc: 0.9977 - val_loss: 0.1096 - val_acc: 0.9809\n",
      "Epoch 15/20\n",
      "60000/60000 [==============================] - 3s 52us/step - loss: 0.0061 - acc: 0.9981 - val_loss: 0.1114 - val_acc: 0.9793\n",
      "Epoch 16/20\n",
      "60000/60000 [==============================] - 3s 53us/step - loss: 0.0055 - acc: 0.9981 - val_loss: 0.1132 - val_acc: 0.9798\n",
      "Epoch 17/20\n",
      "60000/60000 [==============================] - 3s 51us/step - loss: 0.0045 - acc: 0.9985 - val_loss: 0.1156 - val_acc: 0.9798\n",
      "Epoch 18/20\n",
      "60000/60000 [==============================] - 3s 53us/step - loss: 0.0045 - acc: 0.9987 - val_loss: 0.1255 - val_acc: 0.9808\n",
      "Epoch 19/20\n",
      "60000/60000 [==============================] - 3s 53us/step - loss: 0.0049 - acc: 0.9985 - val_loss: 0.1113 - val_acc: 0.9813\n",
      "Epoch 20/20\n",
      "60000/60000 [==============================] - 3s 53us/step - loss: 0.0039 - acc: 0.9987 - val_loss: 0.1238 - val_acc: 0.9803\n"
     ]
    }
   ],
   "source": [
    "history=model.fit(x=train_data,y=train_labels_one_hot,batch_size=256,epochs=20,verbose=1,validation_data=(test_data,test_labels_one_hot))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting the training and validation losses, to see if the model is being overfitted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Accuracy Curves')"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1262519d6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x126efc06f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "#Checking for overfitting\n",
    "\n",
    "#Plot the Loss Curves\n",
    "plt.figure(figsize=[8,6])\n",
    "plt.plot(history.history['loss'],'r',linewidth=3.0)\n",
    "plt.plot(history.history['val_loss'],'b',linewidth=3.0)\n",
    "plt.legend(['Training loss', 'Validation Loss'],fontsize=18)\n",
    "plt.xlabel('Epochs ',fontsize=16)\n",
    "plt.ylabel('Loss',fontsize=16)\n",
    "plt.title('Loss Curves',fontsize=16)\n",
    " \n",
    "#Plot the Accuracy Curves\n",
    "plt.figure(figsize=[8,6])\n",
    "plt.plot(history.history['acc'],'r',linewidth=3.0)\n",
    "plt.plot(history.history['val_acc'],'b',linewidth=3.0)\n",
    "plt.legend(['Training Accuracy', 'Validation Accuracy'],fontsize=18)\n",
    "plt.xlabel('Epochs ',fontsize=16)\n",
    "plt.ylabel('Accuracy',fontsize=16)\n",
    "plt.title('Accuracy Curves',fontsize=16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**We can see that the validation accuracy is far from the training accuracy**\n",
    "\n",
    "This means that our model won't perform very well on unknown data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reducing overfitting:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "#To reduce overfitting\n",
    "from keras.layers import Dropout\n",
    "\n",
    "model2=Sequential()\n",
    "model2.add(Dense(512,activation='relu',input_shape=(dimdata,)))\n",
    "model2.add(Dropout(0.5))\n",
    "model2.add(Dense(512,activation='relu'))\n",
    "model2.add(Dropout(0.5))\n",
    "model2.add(Dense(nClasses,activation='softmax'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing with this new network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 60000 samples, validate on 10000 samples\n",
      "Epoch 1/20\n"
     ]
    },
    {
     "ename": "InternalError",
     "evalue": "Blas GEMM launch failed : a.shape=(256, 784), b.shape=(784, 512), m=256, n=512, k=784\n\t [[Node: dense_1/MatMul = MatMul[T=DT_FLOAT, transpose_a=false, transpose_b=false, _device=\"/job:localhost/replica:0/task:0/device:GPU:0\"](_arg_dense_1_input_0_0/_39, dense_1/kernel/read)]]\n\t [[Node: dense_3/BiasAdd/_45 = _Recv[client_terminated=false, recv_device=\"/job:localhost/replica:0/task:0/device:CPU:0\", send_device=\"/job:localhost/replica:0/task:0/device:GPU:0\", send_device_incarnation=1, tensor_name=\"edge_84_dense_3/BiasAdd\", tensor_type=DT_FLOAT, _device=\"/job:localhost/replica:0/task:0/device:CPU:0\"]()]]\n\nCaused by op 'dense_1/MatMul', defined at:\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\runpy.py\", line 193, in _run_module_as_main\n    \"__main__\", mod_spec)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\runpy.py\", line 85, in _run_code\n    exec(code, run_globals)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\ipykernel_launcher.py\", line 16, in <module>\n    app.launch_new_instance()\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\traitlets\\config\\application.py\", line 658, in launch_instance\n    app.start()\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\ipykernel\\kernelapp.py\", line 486, in start\n    self.io_loop.start()\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\tornado\\platform\\asyncio.py\", line 127, in start\n    self.asyncio_loop.run_forever()\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\asyncio\\base_events.py\", line 421, in run_forever\n    self._run_once()\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\asyncio\\base_events.py\", line 1425, in _run_once\n    handle._run()\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\asyncio\\events.py\", line 127, in _run\n    self._callback(*self._args)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\tornado\\platform\\asyncio.py\", line 117, in _handle_events\n    handler_func(fileobj, events)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\tornado\\stack_context.py\", line 276, in null_wrapper\n    return fn(*args, **kwargs)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\zmq\\eventloop\\zmqstream.py\", line 450, in _handle_events\n    self._handle_recv()\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\zmq\\eventloop\\zmqstream.py\", line 480, in _handle_recv\n    self._run_callback(callback, msg)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\zmq\\eventloop\\zmqstream.py\", line 432, in _run_callback\n    callback(*args, **kwargs)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\tornado\\stack_context.py\", line 276, in null_wrapper\n    return fn(*args, **kwargs)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\ipykernel\\kernelbase.py\", line 283, in dispatcher\n    return self.dispatch_shell(stream, msg)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\ipykernel\\kernelbase.py\", line 233, in dispatch_shell\n    handler(stream, idents, msg)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\ipykernel\\kernelbase.py\", line 399, in execute_request\n    user_expressions, allow_stdin)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\ipykernel\\ipkernel.py\", line 208, in do_execute\n    res = shell.run_cell(code, store_history=store_history, silent=silent)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\ipykernel\\zmqshell.py\", line 537, in run_cell\n    return super(ZMQInteractiveShell, self).run_cell(*args, **kwargs)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 2662, in run_cell\n    raw_cell, store_history, silent, shell_futures)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 2785, in _run_cell\n    interactivity=interactivity, compiler=compiler, result=result)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 2903, in run_ast_nodes\n    if self.run_code(code, result):\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 2963, in run_code\n    exec(code_obj, self.user_global_ns, self.user_ns)\n  File \"<ipython-input-15-6064703ad0fc>\", line 5, in <module>\n    model2.add(Dense(512,activation='relu',input_shape=(dimdata,)))\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\keras\\models.py\", line 467, in add\n    layer(x)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\keras\\engine\\topology.py\", line 619, in __call__\n    output = self.call(inputs, **kwargs)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\keras\\layers\\core.py\", line 855, in call\n    output = K.dot(inputs, self.kernel)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\keras\\backend\\tensorflow_backend.py\", line 1075, in dot\n    out = tf.matmul(x, y)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\tensorflow\\python\\ops\\math_ops.py\", line 1891, in matmul\n    a, b, transpose_a=transpose_a, transpose_b=transpose_b, name=name)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\tensorflow\\python\\ops\\gen_math_ops.py\", line 2436, in _mat_mul\n    name=name)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\tensorflow\\python\\framework\\op_def_library.py\", line 787, in _apply_op_helper\n    op_def=op_def)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\tensorflow\\python\\framework\\ops.py\", line 2956, in create_op\n    op_def=op_def)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\tensorflow\\python\\framework\\ops.py\", line 1470, in __init__\n    self._traceback = self._graph._extract_stack()  # pylint: disable=protected-access\n\nInternalError (see above for traceback): Blas GEMM launch failed : a.shape=(256, 784), b.shape=(784, 512), m=256, n=512, k=784\n\t [[Node: dense_1/MatMul = MatMul[T=DT_FLOAT, transpose_a=false, transpose_b=false, _device=\"/job:localhost/replica:0/task:0/device:GPU:0\"](_arg_dense_1_input_0_0/_39, dense_1/kernel/read)]]\n\t [[Node: dense_3/BiasAdd/_45 = _Recv[client_terminated=false, recv_device=\"/job:localhost/replica:0/task:0/device:CPU:0\", send_device=\"/job:localhost/replica:0/task:0/device:GPU:0\", send_device_incarnation=1, tensor_name=\"edge_84_dense_3/BiasAdd\", tensor_type=DT_FLOAT, _device=\"/job:localhost/replica:0/task:0/device:CPU:0\"]()]]\n",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mInternalError\u001b[0m                             Traceback (most recent call last)",
      "\u001b[1;32mC:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\tensorflow\\python\\client\\session.py\u001b[0m in \u001b[0;36m_do_call\u001b[1;34m(self, fn, *args)\u001b[0m\n\u001b[0;32m   1322\u001b[0m     \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1323\u001b[1;33m       \u001b[1;32mreturn\u001b[0m \u001b[0mfn\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1324\u001b[0m     \u001b[1;32mexcept\u001b[0m \u001b[0merrors\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mOpError\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\tensorflow\\python\\client\\session.py\u001b[0m in \u001b[0;36m_run_fn\u001b[1;34m(session, feed_dict, fetch_list, target_list, options, run_metadata)\u001b[0m\n\u001b[0;32m   1301\u001b[0m                                    \u001b[0mfeed_dict\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfetch_list\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtarget_list\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1302\u001b[1;33m                                    status, run_metadata)\n\u001b[0m\u001b[0;32m   1303\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\tensorflow\\python\\framework\\errors_impl.py\u001b[0m in \u001b[0;36m__exit__\u001b[1;34m(self, type_arg, value_arg, traceback_arg)\u001b[0m\n\u001b[0;32m    472\u001b[0m             \u001b[0mcompat\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mas_text\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mc_api\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mTF_Message\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstatus\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstatus\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 473\u001b[1;33m             c_api.TF_GetCode(self.status.status))\n\u001b[0m\u001b[0;32m    474\u001b[0m     \u001b[1;31m# Delete the underlying status object from memory otherwise it stays alive\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mInternalError\u001b[0m: Blas GEMM launch failed : a.shape=(256, 784), b.shape=(784, 512), m=256, n=512, k=784\n\t [[Node: dense_1/MatMul = MatMul[T=DT_FLOAT, transpose_a=false, transpose_b=false, _device=\"/job:localhost/replica:0/task:0/device:GPU:0\"](_arg_dense_1_input_0_0/_39, dense_1/kernel/read)]]\n\t [[Node: dense_3/BiasAdd/_45 = _Recv[client_terminated=false, recv_device=\"/job:localhost/replica:0/task:0/device:CPU:0\", send_device=\"/job:localhost/replica:0/task:0/device:GPU:0\", send_device_incarnation=1, tensor_name=\"edge_84_dense_3/BiasAdd\", tensor_type=DT_FLOAT, _device=\"/job:localhost/replica:0/task:0/device:CPU:0\"]()]]",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[1;31mInternalError\u001b[0m                             Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-16-6fbf03433800>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[0mmodel2\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcompile\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0moptimizer\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'rmsprop'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mloss\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'categorical_crossentropy'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmetrics\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'accuracy'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mhistory2\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mmodel2\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtrain_data\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtrain_labels_one_hot\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mbatch_size\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m256\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mepochs\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m20\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mverbose\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvalidation_data\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtest_data\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtest_labels_one_hot\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32mC:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\keras\\models.py\u001b[0m in \u001b[0;36mfit\u001b[1;34m(self, x, y, batch_size, epochs, verbose, callbacks, validation_split, validation_data, shuffle, class_weight, sample_weight, initial_epoch, steps_per_epoch, validation_steps, **kwargs)\u001b[0m\n\u001b[0;32m    961\u001b[0m                               \u001b[0minitial_epoch\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0minitial_epoch\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    962\u001b[0m                               \u001b[0msteps_per_epoch\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0msteps_per_epoch\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 963\u001b[1;33m                               validation_steps=validation_steps)\n\u001b[0m\u001b[0;32m    964\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    965\u001b[0m     def evaluate(self, x=None, y=None,\n",
      "\u001b[1;32mC:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\keras\\engine\\training.py\u001b[0m in \u001b[0;36mfit\u001b[1;34m(self, x, y, batch_size, epochs, verbose, callbacks, validation_split, validation_data, shuffle, class_weight, sample_weight, initial_epoch, steps_per_epoch, validation_steps, **kwargs)\u001b[0m\n\u001b[0;32m   1703\u001b[0m                               \u001b[0minitial_epoch\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0minitial_epoch\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1704\u001b[0m                               \u001b[0msteps_per_epoch\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0msteps_per_epoch\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1705\u001b[1;33m                               validation_steps=validation_steps)\n\u001b[0m\u001b[0;32m   1706\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1707\u001b[0m     def evaluate(self, x=None, y=None,\n",
      "\u001b[1;32mC:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\keras\\engine\\training.py\u001b[0m in \u001b[0;36m_fit_loop\u001b[1;34m(self, f, ins, out_labels, batch_size, epochs, verbose, callbacks, val_f, val_ins, shuffle, callback_metrics, initial_epoch, steps_per_epoch, validation_steps)\u001b[0m\n\u001b[0;32m   1233\u001b[0m                         \u001b[0mins_batch\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mins_batch\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtoarray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1234\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1235\u001b[1;33m                     \u001b[0mouts\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mins_batch\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1236\u001b[0m                     \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mouts\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlist\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1237\u001b[0m                         \u001b[0mouts\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mouts\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\keras\\backend\\tensorflow_backend.py\u001b[0m in \u001b[0;36m__call__\u001b[1;34m(self, inputs)\u001b[0m\n\u001b[0;32m   2476\u001b[0m         \u001b[0msession\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mget_session\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2477\u001b[0m         updated = session.run(fetches=fetches, feed_dict=feed_dict,\n\u001b[1;32m-> 2478\u001b[1;33m                               **self.session_kwargs)\n\u001b[0m\u001b[0;32m   2479\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0mupdated\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0moutputs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2480\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\tensorflow\\python\\client\\session.py\u001b[0m in \u001b[0;36mrun\u001b[1;34m(self, fetches, feed_dict, options, run_metadata)\u001b[0m\n\u001b[0;32m    887\u001b[0m     \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    888\u001b[0m       result = self._run(None, fetches, feed_dict, options_ptr,\n\u001b[1;32m--> 889\u001b[1;33m                          run_metadata_ptr)\n\u001b[0m\u001b[0;32m    890\u001b[0m       \u001b[1;32mif\u001b[0m \u001b[0mrun_metadata\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    891\u001b[0m         \u001b[0mproto_data\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtf_session\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mTF_GetBuffer\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrun_metadata_ptr\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\tensorflow\\python\\client\\session.py\u001b[0m in \u001b[0;36m_run\u001b[1;34m(self, handle, fetches, feed_dict, options, run_metadata)\u001b[0m\n\u001b[0;32m   1118\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mfinal_fetches\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0mfinal_targets\u001b[0m \u001b[1;32mor\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mhandle\u001b[0m \u001b[1;32mand\u001b[0m \u001b[0mfeed_dict_tensor\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1119\u001b[0m       results = self._do_run(handle, final_targets, final_fetches,\n\u001b[1;32m-> 1120\u001b[1;33m                              feed_dict_tensor, options, run_metadata)\n\u001b[0m\u001b[0;32m   1121\u001b[0m     \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1122\u001b[0m       \u001b[0mresults\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\tensorflow\\python\\client\\session.py\u001b[0m in \u001b[0;36m_do_run\u001b[1;34m(self, handle, target_list, fetch_list, feed_dict, options, run_metadata)\u001b[0m\n\u001b[0;32m   1315\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mhandle\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1316\u001b[0m       return self._do_call(_run_fn, self._session, feeds, fetches, targets,\n\u001b[1;32m-> 1317\u001b[1;33m                            options, run_metadata)\n\u001b[0m\u001b[0;32m   1318\u001b[0m     \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1319\u001b[0m       \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_do_call\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0m_prun_fn\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_session\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mhandle\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfeeds\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfetches\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\tensorflow\\python\\client\\session.py\u001b[0m in \u001b[0;36m_do_call\u001b[1;34m(self, fn, *args)\u001b[0m\n\u001b[0;32m   1334\u001b[0m         \u001b[1;32mexcept\u001b[0m \u001b[0mKeyError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1335\u001b[0m           \u001b[1;32mpass\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1336\u001b[1;33m       \u001b[1;32mraise\u001b[0m \u001b[0mtype\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0me\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnode_def\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mop\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmessage\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1337\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1338\u001b[0m   \u001b[1;32mdef\u001b[0m \u001b[0m_extend_graph\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mInternalError\u001b[0m: Blas GEMM launch failed : a.shape=(256, 784), b.shape=(784, 512), m=256, n=512, k=784\n\t [[Node: dense_1/MatMul = MatMul[T=DT_FLOAT, transpose_a=false, transpose_b=false, _device=\"/job:localhost/replica:0/task:0/device:GPU:0\"](_arg_dense_1_input_0_0/_39, dense_1/kernel/read)]]\n\t [[Node: dense_3/BiasAdd/_45 = _Recv[client_terminated=false, recv_device=\"/job:localhost/replica:0/task:0/device:CPU:0\", send_device=\"/job:localhost/replica:0/task:0/device:GPU:0\", send_device_incarnation=1, tensor_name=\"edge_84_dense_3/BiasAdd\", tensor_type=DT_FLOAT, _device=\"/job:localhost/replica:0/task:0/device:CPU:0\"]()]]\n\nCaused by op 'dense_1/MatMul', defined at:\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\runpy.py\", line 193, in _run_module_as_main\n    \"__main__\", mod_spec)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\runpy.py\", line 85, in _run_code\n    exec(code, run_globals)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\ipykernel_launcher.py\", line 16, in <module>\n    app.launch_new_instance()\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\traitlets\\config\\application.py\", line 658, in launch_instance\n    app.start()\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\ipykernel\\kernelapp.py\", line 486, in start\n    self.io_loop.start()\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\tornado\\platform\\asyncio.py\", line 127, in start\n    self.asyncio_loop.run_forever()\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\asyncio\\base_events.py\", line 421, in run_forever\n    self._run_once()\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\asyncio\\base_events.py\", line 1425, in _run_once\n    handle._run()\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\asyncio\\events.py\", line 127, in _run\n    self._callback(*self._args)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\tornado\\platform\\asyncio.py\", line 117, in _handle_events\n    handler_func(fileobj, events)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\tornado\\stack_context.py\", line 276, in null_wrapper\n    return fn(*args, **kwargs)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\zmq\\eventloop\\zmqstream.py\", line 450, in _handle_events\n    self._handle_recv()\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\zmq\\eventloop\\zmqstream.py\", line 480, in _handle_recv\n    self._run_callback(callback, msg)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\zmq\\eventloop\\zmqstream.py\", line 432, in _run_callback\n    callback(*args, **kwargs)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\tornado\\stack_context.py\", line 276, in null_wrapper\n    return fn(*args, **kwargs)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\ipykernel\\kernelbase.py\", line 283, in dispatcher\n    return self.dispatch_shell(stream, msg)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\ipykernel\\kernelbase.py\", line 233, in dispatch_shell\n    handler(stream, idents, msg)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\ipykernel\\kernelbase.py\", line 399, in execute_request\n    user_expressions, allow_stdin)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\ipykernel\\ipkernel.py\", line 208, in do_execute\n    res = shell.run_cell(code, store_history=store_history, silent=silent)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\ipykernel\\zmqshell.py\", line 537, in run_cell\n    return super(ZMQInteractiveShell, self).run_cell(*args, **kwargs)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 2662, in run_cell\n    raw_cell, store_history, silent, shell_futures)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 2785, in _run_cell\n    interactivity=interactivity, compiler=compiler, result=result)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 2903, in run_ast_nodes\n    if self.run_code(code, result):\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\IPython\\core\\interactiveshell.py\", line 2963, in run_code\n    exec(code_obj, self.user_global_ns, self.user_ns)\n  File \"<ipython-input-15-6064703ad0fc>\", line 5, in <module>\n    model2.add(Dense(512,activation='relu',input_shape=(dimdata,)))\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\keras\\models.py\", line 467, in add\n    layer(x)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\keras\\engine\\topology.py\", line 619, in __call__\n    output = self.call(inputs, **kwargs)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\keras\\layers\\core.py\", line 855, in call\n    output = K.dot(inputs, self.kernel)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\keras\\backend\\tensorflow_backend.py\", line 1075, in dot\n    out = tf.matmul(x, y)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\tensorflow\\python\\ops\\math_ops.py\", line 1891, in matmul\n    a, b, transpose_a=transpose_a, transpose_b=transpose_b, name=name)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\tensorflow\\python\\ops\\gen_math_ops.py\", line 2436, in _mat_mul\n    name=name)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\tensorflow\\python\\framework\\op_def_library.py\", line 787, in _apply_op_helper\n    op_def=op_def)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\tensorflow\\python\\framework\\ops.py\", line 2956, in create_op\n    op_def=op_def)\n  File \"C:\\Everything\\Software\\Python\\Anaconda\\Files\\lib\\site-packages\\tensorflow\\python\\framework\\ops.py\", line 1470, in __init__\n    self._traceback = self._graph._extract_stack()  # pylint: disable=protected-access\n\nInternalError (see above for traceback): Blas GEMM launch failed : a.shape=(256, 784), b.shape=(784, 512), m=256, n=512, k=784\n\t [[Node: dense_1/MatMul = MatMul[T=DT_FLOAT, transpose_a=false, transpose_b=false, _device=\"/job:localhost/replica:0/task:0/device:GPU:0\"](_arg_dense_1_input_0_0/_39, dense_1/kernel/read)]]\n\t [[Node: dense_3/BiasAdd/_45 = _Recv[client_terminated=false, recv_device=\"/job:localhost/replica:0/task:0/device:CPU:0\", send_device=\"/job:localhost/replica:0/task:0/device:GPU:0\", send_device_incarnation=1, tensor_name=\"edge_84_dense_3/BiasAdd\", tensor_type=DT_FLOAT, _device=\"/job:localhost/replica:0/task:0/device:CPU:0\"]()]]\n"
     ]
    }
   ],
   "source": [
    "model2.compile(optimizer='rmsprop', loss='categorical_crossentropy', metrics=['accuracy'])\n",
    "history2=model2.fit(train_data, train_labels_one_hot, batch_size=256, epochs=20, verbose=1, validation_data=(test_data, test_labels_one_hot))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting the training and validation losses, to see if the model is being overfitted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Plot the Loss Curves\n",
    "plt.figure(figsize=[8,6])\n",
    "plt.plot(history2.history['loss'],'r',linewidth=3.0)\n",
    "plt.plot(history2.history['val_loss'],'b',linewidth=3.0)\n",
    "plt.legend(['Training loss', 'Validation Loss'],fontsize=18)\n",
    "plt.xlabel('Epochs ',fontsize=16)\n",
    "plt.ylabel('Loss',fontsize=16)\n",
    "plt.title('Loss Curves',fontsize=16)\n",
    " \n",
    "#Plot the Accuracy Curves\n",
    "plt.figure(figsize=[8,6])\n",
    "plt.plot(history2.history['acc'],'r',linewidth=3.0)\n",
    "plt.plot(history2.history['val_acc'],'b',linewidth=3.0)\n",
    "plt.legend(['Training Accuracy', 'Validation Accuracy'],fontsize=18)\n",
    "plt.xlabel('Epochs ',fontsize=16)\n",
    "plt.ylabel('Accuracy',fontsize=16)\n",
    "plt.title('Accuracy Curves',fontsize=16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Much better now, less overfitting, validation loss is not increasing,**\n",
    "\n",
    "This model is generally better for unseen data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing the accuracy of our model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(\"Accuracy of the model: %.2f%%\"%(model2.evaluate(test_data, test_labels_one_hot)[1]*100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting some image predictions from our neural model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "img_shape=(28,28)\n",
    "plt.figure(figsize=(15, 15))\n",
    "def plot_images(images, cls_true, cls_pred=None):\n",
    "    assert len(images) == len(cls_true) == 9\n",
    "    \n",
    "    # Create figure with 3x3 sub-plots.\n",
    "    fig, axes = plt.subplots(3, 3)\n",
    "    fig.subplots_adjust(hspace=0.3, wspace=0.3)\n",
    "\n",
    "    for i, ax in enumerate(axes.flat):\n",
    "        # Plot image.\n",
    "        ax.imshow(images[i].reshape(img_shape), cmap='binary')\n",
    "\n",
    "        # Show true and predicted classes.\n",
    "        if cls_pred is None:\n",
    "            xlabel = \"True: {0}\".format(cls_true[i])\n",
    "        else:\n",
    "            xlabel = \"True: {0}, Pred: {1}\".format(np.argmax(cls_true[i]), cls_pred[i])\n",
    "\n",
    "        # Show the classes as the label on the x-axis.\n",
    "        ax.set_xlabel(xlabel)\n",
    "        \n",
    "        # Remove ticks from the plot.\n",
    "        ax.set_xticks([])\n",
    "        ax.set_yticks([])\n",
    "    \n",
    "    # Ensure the plot is shown correctly with multiple plots\n",
    "    # in a single Notebook cell.\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "images = test_data[:9]\n",
    "cls_true = test_labels_one_hot[:9]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred=model2.predict(x=images)\n",
    "cls_pred=np.argmax(y_pred,axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_images(images=images,\n",
    "            cls_true=cls_true,\n",
    "           cls_pred=cls_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hence we have used Neural Networks to successfully predict handwritten image classes, with pretty high accuracy"
   ]
  }
 ],
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