README.ipynb

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   "source": [
    "# Neural Network from Scratch Performance Analysis\n",
    "\n",
    "Quick analysis of a neural network I programmed with basic functions and numpy vs a state of the art tensorflow implementation. Both models will use sigmoid functions and have 2 hidden layers with 30 neurons each and be trained on the MNIST database\n"
   ],
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   "metadata": {}
  },
  {
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   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from network import Network\n",
    "from tensorflow import keras\n",
    "import tensorflow as tf\n",
    "import mnist, matplotlib, os, time, seaborn\n",
    "%matplotlib inline\n",
    "\n",
    "#Disable GPU tensorflow\n",
    "os.environ['CUDA_VISIBLE_DEVICES'] = '-1'\n",
    "\n",
    "#Load data\n",
    "x_train, t_train, x_test, t_test = mnist.load()\n",
    "#one_hot_encode labels\n",
    "y_train = np.zeros((60000, 10))\n",
    "y_test = np.zeros((10000, 10))\n",
    "for i in range(60000):\n",
    "    y_train[i, t_train[i]] = 1\n",
    "for i in range(10000):\n",
    "    y_test[i, t_test[i]] = 1\n",
    "#normalize images\n",
    "x_train = x_train / 255\n",
    "x_test = x_test / 255\n",
    "\n",
    "epochs = 15\n",
    "activation_function = 'sigmoid'\n",
    "alpha = .5"
   ]
  },
  {
   "source": [
    "## 1 Import packages and load data. \n"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "test_network = Network()\n",
    "test_network.set_input(784)\n",
    "test_network.set_output(10)\n",
    "test_network.add_hidden_layers(1, 30, activation_function)\n",
    "test_network.add_hidden_layers(1, 15, activation_function)\n",
    "test_network.set_output_activation_function(activation_function)\n",
    "test_network.set_error_function('mean squared error')\n",
    "test_network.set_gradient_descent_algorithm('stochastic')\n",
    "test_network.set_alpha(alpha)\n",
    "test_network.compile_network()\n",
    "start_time = time.time()\n",
    "test_network.train(x_train, y_train, x_test, y_test, epochs)\n",
    "custom_network_time = time.time() - start_time"
   ],
   "cell_type": "code",
   "metadata": {
    "tags": []
   },
   "execution_count": 3,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Epoch: 1. Accuracy: 89.07000000000001%\nEpoch: 2. Accuracy: 91.36%\nEpoch: 3. Accuracy: 91.44%\nEpoch: 4. Accuracy: 91.83%\nEpoch: 5. Accuracy: 92.17999999999999%\nEpoch: 6. Accuracy: 93.67%\nEpoch: 7. Accuracy: 93.58999999999999%\nEpoch: 8. Accuracy: 93.32000000000001%\nEpoch: 9. Accuracy: 93.51%\nEpoch: 10. Accuracy: 93.87%\nEpoch: 11. Accuracy: 93.89999999999999%\nEpoch: 12. Accuracy: 94.21000000000001%\nEpoch: 13. Accuracy: 93.67999999999999%\nEpoch: 14. Accuracy: 94.24%\nEpoch: 15. Accuracy: 93.61%\n"
    }
   ]
  },
  {
   "source": [
    "## 2 Create and test custom network"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "model = keras.Sequential([\n",
    "        keras.layers.Dense(30, activation = activation_function, input_shape = (784,), kernel_initializer=keras.initializers.RandomNormal(mean = 0, stddev = 1)),\n",
    "        keras.layers.Dense(15, activation = activation_function, kernel_initializer=keras.initializers.RandomNormal(mean = 0, stddev = 1)),\n",
    "        keras.layers.Dense(10, activation = activation_function, kernel_initializer=keras.initializers.RandomNormal(mean = 0, stddev = 1))\n",
    "    ])\n",
    "model.compile(optimizer = keras.optimizers.SGD(learning_rate = alpha), loss = keras.losses.mean_squared_error, metrics =  [keras.metrics.categorical_accuracy])\n",
    "start_time = time.time()\n",
    "history = model.fit(x_train, y_train, batch_size = 1, epochs = epochs, validation_data = (x_test, y_test), verbose = 0)\n",
    "keras_time = time.time() - start_time"
   ]
  },
  {
   "source": [
    "## 3 Create and test Keras network"
   ],
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   }
  },
  {
   "cell_type": "code",
   "execution_count": 4,
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   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Custom network training time: 257.23 \nKeras training time: 371.74\n"
    },
    {
     "output_type": "display_data",
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "data = pd.DataFrame({\"Epoch\":range(1, epochs+1), \"Custom Network\":test_network.history, \"Keras Network\":history.history['categorical_accuracy']})\n",
    "data = data.melt(id_vars = 'Epoch', value_vars = ['Keras Network', 'Custom Network'])\n",
    "seaborn.set()\n",
    "plot = seaborn.lineplot(x = 'Epoch', y = 'value', hue = 'variable', data = data)\n",
    "print(f'Custom network training time: {custom_network_time:.2f} \\nKeras training time: {keras_time:.2f}')\n",
    "\n"
   ]
  },
  {
   "source": [
    "## 4 Graph data and analyze results\n",
    "While this graph only shows one trial, I ran a few more just to validate the results and the graphs came up very similar. While my network started with a higher accuracy, it gained less accuracy and also regressed as the training went on in comparison to the Keras network which had a much smoother curve. I am relatively confident that both neural networks were initalized the same way (random normal weight distribution, same activations, etc.) so this difference can be attributed to either optimizations done by Tensorflow or flaws in my code. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  }
 ]
}