neuralnetworks.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Common Activation Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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mcO218O7S/ZdMqk57eztDhw4FGJpSau/LuUrzsYmI04GvA5ssrMCQpL6aOjXv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\nqguLDEmSVBcWGZIkqS7+P8vWRtzEd2QpAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e70aac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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eCOuuC5s6xZ+kVootPPoCzeM7vkx2OyvA82SDQyXVqIULs8LjgAMgYsnnS6ot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\n9w8cCCuuCGecMYPzz5/c7nX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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e8bc5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SpArKhK99DU46qVjob2tSmQGxkiTpeb/9Ldx5J/zqV2VXMvDsOZEkqYK+9jV4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\n/QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e9b9a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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neX1tMrPyUumSVJXrZUida+cf8GOAp7WOrweeXn85kjQYzGVI9WhnRGM58IaI\n+C7F2hlbtNbReALDmpKazFyGVJ92Go2PUuw38nmKvMRPp3lNtK6tM801SRp45jKkes250cjMxREx\nDmwNXEmxudmvulWYJPWDuQypXm2to5GZK4GrWpuaXZiZD63teySpKcxlSPWrugT5yXUXIkn9ZC5D\n6o52Fuy6G3hOZt4VEfcw+4Jdm9RRnCT1grkMqXvaGdFYBKwsHXe2SYokDQhzGVL3tBMGPbl0fFJX\nqpGkHjOXIXVXpRU3I+KxiNhsmvObRsRjnZclSd1nLkPqvqq7t8YM558KPFzxnpLUM+YypN5oq9GI\niENahwnsHxH3ly6vA/wR8POaapOkrjGXIfVGuyMai1p/B8WOquVpkoeBG1rnJWlgmcuQeqfdBbu2\nBYiIc4E/z8x7ulKVJHWJuQypt6ou2PXSuguRpG4zlyH1XtWnTv4tIt4/zfn3RsS/dl6WJNVvMpex\neLG5DKlXKjUawB7AmdOc/z5FIFSSBoq5DKk/qjYav8X0j7E+AjytejmSVD9zGVL/VG00rgLeNM35\nNwNXVy9HkupVzmUsXWouQ+q1qgt2fQT4ZkQ8CzindW5PYCHwxjoKk6Q6uF6G1F9Vnzo5IyJeDxwO\n/AXwa+BK4OWZeV6N9UlSZeYypP6rOqJBZp7J9IFQSeo7cxnSYKjcaETERhSjGdsBn8rMuyNiAXB7\nZt5SV4GS1C7Xy5AGR6VGIyJ2Bn4IrAC2Ab4C3A38GbA1sF9N9UlS28xlSIOj6lMnxwAnZeb2wIOl\n89/DdTQk9ZG5DGmwVG00fh/48jTnbwE2r16OJFVnLkMaPFUzGg8y/cJczwXurF6OJFVjLkMaTFVH\nNE4HjoqIdVtfZ0RsBXwC+GYtlUlSG9zHRBpMVRuN/ws8HbgDWB84D7gWWAkcUU9pkjQ35jKkwdX2\n1ElrFON04ADgd4EFFA3LRGb+sN7yJGl25jKkwdZ2o5GZj0TE84DHMvMcfrMEuST1lLkMafBVnTo5\nBfibOguRpHaZy5AGX9WnTp4C7B8RewGXAqvKFzPz7zstTJJmYy5DaoaqjcbzgInW8dTfI7J6OZK0\nduYypOaounvrS+suRJLmwlyG1CyVN1WTpH5wHxOpWaqGQSWp58xlSM1joyGpEcxlSM3k1ImkgWcu\nQ2ouGw1JA89chtRcTp1IGmjmMqRms9GQNLDMZUjN59SJpIFkLkMaDjYakgaSuQxpODh1ImngmMuQ\nhoeNhqS35yrkAAAFtklEQVSBYi5DGi5OnUgaGOYypOFjoyFpYJjLkIaPUyeSBoK5DGk42WhI6jtz\nGdLwstFQY4yPj/e7BNVo8vMs5zKWLjWX0VT+fGomjWo0IuLgiLguIn4dET+NiJf0uyb1jv8hGy6T\nn+dkLmPxYnMZTebPp2bSmEYjIt4EHAt8BHghcAHwvYjYoq+FSarMXIY0/BrTaACLgBMy88TM/EVm\nLgJuBt7Z57okVfDoo+YypFHQiMdbI2JdYAz4+JRLPwBe3PuKJHUiE668ElascL0Madg1otEAng6s\nA9w+5fztwObTvH49gNNOu4ZLL+1yZeqZG29cweLFE/0uQzW44gq45ZYVfOxjE9x/P0z4sTbeihUr\nmPCDHArXXHPN5OF6ddwvMrOO+3RVRDwDuAX4P5n549L5w4F9M3OnKa9/C/D13lYpSdJQ2Sczl3R6\nk6aMaNwFPMYTRy8244mjHABnAfsANwAPdrUySZKGy3rANhT/lnasESMaABFxCXBpZr67dO6/gG9n\n5hH9q0ySJM2kKSMaAMcAp0TEMuBi4B3AlsCX+lqVJEmaUWMajcxcGhGbAEcCzwCuAvbOzJv7W5kk\nSZpJY6ZOJElS8zRpwS5JktQwNhqSJKlrhq7RiIjDI+LCiFgVEXfP8JotI+I7EXF/RNwZEZ+NiMbk\nVUZdRNwQEatLfx6LiH/qd12aGzdHHB4R8cEpP4urI2J5v+vS3ETE7hFxRkTc0vrsXjvNa/6xdf2B\niDg3Inaa7l6zGbpGA1gXWAp8cbqLEfEk4LvA+hTLl78JeAPw6V4VqI4l8AHgdyjWVnkG8NG+VqQ5\ncXPEoXQVv/lZ3Bx4fn/LURs2AC4H3kXx39U1RMT7gPcABwO7ArcBZ0fEBu28ydCGQSPircCxmbnJ\nlPN7A2cAW2Tm7a1zbwJOBDbLzPt7XqzaEhHXU3y2x/W7FrVnhvVwrga+5Xo4zRMRHwRel5kL+l2L\nOhMRq4HXZ+YZpXPLgWMy81Otr59CsUjmoZl5wlzvPYwjGmuzG3DVZJPRchbFSmhj/SlJFbwvIu6K\niMta02Xr9rsgza60OeLZUy65OWKzbd8aWr8uIsYjYtt+F6TOtT7HzSn9vGbmw8B5tPnzOoq5hM2Z\nsmx5Zt4bEQ8z/QZtGjyfASaAe4A/AD5BsVzugX2sSWvX7uaIGnyXAPsB/00xfXIkcFFE7JSZ9/S1\nMnVqc4rplOl+Xrdq50aNGNGYIXA0NQzYztDddPNFMcN59UA7n3FmfjYzz8/MqzLzq8BBwN9ExMb9\n/V+hOZr6c+bPXkNl5lmZ+a3M/K/MPAd4devSW/tZl2rV8c9rU0Y0PgeMr+U1N8zxXrdR/Bb8uIjY\niCJEOt0GbeqNTj7jSyj+z/9s4Kc11qR6tbs5ohomMx+IiJ8B2/e7FnXsNor/rk6dBWj757URjUZm\n3g1M+6hqBRcDh0fE75RyGq+k2OV1WU3voTZ1+BkvoOiwb62vItUtMx9p7VW0F3B66dJewLf7U5Xq\nFBFPBXYEftTvWtSZzLw+Im6j+Pm8Ah4Pg+4BvLedezWi0WhHRGwJbAJsDawTES9oXbo2M1dRBM+u\nBr4WEYcCmwJHA4t94mTwRcRuFIHec4EVFKNTxwCnZ+b/9rM2zYmbIw6RiDga+A5wE0VG4wPAhsDJ\n/axLc9N6TPXZFCMXANu1/s28u7WP2GcofjG/FrgWOBxYxdpHn9cwdI0G8GGKcNKkidbfLwV+lJmr\nI+LVwBconuH/NfB12uzQ1DcPUax9chTwVOBG4MsUzaIGnJsjDp0tgCUUQd87KaYxd/PzbIxdKX5p\ny9afyfWkTgbenpmfjIj1gOOBjYEfA69o/dI+Z0O7joYkSeq/Rjx1IkmSmslGQ5IkdY2NhiRJ6hob\nDUmS1DU2GpIkqWtsNCRJUtfYaEiSpK6x0ZAkSV1joyFJkrrGRkOSJHWNjYYkSeqa/w9W/4sgrMkD\nfgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10eb55908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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pUhg3DsaOzTuJpHIo9qK9qyLilxGxR8eBiDgUeBj4eEmSSVIf3LNHqm3FlpRjgL2AxyPi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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10eb55f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from math import tanh\n",
    "from matplotlib import pyplot as plt\n",
    "i = np.arange(-10, 10, .1)\n",
    "\n",
    "def softplus(x):\n",
    "    return np.log(1 + np.exp(x))\n",
    "\n",
    "plt.plot(i, softplus(i))\n",
    "plt.ylabel('softplus(x)')\n",
    "plt.show()\n",
    "\n",
    "def logistic_sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "\n",
    "plt.plot(i, logistic_sigmoid(i))\n",
    "plt.ylabel('logistic_sigmoid(x)')\n",
    "plt.show()\n",
    "\n",
    "def softmax(x):\n",
    "    e_x = np.exp(x - np.max(x))\n",
    "    return e_x / e_x.sum()\n",
    "\n",
    "plt.plot(i, softmax(i))\n",
    "plt.ylabel('softmax(x)')\n",
    "plt.show()\n",
    "\n",
    "def rectified_linear_activation_function(z):\n",
    "    return max([0, z])\n",
    "\n",
    "plt.plot(i, list(map(rectified_linear_activation_function, i)))\n",
    "plt.ylabel('rectified_linear_activation_function(x)')\n",
    "plt.show()\n",
    "\n",
    "plt.plot(i, list(map(tanh, i)))\n",
    "plt.ylabel('tanh(x)')\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### XOR as a Neural Network in Numpy, Keras (TensorFlow), TensorFlow, and PyTorch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "XOR with Numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[0],\n",
       "        [1],\n",
       "        [1],\n",
       "        [0]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "X = np.matrix([[0, 0],\n",
    "               [0, 1],\n",
    "               [1, 0],\n",
    "               [1, 1]])\n",
    "W = np.matrix([[1, 1],\n",
    "               [1, 1]])\n",
    "c = np.array([0, -1])\n",
    "w = np.matrix([[1],\n",
    "               [-2]])\n",
    "\n",
    "A_in = (X * W + c)\n",
    "A_out = np.matrix([list(rectified_linear_activation_function(y) for y in x) for x in A_in.tolist()])\n",
    "A_out * w"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "XOR with Keras"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4/4 [==============================] - 0s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[0],\n",
       "       [1],\n",
       "       [1],\n",
       "       [0]], dtype=int32)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import keras\n",
    "\n",
    "model = keras.models.Sequential()\n",
    "model.add(keras.layers.core.Dense(2, activation='relu', input_shape=(2,)))\n",
    "model.add(keras.layers.core.Dense(1)) # linear is the default activation (https://keras.io/activations/)\n",
    "model.set_weights([\n",
    "    np.array([[1 , 1], [1,  1]]),\n",
    "    np.array([ 0, -1]),\n",
    "    np.array([[1], [-2]]),\n",
    "    np.array([ 0])\n",
    "])\n",
    "model.predict_classes(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "XOR with TensorFlow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.],\n",
       "       [ 1.],\n",
       "       [ 1.],\n",
       "       [ 0.]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "\n",
    "tfX = tf.constant(X, dtype='float64')\n",
    "tfW = tf.Variable(W, dtype='float64')\n",
    "tfc = tf.Variable(c, dtype='float64')\n",
    "tfw = tf.Variable(w, dtype='float64')\n",
    "\n",
    "node1 = tf.matmul(tfX, tfW)\n",
    "node2 = tf.add(node1, tfc)\n",
    "node3 = tf.nn.relu(node2)\n",
    "node4 = tf.matmul(node3, tfw)\n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "sess = tf.Session()\n",
    "sess.run(init)\n",
    "sess.run(node4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "XOR with PyTorch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Variable containing:\n",
       " 0\n",
       " 1\n",
       " 1\n",
       " 0\n",
       "[torch.FloatTensor of size 4x1]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from torch import Tensor\n",
    "from torch.autograd import Variable\n",
    "from torch.nn import Module, Linear, Parameter \n",
    "from torch.nn.functional import relu\n",
    "\n",
    "class Net(Module):\n",
    "    def __init__(self):\n",
    "        super(Net, self).__init__()\n",
    "        self.fc1 = Linear(2, 2)\n",
    "        self.fc2 = Linear(2, 1)\n",
    "    def forward(self, x):\n",
    "        x = relu(self.fc1(x))\n",
    "        x = self.fc2(x)\n",
    "        return x\n",
    "\n",
    "net = Net()\n",
    "\n",
    "net.fc1.weight = Parameter(Tensor([[1, 1],\n",
    "                                   [1, 1]]))\n",
    "net.fc1.bias = Parameter(Tensor([[0, -1]]))\n",
    "net.fc2.weight = Parameter(Tensor([[1, -2]]))\n",
    "net.fc2.bias = Parameter(Tensor([[0]]))\n",
    "\n",
    "input = Variable(Tensor([[0, 0],\n",
    "                         [0, 1],\n",
    "                         [1, 0],\n",
    "                         [1, 1]]))\n",
    "out = net(input)\n",
    "out"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Neural Network w/ Loss Function, Gradient, and Optimization defined with Sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "forward: w*x\n",
      "loss: (w*x - y)**2\n",
      "gradient: 2*x*(w*x - y)\n",
      "w: 2\n",
      "learning_rate: 0.01 \n",
      "\n",
      "x: 1 y: 2 w: 2\n",
      "gradient: 0.e-141\n",
      "x: 2 y: 4 w: 2.00000000000000\n",
      "gradient: 0.e-140\n",
      "x: 3 y: 6 w: 2.00000000000000\n",
      "gradient: 0.e-140\n",
      "loss: 4.62129760221396e-274 \n",
      "\n",
      "x: 1 y: 2 w: 2.00000000000000\n",
      "gradient: 0.e-141\n",
      "x: 2 y: 4 w: 2.00000000000000\n",
      "gradient: 0.e-140\n",
      "x: 3 y: 6 w: 2.00000000000000\n",
      "gradient: 0.e-140\n",
      "loss: 4.62129760221396e-274 \n",
      "\n",
      "x: 1 y: 2 w: 2.00000000000000\n",
      "gradient: 0.e-141\n",
      "x: 2 y: 4 w: 2.00000000000000\n",
      "gradient: 0.e-140\n",
      "x: 3 y: 6 w: 2.00000000000000\n",
      "gradient: 0.e-140\n",
      "loss: 4.62129760221396e-274 \n",
      "\n",
      "x: 1 y: 2 w: 2.00000000000000\n",
      "gradient: 0.e-141\n",
      "x: 2 y: 4 w: 2.00000000000000\n",
      "gradient: 0.e-140\n",
      "x: 3 y: 6 w: 2.00000000000000\n",
      "gradient: 0.e-140\n",
      "loss: 4.62129760221396e-274 \n",
      "\n",
      "x: 1 y: 2 w: 2.00000000000000\n",
      "gradient: 0.e-141\n",
      "x: 2 y: 4 w: 2.00000000000000\n",
      "gradient: 0.e-140\n",
      "x: 3 y: 6 w: 2.00000000000000\n",
      "gradient: 0.e-140\n",
      "loss: 4.62129760221396e-274 \n",
      "\n",
      "x: 1 y: 2 w: 2.00000000000000\n",
      "gradient: 0.e-141\n",
      "x: 2 y: 4 w: 2.00000000000000\n",
      "gradient: 0.e-140\n",
      "x: 3 y: 6 w: 2.00000000000000\n",
      "gradient: 0.e-140\n",
      "loss: 4.62129760221396e-274 \n",
      "\n",
      "x: 1 y: 2 w: 2.00000000000000\n",
      "gradient: 0.e-141\n",
      "x: 2 y: 4 w: 2.00000000000000\n",
      "gradient: 0.e-140\n",
      "x: 3 y: 6 w: 2.00000000000000\n",
      "gradient: 0.e-140\n",
      "loss: 4.62129760221396e-274 \n",
      "\n",
      "x: 1 y: 2 w: 2.00000000000000\n",
      "gradient: 0.e-141\n",
      "x: 2 y: 4 w: 2.00000000000000\n",
      "gradient: 0.e-140\n",
      "x: 3 y: 6 w: 2.00000000000000\n",
      "gradient: 0.e-140\n",
      "loss: 4.62129760221396e-274 \n",
      "\n",
      "x: 1 y: 2 w: 2.00000000000000\n",
      "gradient: 0.e-141\n",
      "x: 2 y: 4 w: 2.00000000000000\n",
      "gradient: 0.e-140\n",
      "x: 3 y: 6 w: 2.00000000000000\n",
      "gradient: 0.e-140\n",
      "loss: 4.62129760221396e-274 \n",
      "\n",
      "x: 1 y: 2 w: 2.00000000000000\n",
      "gradient: 0.e-141\n",
      "x: 2 y: 4 w: 2.00000000000000\n",
      "gradient: 0.e-140\n",
      "x: 3 y: 6 w: 2.00000000000000\n",
      "gradient: 0.e-140\n",
      "loss: 4.62129760221396e-274 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import sympy\n",
    "\n",
    "x_data = np.array([1, 2, 3])\n",
    "y_data = np.array([2, 4, 6])\n",
    "\n",
    "x, y, w, y_pred = sympy.symbols('x y w y_pred')\n",
    "y_pred = x * w\n",
    "print('forward:', y_pred)\n",
    "loss = (y_pred - y)**2\n",
    "print('loss:', loss)\n",
    "gradient = sympy.diff(loss, w)\n",
    "print('gradient:', gradient)\n",
    "\n",
    "w_in = np.random.randint(0,3)\n",
    "print('w:', w_in)\n",
    "learning_rate = 0.01\n",
    "print('learning_rate:', learning_rate, '\\n')\n",
    "for epoch in range(10):\n",
    "    for x_in, y_in in zip(x_data, y_data):\n",
    "        print('x:', x_in, 'y:', y_in, 'w:', w_in)\n",
    "        grad = gradient.evalf(subs={x: x_in, y: y_in, w: w_in})\n",
    "        print('gradient:', grad)\n",
    "        w_in = w_in - learning_rate * grad\n",
    "        l = loss.evalf(subs={x: x_in, y: y_in, w: w_in})\n",
    "    print('loss:', l, '\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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