thearn/gradient.ipynb

## gradient.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "import keras\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from keras.layers import Dense, Dropout, Activation\n",
    "from keras.models import Sequential\n",
    "import keras.backend as K\n",
    "import tensorflow as tf\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define model & data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x126bf4eb8>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Iax2vtY7SWkf5+vpeZ8mOra2vJ1OHtGPFzhOsOyR/AYqGI/1cHnPXHOa2zq24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\n6QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x124619278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(x):\n",
    "    # quadratic\n",
    "    return ((x - 5)**2)/25.0\n",
    "\n",
    "def df(x):\n",
    "    # derivative of quadratic is linear\n",
    "    return 2*(x - 5) / 25.0\n",
    "\n",
    "# sample size\n",
    "n = 1000\n",
    "# these will be my training data sets, with regular sampling\n",
    "x = np.linspace(0,10,n)\n",
    "y = f(x)\n",
    "\n",
    "# normalize\n",
    "x = x / 10\n",
    "\n",
    "# get test data too, but randomly sampled\n",
    "x_test = 10*np.random.ranf(20)\n",
    "y_test = f(x_test)\n",
    "x_test = x_test / 10\n",
    "\n",
    "plt.plot(x,y, label='training points')\n",
    "plt.plot(x_test,y_test, 'ko', label='test data')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define and run tiny nonlinear regression NN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x127033e48>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = Sequential()\n",
    "# 1d input\n",
    "model.add(Dense(64, input_dim=1, activation='relu'))\n",
    "model.add(Activation(\"linear\"))\n",
    "model.add(Dense(32, activation='relu'))\n",
    "model.add(Activation(\"linear\"))\n",
    "model.add(Dense(32, activation='relu'))\n",
    "# 1d output\n",
    "model.add(Dense(1))\n",
    "\n",
    "# minimize mse\n",
    "model.compile(loss='mse', optimizer='adam', metrics=[\"accuracy\"])\n",
    "\n",
    "\n",
    "model.fit(x, y,\n",
    "          batch_size=10,\n",
    "          epochs=25,\n",
    "          verbose=0,\n",
    "          validation_data=(x_test, y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot performance (not bad, not perfect but really just an example model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x127386f60>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ECH+6tpPVJSkP8Z8NP/P0V9sY0a0VU4d1tLocdZ4cCfefgZo/smOqt51CRLoC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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x124622860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_result = model.predict(x_test)\n",
    "plt.plot(x,y, label='exact')\n",
    "plt.plot(x_test, y_result, 'go', label='predictions')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Derivatives\n",
    "I know Theano/TF are built around the idea of easily getting derivatives of loss functions w.r.t weights. But what I specifically want to extract is what the model things dy/dx is at a given point"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x124622400>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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05XY+XneAhoGV+WRkV25qWsfTZRnjUwoMBhFZDuR1fD728hlVVRHRPMahqtlA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1246226a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, df(x), label='dy/dx exact')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not sure where to start though... almost everything that I see is based on getting d_loss / d_weight\n",
    "\n",
    "I could work with that on the first layer though, using the chain rule\n",
    "\n",
    "Just shooting in the dark down below"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "weights = model.trainable_weights # weight tensors\n",
    "weights = [weight for weight in weights] # filter down weights tensors to only ones which are trainable\n",
    "gradients = model.optimizer.get_gradients(model.output, weights) # gradient tensors\n",
    "\n",
    "input_tensors = [model.inputs[0], # input data\n",
    "]\n",
    "\n",
    "get_gradients = K.function(inputs=input_tensors, outputs=gradients)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "Cannot feed value of shape (1000,) for Tensor 'dense_1_input:0', which has shape '(?, 1)'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-44-7d09280de900>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mget_gradients\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/Users/tahearn1/anaconda3/lib/python3.6/site-packages/keras/backend/tensorflow_backend.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, inputs)\u001b[0m\n\u001b[1;32m   2227\u001b[0m         \u001b[0msession\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_session\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2228\u001b[0m         updated = session.run(self.outputs + [self.updates_op],\n\u001b[0;32m-> 2229\u001b[0;31m                               feed_dict=feed_dict)\n\u001b[0m\u001b[1;32m   2230\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mupdated\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moutputs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2231\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/tahearn1/anaconda3/lib/python3.6/site-packages/tensorflow/python/client/session.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self, fetches, feed_dict, options, run_metadata)\u001b[0m\n\u001b[1;32m    776\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    777\u001b[0m       result = self._run(None, fetches, feed_dict, options_ptr,\n\u001b[0;32m--> 778\u001b[0;31m                          run_metadata_ptr)\n\u001b[0m\u001b[1;32m    779\u001b[0m       \u001b[0;32mif\u001b[0m \u001b[0mrun_metadata\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    780\u001b[0m         \u001b[0mproto_data\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtf_session\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mTF_GetBuffer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrun_metadata_ptr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/tahearn1/anaconda3/lib/python3.6/site-packages/tensorflow/python/client/session.py\u001b[0m in \u001b[0;36m_run\u001b[0;34m(self, handle, fetches, feed_dict, options, run_metadata)\u001b[0m\n\u001b[1;32m    959\u001b[0m                 \u001b[0;34m'Cannot feed value of shape %r for Tensor %r, '\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    960\u001b[0m                 \u001b[0;34m'which has shape %r'\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 961\u001b[0;31m                 % (np_val.shape, subfeed_t.name, str(subfeed_t.get_shape())))\n\u001b[0m\u001b[1;32m    962\u001b[0m           \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgraph\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mis_feedable\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msubfeed_t\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    963\u001b[0m             \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Tensor %s may not be fed.'\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0msubfeed_t\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: Cannot feed value of shape (1000,) for Tensor 'dense_1_input:0', which has shape '(?, 1)'"
     ]
    }
   ],
   "source": [
    "\n",
    "get_gradients([x])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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