forceSparseWeights.ipynb

{
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  "metadata": {
    "colab": {
      "name": "forceSparseWeights.ipynb",
      "version": "0.3.2",
      "provenance": []
    },
    "kernelspec": {
      "name": "python2",
      "display_name": "Python 2"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "[View in Colaboratory](https://colab.research.google.com/github/rex-yue-wu/Notebooks/blob/master/forceSparseWeights.ipynb)"
      ]
    },
    {
      "metadata": {
        "id": "S_Nc8qsiP97e",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "import keras\n",
        "import tensorflow as tf\n",
        "from keras import backend as K\n",
        "import numpy as np \n",
        "from keras.layers import Input, Conv1D, Conv3D, SimpleRNN, Conv2D, Reshape, Permute, TimeDistributed\n",
        "from keras.models import Model\n",
        "from keras.constraints import Constraint\n",
        "from keras.callbacks import Callback\n",
        "from matplotlib import pyplot\n",
        "from copy import deepcopy"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "9TZ9J4tt_s9k",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# Define our custom constraints to force small weights to zeros \n",
        "# and callbacks to monitor weight sparsity"
      ]
    },
    {
      "metadata": {
        "id": "UkkRacOqQDvo",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "class NoSmallWeights(Constraint) :\n",
        "    def __init__(self, th_val=1e-3 ):\n",
        "        self.th_val = th_val\n",
        "    def __call__(self, w):\n",
        "        w *= K.cast(K.greater_equal(w, self.th_val), K.floatx())\n",
        "        return w        \n",
        "\n",
        "class ShowSparsity( Callback ) :\n",
        "    def __init__( self, th_val=1e-3 ) :\n",
        "        self.th_val = th_val\n",
        "    def on_epoch_end( self, epoch, logs ) :\n",
        "        w_list = self.model.get_weights()\n",
        "        w_list = sum( [], w_list )\n",
        "        denominator = 0.\n",
        "        numerator = 0.\n",
        "        for w in w_list :\n",
        "            if w.ndim > 1 :\n",
        "                denominator += w.size\n",
        "                numerator += np.sum( w < self.th_val )\n",
        "        print \"Epoch {:05d}, sparsity = {:.4f}\".format( epoch, numerator/denominator )\n",
        "            "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "CBOtmaA1_6xm",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# Use MNIST as an exmaple"
      ]
    },
    {
      "metadata": {
        "id": "j0_0Bq8kYa7M",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 88
        },
        "outputId": "0ccf2d2e-1a08-42c8-ff87-8a59f06da18a"
      },
      "cell_type": "code",
      "source": [
        "from keras.datasets import mnist\n",
        "from keras.models import Sequential\n",
        "from keras.layers.core import Dense, Dropout, Activation\n",
        "from keras.utils import np_utils\n",
        "nb_classes = 10\n",
        "\n",
        "# the data, shuffled and split between tran and test sets\n",
        "(X_train, y_train), (X_test, y_test) = mnist.load_data()\n",
        "print(\"X_train original shape\", X_train.shape)\n",
        "print(\"y_train original shape\", y_train.shape)\n",
        "\n",
        "X_train = X_train.reshape(60000, 784)\n",
        "X_test = X_test.reshape(10000, 784)\n",
        "X_train = X_train.astype('float32')\n",
        "X_test = X_test.astype('float32')\n",
        "X_train /= 255\n",
        "X_test /= 255\n",
        "print(\"Training matrix shape\", X_train.shape)\n",
        "print(\"Testing matrix shape\", X_test.shape)\n",
        "\n",
        "Y_train = np_utils.to_categorical(y_train, nb_classes)\n",
        "Y_test = np_utils.to_categorical(y_test, nb_classes)"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "('X_train original shape', (60000, 28, 28))\n",
            "('y_train original shape', (60000,))\n",
            "('Training matrix shape', (60000, 784))\n",
            "('Testing matrix shape', (10000, 784))\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "XJqtgL1EADj4",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# Define a testing network architecture\n",
        "\n",
        "- support l1 regularization\n",
        "- support forcing small weights to zeros during training\n",
        "\n",
        "## NOTE: this network architecture is NOT optimal, but we only use it to demonstrate the idea."
      ]
    },
    {
      "metadata": {
        "id": "XYkBuplJuJwg",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "from keras.regularizers import l1\n",
        "def create_model( th_val, l1_coef=0 ) :\n",
        "    \n",
        "    smodel = Sequential()\n",
        "    smodel.add(Dense(512, input_shape=(784,), use_bias=False,\n",
        "               kernel_constraint = NoSmallWeights(th_val) if (th_val is not None) else None, \n",
        "               kernel_regularizer=l1(l1_coef)))\n",
        "    smodel.add(Activation('tanh'))\n",
        "    smodel.add(Dropout(0.2))  \n",
        "    smodel.add(Dense(512, use_bias=False,      \n",
        "               kernel_constraint=NoSmallWeights(th_val) if (th_val is not None) else None, \n",
        "               kernel_regularizer=l1(l1_coef)))\n",
        "    smodel.add(Activation('tanh'))\n",
        "    smodel.add(Dropout(0.2))\n",
        "    smodel.add(Dense(10, use_bias=False, \n",
        "               kernel_constraint=NoSmallWeights(th_val) if (th_val is not None) else None, \n",
        "               kernel_regularizer=l1(l1_coef)))\n",
        "    smodel.add(Activation('softmax')) \n",
        "    smodel.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])\n",
        "    return smodel"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "VVQk8rUtumMU",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1032
        },
        "outputId": "ccdece86-1d10-4320-b808-c5bd414581aa"
      },
      "cell_type": "code",
      "source": [
        "all_model_weights = []\n",
        "th_val_list = [None, 0, 1e-5, 1e-4, 1e-3, 1e-2 ]\n",
        "for th_val in th_val_list :\n",
        "    print \"-\" * 50\n",
        "    print \"th_val =\", th_val\n",
        "    print \"-\" * 50\n",
        "    smodel = create_model( th_val, l1_coef=1e-4 )\n",
        "    smodel.fit(X_train, Y_train,\n",
        "              batch_size=128, nb_epoch=5,\n",
        "              verbose=0, callbacks=[ShowSparsity((th_val or 0) +K.epsilon())],\n",
        "              validation_data=(X_test, Y_test))\n",
        "    print \"testing accuracy =\", smodel.evaluate( X_test, Y_test, verbose=0 )[1]\n",
        "    all_model_weights.append( smodel.get_weights() )"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "--------------------------------------------------\n",
            "th_val = None\n",
            "--------------------------------------------------\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python2.7/dist-packages/keras/models.py:981: UserWarning: The `nb_epoch` argument in `fit` has been renamed `epochs`.\n",
            "  warnings.warn('The `nb_epoch` argument in `fit` '\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Epoch 00000, sparsity = 0.5033\n",
            "Epoch 00001, sparsity = 0.5007\n",
            "Epoch 00002, sparsity = 0.5005\n",
            "Epoch 00003, sparsity = 0.5016\n",
            "Epoch 00004, sparsity = 0.5003\n",
            "testing accuracy = 0.9599\n",
            "--------------------------------------------------\n",
            "th_val = 0\n",
            "--------------------------------------------------\n",
            "Epoch 00000, sparsity = 0.8736\n",
            "Epoch 00001, sparsity = 0.8729\n",
            "Epoch 00002, sparsity = 0.8530\n",
            "Epoch 00003, sparsity = 0.8476\n",
            "Epoch 00004, sparsity = 0.8457\n",
            "testing accuracy = 0.9309\n",
            "--------------------------------------------------\n",
            "th_val = 1e-05\n",
            "--------------------------------------------------\n",
            "Epoch 00000, sparsity = 0.8738\n",
            "Epoch 00001, sparsity = 0.8611\n",
            "Epoch 00002, sparsity = 0.8653\n",
            "Epoch 00003, sparsity = 0.8621\n",
            "Epoch 00004, sparsity = 0.8369\n",
            "testing accuracy = 0.9312\n",
            "--------------------------------------------------\n",
            "th_val = 0.0001\n",
            "--------------------------------------------------\n",
            "Epoch 00000, sparsity = 0.8804\n",
            "Epoch 00001, sparsity = 0.8813\n",
            "Epoch 00002, sparsity = 0.8729\n",
            "Epoch 00003, sparsity = 0.8621\n",
            "Epoch 00004, sparsity = 0.8644\n",
            "testing accuracy = 0.927\n",
            "--------------------------------------------------\n",
            "th_val = 0.001\n",
            "--------------------------------------------------\n",
            "Epoch 00000, sparsity = 0.9528\n",
            "Epoch 00001, sparsity = 0.9662\n",
            "Epoch 00002, sparsity = 0.9712\n",
            "Epoch 00003, sparsity = 0.9732\n",
            "Epoch 00004, sparsity = 0.9766\n",
            "testing accuracy = 0.9264\n",
            "--------------------------------------------------\n",
            "th_val = 0.01\n",
            "--------------------------------------------------\n",
            "Epoch 00000, sparsity = 0.9762\n",
            "Epoch 00001, sparsity = 0.9823\n",
            "Epoch 00002, sparsity = 0.9849\n",
            "Epoch 00003, sparsity = 0.9864\n",
            "Epoch 00004, sparsity = 0.9874\n",
            "testing accuracy = 0.9132\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "9o7bBljOAnUi",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# Evaluate model performance before and after setting small weights to zero"
      ]
    },
    {
      "metadata": {
        "id": "zopwDo307FME",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def set_small_weights_zeros( w_list, th_val ) :\n",
        "    denominator = 0.\n",
        "    numerator = 0.\n",
        "    for w in w_list :\n",
        "        denominator += w.size\n",
        "        numerator += np.sum(w<th_val)\n",
        "        w[w<th_val] = 0.\n",
        "    return numerator/denominator\n",
        "        "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "R6nvNGd0usWE",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 485
        },
        "outputId": "860ccdc7-fccd-4025-f48d-99a05bbc5aef"
      },
      "cell_type": "code",
      "source": [
        "results = []\n",
        "for w_list in all_model_weights :\n",
        "    # evaluate model before setting small weights to zeros\n",
        "    smodel.set_weights( w_list )\n",
        "    loss, acc =  smodel.evaluate( X_test, Y_test, verbose=0 )\n",
        "    # set small weights to zeros and compute sparisty\n",
        "    w0_list = deepcopy(w_list)\n",
        "    sparsity = set_small_weights_zeros( w0_list, th_val=K.epsilon() )\n",
        "    # re-evaluate model after setting small weights to zeros\n",
        "    smodel.set_weights( w0_list )\n",
        "    loss0, acc0 =  smodel.evaluate( X_test, Y_test, verbose=0 )\n",
        "    results.append( [sparsity, acc, acc0] )\n",
        "    \n",
        "    \n",
        "pyplot.plot( np.row_stack( results ) ) \n",
        "pyplot.legend(['model sparsity', 'accuracy w/o zero-out', 'accuracy w/ zero-out'], fontsize=16)\n",
        "pyplot.xlabel( 'th_val used in model')\n",
        "pyplot.xticks( range(6), [ str(v) for v in th_val_list ] )"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "([<matplotlib.axis.XTick at 0x7fc5462b9190>,\n",
              "  <matplotlib.axis.XTick at 0x7fc5a5e0d1d0>,\n",
              "  <matplotlib.axis.XTick at 0x7fc54627cb90>,\n",
              "  <matplotlib.axis.XTick at 0x7fc54628f090>,\n",
              "  <matplotlib.axis.XTick at 0x7fc54627c6d0>,\n",
              "  <matplotlib.axis.XTick at 0x7fc5462caf10>],\n",
              " <a list of 6 Text xticklabel objects>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        },
        {
          "output_type": "display_data",
          "data": {
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EPgnhRmitfmAAT0U5Zduz0PeKR989rsX2K4QQIvRpG7PSokWL2LJlCyqVinnz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\ngPj43jz44B+YM2c2WVnbGDB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gMBgYOnQ4W7ZksHlzuv8quKSkmN27d/LQQ/P825tMZn9o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\nXd3o3r0HmZlXSU9PIzr6JLa2drRv3wEwTMoaMmR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8vLzKnMfb21v9/PPPZeozZswYderU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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fc54639bd10>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}