working-with-samples-of-distributions-over-convolutional-kernels.ipynb

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   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
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   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import tensorflow as tf\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from tensorflow.examples.tutorials.mnist import input_data as mnist_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1.2.1'"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tf.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sess = tf.InteractiveSession()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extracting /home/tiao/Desktop/MNIST/train-images-idx3-ubyte.gz\n",
      "Extracting /home/tiao/Desktop/MNIST/train-labels-idx1-ubyte.gz\n",
      "Extracting /home/tiao/Desktop/MNIST/t10k-images-idx3-ubyte.gz\n",
      "Extracting /home/tiao/Desktop/MNIST/t10k-labels-idx1-ubyte.gz\n"
     ]
    }
   ],
   "source": [
    "mnist = mnist_data.read_data_sets(\"/home/tiao/Desktop/MNIST\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50, 28, 28, 1)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 50 single-channel (grayscale) 28x28 images\n",
    "x = mnist.train.images[:50].reshape(-1, 28, 28, 1)\n",
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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   "source": [
    "fig, ax = plt.subplots(figsize=(5, 5))\n",
    "\n",
    "# showing an arbitrarily chosen image\n",
    "ax.imshow(np.squeeze(x[5], axis=-1), cmap='gray')\n",
    "\n",
    "plt.show()"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standard 2D Convolution with `conv2d`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5, 5, 1, 32]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 32 kernels of size 5x5x1\n",
    "kernel = tf.truncated_normal([5, 5, 1, 32], stddev=0.1)\n",
    "kernel.get_shape().as_list()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[50, 28, 28, 32]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_conved = tf.nn.conv2d(x, kernel, \n",
    "                        strides=[1, 1, 1, 1], \n",
    "                        padding='SAME')\n",
    "x_conved.get_shape().as_list()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(28, 28)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_conved[5, ..., 0].eval().shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
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       "<matplotlib.figure.Figure at 0x7f1a405177b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(9, 4))\n",
    "\n",
    "# showing what the 0th filter looks like\n",
    "ax1.imshow(kernel[..., 0, 0].eval(), cmap='gray')\n",
    "\n",
    "# show the previous arbitrarily chosen image\n",
    "# convolved with the 0th filter\n",
    "ax2.imshow(x_conved[5, ..., 0].eval(), cmap='gray')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sample from a Distribution over Kernels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[8, 5, 5, 1, 32]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 8x32 kernels of size 5x5x1\n",
    "kernels = tf.truncated_normal([8, 5, 5, 1, 32], stddev=0.1)\n",
    "kernels.get_shape().as_list()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Approach 1: Map over samples with `conv2d`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[8, 50, 28, 28, 1]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_tiled = tf.tile(tf.expand_dims(x, 0), [8, 1, 1, 1, 1])\n",
    "x_tiled.get_shape().as_list()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[50, 28, 28, 32]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tf.nn.conv2d(x_tiled[0], kernels[0], \n",
    "             strides=[1, 1, 1, 1], \n",
    "             padding='SAME').get_shape().as_list()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[8, 50, 28, 28, 32]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_conved1 = tf.map_fn(lambda args: tf.nn.conv2d(*args, strides=[1, 1, 1, 1], padding='SAME'),\n",
    "                      elems=(x_tiled, kernels), dtype=tf.float32)\n",
    "x_conved1.get_shape().as_list()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Approach 2: Flattening"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5, 5, 1, 256]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kernels_flat = tf.reshape(tf.transpose(kernels, \n",
    "                                       perm=(1, 2, 3, 4, 0)), \n",
    "                          shape=(5, 5, 1, 32*8))\n",
    "kernels_flat.get_shape().as_list()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[8, 50, 28, 28, 32]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_conved2 = tf.transpose(tf.reshape(tf.nn.conv2d(x, kernels_flat, \n",
    "                                                 strides=[1, 1, 1, 1], \n",
    "                                                 padding='SAME'), \n",
    "                                    shape=(50, 28, 28, 32, 8)), \n",
    "                         perm=(4, 0, 1, 2, 3))\n",
    "x_conved2.get_shape().as_list()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tf.reduce_all(tf.equal(x_conved1, x_conved2)).eval()"
   ]
  }
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   "slug": "working-with-samples-of-distributions-over-convolutional-kernels",
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   "title": "Working with Samples of Distributions over Convolutional Kernels",
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