note-on-conv-masking.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Note on Masked Convolutions\n",
    "\n",
    "A major motivation for using two stacks (a horizontal and vertical stack) suggested by van den Oord et al. is\n",
    "to avoid a blind spot (see figure 1 in van den Oord et al. 2016).  However, the figure is misleading.  It suggests two convolutions\n",
    "of the form:\n",
    "\n",
    "```\n",
    "1 1 1 1 1\n",
    "1 1 1 1 1\n",
    "0 0 0 0 0\n",
    "0 0 0 0 0\n",
    "0 0 0 0 0\n",
    "```\n",
    "(for the first layer's vertical conv)\n",
    "\n",
    "and\n",
    "```\n",
    "1 1 0 0 0\n",
    "```\n",
    "(for the first layer's horizontal conv)\n",
    "\n",
    "For subsequent conv's, the center pixel can be included without including information about that pixel in the input,\n",
    "suggesting the use of\n",
    "```\n",
    "1 1 1 1 1\n",
    "1 1 1 1 1\n",
    "0 0 1 0 0\n",
    "0 0 0 0 0\n",
    "0 0 0 0 0\n",
    "```\n",
    "(for the subsequent layers' vertical conv)\n",
    "\n",
    "and\n",
    "```\n",
    "1 1 1 0 0\n",
    "```\n",
    "(for the subsequent layers' horizontal conv)\n",
    "\n",
    "Turukin, in his blog post, even uses:\n",
    "```\n",
    "1 1 1 1 1\n",
    "1 1 1 1 1\n",
    "1 1 1 0 0\n",
    "0 0 0 0 0\n",
    "0 0 0 0 0\n",
    "```\n",
    "for subsequent vertical convolutions, as that does not break the autoregressive dependence structure.\n",
    "\n",
    "I take it a step farther and use\n",
    "```\n",
    "1 1 1 1 1\n",
    "1 1 1 1 1\n",
    "1 1 1 1 1\n",
    "0 0 0 0 0\n",
    "0 0 0 0 0\n",
    "```\n",
    "for my subsequent vertical convolutions (which I believe the authors of van den Oord intended); I show in\n",
    "this notebook that it is the only formulation of secondary vertical\n",
    "convolution masks that prevents blindspots while maintaining the autoregressive dependency structure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from models.mnist_pixelcnn import *\n",
    "import matplotlib.pyplot as plt\n",
    "def show_tensor(tensor):\n",
    "    plt.imshow(tensor.cpu().numpy())\n",
    "    plt.colorbar()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_experiment(mask_mode, horizontal_n_by_n=False):\n",
    "    model = MNIST_PixelCNNNew(levels=2, layers=5, mask_mode=mask_mode, horizontal_2d_convs=horizontal_n_by_n)\n",
    "    for param in model.parameters():\n",
    "        if len(param.size()) == 4:\n",
    "            param.data.fill_(1)\n",
    "        else:\n",
    "            param.data.fill_(0)\n",
    "    test = torch.zeros(1, 1, 28, 28)\n",
    "    test[0, 0, 14, 14] = 1\n",
    "    test = Variable(test, requires_grad=False)\n",
    "    plt.title(\"PixelCNN Input\")\n",
    "    show_tensor(test.data[0,0])\n",
    "    logits = model(test)\n",
    "    plt.title(\"PixelCNN Output Channel 1\")\n",
    "    show_tensor(logits.data[0,0,0])\n",
    "    plt.title(\"PixelCNN Output Channel 2\")\n",
    "    show_tensor(logits.data[0,1,0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Experiments\n",
    "\n",
    "For the experiments, I set all biases to zero and set the kernel matrices all to 1.  I use an image of all zeros with a single non-zero pixel (value 1) in the center.  I then run it through the gated convolutional network.  All non-zero pixels in the output show where information from the center pixel has propogated.\n",
    "\n",
    "### Experiment 1: Masks Implied by Figure 1 of van den Oord et al.\n",
    "\n",
    "I believe that in theory, in order to propose the use of a vertical and horizontal stack, van den Oord must have used the convolutions I used below (labeled \"noblind\"), but figure 1 of the paper seems to suggest kernel masks of the following form:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A VERTICAL MASKED CONV: 7 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]]\n",
      "A HORIZONTAL MASKED CONV: 1 x 7. Mask:\n",
      "[[ 1.  1.  1.  0.  0.  0.  0.]]\n",
      "B VERTICAL MASKED CONV: 7 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]]\n",
      "B HORIZONTAL MASKED CONV: 1 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  0.  0.  0.]]\n",
      "B VERTICAL MASKED CONV: 7 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]]\n",
      "B HORIZONTAL MASKED CONV: 1 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  0.  0.  0.]]\n",
      "B VERTICAL MASKED CONV: 7 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]]\n",
      "B HORIZONTAL MASKED CONV: 1 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  0.  0.  0.]]\n",
      "B VERTICAL MASKED CONV: 7 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]]\n",
      "B HORIZONTAL MASKED CONV: 1 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  0.  0.  0.]]\n"
     ]
    },
    {
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fBH69V9KCjHFFRBeDmg5h+xCwCdgG3Alca3uXpIskvWG28aXFFRFTDXDmfLnQ6NZJxy6Y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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fac08728a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fac063cb160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fac04d6ce80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "run_experiment(\"fig1-van-den-oord\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, this masking suffers from the blind spot noted by van den Oord.\n",
    "\n",
    "### Experiment 2: Masks used by Sergei Turukin's blog post\n",
    "\n",
    "In Sergei Turukin's [blog post](http://sergeiturukin.com/2017/02/24/gated-pixelcnn.html), he recommended masks of the following form:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A VERTICAL MASKED CONV: 7 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]]\n",
      "A HORIZONTAL MASKED CONV: 1 x 7. Mask:\n",
      "[[ 1.  1.  1.  0.  0.  0.  0.]]\n",
      "B VERTICAL MASKED CONV: 7 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]]\n",
      "B HORIZONTAL MASKED CONV: 1 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  0.  0.  0.]]\n",
      "B VERTICAL MASKED CONV: 7 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]]\n",
      "B HORIZONTAL MASKED CONV: 1 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  0.  0.  0.]]\n",
      "B VERTICAL MASKED CONV: 7 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]]\n",
      "B HORIZONTAL MASKED CONV: 1 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  0.  0.  0.]]\n",
      "B VERTICAL MASKED CONV: 7 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]]\n",
      "B HORIZONTAL MASKED CONV: 1 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  0.  0.  0.]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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fBH69V9KCjHFFRBeDmg5h+xCwCdgG3Alca3uXpIskvWG28aXFFRFTDXDmfLnQ6NZJxy6Y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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fac04d08b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fac05714c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fac04c9ff98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "run_experiment(\"turukin\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These also suffer from a blindspot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Experiment 3: No blindspot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A VERTICAL MASKED CONV: 7 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]]\n",
      "A HORIZONTAL MASKED CONV: 1 x 7. Mask:\n",
      "[[ 1.  1.  1.  0.  0.  0.  0.]]\n",
      "B VERTICAL MASKED CONV: 7 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]]\n",
      "B HORIZONTAL MASKED CONV: 1 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  0.  0.  0.]]\n",
      "B VERTICAL MASKED CONV: 7 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]]\n",
      "B HORIZONTAL MASKED CONV: 1 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  0.  0.  0.]]\n",
      "B VERTICAL MASKED CONV: 7 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]]\n",
      "B HORIZONTAL MASKED CONV: 1 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  0.  0.  0.]]\n",
      "B VERTICAL MASKED CONV: 7 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]]\n",
      "B HORIZONTAL MASKED CONV: 1 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  0.  0.  0.]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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fBH69V9KCjHFFRBeDmg5h+xCwCdgG3Alca3uXpIskvWG28aXFFRFTDXDmfLnQ6NZJxy6Y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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fac05645630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fac056839b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fac084a4ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "run_experiment(\"noblind\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see there is no blind spot for these masks.\n",
    "\n",
    "## BONUS: Experiment 4: NxN convolution in HORIZONTAL stack\n",
    "\n",
    "In addition, you can make convolutions in the horizontal stack $N \\times N$ instead of $1 \\times N$ so long as you use a kernel mask like that suggested by Turukin in his blog post:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A VERTICAL MASKED CONV: 7 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]]\n",
      "A HORIZONTAL MASKED CONV: 7 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]]\n",
      "B VERTICAL MASKED CONV: 7 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]]\n",
      "B HORIZONTAL MASKED CONV: 7 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]]\n",
      "B VERTICAL MASKED CONV: 7 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]]\n",
      "B HORIZONTAL MASKED CONV: 7 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]]\n",
      "B VERTICAL MASKED CONV: 7 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]]\n",
      "B HORIZONTAL MASKED CONV: 7 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]]\n",
      "B VERTICAL MASKED CONV: 7 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]]\n",
      "B HORIZONTAL MASKED CONV: 7 x 7. Mask:\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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fBH69V9KCjHFFRBeDmg5h+xCwCdgG3Alca3uXpIskvWG28aXFFRFTDXDmfLnQ6NZJxy6Y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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fac063bdba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fac05604fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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37k/5D2vmcwx7QCEiQtKAMTwiVgIrAV6tqSUYgzErvyH8ou6OiHkDHUz98UuAI4BngO9R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\nJQc3MyslBzczKyUHNzMrpf8PLeZ8higWOCMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fac056bee10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "run_experiment(\"noblind\", horizontal_n_by_n=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Though this results in the same receptive field, I intuitively think this will make it easier for left-to-right diagonal information to be passed through the network."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}