conv.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "dim_x, dim_y, colors=10,11,5\n",
    "kernel_x, kernel_y, in_colors, out_colors=2,3,colors, 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "im=np.random.rand(dim_x, dim_y, colors)\n",
    "weights=np.random.rand(kernel_x, kernel_y, in_colors, out_colors)\n",
    "\n",
    "debug_weights=np.random.rand(*(dim_x-kernel_x+1, dim_y-kernel_y+1, out_colors))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 11, 5)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "im.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def forward(im, weights):\n",
    "    kernel_x, kernel_y, in_colors, out_colors=weights.shape\n",
    "    dim_x, dim_y, colors=im.shape\n",
    "    \n",
    "    \n",
    "    out=np.empty((dim_x-kernel_x+1, dim_y-kernel_y+1, out_colors))\n",
    "    \n",
    "    for i in range(out.shape[0]):\n",
    "        for j in range(out.shape[1]):\n",
    "            crop=im[i:i+kernel_x, j:j+kernel_y]\n",
    "            #expand crops so the dimensions match\n",
    "            crop=np.expand_dims(crop, axis=-1)\n",
    "            \n",
    "            res=crop*weights\n",
    "            \n",
    "            #sum everything except the output\n",
    "            res=np.apply_over_axes(np.sum, res, [0,1,2]).reshape(-1)\n",
    "            \n",
    "            out[i,j]=res\n",
    "            \n",
    "    return out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "out=forward(im, weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(9, 9, 4)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "debug_out=np.sum(out*debug_weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1202.8937344394294"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "debug_out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "debug_shape=debug_weights.shape\n",
    "\n",
    "padded=np.zeros((debug_shape[0]+2*(kernel_x-1), debug_shape[1]+2*(kernel_y-1), out_colors))\n",
    "padded[kernel_x-1:kernel_x-1+debug_shape[0], kernel_y-1:kernel_y-1+debug_shape[1]]=debug_weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f6ce875cac8>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ceaa4e0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow((padded>0).sum(axis=-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "backward_weights=weights[::-1,::-1].transpose((0,1,3,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "grads=forward(padded, backward_weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 11, 5)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grads.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "eps=1e-4\n",
    "tol=1e-8\n",
    "\n",
    "for idx in np.ndindex(im.shape):\n",
    "    d_im=im.copy()\n",
    "    d_im[idx]+=eps\n",
    "    d_out=forward(d_im, weights)\n",
    "    d_debug_out=np.sum(d_out*debug_weights)\n",
    "\n",
    "    grad=(d_debug_out-debug_out)/eps\n",
    "    \n",
    "    assert np.abs(grad-grads[idx])<tol, idx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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