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| 1 | +{ |
| 2 | + "cells": [ |
| 3 | + { |
| 4 | + "cell_type": "markdown", |
| 5 | + "metadata": {}, |
| 6 | + "source": [ |
| 7 | + "# Theano tensor 模块：conv 子模块" |
| 8 | + ] |
| 9 | + }, |
| 10 | + { |
| 11 | + "cell_type": "markdown", |
| 12 | + "metadata": {}, |
| 13 | + "source": [ |
| 14 | + "`conv` 是 `tensor` 中处理卷积神经网络的子模块。" |
| 15 | + ] |
| 16 | + }, |
| 17 | + { |
| 18 | + "cell_type": "markdown", |
| 19 | + "metadata": {}, |
| 20 | + "source": [ |
| 21 | + "## 卷积" |
| 22 | + ] |
| 23 | + }, |
| 24 | + { |
| 25 | + "cell_type": "markdown", |
| 26 | + "metadata": {}, |
| 27 | + "source": [ |
| 28 | + "这里只介绍二维卷积：\n", |
| 29 | + "\n", |
| 30 | + "`T.nnet.conv2d(input, filters, input_shape=None, filter_shape=None, border_mode='valid', subsample=(1, 1), filter_flip=True, image_shape=None, **kwargs)`\n", |
| 31 | + "\n", |
| 32 | + "`conv2d` 函数接受两个输入：\n", |
| 33 | + "\n", |
| 34 | + "- `4D` 张量 `input`，其形状如下：\n", |
| 35 | + " \n", |
| 36 | + " `[b, ic, i0, i1]`\n", |
| 37 | + " \n", |
| 38 | + " \n", |
| 39 | + "- `4D` 张量 `filter` ，其形状如下：\n", |
| 40 | + " \n", |
| 41 | + " `[oc, ic, f0, f1]`\n", |
| 42 | + " \n", |
| 43 | + "`border_mode` 控制输出大小：\n", |
| 44 | + "\n", |
| 45 | + "- `'valid'`：输出形状：\n", |
| 46 | + "\n", |
| 47 | + " `[b, oc, i0 - f0 + 1, i1 - f1 + 1]`\n", |
| 48 | + " \n", |
| 49 | + "- `'full'`：输出形状：\n", |
| 50 | + "\n", |
| 51 | + " `[b, oc, i0 + f0 - 1, i1 + f1 - 1]`" |
| 52 | + ] |
| 53 | + }, |
| 54 | + { |
| 55 | + "cell_type": "markdown", |
| 56 | + "metadata": {}, |
| 57 | + "source": [ |
| 58 | + "## 池化" |
| 59 | + ] |
| 60 | + }, |
| 61 | + { |
| 62 | + "cell_type": "markdown", |
| 63 | + "metadata": {}, |
| 64 | + "source": [ |
| 65 | + "池化操作：\n", |
| 66 | + "\n", |
| 67 | + "`T.signal.downsample.max_pool_2d(input, ds, ignore_border=None, st=None, padding=(0, 0), mode='max')`\n", |
| 68 | + "\n", |
| 69 | + "`input` 池化操作在其最后两维进行。\n", |
| 70 | + "\n", |
| 71 | + "`ds` 是池化区域的大小，用长度为 2 的元组表示。\n", |
| 72 | + "\n", |
| 73 | + "`ignore_border` 设为 `Ture` 时，`(5, 5)` 在 `(2, 2)` 的池化下会变成 `(2, 2)`（5 % 2 == 1，多余的 1 个被舍去了），否则是 `(3, 3)`。" |
| 74 | + ] |
| 75 | + }, |
| 76 | + { |
| 77 | + "cell_type": "markdown", |
| 78 | + "metadata": {}, |
| 79 | + "source": [ |
| 80 | + "## MNIST 卷积神经网络形状详解" |
| 81 | + ] |
| 82 | + }, |
| 83 | + { |
| 84 | + "cell_type": "markdown", |
| 85 | + "metadata": {}, |
| 86 | + "source": [ |
| 87 | + "```python\n", |
| 88 | + "def model(X, w, w2, w3, w4, p_drop_conv, p_drop_hidden):\n", |
| 89 | + " \n", |
| 90 | + " # X: 128 * 1 * 28 * 28\n", |
| 91 | + " # w: 32 * 1 * 3 * 3\n", |
| 92 | + " # full mode\n", |
| 93 | + " # l1a: 128 * 32 * (28 + 3 - 1) * (28 + 3 - 1)\n", |
| 94 | + " l1a = rectify(conv2d(X, w, border_mode='full'))\n", |
| 95 | + " # l1a: 128 * 32 * 30 * 30\n", |
| 96 | + " # ignore_border False\n", |
| 97 | + " # l1: 128 * 32 * (30 / 2) * (30 / 2)\n", |
| 98 | + " l1 = max_pool_2d(l1a, (2, 2), ignore_border=False)\n", |
| 99 | + " l1 = dropout(l1, p_drop_conv)\n", |
| 100 | + "\n", |
| 101 | + " # l1: 128 * 32 * 15 * 15\n", |
| 102 | + " # w2: 64 * 32 * 3 * 3\n", |
| 103 | + " # valid mode\n", |
| 104 | + " # l2a: 128 * 64 * (15 - 3 + 1) * (15 - 3 + 1)\n", |
| 105 | + " l2a = rectify(conv2d(l1, w2)) \n", |
| 106 | + " # l2a: 128 * 64 * 13 * 13\n", |
| 107 | + " # l2: 128 * 64 * (13 / 2 + 1) * (13 / 2 + 1)\n", |
| 108 | + " l2 = max_pool_2d(l2a, (2, 2), ignore_border=False)\n", |
| 109 | + " l2 = dropout(l2, p_drop_conv)\n", |
| 110 | + "\n", |
| 111 | + " # l2: 128 * 64 * 7 * 7\n", |
| 112 | + " # w3: 128 * 64 * 3 * 3\n", |
| 113 | + " # l3a: 128 * 128 * (7 - 3 + 1) * (7 - 3 + 1)\n", |
| 114 | + " l3a = rectify(conv2d(l2, w3))\n", |
| 115 | + " # l3a: 128 * 128 * 5 * 5\n", |
| 116 | + " # l3b: 128 * 128 * (5 / 2 + 1) * (5 / 2 + 1)\n", |
| 117 | + " l3b = max_pool_2d(l3a, (2, 2), ignore_border=False) \n", |
| 118 | + " # l3b: 128 * 128 * 3 * 3\n", |
| 119 | + " # l3: 128 * (128 * 3 * 3)\n", |
| 120 | + " l3 = T.flatten(l3b, outdim=2)\n", |
| 121 | + " l3 = dropout(l3, p_drop_conv)\n", |
| 122 | + " \n", |
| 123 | + " # l3: 128 * (128 * 3 * 3)\n", |
| 124 | + " # w4: (128 * 3 * 3) * 625\n", |
| 125 | + " # l4: 128 * 625\n", |
| 126 | + " l4 = rectify(T.dot(l3, w4))\n", |
| 127 | + " l4 = dropout(l4, p_drop_hidden)\n", |
| 128 | + "\n", |
| 129 | + " # l5: 128 * 625\n", |
| 130 | + " # w5: 625 * 10\n", |
| 131 | + " # pyx: 128 * 10\n", |
| 132 | + " pyx = softmax(T.dot(l4, w_o))\n", |
| 133 | + " return l1, l2, l3, l4, pyx\n", |
| 134 | + "```" |
| 135 | + ] |
| 136 | + } |
| 137 | + ], |
| 138 | + "metadata": { |
| 139 | + "kernelspec": { |
| 140 | + "display_name": "Python 2", |
| 141 | + "language": "python", |
| 142 | + "name": "python2" |
| 143 | + }, |
| 144 | + "language_info": { |
| 145 | + "codemirror_mode": { |
| 146 | + "name": "ipython", |
| 147 | + "version": 2 |
| 148 | + }, |
| 149 | + "file_extension": ".py", |
| 150 | + "mimetype": "text/x-python", |
| 151 | + "name": "python", |
| 152 | + "nbconvert_exporter": "python", |
| 153 | + "pygments_lexer": "ipython2", |
| 154 | + "version": "2.7.6" |
| 155 | + } |
| 156 | + }, |
| 157 | + "nbformat": 4, |
| 158 | + "nbformat_minor": 0 |
| 159 | +} |
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