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93 lines
2.5 KiB
Markdown
93 lines
2.5 KiB
Markdown
# Theano tensor 模块：conv 子模块
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`conv` 是 `tensor` 中处理卷积神经网络的子模块。
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## 卷积
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这里只介绍二维卷积：
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`T.nnet.conv2d(input, filters, input_shape=None, filter_shape=None, border_mode='valid', subsample=(1, 1), filter_flip=True, image_shape=None, **kwargs)`
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`conv2d` 函数接受两个输入：
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* `4D` 张量 `input`，其形状如下：
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`[b, ic, i0, i1]`
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* `4D` 张量 `filter` ，其形状如下：
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`[oc, ic, f0, f1]`
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`border_mode` 控制输出大小：
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* `'valid'`：输出形状：
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`[b, oc, i0 - f0 + 1, i1 - f1 + 1]`
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* `'full'`：输出形状：
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`[b, oc, i0 + f0 - 1, i1 + f1 - 1]`
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## 池化
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池化操作：
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`T.signal.downsample.max_pool_2d(input, ds, ignore_border=None, st=None, padding=(0, 0), mode='max')`
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`input` 池化操作在其最后两维进行。
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`ds` 是池化区域的大小，用长度为 2 的元组表示。
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`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)`。
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## MNIST 卷积神经网络形状详解
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```py
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def model(X, w, w2, w3, w4, p_drop_conv, p_drop_hidden):
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# X: 128 * 1 * 28 * 28
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# w: 32 * 1 * 3 * 3
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# full mode
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# l1a: 128 * 32 * (28 + 3 - 1) * (28 + 3 - 1)
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l1a = rectify(conv2d(X, w, border_mode='full'))
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# l1a: 128 * 32 * 30 * 30
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# ignore_border False
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# l1: 128 * 32 * (30 / 2) * (30 / 2)
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l1 = max_pool_2d(l1a, (2, 2), ignore_border=False)
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l1 = dropout(l1, p_drop_conv)
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# l1: 128 * 32 * 15 * 15
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# w2: 64 * 32 * 3 * 3
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# valid mode
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# l2a: 128 * 64 * (15 - 3 + 1) * (15 - 3 + 1)
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l2a = rectify(conv2d(l1, w2))
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# l2a: 128 * 64 * 13 * 13
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# l2: 128 * 64 * (13 / 2 + 1) * (13 / 2 + 1)
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l2 = max_pool_2d(l2a, (2, 2), ignore_border=False)
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l2 = dropout(l2, p_drop_conv)
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# l2: 128 * 64 * 7 * 7
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# w3: 128 * 64 * 3 * 3
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# l3a: 128 * 128 * (7 - 3 + 1) * (7 - 3 + 1)
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l3a = rectify(conv2d(l2, w3))
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# l3a: 128 * 128 * 5 * 5
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# l3b: 128 * 128 * (5 / 2 + 1) * (5 / 2 + 1)
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l3b = max_pool_2d(l3a, (2, 2), ignore_border=False)
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# l3b: 128 * 128 * 3 * 3
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# l3: 128 * (128 * 3 * 3)
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l3 = T.flatten(l3b, outdim=2)
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l3 = dropout(l3, p_drop_conv)
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# l3: 128 * (128 * 3 * 3)
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# w4: (128 * 3 * 3) * 625
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# l4: 128 * 625
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l4 = rectify(T.dot(l3, w4))
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l4 = dropout(l4, p_drop_hidden)
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# l5: 128 * 625
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# w5: 625 * 10
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# pyx: 128 * 10
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pyx = softmax(T.dot(l4, w_o))
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return l1, l2, l3, l4, pyx
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``` |