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Theano 实例：卷积神经网络
import theano import theano.tensor as T from theano.sandbox.rng_mrg import MRG_RandomStreams as RandomStreams import numpy as np from load import mnist srng = RandomStreams()
Using gpu device 1: Tesla C2075 (CNMeM is disabled)
从前一节导入有用的函数：
def floatX(X): return np.asarray(X, dtype=theano.config.floatX) def init_weights(shape): return theano.shared(floatX(np.random.randn(*shape) * 0.01)) def rectify(X): return T.maximum(X, 0.) def softmax(X): e_x = T.exp(X - X.max(axis=1).dimshuffle(0, 'x')) return e_x / e_x.sum(axis=1).dimshuffle(0, 'x') def dropout(X, p=0.): if p > 0: retain_prob = 1 - p X *= srng.binomial(X.shape, p=retain_prob, dtype=theano.config.floatX) X /= retain_prob return X def RMSprop(cost, params, lr=0.001, rho=0.9, epsilon=1e-6): grads = T.grad(cost=cost, wrt=params) updates = [] for p, g in zip(params, grads): acc = theano.shared(p.get_value() * 0.) acc_new = rho * acc + (1 - rho) * g ** 2 gradient_scaling = T.sqrt(acc_new + epsilon) g = g / gradient_scaling updates.append((acc, acc_new)) updates.append((p, p - lr * g)) return updates
与前一节不同，我们使用卷积神经网络来实现这次的模型，为此，我们需要导入 2 维的卷积和池化函数：
from theano.tensor.nnet.conv import conv2d from theano.tensor.signal.downsample import max_pool_2d
conv2d 函数接受两个输入：
-
对应输入的
4D张量，其形状如下：[mini-batch size, number of feature maps at layer m-1, image height, image width] -
对应参数矩阵的
4D张量，其形状如下：[number of feature maps at layer m, number of feature maps at layer m-1, filter height, filter width]
为了对图像使用卷积，我们需要将图像转化为原始的 28 × 28 大小，同时添加一维表示图像的通道数（黑白图像为 1）：
trX, teX, trY, teY = mnist(onehot=True) trX = trX.reshape(-1, 1, 28, 28) teX = teX.reshape(-1, 1, 28, 28)
注意，对于 reshape 方法，传入的参数是 -1 表示该维的维度将根据其他参数自动计算。
模型首先进行三层卷积加池化操作，然后在第三层的输出中加一个全连结层，最后在第四层加上一个 softmax 层：
def model(X, w, w2, w3, w4, p_drop_conv, p_drop_hidden): # X: 128 * 1 * 28 * 28 # w: 32 * 1 * 3 * 3 # full mode # l1a: 128 * 32 * (28 + 3 - 1) * (28 + 3 - 1) l1a = rectify(conv2d(X, w, border_mode='full')) # l1a: 128 * 32 * 30 * 30 # ignore_border False # l1: 128 * 32 * (30 / 2) * (30 / 2) l1 = max_pool_2d(l1a, (2, 2), ignore_border=False) l1 = dropout(l1, p_drop_conv) # l1: 128 * 32 * 15 * 15 # w2: 64 * 32 * 3 * 3 # valid mode # l2a: 128 * 64 * (15 - 3 + 1) * (15 - 3 + 1) l2a = rectify(conv2d(l1, w2)) # l2a: 128 * 64 * 13 * 13 # l2: 128 * 64 * (13 / 2 + 1) * (13 / 2 + 1) l2 = max_pool_2d(l2a, (2, 2), ignore_border=False) l2 = dropout(l2, p_drop_conv) # l2: 128 * 64 * 7 * 7 # w3: 128 * 64 * 3 * 3 # l3a: 128 * 128 * (7 - 3 + 1) * (7 - 3 + 1) l3a = rectify(conv2d(l2, w3)) # l3a: 128 * 128 * 5 * 5 # l3b: 128 * 128 * (5 / 2 + 1) * (5 / 2 + 1) l3b = max_pool_2d(l3a, (2, 2), ignore_border=False) # l3b: 128 * 128 * 3 * 3 # l3: 128 * (128 * 3 * 3) l3 = T.flatten(l3b, outdim=2) l3 = dropout(l3, p_drop_conv) # l3: 128 * (128 * 3 * 3) # w4: (128 * 3 * 3) * 625 # l4: 128 * 625 l4 = rectify(T.dot(l3, w4)) l4 = dropout(l4, p_drop_hidden) # l5: 128 * 625 # w5: 625 * 10 # pyx: 128 * 10 pyx = softmax(T.dot(l4, w_o)) return l1, l2, l3, l4, pyx
定义符号变量：
X = T.ftensor4() Y = T.fmatrix() w = init_weights((32, 1, 3, 3)) w2 = init_weights((64, 32, 3, 3)) w3 = init_weights((128, 64, 3, 3)) w4 = init_weights((128 * 3 * 3, 625)) w_o = init_weights((625, 10))
使用带 dropout 的模型进行训练：
noise_l1, noise_l2, noise_l3, noise_l4, noise_py_x = model(X, w, w2, w3, w4, 0.2, 0.5)
使用不带 dropout 的模型进行预测：
l1, l2, l3, l4, py_x = model(X, w, w2, w3, w4, 0., 0.) y_x = T.argmax(py_x, axis=1)
定义损失函数和迭代规则：
cost = T.mean(T.nnet.categorical_crossentropy(noise_py_x, Y)) params = [w, w2, w3, w4, w_o] updates = RMSprop(cost, params, lr=0.001)
开始训练：
train = theano.function(inputs=[X, Y], outputs=cost, updates=updates, allow_input_downcast=True) predict = theano.function(inputs=[X], outputs=y_x, allow_input_downcast=True) for i in range(50): for start, end in zip(range(0, len(trX), 128), range(128, len(trX), 128)): cost = train(trX[start:end], trY[start:end]) print "iter {:03d}, {:.3f}".format(i + 1, np.mean(np.argmax(teY, axis=1) == predict(teX)))
iter 001, 0.917 iter 002, 0.974 iter 003, 0.983 iter 004, 0.984 iter 005, 0.987 iter 006, 0.989 iter 007, 0.991 iter 008, 0.993 iter 009, 0.991 iter 010, 0.992 iter 011, 0.993 iter 012, 0.992 iter 013, 0.992 iter 014, 0.992 iter 015, 0.993 iter 016, 0.992 iter 017, 0.994 iter 018, 0.993 iter 019, 0.993 iter 020, 0.994 iter 021, 0.993 iter 022, 0.993 iter 023, 0.993 iter 024, 0.992 iter 025, 0.994 iter 026, 0.993 iter 027, 0.994 iter 028, 0.993 iter 029, 0.993 iter 030, 0.994 iter 031, 0.994 iter 032, 0.993 iter 033, 0.994 iter 034, 0.994 iter 035, 0.994 iter 036, 0.994 iter 037, 0.994 iter 038, 0.993 iter 039, 0.994 iter 040, 0.994 iter 041, 0.994 iter 042, 0.994 iter 043, 0.995 iter 044, 0.994 iter 045, 0.994 iter 046, 0.994 iter 047, 0.995 iter 048, 0.994 iter 049, 0.994 iter 050, 0.995
