20个feature maps
pooling layer：作为图像压缩，将图像信息缩小
隐藏层: 100个神经元
训练60个epochs
学习率 = 0.1
mini-batch size: 10
>>>import network3
>>>from network3 import Network
>>>from network3 import ConvPoolLayer,FullyConnectedLayer,SoftmaxLayer
>>>training_data,validation_data,test_data=network3.load_data_shared()
>>>mini_batch_size=10
>>>net = Network([FullyConnectedLayer(n_in=784,n_out=100),
SoftmaxLayer(n_in=100,n_out=10)],mini_batch_size)
>>>net.SGD(training_data,60,mini_batch_size,0.1,validation_data,test_data)
结果: 97.8 accuracy
这次: 没有regularization, 上次有
这次: softmax 上次: sigmoid + cross-entropy
[ConvPoolLayer(image_shape=(mini_batch_size,1,28,28),
FullyConnectedLayer(n_in=20*12*12,n_out=100),
SoftmaxLayer(n_in=100,n_out=10)],mini_batch_size)
>>>net.SGD(training_data,60,mini_batch_size,0.1,validation_data,test_data)
准确率: 98.78 比上次有显著提高
再加入一层convolution (共两层):
>>>net=Network(
[ConvPoolLayer(image_shape=(mini_batch_size,1,28,28),
filter_shape=(20,1,5,5),
poolsize=(2,2)),
ConvPoolLayer(image_shape=(mini_batch_size,20,12,12),
filter_shape=(40,20,5,5),
poolsize=(2,2)),
FullyConnectedLayer(n_in=40*4*4,n_out=100),
SoftmaxLayer(n_in=100,n_out=10)],mini_batch_size)
>>>net.SGD(training_data,60,mini_batch_size,0.1,validation_data,test_data)
准确率: 99.06% (再一次刷新)
用Rectified Linear Units代替sigmoid:
f(z) = max(0, z)
>>>net=Network(
[ConvPoolLayer(image_shape=(mini_batch_size,1,28,28),
filter_shape=(20,1,5,5),
poolsize=(2,2),
activation_fn=ReLU),
ConvPoolLayer(image_shape=(mini_batch_size,20,12,12),
filter_shape=(40,20,5,5),
poolsize=(2,2),activation_fn=ReLU),
FullyConnectedLayer(n_in=40*4*4,n_out=100,activation_fn=ReLU),
SoftmaxLayer(n_in=100,n_out=10)],
mini_batch_size)
>>>net.SGD(training_data,60,mini_batch_size,0.03,validation_data,test_data,lmbda=0.1)
准确率: 99.23 比之前用sigmoid函数的99.06%稍有提高
扩大训练集: 每个图像向上,下,左,右移动一个像素
总训练集: 50,000 * 5 = 250,000
$ python expand_mnist.py
>>>expanded_training_data,_,_=network3.load_data_shared("../data/mnist_expanded.pkl.gz")
>>>net=Network([ConvPoolLayer(image_shape=(mini_batch_size,1,28,28),
filter_shape=(20,1,5,5),
poolsize=(2,2),
activation_fn=ReLU),
ConvPoolLayer(image_shape=(mini_batch_size,20,12,12),
filter_shape=(40,20,5,5),
poolsize=(2,2),activation_fn=ReLU),
FullyConnectedLayer(n_in=40*4*4,n_out=100,activation_fn=ReLU),
SoftmaxLayer(n_in=100,n_out=10)],mini_batch_size)
>>>net.SGD(expanded_training_data,60,mini_batch_size,0.03,validation_data,test_data,lmbda=0.1)
结果: 99.37%
加入一个100个神经元的隐藏层在fully-connected层:
>>>net=Network([
ConvPoolLayer(image_shape=(mini_batch_size,1,28,28),
filter_shape=(20,1,5,5),
poolsize=(2,2),
activation_fn=ReLU),
ConvPoolLayer(image_shape=(mini_batch_size,20,12,12),
filter_shape=(40,20,5,5),
poolsize=(2,2),
activation_fn=ReLU),
FullyConnectedLayer(n_in=40*4*4,n_out=100,activation_fn=ReLU),
FullyConnectedLayer(n_in=100,n_out=100,activation_fn=ReLU),
SoftmaxLayer(n_in=100,n_out=10)],mini_batch_size)
>>>net.SGD(expanded_training_data,60,mini_batch_size,0.03,validation_data,test_data,lmbda=0.1)
结果: 99.43%, 并没有大的提高有可能overfit
加上dropout到最后一个fully-connected层:
>>>expanded_training_data,_,_=network3.load_data_shared("../data/mnist_expanded.pkl.gz")
>>>net=Network([
ConvPoolLayer(image_shape=(mini_batch_size,1,28,28),
filter_shape=(20,1,5,5),
poolsize=(2,2),activation_fn=ReLU),
ConvPoolLayer(image_shape=(mini_batch_size,20,12,12),
filter_shape=(40,20,5,5),poolsize=(2,2),activation_fn=ReLU),
FullyConnectedLayer(n_in=40*4*4,n_out=1000,activation_fn=ReLU,p_dropout=0.5),
FullyConnectedLayer(n_in=1000,n_out=1000,activation_fn=ReLU,p_dropout=0.5),
SoftmaxLayer(n_in=1000,n_out=10,p_dropout=0.5)],mini_batch_size)
>>>net.SGD(expanded_training_data,40,mini_batch_size,0.03,validation_data,test_data)
结果: 99.60% 显著提高
epochs: 减少到了40
隐藏层有 1000 个神经元
Ensemble of network: 训练多个神经网络, 投票决定结果, 有时会提高
误识别的图像:
CNN本身的convolution层对于overfitting有防止作用: 共享的权重造成convolution filter强迫对于整个图像进行学习
为什么可以克服深度学习里面的一些困难?
用CNN大大减少了参数数量
用dropout减少了overfitting
用Rectified Linear Units代替了sigmoid，避免了overfitting，不同层学习率差别大的问题
用GPU计算更快, 每次更新较少, 但是可以训练很多次
目前的深度神经网络有多深？ (多少层)？
最多有20多层。
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