theano实现使用自适应的 Dropout 方法来动态调整VGG网络的 Dropout 概率值

自适应 Dropout 方法可以根据网络的不同层次和输入数据的特征，动态调整 Dropout 概率值，从而提高模型的泛化能力。在 Theano 框架中，可以通过以下代码实现使用自适应 Dropout 方法来动态调整 VGG 网络的 Dropout 概率值：

import theano
import theano.tensor as T
from theano.sandbox.rng_mrg import MRG_RandomStreams

def dropout(input, p, rng):
    srng = MRG_RandomStreams(rng.randint(999999))
    mask = srng.binomial(n=1, p=1-p, size=input.shape, dtype=theano.config.floatX)
    output = input * mask
    return output

def adaptive_dropout(input, p, rng):
    p = 0.5 * p
    if input.ndim == 4:
        input_shape = input.shape
        input = T.flatten(input, 2)
        mean = T.mean(input, axis=1, keepdims=True)
        var = T.var(input, axis=1, keepdims=True)
        alpha = theano.shared(np.ones((input_shape[1], 1), dtype=theano.config.floatX))
        rho = theano.shared(np.ones((input_shape[1], 1), dtype=theano.config.floatX))
        alpha_new = T.nnet.sigmoid(T.dot(alpha, T.log(1+T.exp(rho*(var-mean**2)/mean**2))))
        p_new = 1 - alpha_new
        output = dropout(input, p_new, rng)
        output_shape = (input_shape[0], input_shape[1], input_shape[2], input_shape[3])
        output = T.reshape(output, output_shape)
        return output
    else:
        return dropout(input, p, rng)

其中，`dropout` 函数实现了标准的 Dropout 方法；`adaptive_dropout` 函数实现了自适应 Dropout 方法。在自适应 Dropout 方法中，首先将 Dropout 概率值减半，然后计算输入数据在每个通道上的均值和方差，并通过一个神经网络计算每个通道的 `alpha` 值。最后，根据 `alpha` 值计算新的 Dropout 概率值，然后应用 Dropout。

在 VGG 网络中使用自适应 Dropout 方法，可以在每个卷积层和全连接层后添加一个自适应 Dropout 层，如下所示：

import numpy as np
import lasagne

def build_vgg(input_var=None):
    network = lasagne.layers.InputLayer(shape=(None, 3, 224, 224), input_var=input_var)
    network = lasagne.layers.Conv2DLayer(network, num_filters=64, filter_size=(3, 3), pad=1, flip_filters=False)
    network = adaptive_dropout(network, p=0.3, rng=np.random.RandomState(1234))
    network = lasagne.layers.Conv2DLayer(network, num_filters=64, filter_size=(3, 3), pad=1, flip_filters=False)
    network = adaptive_dropout(network, p=0.3, rng=np.random.RandomState(1234))
    network = lasagne.layers.Pool2DLayer(network, pool_size=(2, 2), mode='max')
    network = lasagne.layers.Conv2DLayer(network, num_filters=128, filter_size=(3, 3), pad=1, flip_filters=False)
    network = adaptive_dropout(network, p=0.4, rng=np.random.RandomState(1234))
    network = lasagne.layers.Conv2DLayer(network, num_filters=128, filter_size=(3, 3), pad=1, flip_filters=False)
    network = adaptive_dropout(network, p=0.4, rng=np.random.RandomState(1234))
    network = lasagne.layers.Pool2DLayer(network, pool_size=(2, 2), mode='max')
    network = lasagne.layers.Conv2DLayer(network, num_filters=256, filter_size=(3, 3), pad=1, flip_filters=False)
    network = adaptive_dropout(network, p=0.4, rng=np.random.RandomState(1234))
    network = lasagne.layers.Conv2DLayer(network, num_filters=256, filter_size=(3, 3), pad=1, flip_filters=False)
    network = adaptive_dropout(network, p=0.4, rng=np.random.RandomState(1234))
    network = lasagne.layers.Conv2DLayer(network, num_filters=256, filter_size=(3, 3), pad=1, flip_filters=False)
    network = adaptive_dropout(network, p=0.4, rng=np.random.RandomState(1234))
    network = lasagne.layers.Pool2DLayer(network, pool_size=(2, 2), mode='max')
    network = lasagne.layers.Conv2DLayer(network, num_filters=512, filter_size=(3, 3), pad=1, flip_filters=False)
    network = adaptive_dropout(network, p=0.4, rng=np.random.RandomState(1234))
    network = lasagne.layers.Conv2DLayer(network, num_filters=512, filter_size=(3, 3), pad=1, flip_filters=False)
    network = adaptive_dropout(network, p=0.4, rng=np.random.RandomState(1234))
    network = lasagne.layers.Conv2DLayer(network, num_filters=512, filter_size=(3, 3), pad=1, flip_filters=False)
    network = adaptive_dropout(network, p=0.4, rng=np.random.RandomState(1234))
    network = lasagne.layers.Pool2DLayer(network, pool_size=(2, 2), mode='max')
    network = lasagne.layers.Conv2DLayer(network, num_filters=512, filter_size=(3, 3), pad=1, flip_filters=False)
    network = adaptive_dropout(network, p=0.4, rng=np.random.RandomState(1234))
    network = lasagne.layers.Conv2DLayer(network, num_filters=512, filter_size=(3, 3), pad=1, flip_filters=False)
    network = adaptive_dropout(network, p=0.4, rng=np.random.RandomState(1234))
    network = lasagne.layers.Conv2DLayer(network, num_filters=512, filter_size=(3, 3), pad=1, flip_filters=False)
    network = adaptive_dropout(network, p=0.4, rng=np.random.RandomState(1234))
    network = lasagne.layers.Pool2DLayer(network, pool_size=(2, 2), mode='max')
    network = lasagne.layers.DenseLayer(network, num_units=4096)
    network = adaptive_dropout(network, p=0.5, rng=np.random.RandomState(1234))
    network = lasagne.layers.DenseLayer(network, num_units=4096)
    network = adaptive_dropout(network, p=0.5, rng=np.random.RandomState(1234))
    network = lasagne.layers.DenseLayer(network, num_units=1000, nonlinearity=lasagne.nonlinearities.softmax)
    return network

其中，`adaptive_dropout` 函数的参数 `p` 表示初始的 Dropout 概率值，`rng` 表示随机数生成器。在 VGG 网络中，每个卷积层和全连接层后添加一个自适应 Dropout 层，并根据不同层次的特征动态调整 Dropout 概率值。这样可以提高模型的泛化能力，防止过拟合。