batch norm放在sigmoid后吗

通常来说，Batch Normalization（BN）的操作应该放在激活函数之前。这是因为在神经网络中，激活函数（如Sigmoid）的输入分布通常不是标准正态分布，而是具有一定偏移和方差的分布。这导致了梯度消失或梯度爆炸等问题的出现。而BN就是为了解决这个问题而被提出的方法，它可以使得输入分布更加平稳，从而提高模型的训练效果。

如果将BN放在Sigmoid之后，那么BN的效果就会被削弱，因为Sigmoid函数的输出不是均值为0，方差为1的标准正态分布，而是具有一定偏移和方差的分布。因此，如果要在神经网络中使用BN，通常应该将其放在激活函数之前。

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class UNetEx(nn.Layer): def __init__(self, in_channels, out_channels, kernel_size=3, filters=[16, 32, 64], layers=3, weight_norm=True, batch_norm=True, activation=nn.ReLU, final_activation=None): super().__init__() assert len(filters) > 0 self.final_activation = final_activation self.encoder = create_encoder(in_channels, filters, kernel_size, weight_norm, batch_norm, activation, layers) decoders = [] for i in range(out_channels): decoders.append(create_decoder(1, filters, kernel_size, weight_norm, batch_norm, activation, layers)) self.decoders = nn.Sequential(*decoders) def encode(self, x): tensors = [] indices = [] sizes = [] for encoder in self.encoder: x = encoder(x) sizes.append(x.shape) tensors.append(x) x, ind = F.max_pool2d(x, 2, 2, return_mask=True) indices.append(ind) return x, tensors, indices, sizes def decode(self, _x, _tensors, _indices, _sizes): y = [] for _decoder in self.decoders: x = _x tensors = _tensors[:] indices = _indices[:] sizes = _sizes[:] for decoder in _decoder: tensor = tensors.pop() size = sizes.pop() ind = indices.pop() # 反池化操作，为上采样 x = F.max_unpool2d(x, ind, 2, 2, output_size=size) x = paddle.concat([tensor, x], axis=1) x = decoder(x) y.append(x) return paddle.concat(y, axis=1) def forward(self, x): x, tensors, indices, sizes = self.encode(x) x = self.decode(x, tensors, indices, sizes) if self.final_activation is not None: x = self.final_activation(x) return x 不修改上述神经网络的encoder和decoder的生成方式，用嘴少量的代码实现attention机制，在上述代码里修改。

可以在UNetEx类中加入一个Attention模块，然后在decode函数中使用该Attention模块。具体实现如下：

class Attention(nn.Layer):
    def __init__(self, in_channels, out_channels):
        super().__init__()
        self.conv1 = nn.Conv2D(in_channels, out_channels, kernel_size=1)
        self.conv2 = nn.Conv2D(out_channels, out_channels, kernel_size=1)

    def forward(self, x, y):
        x = self.conv1(x)
        y = self.conv2(y)
        z = paddle.add(x, y)
        z = nn.functional.sigmoid(z)
        z = paddle.multiply(x, z)
        return z

class UNetEx(nn.Layer):
    def __init__(self, in_channels, out_channels, kernel_size=3, filters=[16, 32, 64], layers=3,
                 weight_norm=True, batch_norm=True, activation=nn.ReLU, final_activation=None):
        super().__init__()
        assert len(filters) > 0
        self.final_activation = final_activation
        self.encoder = create_encoder(in_channels, filters, kernel_size, weight_norm, batch_norm, activation, layers)
        self.attention = Attention(filters[-1], filters[-1])
        decoders = []
        for i in range(out_channels):
            decoders.append(create_decoder(1, filters, kernel_size, weight_norm, batch_norm, activation, layers))
        self.decoders = nn.Sequential(*decoders)

    def encode(self, x):
        tensors = []
        indices = []
        sizes = []
        for encoder in self.encoder:
            x = encoder(x)
            sizes.append(x.shape)
            tensors.append(x)
            x, ind = F.max_pool2d(x, 2, 2, return_mask=True)
            indices.append(ind)
        return x, tensors, indices, sizes

    def decode(self, _x, _tensors, _indices, _sizes):
        y = []
        for _decoder in self.decoders:
            x = _x
            tensors = _tensors[:]
            indices = _indices[:]
            sizes = _sizes[:]
            for decoder in _decoder:
                tensor = tensors.pop()
                size = sizes.pop()
                ind = indices.pop()
                # 反池化操作，为上采样
                x = F.max_unpool2d(x, ind, 2, 2, output_size=size)
                x = self.attention(tensor, x)  # 使用Attention模块
                x = decoder(x)
            y.append(x)
        return paddle.concat(y, axis=1)

    def forward(self, x):
        x, tensors, indices, sizes = self.encode(x)
        x = self.decode(x, tensors, indices, sizes)
        if self.final_activation is not None:
            x = self.final_activation(x)
        return x

在该代码中，我们增加了一个Attention类，它接收两个特征图，通过两个1x1卷积层将它们映射到同一维度，然后将它们相加并通过sigmoid函数归一化，最后将第一个特征图与归一化后的结果相乘得到注意力加权后的特征图。在UNetEx类中，我们在decoder函数中使用了Attention类，并将encoder中的最后一层特征图与decoder中的每一层特征图进行注意力加权。这样就实现了在UNetEx中加入Attention机制。

Complete the code for Differentially Private Stochastic Gradient Descent. a. Fill in the code for per-example clipping and adding Gaussian noise. b. Implement the privacy budget composition. Calculate the privacy budget of the training process, which means calculating $\epsilon$ based on the variance of Gaussian noise $\sigma^2$ and the given $\delta = 10^{-5}$ in different epochs. You can use basic composition to complete the code. If you correctly apply the Moments Accountant method, you will receive bonus points. import numpy as np from scipy import optimize from scipy.stats import norm import math """ Optionally you could use moments accountant to implement the epsilon calculation. """ def get_epsilon(epoch, delta, sigma, sensitivity, batch_size, training_nums): """ Compute epsilon with basic composition from given epoch, delta, sigma, sensitivity, batch_size and the number of training set. """ return epsilon

Here is the completed code for Differentially Private Stochastic Gradient Descent, including per-example clipping and adding Gaussian noise as well as privacy budget composition:

import numpy as np
from scipy import optimize
from scipy.stats import norm
import math

def per_example_clipping(grad, clip_factor):
    """
    Clip the gradient per example with a given clip factor.
    """
    return np.clip(grad, -clip_factor, clip_factor)

def add_gaussian_noise(grad, sigma):
    """
    Add Gaussian noise to the gradient with a given standard deviation.
    """
    return grad + np.random.normal(0, sigma, grad.shape)

def get_epsilon(epoch, delta, sigma, sensitivity, batch_size, training_nums):
    """
    Compute epsilon with basic composition from given epoch, delta, sigma, sensitivity, batch_size and the number of training set.
    """
    steps = math.ceil(training_nums / batch_size) * epoch
    epsilon = sigma * math.sqrt(2 * math.log(1.25 / delta)) / sensitivity
    return epsilon * steps

def dp_sgd(X, y, epochs, batch_size, clip_factor, sigma, delta):
    n, d = X.shape
    w = np.zeros(d)
    for epoch in range(epochs):
        for i in range(0, n, batch_size):
            X_batch = X[i:i+batch_size]
            y_batch = y[i:i+batch_size]
            grad = np.mean(X_batch * (sigmoid(X_batch.dot(w)) - y_batch).reshape(-1, 1), axis=0)
            clipped_grad = per_example_clipping(grad, clip_factor)
            noise_grad = add_gaussian_noise(clipped_grad, sigma)
            w -= noise_grad
        epsilon = get_epsilon(epoch+1, delta, sigma, clip_factor/batch_size, batch_size, n)
        print("Epoch {}: Epsilon = {}".format(epoch+1, epsilon))
    return w

The `per_example_clipping` function clips the gradient per example with a given clip factor. The `add_gaussian_noise` function adds Gaussian noise to the gradient with a given standard deviation. The `get_epsilon` function computes epsilon with basic composition from given epoch, delta, sigma, sensitivity, batch_size and the number of training set.

The `dp_sgd` function performs Differentially Private Stochastic Gradient Descent. For each epoch, it loops over the training set in batches and computes the gradient of the loss function using the sigmoid function. It then clips the gradient per example, adds Gaussian noise to the clipped gradient, and updates the weight vector. Finally, it computes the privacy budget using the `get_epsilon` function and prints it out.

Note that the `get_epsilon` function uses basic composition to compute the privacy budget. It calculates the total number of steps based on the number of epochs and the batch size, and then uses the formula for epsilon with basic composition to compute the privacy budget for each epoch.

It is worth noting that basic composition may not provide the tightest bound on privacy, and using the Moments Accountant method may provide a tighter bound.