Pytorch：如何将 L1 正则化器添加到激活中？

Question

我想将 L1 正则化器添加到 ReLU 的激活输出中。 更一般地，如何将正则化器仅添加到网络中的特定层？

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相关资料：

• This similar post 指的是添加L2正则化，但它似乎将正则化惩罚添加到网络的所有层。

• nn.modules.loss.L1Loss() 似乎相关，但我还不明白如何使用它。

• 遗留模块L1Penalty 似乎也很重要，但为什么它被弃用了？

Answer 1

这里是你如何做到这一点：

• 在您要应用 L1 正则化的模块的前向返回最终输出和层输出中
• loss 变量将是输出 w.r.t 的交叉熵损失的总和。目标和 L1 处罚。

这是一个示例代码

import torch
from torch.autograd import Variable
from torch.nn import functional as F


class MLP(torch.nn.Module):
    def __init__(self):
        super(MLP, self).__init__()
        self.linear1 = torch.nn.Linear(128, 32)
        self.linear2 = torch.nn.Linear(32, 16)
        self.linear3 = torch.nn.Linear(16, 2)

    def forward(self, x):
        layer1_out = F.relu(self.linear1(x))
        layer2_out = F.relu(self.linear2(layer1_out))
        out = self.linear3(layer2_out)
        return out, layer1_out, layer2_out

batchsize = 4
lambda1, lambda2 = 0.5, 0.01

model = MLP()
optimizer = torch.optim.SGD(model.parameters(), lr=1e-4)

# usually following code is looped over all batches 
# but let's just do a dummy batch for brevity

inputs = Variable(torch.rand(batchsize, 128))
targets = Variable(torch.ones(batchsize).long())

optimizer.zero_grad()
outputs, layer1_out, layer2_out = model(inputs)
cross_entropy_loss = F.cross_entropy(outputs, targets)

all_linear1_params = torch.cat([x.view(-1) for x in model.linear1.parameters()])
all_linear2_params = torch.cat([x.view(-1) for x in model.linear2.parameters()])
l1_regularization = lambda1 * torch.norm(all_linear1_params, 1)
l2_regularization = lambda2 * torch.norm(all_linear2_params, 2)

loss = cross_entropy_loss + l1_regularization + l2_regularization
loss.backward()
optimizer.step()

Answer 2

@Sasank Chilamkurthy 正则化应该是模型每一层的权重参数，而不是每一层的输出。请看下面： Regularization

import torch
from torch.autograd import Variable
from torch.nn import functional as F


class MLP(torch.nn.Module):
    def __init__(self):
        super(MLP, self).__init__()
        self.linear1 = torch.nn.Linear(128, 32)
        self.linear2 = torch.nn.Linear(32, 16)
        self.linear3 = torch.nn.Linear(16, 2)
    def forward(self, x):
        layer1_out = F.relu(self.linear1(x))
        layer2_out = F.relu(self.linear2(layer1_out))
        out = self.linear3(layer2_out)
        return out

batchsize = 4
lambda1, lambda2 = 0.5, 0.01

model = MLP()
optimizer = torch.optim.SGD(model.parameters(), lr=1e-4)

inputs = Variable(torch.rand(batchsize, 128))
targets = Variable(torch.ones(batchsize).long())
l1_regularization, l2_regularization = torch.tensor(0), torch.tensor(0)

optimizer.zero_grad()
outputs = model(inputs)
cross_entropy_loss = F.cross_entropy(outputs, targets)
for param in model.parameters():
    l1_regularization += torch.norm(param, 1)**2
    l2_regularization += torch.norm(param, 2)**2

loss = cross_entropy_loss + l1_regularization + l2_regularization
loss.backward()
optimizer.step()

Answer 3

我认为原帖想要对 ReLU 的输出进行正则化，所以正则化器应该在输出上，而不是网络的权重上。它们不一样！

• 使用 l1-norm 正则化权重正在训练具有稀疏权重的神经网络

• 使用 l1-norm 正则化层的输出正在训练一个网络，该网络具有该特定层的稀疏输出。

以上这些答案（包括已接受的答案）都没有抓住重点，或者我误解了原始帖子的问题。

Answer 4

所有（其他当前）响应在某种程度上都是不正确的，因为问题是关于向激活添加正则化。 This one 最接近，因为它建议对输出的范数求和，这是正确的，但代码对权重的范数求和，这是不正确的。

正确的方法不是修改网络代码，而是通过前向钩子捕获输出，如OutputHook 类。从那里，输出的范数的总和很简单，但需要注意每次迭代清除捕获的输出。

import torch


class OutputHook(list):
    """ Hook to capture module outputs.
    """
    def __call__(self, module, input, output):
        self.append(output)


class MLP(torch.nn.Module):
    def __init__(self):
        super(MLP, self).__init__()
        self.linear1 = torch.nn.Linear(128, 32)
        self.linear2 = torch.nn.Linear(32, 16)
        self.linear3 = torch.nn.Linear(16, 2)
        # Instantiate ReLU, so a hook can be registered to capture its output.
        self.relu = torch.nn.ReLU()

    def forward(self, x):
        layer1_out = self.relu(self.linear1(x))
        layer2_out = self.relu(self.linear2(layer1_out))
        out = self.linear3(layer2_out)
        return out


batch_size = 4
l1_lambda = 0.01

model = MLP()
optimizer = torch.optim.SGD(model.parameters(), lr=1e-4)
# Register hook to capture the ReLU outputs. Non-trivial networks will often
# require hooks to be applied more judiciously.
output_hook = OutputHook()
model.relu.register_forward_hook(output_hook)

inputs = torch.rand(batch_size, 128)
targets = torch.ones(batch_size).long()

optimizer.zero_grad()
outputs = model(inputs)
cross_entropy_loss = torch.nn.functional.cross_entropy(outputs, targets)

# Compute the L1 penalty over the ReLU outputs captured by the hook.
l1_penalty = 0.
for output in output_hook:
    l1_penalty += torch.norm(output, 1)
l1_penalty *= l1_lambda

loss = cross_entropy_loss + l1_penalty
loss.backward()
optimizer.step()
output_hook.clear()

Answer 5

您可以使用以下代码将模型my_layer 的单层权重的 L1 正则化应用于损失函数：

def l1_penalty(params, l1_lambda=0.001):
    """Returns the L1 penalty of the params."""
    l1_norm = sum(p.abs().sum() for p in params)
    return l1_lambda*l1_norm

loss = loss_fn(outputs, labels) + l1_penalty(my_layer.parameters())