一起读《动手学深度学习（PyTorch版）》- 权重衰减（weight decay）
<div class='showpostmsg'><article data-content="[{"type":"block","id":"3060-1621846615933","name":"paragraph","data":{},"nodes":[{"type":"text","id":"p5PQ-1621846617594","leaves":[{"text":"weight-decay，用于解决过拟合问题，其中用到范数，将权重进行欧几里得范数，得到惩罚函数为 Sum(w^2) / 2，要保证权重向量比较小， 最常用方法是将其范数作为惩罚项加到最小化损失的问题中，将原来的训练目标最小化训练标签上的预测损失， 调整为最小化预测损失和惩罚项之和。现在，如果权重向量增长的太大， 优化算法会更集中于最小化权重范数","marks":[]}]}],"state":{}}]"><p>weight-decay，用于解决过拟合问题，其中用到范数，将权重进行欧几里得范数，得到惩罚函数为 Sum(w^2) / 2，要保证权重向量比较小， 最常用方法是将其范数作为惩罚项加到最小化损失的问题中，将原来的训练目标最小化训练标签上的预测损失， 调整为最小化预测损失和惩罚项之和。现在，如果权重向量增长的太大， 优化算法会更集中于最小化权重范数</p>
<p> </p>
<article data-content="[{"type":"block","id":"64Ob-1730025844954","name":"paragraph","data":{},"nodes":[{"type":"text","id":"RyZl-1730025844953","leaves":[{"text":"损失函数","marks":[]}]}],"state":{}}]">
<p>损失函数</p>
<p> </p>
<article data-content="[{"type":"block","id":"xWiX-1730026079009","name":"paragraph","data":{},"nodes":[{"type":"text","id":"Jzc6-1730026079008","leaves":[{"text":"预测损失和惩罚项之和","marks":[]}]}],"state":{}}]">
<p>预测损失和惩罚项之和</p>
<pre>
<code>import torch
import torchvision
from torch.utils import data
from torchvision import transforms
import matplotlib.pyplot as plt
from torch import nn
def get_dataloader_workers():
return 6
class Accumulator:
def __init__(self, n) -> None:
self.data = *n
def add(self, *args):
# args is a tupe
self.data =
def reset(self):
self.data = * len(self.data)
def __getitem__(self, idx):
return self.data
def set_axes(axes, xlabel, ylabel, xlim, ylim, xscale, yscale, legend):
axes.set_xlabel(xlabel)
axes.set_ylabel(ylabel)
axes.set_xscale(xscale)
axes.set_yscale(yscale)
axes.set_xlim(xlim)
axes.set_ylim(ylim)
if legend:
axes.legend(legend)
axes.grid()
class Animator:
def __init__(self, xlabel=None, ylabel=None, legend=None, xlim=None, ylim=None,
xscale='linear', yscale='linear',fmts=('-','m--','g-.','r:'), nrows=1, ncols=1, figsize=(3.5, 2.5)):
if legend is None:
legend = []
self.fig, self.axes = plt.subplots(nrows, ncols, figsize=figsize)
if nrows * ncols == 1:
self.axes =
self.config_axes = lambda: set_axes(self.axes, xlabel, ylabel, xlim, ylim, xscale, yscale, legend)
self.X, self.Y, self.fmts = None, None, fmts
def add(self, x, y):
if not hasattr(y, "__len__"):
y=
n = len(y)
if not hasattr(x, "__len__"):
x = * n
if not self.X:
self.X = [[] for _ in range(n)]
if not self.Y:
self.Y = [[] for _ in range(n)]
for i, (a,b) in enumerate(zip(x, y)):
if a is not None and b is not None:
self.X.append(a)
self.Y.append(b)
self.axes.cla()
for x, y, fmt in zip(self.X, self.Y, self.fmts):
self.axes.plot(x, y, fmt)
self.config_axes()
def evaluate_loss(net, data_iter, loss):
metric = Accumulator(2)
for X, y in data_iter:
out = net(X)
y = y.reshape(out.shape)
l = loss(out, y)
metric.add(l.sum(), l.numel())
return metric / metric
def load_array(data_arrays, batch_size, is_train=True):
dataset = data.TensorDataset(*data_arrays)
return data.DataLoader(dataset, batch_size, shuffle=is_train, num_workers=get_dataloader_workers())
def synthetic_data(w, b, num_examples):
X = torch.normal(0, 1, (num_examples, len(w)))
y = torch.matmul(X, w) + b
y += torch.normal(0, 0.01, y.shape)
return X, y.reshape((-1, 1))
n_train, n_test, num_inputs, batch_size = 20, 100, 200, 5
true_w, true_b = torch.ones((num_inputs, 1)) * 0.01, 0.05
train_data = synthetic_data(true_w, true_b, n_train)
train_iter = load_array(train_data, batch_size)
test_data = synthetic_data(true_w, true_b, n_test)
test_iter = load_array(test_data, batch_size, is_train=False)
def train_concise(wd):
net = nn.Sequential(nn.Linear(num_inputs, 1))
for param in net.parameters():
param.data.normal_()
loss = nn.MSELoss(reduction='none')
num_epochs, lr = 100, 0.003
trainer = torch.optim.SGD([
{"params":net.weight,'weight_decay': wd},
{"params":net.bias}], lr=lr)
animator = Animator(xlabel='epochs', ylabel='loss', yscale='log',
xlim=, legend=['train', 'test'])
for epoch in range(num_epochs):
for X, y in train_iter:
trainer.zero_grad()
l = loss(net(X), y)
l.mean().backward()
trainer.step()
if (epoch + 1) % 5 == 0:
animator.add(epoch + 1,
(evaluate_loss(net, train_iter, loss),
evaluate_loss(net, test_iter, loss)))
print('weight', net.weight.norm().item())
train_concise(0)
plt.show()</code></pre>
<p> </p>
<article data-content="[{"type":"block","id":"neBp-1730026310109","name":"paragraph","data":{},"nodes":[{"type":"text","id":"dWm6-1730026310108","leaves":[{"text":"可以看到，当不启用权重衰减时，测试loss基本不下降，也就是过拟合的现象","marks":[]}]}],"state":{}}]">
<p>可以看到，当不启用权重衰减时，测试loss基本不下降，也就是过拟合的现象</p>
<pre>
<code>train_concise(5)</code></pre>
<p> </p>
<article data-content="[{"type":"block","id":"9z0p-1730026506587","name":"paragraph","data":{},"nodes":[{"type":"text","id":"mgOS-1730026506585","leaves":[{"text":"启用权重衰减，控制量为5时，可以看到实际的测试loss也是逐渐减小的","marks":[]}]}],"state":{}}]">
<p>启用权重衰减，控制量为5时，可以看到实际的测试loss也是逐渐减小的</p>
<p> </p>
<article data-content="[{"type":"block","id":"niHE-1730027318588","name":"paragraph","data":{},"nodes":[{"type":"text","id":"rDgj-1730027318586","leaves":[{"text":"继续增强权重衰减的效果","marks":[]}]}],"state":{}}]">
<p>继续增强权重衰减的效果</p>
</article>
</article>
</article>
</article>
</article>
</article>
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