简单性的另一个深刻维度在于其平滑性特质，这一特性强调了函数在面对输入数据的微小波动时不应产生剧烈的反应或输出的大幅变化。在机器学习与深度神经网络的领域中，追求模型的平滑性对于提升泛化能力、减少过拟合现象至关重要。平滑性要求模型不仅能够很好地拟合训练数据，还能在未见过的数据上保持稳定的预测性能。
暂退法（Dropout），作为训练神经网络时的一种创新技术，正是基于这一理念而设计的。在前向传播的过程中，暂退法不仅计算每一内部层的输出，还故意向这些层中注入随机噪声，具体做法是按照一定概率随机“丢弃”或暂时忽略网络中的一部分神经元。之所以将这种技术命名为“暂退法”（Dropout），是因为从直观上看，它仿佛是在训练过程中的每一个迭代步骤中，随机地“丢弃”或关闭了一部分神经元的连接。这种随机性的引入，有效地打破了神经网络训练过程中可能形成的固定模式或路径依赖，促使网络能够探索到更多的可能性，进而提升了模型的泛化性能和鲁棒性。通过不断地在训练过程中实施暂退，网络逐渐学会了如何在缺少部分信息的情况下仍然能够做出准确的预测，这对于提高模型在实际应用中的表现具有重要意义。
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
def load_data_fashion_mnist(batch_size, resize=None):
trans = [transforms.ToTensor()]
if resize:
trans.insert(0, transforms.Resize(resize))
trans = transforms.Compose(trans)
mnist_train = torchvision.datasets.FashionMNIST(root="./data", train=True, transform=trans, download=True)
mnist_test = torchvision.datasets.FashionMNIST(root="./data", train=False, transform=trans, download=True)
return (data.DataLoader(mnist_train, batch_size, shuffle=True, num_workers=get_dataloader_workers()),
data.DataLoader(mnist_test, batch_size, shuffle=False, num_workers=get_dataloader_workers()))
def accurancy(y_hat, y):
if len(y_hat.shape) > 1 and y_hat.shape[1] > 1:
y_hat = y_hat.argmax(axis=1)
cmp = y_hat.type(y.dtype) == y
return float(cmp.type(y.dtype).sum())
class Accumulator:
def __init__(self, n) -> None:
self.data = [0.0]*n
def add(self, *args):
self.data = [a + float(b) for a, b in zip(self.data, args)]
def reset(self):
self.data = [0.0] * len(self.data)
def __getitem__(self, idx):
return self.data[idx]
def evaluate_accurancy(net, data_iter):
if isinstance(net, torch.nn.Module):
net.eval()
metric = Accumulator(2)
with torch.no_grad():
for X, y in data_iter:
metric.add(accurancy(net(X), y), y.numel())
return metric[0] / metric[1]
def train_epoch_ch3(net, train_iter, loss, updater):
if isinstance(net, torch.nn.Module):
net.train()
metric = Accumulator(3)
for X, y in train_iter:
y_hat = net(X)
l = loss(y_hat, y)
if isinstance(updater, torch.optim.Optimizer):
updater.zero_grad()
l.mean().backward()
updater.step()
else:
l.sum().backward()
updater(X.shape[0])
metric.add(float(l.sum()), accurancy(y_hat, y), y.numel())
return metric[0] / metric[1], metric[1] / metric[2]
def set_axes(axes, xlable, ylable, xlim, ylim, xscale, yscale, legend):
axes.set_xlabel(xlable)
axes.set_ylabel(ylable)
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, xlable=None, ylable=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.axes, ]
self.config_axes = lambda: set_axes(self.axes[0], xlable, ylable, 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=[y]
n = len(y)
if not hasattr(x, "__len__"):
x = [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[i].append(a)
self.Y[i].append(b)
self.axes[0].cla()
for x, y, fmt in zip(self.X, self.Y, self.fmts):
self.axes[0].plot(x, y, fmt)
self.config_axes()
def train_ch3(net, train_iter, test_iter, loss, num_epochs, updater):
animator = Animator(xlable='epoch', xlim=[1, num_epochs], ylim=[0.3, 0.9], legend=['train loss', "train acc", "test acc"])
for epoch in range(num_epochs):
train_metrics = train_epoch_ch3(net, train_iter, loss, updater)
test_acc = evaluate_accurancy(net, test_iter)
animator.add(epoch+1, train_metrics+(test_acc, ))
train_loss, train_acc = train_metrics
assert train_loss < 0.5, train_loss
assert train_acc < 1 and train_acc > 0.7, train_acc
assert test_acc < 1 and test_acc > 0.7, test_acc
dropout1, dropout2 = 0.2, 0.5
num_epochs, lr, batch_size = 10, 0.5, 256
loss = nn.CrossEntropyLoss(reduction='none')
train_iter, test_iter = load_data_fashion_mnist(batch_size)
net = nn.Sequential(nn.Flatten(),
nn.Linear(784, 256),
nn.ReLU(),
nn.Dropout(dropout1),
nn.Linear(256, 256),
nn.ReLU(),
nn.Dropout(dropout2),
nn.Linear(256, 10))
def init_weights(m):
if type(m) == nn.Linear:
nn.init.normal_(m.weight, std=0.01)
net.apply(init_weights)
trainer = torch.optim.SGD(net.parameters(), lr=lr)
train_ch3(net, train_iter, test_iter, loss, num_epochs, trainer)
plt.show()
