问题一，若设置gamma=1，则states无法更新，学习率为固定的值，由于之前states初始化为0，将使得学习率过大，从而导致无法收敛，loss=nan
为什么在11.6节中使用泄露平均值的时候第二项系数为1，而这里第二项系数是(1-\gamma)呢，只是因为是平方项所以用更小的系数去约束它吗？那么是不是其实不一定要用(1-\gamma)呢？如果是因为“平均值”的定义，那么11.6节的公式是否存在错误？
# 练习2
def rmsprop_2d(x1, x2, s1, s2):
g1, g2, eps = 0.2 * x1 + 0.2 * x2 + 4 * x1 - 4 * x2, 0.2 * x1 + 0.2 * x2 - 4 * x1 + 4 * x2, 1e-6
s1 = gamma * s1 + (1 - gamma) * g1 ** 2
s2 = gamma * s2 + (1 - gamma) * g2 ** 2
x1 -= eta / math.sqrt(s1 + eps) * g1
x2 -= eta / math.sqrt(s2 + eps) * g2
return x1, x2, s1, s2
def f_2d(x1, x2):
return 0.1 * (x1+x2) ** 2 + 2 * (x1-x2) ** 2
eta, gamma = 0.6, 0.9
d2l.show_trace_2d(f_2d, d2l.train_2d(rmsprop_2d))
# 练习3
# AlexNet
from torch import nn
from d2l import torch as d2l
net = nn.Sequential(
nn.Conv2d(1, 6, kernel_size=5, padding=2), nn.Sigmoid(),
nn.AvgPool2d(kernel_size=2, stride=2),
nn.Conv2d(6, 16, kernel_size=5), nn.Sigmoid(),
nn.AvgPool2d(kernel_size=2, stride=2),
nn.Flatten(),
nn.Linear(16 * 5 * 5, 120), nn.Sigmoid(),
nn.Linear(120, 84), nn.Sigmoid(),
nn.Linear(84, 10))
def train_ch6_2(net, train_iter, test_iter, num_epochs, lr, alpha, device):
"""用GPU训练模型(在第六章定义)"""
def init_weights(m):
if type(m) == nn.Linear or type(m) == nn.Conv2d:
nn.init.xavier_uniform_(m.weight)
net.apply(init_weights)
print('training on', device)
net.to(device)
optimizer = torch.optim.RMSprop(net.parameters(), lr=lr, alpha=alpha)
# optimizer = torch.optim.SGD(net.parameters(), lr=lr)
loss = nn.CrossEntropyLoss()
animator = d2l.Animator(xlabel='epoch', xlim=[1, num_epochs],
legend=['train loss', 'train acc', 'test acc'])
timer, num_batches = d2l.Timer(), len(train_iter)
for epoch in range(num_epochs):
# 训练损失之和，训练准确率之和，样本数
metric = d2l.Accumulator(3)
net.train()
for i, (X, y) in enumerate(train_iter):
timer.start()
optimizer.zero_grad()
X, y = X.to(device), y.to(device)
y_hat = net(X)
l = loss(y_hat, y)
l.backward()
optimizer.step()
with torch.no_grad():
metric.add(l * X.shape[0], d2l.accuracy(y_hat, y), X.shape[0])
timer.stop()
train_l = metric[0] / metric[2]
train_acc = metric[1] / metric[2]
if (i + 1) % (num_batches // 5) == 0 or i == num_batches - 1:
animator.add(epoch + (i + 1) / num_batches,
(train_l, train_acc, None))
test_acc = d2l.evaluate_accuracy_gpu(net, test_iter)
animator.add(epoch + 1, (None, None, test_acc))
print(f'loss {train_l:.3f}, train acc {train_acc:.3f}, '
f'test acc {test_acc:.3f}')
print(f'{metric[2] * num_epochs / timer.sum():.1f} examples/sec '
f'on {str(device)}')
batch_size = 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size=batch_size)
lr, alpha, num_epochs = 0.9, 0.6, 10
train_ch6_2(net, train_iter, test_iter, num_epochs, lr, alpha, d2l.try_gpu())
效果很差的样子，不知道是不是正常的
发现问题了，学习率应该用0.01，只有SGD能用零点几的学习率