low precision training 的代码

下面是一个使用 PyTorch 实现的 low precision training 的示例代码：

import torch
import torch.nn as nn
import torch.optim as optim
from torch.autograd import Variable

# 定义一个使用半精度浮点数的模型
class LowPrecisionModel(nn.Module):
    def __init__(self):
        super(LowPrecisionModel, self).__init__()
        self.fc1 = nn.Linear(784, 512)
        self.fc2 = nn.Linear(512, 10)

    def forward(self, x):
        x = x.view(-1, 784)
        x = nn.functional.relu(self.fc1(x))
        x = nn.functional.relu(self.fc2(x))
        return x

# 定义一个使用半精度浮点数的优化器
class LowPrecisionOptimizer(optim.SGD):
    def __init__(self, params, lr=0.01, momentum=0.9, weight_decay=0, nesterov=False):
        super(LowPrecisionOptimizer, self).__init__(params, lr=lr, momentum=momentum, weight_decay=weight_decay, nesterov=nesterov)

    def step(self, closure=None):
        for group in self.param_groups:
            for p in group['params']:
                if p.grad is None:
                    continue
                grad = p.grad.data.float()
                p.data = p.data.half()
                grad = grad.half()
                state = self.state[p]
                if 'momentum_buffer' not in state:
                    state['momentum_buffer'] = torch.zeros_like(p.data)
                buf = state['momentum_buffer']
                buf.mul_(group['momentum']).add_(grad)
                if group['nesterov']:
                    grad = grad.add(group['momentum'] * buf)
                else:
                    grad = buf
                p.data.add_(-group['lr'], grad)
        return loss

# 加载数据集
train_loader = torch.utils.data.DataLoader(
    torchvision.datasets.MNIST('data', train=True, download=True,
                               transform=torchvision.transforms.Compose([
                                   torchvision.transforms.ToTensor(),
                                   torchvision.transforms.Normalize(
                                       (0.1307,), (0.3081,))
                               ])),
    batch_size=64, shuffle=True)

# 初始化模型和优化器
model = LowPrecisionModel()
optimizer = LowPrecisionOptimizer(model.parameters(), lr=0.01)

# 训练模型
for epoch in range(10):
    for batch_idx, (data, target) in enumerate(train_loader):
        data, target = Variable(data), Variable(target)
        optimizer.zero_grad()
        output = model(data)
        loss = nn.functional.cross_entropy(output, target)
        loss.backward()
        optimizer.step()
        if batch_idx % 100 == 0:
            print('Train Epoch: {} [{}/{} ({:.0f}%)]\tLoss: {:.6f}'.format(
                epoch, batch_idx * len(data), len(train_loader.dataset),
                100. * batch_idx / len(train_loader), loss.data.item()))

在这个示例代码中，我们定义了一个名为 `LowPrecisionModel` 的模型，它使用半精度浮点数进行计算。我们还定义了一个名为 `LowPrecisionOptimizer` 的优化器，它可以将模型参数和梯度转换为半精度浮点数进行计算。在训练过程中，我们使用 `LowPrecisionOptimizer` 优化器来更新模型参数，以达到低精度训练的效果。