使用自定义函数融合卷积和批量归一化

创建日期：2021 年 7 月 22 日 | 最后更新：2023 年 4 月 18 日 | 最后验证：2024 年 11 月 5 日

将相邻的卷积层和批量归一化层融合在一起通常是一种推理时优化，以提高运行时间。这通常是通过完全消除批量归一化层并更新前一个卷积层的权重和偏置来实现的 [0]。然而，这种技术不适用于模型训练。

在本教程中，我们将展示一种不同的层融合技术，该技术可以在训练期间应用。这种优化的目标不是提高运行时间，而是减少内存使用。

这种优化背后的想法是认识到卷积和批量归一化（以及许多其他算子）在前向传播期间都需要保存输入的副本以供反向传播使用。对于大批量大小，这些保存的输入占用了大部分内存，因此能够避免为每一对卷积和批量归一化分配另一个输入张量可以显著减少内存消耗。

在本教程中，我们通过将卷积和批量归一化组合成一个单一的层（作为自定义函数）来避免这种额外的分配。在这个组合层的前向传播中，我们像往常一样执行卷积和批量归一化，唯一的区别是我们只保存卷积的输入。为了获得批量归一化的输入（这是通过它进行反向传播所必需的），我们在反向传播过程中再次重新计算卷积的前向传播。

需要注意的是，这种优化的使用是具有情境性的。虽然（通过避免保存一个缓冲区）我们在前向传播结束时总是减少了内存分配，但在某些情况下，分配的峰值内存可能实际上并没有减少。详情请参阅最后一节。

为了简化，在本教程中，我们硬编码了 Conv2D 的 bias=False、stride=1、padding=0、dilation=1 和 groups=1。对于 BatchNorm2D，我们硬编码了 eps=1e-3、momentum=0.1、affine=False 和 track_running_statistics=False。另一个小区别是，我们在计算批量归一化时，在平方根之外的分母中添加了 epsilon。

[0] https://nenadmarkus.com/p/fusing-batchnorm-and-conv/

卷积的反向传播公式实现

实现自定义函数需要我们自己实现反向传播。在这种情况下，我们需要 Conv2D 和 BatchNorm2D 的反向传播公式。最终我们将它们链接到我们统一的反向函数中，但在下面我们首先将它们实现为自己的自定义函数，以便我们可以分别验证它们的正确性

import torch
from torch.autograd.function import once_differentiable
import torch.nn.functional as F

def convolution_backward(grad_out, X, weight):
    grad_input = F.conv2d(X.transpose(0, 1), grad_out.transpose(0, 1)).transpose(0, 1)
    grad_X = F.conv_transpose2d(grad_out, weight)
    return grad_X, grad_input

class Conv2D(torch.autograd.Function):
    @staticmethod
    def forward(ctx, X, weight):
        ctx.save_for_backward(X, weight)
        return F.conv2d(X, weight)

    # Use @once_differentiable by default unless we intend to double backward
    @staticmethod
    @once_differentiable
    def backward(ctx, grad_out):
        X, weight = ctx.saved_tensors
        return convolution_backward(grad_out, X, weight)

使用 gradcheck 进行测试时，重要的是使用双精度浮点数

weight = torch.rand(5, 3, 3, 3, requires_grad=True, dtype=torch.double)
X = torch.rand(10, 3, 7, 7, requires_grad=True, dtype=torch.double)
torch.autograd.gradcheck(Conv2D.apply, (X, weight))

True

批量归一化的反向传播公式实现

批量归一化有两种模式：训练模式和 eval 模式。在训练模式下，样本统计信息是输入的函数。在 eval 模式下，我们使用保存的运行统计信息，这些统计信息不是输入的函数。这使得非训练模式的反向传播显著简化。下面我们只实现和测试训练模式的情况。

def unsqueeze_all(t):
    # Helper function to ``unsqueeze`` all the dimensions that we reduce over
    return t[None, :, None, None]

def batch_norm_backward(grad_out, X, sum, sqrt_var, N, eps):
    # We use the formula: ``out = (X - mean(X)) / (sqrt(var(X)) + eps)``
    # in batch norm 2D forward. To simplify our derivation, we follow the
    # chain rule and compute the gradients as follows before accumulating
    # them all into a final grad_input.
    #  1) ``grad of out wrt var(X)`` * ``grad of var(X) wrt X``
    #  2) ``grad of out wrt mean(X)`` * ``grad of mean(X) wrt X``
    #  3) ``grad of out wrt X in the numerator`` * ``grad of X wrt X``
    # We then rewrite the formulas to use as few extra buffers as possible
    tmp = ((X - unsqueeze_all(sum) / N) * grad_out).sum(dim=(0, 2, 3))
    tmp *= -1
    d_denom = tmp / (sqrt_var + eps)**2  # ``d_denom = -num / denom**2``
    # It is useful to delete tensors when you no longer need them with ``del``
    # For example, we could've done ``del tmp`` here because we won't use it later
    # In this case, it's not a big difference because ``tmp`` only has size of (C,)
    # The important thing is avoid allocating NCHW-sized tensors unnecessarily
    d_var = d_denom / (2 * sqrt_var)  # ``denom = torch.sqrt(var) + eps``
    # Compute ``d_mean_dx`` before allocating the final NCHW-sized grad_input buffer
    d_mean_dx = grad_out / unsqueeze_all(sqrt_var + eps)
    d_mean_dx = unsqueeze_all(-d_mean_dx.sum(dim=(0, 2, 3)) / N)
    # ``d_mean_dx`` has already been reassigned to a C-sized buffer so no need to worry

    # ``(1) unbiased_var(x) = ((X - unsqueeze_all(mean))**2).sum(dim=(0, 2, 3)) / (N - 1)``
    grad_input = X * unsqueeze_all(d_var * N)
    grad_input += unsqueeze_all(-d_var * sum)
    grad_input *= 2 / ((N - 1) * N)
    # (2) mean (see above)
    grad_input += d_mean_dx
    # (3) Add 'grad_out / <factor>' without allocating an extra buffer
    grad_input *= unsqueeze_all(sqrt_var + eps)
    grad_input += grad_out
    grad_input /= unsqueeze_all(sqrt_var + eps)  # ``sqrt_var + eps > 0!``
    return grad_input

class BatchNorm(torch.autograd.Function):
    @staticmethod
    def forward(ctx, X, eps=1e-3):
        # Don't save ``keepdim`` values for backward
        sum = X.sum(dim=(0, 2, 3))
        var = X.var(unbiased=True, dim=(0, 2, 3))
        N = X.numel() / X.size(1)
        sqrt_var = torch.sqrt(var)
        ctx.save_for_backward(X)
        ctx.eps = eps
        ctx.sum = sum
        ctx.N = N
        ctx.sqrt_var = sqrt_var
        mean = sum / N
        denom = sqrt_var + eps
        out = X - unsqueeze_all(mean)
        out /= unsqueeze_all(denom)
        return out

    @staticmethod
    @once_differentiable
    def backward(ctx, grad_out):
        X, = ctx.saved_tensors
        return batch_norm_backward(grad_out, X, ctx.sum, ctx.sqrt_var, ctx.N, ctx.eps)

使用 gradcheck 进行测试

a = torch.rand(1, 2, 3, 4, requires_grad=True, dtype=torch.double)
torch.autograd.gradcheck(BatchNorm.apply, (a,), fast_mode=False)

True

融合卷积和批量归一化

现在大部分工作已经完成，我们可以将它们组合起来。请注意，在 (1) 中，我们只为反向传播保存了一个缓冲区，但这也意味着我们在 (5) 中重新计算卷积的前向传播。此外，请看 (2)、(3)、(4) 和 (6) 中的代码与上面的示例完全相同。

class FusedConvBN2DFunction(torch.autograd.Function):
    @staticmethod
    def forward(ctx, X, conv_weight, eps=1e-3):
        assert X.ndim == 4  # N, C, H, W
        # (1) Only need to save this single buffer for backward!
        ctx.save_for_backward(X, conv_weight)

        # (2) Exact same Conv2D forward from example above
        X = F.conv2d(X, conv_weight)
        # (3) Exact same BatchNorm2D forward from example above
        sum = X.sum(dim=(0, 2, 3))
        var = X.var(unbiased=True, dim=(0, 2, 3))
        N = X.numel() / X.size(1)
        sqrt_var = torch.sqrt(var)
        ctx.eps = eps
        ctx.sum = sum
        ctx.N = N
        ctx.sqrt_var = sqrt_var
        mean = sum / N
        denom = sqrt_var + eps
        # Try to do as many things in-place as possible
        # Instead of `out = (X - a) / b`, doing `out = X - a; out /= b`
        # avoids allocating one extra NCHW-sized buffer here
        out = X - unsqueeze_all(mean)
        out /= unsqueeze_all(denom)
        return out

    @staticmethod
    def backward(ctx, grad_out):
        X, conv_weight, = ctx.saved_tensors
        # (4) Batch norm backward
        # (5) We need to recompute conv
        X_conv_out = F.conv2d(X, conv_weight)
        grad_out = batch_norm_backward(grad_out, X_conv_out, ctx.sum, ctx.sqrt_var,
                                       ctx.N, ctx.eps)
        # (6) Conv2d backward
        grad_X, grad_input = convolution_backward(grad_out, X, conv_weight)
        return grad_X, grad_input, None, None, None, None, None

下一步是将我们的函数式变体封装在一个有状态的 nn.Module 中

import torch.nn as nn
import math

class FusedConvBN(nn.Module):
    def __init__(self, in_channels, out_channels, kernel_size, exp_avg_factor=0.1,
                 eps=1e-3, device=None, dtype=None):
        super(FusedConvBN, self).__init__()
        factory_kwargs = {'device': device, 'dtype': dtype}
        # Conv parameters
        weight_shape = (out_channels, in_channels, kernel_size, kernel_size)
        self.conv_weight = nn.Parameter(torch.empty(*weight_shape, **factory_kwargs))
        # Batch norm parameters
        num_features = out_channels
        self.num_features = num_features
        self.eps = eps
        # Initialize
        self.reset_parameters()

    def forward(self, X):
        return FusedConvBN2DFunction.apply(X, self.conv_weight, self.eps)

    def reset_parameters(self) -> None:
        nn.init.kaiming_uniform_(self.conv_weight, a=math.sqrt(5))

使用 gradcheck 验证我们的反向传播公式的正确性

weight = torch.rand(5, 3, 3, 3, requires_grad=True, dtype=torch.double)
X = torch.rand(2, 3, 4, 4, requires_grad=True, dtype=torch.double)
torch.autograd.gradcheck(FusedConvBN2DFunction.apply, (X, weight))

True

测试我们的新层

使用 FusedConvBN 训练一个基本网络 下面的代码是对此处示例进行一些轻微修改后的结果：https://github.com/pytorch/examples/tree/master/mnist

import torch.optim as optim
from torchvision import datasets, transforms
from torch.optim.lr_scheduler import StepLR

# Record memory allocated at the end of the forward pass
memory_allocated = [[],[]]

class Net(nn.Module):
    def __init__(self, fused=True):
        super(Net, self).__init__()
        self.fused = fused
        if fused:
            self.convbn1 = FusedConvBN(1, 32, 3)
            self.convbn2 = FusedConvBN(32, 64, 3)
        else:
            self.conv1 = nn.Conv2d(1, 32, 3, 1, bias=False)
            self.bn1 = nn.BatchNorm2d(32, affine=False, track_running_stats=False)
            self.conv2 = nn.Conv2d(32, 64, 3, 1, bias=False)
            self.bn2 = nn.BatchNorm2d(64, affine=False, track_running_stats=False)
        self.fc1 = nn.Linear(9216, 128)
        self.dropout = nn.Dropout(0.5)
        self.fc2 = nn.Linear(128, 10)

    def forward(self, x):
        if self.fused:
            x = self.convbn1(x)
        else:
            x = self.conv1(x)
            x = self.bn1(x)
        F.relu_(x)
        if self.fused:
            x = self.convbn2(x)
        else:
            x = self.conv2(x)
            x = self.bn2(x)
        F.relu_(x)
        x = F.max_pool2d(x, 2)
        F.relu_(x)
        x = x.flatten(1)
        x = self.fc1(x)
        x = self.dropout(x)
        F.relu_(x)
        x = self.fc2(x)
        output = F.log_softmax(x, dim=1)
        if fused:
            memory_allocated[0].append(torch.cuda.memory_allocated())
        else:
            memory_allocated[1].append(torch.cuda.memory_allocated())
        return output

def train(model, device, train_loader, optimizer, epoch):
    model.train()
    for batch_idx, (data, target) in enumerate(train_loader):
        data, target = data.to(device), target.to(device)
        optimizer.zero_grad()
        output = model(data)
        loss = F.nll_loss(output, target)
        loss.backward()
        optimizer.step()
        if batch_idx % 2 == 0:
            print('Train Epoch: {} [{}/{} ({:.0f}%)]\tLoss: {:.6f}'.format(
                epoch, batch_idx * len(data), len(train_loader.dataset),
                100. * batch_idx / len(train_loader), loss.item()))

def test(model, device, test_loader):
    model.eval()
    test_loss = 0
    correct = 0
    # Use inference mode instead of no_grad, for free improved test-time performance
    with torch.inference_mode():
        for data, target in test_loader:
            data, target = data.to(device), target.to(device)
            output = model(data)
            # sum up batch loss
            test_loss += F.nll_loss(output, target, reduction='sum').item()
            # get the index of the max log-probability
            pred = output.argmax(dim=1, keepdim=True)
            correct += pred.eq(target.view_as(pred)).sum().item()

    test_loss /= len(test_loader.dataset)

    print('\nTest set: Average loss: {:.4f}, Accuracy: {}/{} ({:.0f}%)\n'.format(
        test_loss, correct, len(test_loader.dataset),
        100. * correct / len(test_loader.dataset)))

use_cuda = torch.cuda.is_available()
device = torch.device("cuda" if use_cuda else "cpu")
train_kwargs = {'batch_size': 2048}
test_kwargs = {'batch_size': 2048}

if use_cuda:
    cuda_kwargs = {'num_workers': 1,
                   'pin_memory': True,
                   'shuffle': True}
    train_kwargs.update(cuda_kwargs)
    test_kwargs.update(cuda_kwargs)

transform = transforms.Compose([
    transforms.ToTensor(),
    transforms.Normalize((0.1307,), (0.3081,))
])
dataset1 = datasets.MNIST('../data', train=True, download=True,
                          transform=transform)
dataset2 = datasets.MNIST('../data', train=False,
                          transform=transform)
train_loader = torch.utils.data.DataLoader(dataset1, **train_kwargs)
test_loader = torch.utils.data.DataLoader(dataset2, **test_kwargs)

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内存使用比较

如果启用了 CUDA，则打印出 fused=True 和 fused=False 的内存使用情况 在 NVIDIA GeForce RTX 3070、NVIDIA CUDA® 深度神经网络库 (cuDNN) 8.0.5 上的示例运行结果：融合后的峰值内存：1.56GB，未融合的峰值内存：2.68GB

需要注意的是，此模型的峰值内存使用情况可能因所使用的具体 cuDNN 卷积算法而异。对于较浅层的模型，融合模型的峰值内存分配甚至可能超过未融合模型！这是因为计算某些 cuDNN 卷积算法所需的内存可能足够高，以至于“隐藏”了你在反向传播开始时通常预期的峰值。

因此，我们也记录并显示了前向传播结束时的内存分配作为近似值，并以此表明对于每个融合的 conv-bn 对，我们确实少分配了一个缓冲区。

from statistics import mean

torch.backends.cudnn.enabled = True

if use_cuda:
    peak_memory_allocated = []

    for fused in (True, False):
        torch.manual_seed(123456)

        model = Net(fused=fused).to(device)
        optimizer = optim.Adadelta(model.parameters(), lr=1.0)
        scheduler = StepLR(optimizer, step_size=1, gamma=0.7)

        for epoch in range(1):
            train(model, device, train_loader, optimizer, epoch)
            test(model, device, test_loader)
            scheduler.step()
        peak_memory_allocated.append(torch.cuda.max_memory_allocated())
        torch.cuda.reset_peak_memory_stats()
    print("cuDNN version:", torch.backends.cudnn.version())
    print()
    print("Peak memory allocated:")
    print(f"fused: {peak_memory_allocated[0]/1024**3:.2f}GB, unfused: {peak_memory_allocated[1]/1024**3:.2f}GB")
    print("Memory allocated at end of forward pass:")
    print(f"fused: {mean(memory_allocated[0])/1024**3:.2f}GB, unfused: {mean(memory_allocated[1])/1024**3:.2f}GB")

Train Epoch: 0 [0/60000 (0%)]   Loss: 2.348850
Train Epoch: 0 [4096/60000 (7%)]        Loss: 7.906041
Train Epoch: 0 [8192/60000 (13%)]       Loss: 3.852560
Train Epoch: 0 [12288/60000 (20%)]      Loss: 2.176885
Train Epoch: 0 [16384/60000 (27%)]      Loss: 1.876234
Train Epoch: 0 [20480/60000 (33%)]      Loss: 1.706322
Train Epoch: 0 [24576/60000 (40%)]      Loss: 1.607102
Train Epoch: 0 [28672/60000 (47%)]      Loss: 1.706126
Train Epoch: 0 [32768/60000 (53%)]      Loss: 1.481350
Train Epoch: 0 [36864/60000 (60%)]      Loss: 1.342697
Train Epoch: 0 [40960/60000 (67%)]      Loss: 1.154232
Train Epoch: 0 [45056/60000 (73%)]      Loss: 1.001995
Train Epoch: 0 [49152/60000 (80%)]      Loss: 1.001608
Train Epoch: 0 [53248/60000 (87%)]      Loss: 0.860608
Train Epoch: 0 [57344/60000 (93%)]      Loss: 0.692767

Test set: Average loss: 0.4204, Accuracy: 8901/10000 (89%)

Train Epoch: 0 [0/60000 (0%)]   Loss: 2.349130
Train Epoch: 0 [4096/60000 (7%)]        Loss: 7.946248
Train Epoch: 0 [8192/60000 (13%)]       Loss: 3.230653
Train Epoch: 0 [12288/60000 (20%)]      Loss: 2.591974
Train Epoch: 0 [16384/60000 (27%)]      Loss: 1.949312
Train Epoch: 0 [20480/60000 (33%)]      Loss: 2.424960
Train Epoch: 0 [24576/60000 (40%)]      Loss: 2.075612
Train Epoch: 0 [28672/60000 (47%)]      Loss: 1.709257
Train Epoch: 0 [32768/60000 (53%)]      Loss: 1.384610
Train Epoch: 0 [36864/60000 (60%)]      Loss: 1.277133
Train Epoch: 0 [40960/60000 (67%)]      Loss: 1.244485
Train Epoch: 0 [45056/60000 (73%)]      Loss: 0.953217
Train Epoch: 0 [49152/60000 (80%)]      Loss: 0.987237
Train Epoch: 0 [53248/60000 (87%)]      Loss: 0.953964
Train Epoch: 0 [57344/60000 (93%)]      Loss: 1.040246

Test set: Average loss: 0.4897, Accuracy: 8488/10000 (85%)

cuDNN version: 90501

Peak memory allocated:
fused: 1.94GB, unfused: 1.50GB
Memory allocated at end of forward pass:
fused: 0.59GB, unfused: 0.96GB