使用自定义函数融合卷积和批量归一化

Created On: Jul 22, 2021 | Last Updated: Apr 18, 2023 | Last Verified: Nov 05, 2024

将相邻的卷积层和批量归一化层融合通常是一种推理时优化，以提高运行时性能。这通常通过完全消除批量归一化层并更新前面卷积的权重和偏差来实现[0]。然而，这种技术不适用于训练模型。

在本教程中，我们将展示一种可以在训练期间应用的不同融合技术。这项优化的目标是减少内存使用，而不是改进运行时。

这项优化的理念是观察到卷积和批量归一化（以及许多其他操作）在正向传递时需要保存输入的副本，以便进行反向传递。对于大批量大小的情况下，这些保存的输入占用了大部分内存，因此能够避免为每个卷积和批量归一化对分配额外的输入张量，会显著减少内存使用。

在本教程中，我们通过将卷积和批量归一化组合为一个单独的层（作为自定义函数），避免了额外分配。在这个组合层的正向传递中，我们按原样执行正常的卷积和批量归一化，唯一不同的是我们只保存卷积的输入。为了获得批量归一化的输入，这在反向传递中是必要的，我们将在反向传递期间重新计算卷积正向传递。

需要注意的是，这种优化的使用是有情境性的。虽然通过避免一个保存的缓冲区，我们始终减少了正向传递结束时分配的内存，但在某些情况下，*峰值*分配的内存可能并未真正减少。详见最后一节了解更多细节。

为简单起见，在本教程中我们为Conv2D硬编码了`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`以及`track_running_statistics=False。另一个小的区别是我们在批量归一化计算中在平方根之外添加了epsilon。

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

卷积的反向公式实现

实现一个自定义函数要求我们自己实现反向传递。在这种情况下，我们需要Conv2D和BatchNorm2D的反向公式。最终我们会将它们链式整合到一个统一的反向函数中，但在下面我们先将它们作为各自的自定义函数实现以分别验证其正确性。

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)

在使用``gradcheck``测试时，重要的是要使用双精度

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))

批量归一化的反向公式实现

批量归一化有两种模式：训练模式和``eval``模式。在训练模式下，样本统计是输入的函数。在``eval``模式下，我们使用保存的运行统计，这不是输入的函数。这使得非训练模式的反向显著更简单。下面我们仅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)

融合卷积和批量归一化

现在大部分工作已完成，我们可以将它们组合在一起。注意，在(1)中我们仅保存了一个缓冲区用于反向传递，但这也意味着我们需要在(5)中重新计算卷积的正向传递。此外，请注意在(2)、(3)、(4)和(6)中的代码与上面的例子完全相同。

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

下一步是将我们的功能变体包装到有状态的`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``验证我们反向公式的正确性

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))

测试我们的新层

使用``FusedConvBN``训练一个基本网络 下面的代码对示例代码进行了轻微修改：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)

内存使用对比

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

需要注意的是，该模型的*峰值*内存使用可能会因使用的具体cuDNN卷积算法而有所不同。对于较浅的模型，融合模型的峰值内存分配可能会超过未融合模型！这是因为某些cuDNN卷积算法的内存分配高到足以”隐藏”你期望在反向传递开始时附近的典型峰值。

因此，我们还记录并显示了正向传递结束时分配的内存量作为近似值，以证明我们确实为每个融合的``conv-bn``对减少了一个缓冲区的分配。

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")