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使用自定义函数融合卷积与批归一化#
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归一化（Batch Norm）层融合在一起，通常是一种用于提高推理运行时性能的优化手段。这种优化通常通过完全消除批归一化层，并更新前序卷积层的权重和偏置来实现 [0]。然而，该技术不适用于模型训练阶段。
在本教程中，我们将展示一种可在训练期间使用的不同融合技术。与提高运行速度不同，此优化的目标是减少内存占用。
该优化的核心思想在于：卷积和批归一化（以及许多其他算子）在正向传播过程中都需要保存一份输入的副本，以供反向传播使用。对于较大的批处理大小（batch size），这些保存的输入占据了大部分内存开销。因此，能够避免为每一对“卷积-批归一化”组合分配额外的输入张量，可以显著降低内存需求。
在本教程中，我们通过将卷积和批归一化合并为单一层（作为自定义函数）来避免这种额外分配。在此组合层的正向传播中，我们按原样执行常规的卷积和批归一化，唯一的区别是我们只保存卷积的输入。为了获得批归一化所需的输入（该输入对于反向传播至关重要），我们在反向传播阶段重新计算卷积的正向传播。
需要注意的是，此优化的使用具有情境性。尽管（通过减少一个缓存区）我们确实减少了正向传播结束时的已分配内存，但在某些情况下，峰值内存占用可能并未真正降低。详情请参阅最后一节。
为简化起见，本教程在 Conv2D 中硬编码了 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 和 track_running_statistics=False。另一个微小的差异是，我们在计算批归一化时，将 epsilon 加在了平方根之外的分母上。
[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行编写反向传播逻辑。在这种情况下，我们需要 Conv2D 和 BatchNorm2D 的反向传播公式。最终，我们会在统一的反向传播函数中将它们串联起来，但在下面，我们首先将它们实现为独立的自定义函数，以便单独验证其正确性。
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)
当使用 gradcheck 进行测试时，务必使用双精度。
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))
True
批归一化的反向传播公式实现#
批归一化有两种模式：训练模式和 eval（评估）模式。在训练模式下，样本统计量是输入的函数。在 eval 模式下，我们使用保存的运行统计量，它们不是输入的函数。这使得非训练模式下的反向传播变得非常简单。下面我们仅实现并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
融合卷积与批归一化#
现在主体工作已完成，我们可以将它们结合在一起。请注意，在 (1) 中，我们只为反向传播保存了一个缓存区，但这也意味着我们在 (5) 中重新计算了卷积的正向传播。同时请注意，在 (2)、(3)、(4) 和 (6) 中，代码与上述示例完全相同。
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 训练一个基础网络。以下代码是在此示例基础上稍作修改后的版本：pytorch/examples
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)
0%| | 0.00/9.91M [00:00<?, ?B/s]
85%|████████▍ | 8.42M/9.91M [00:00<00:00, 84.2MB/s]
100%|██████████| 9.91M/9.91M [00:00<00:00, 89.0MB/s]
0%| | 0.00/28.9k [00:00<?, ?B/s]
100%|██████████| 28.9k/28.9k [00:00<00:00, 3.96MB/s]
0%| | 0.00/1.65M [00:00<?, ?B/s]
100%|██████████| 1.65M/1.65M [00:00<00:00, 86.9MB/s]
0%| | 0.00/4.54k [00:00<?, ?B/s]
100%|██████████| 4.54k/4.54k [00:00<00:00, 29.0MB/s]
内存占用对比#
如果启用了 CUDA，打印 fused=True 和 fused=False 时的内存占用情况。以在 NVIDIA GeForce RTX 3070、NVIDIA CUDA® 深度神经网络库 (cuDNN) 8.0.5 上的运行为例：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，该模型的峰值内存占用可能会根据所使用的特定 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占用有时甚至可能超过未融合模型！这是因为计算某些 cuDNN 卷积算法所分配的内存可能足够大，从而“掩盖”了你通常预期的、出现在反向传播起始点附近的峰值。
因此，我们也记录并显示了正向传播结束时的已分配内存，作为一种近似指标，以证明我们确实为每一对融合的 conv-bn 少分配了一个缓存区。
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: 7.906153
Train Epoch: 0 [8192/60000 (13%)] Loss: 3.855717
Train Epoch: 0 [12288/60000 (20%)] Loss: 2.177739
Train Epoch: 0 [16384/60000 (27%)] Loss: 1.894665
Train Epoch: 0 [20480/60000 (33%)] Loss: 1.795232
Train Epoch: 0 [24576/60000 (40%)] Loss: 1.696847
Train Epoch: 0 [28672/60000 (47%)] Loss: 1.644211
Train Epoch: 0 [32768/60000 (53%)] Loss: 1.232944
Train Epoch: 0 [36864/60000 (60%)] Loss: 1.109315
Train Epoch: 0 [40960/60000 (67%)] Loss: 1.209388
Train Epoch: 0 [45056/60000 (73%)] Loss: 1.256302
Train Epoch: 0 [49152/60000 (80%)] Loss: 1.404235
Train Epoch: 0 [53248/60000 (87%)] Loss: 0.904530
Train Epoch: 0 [57344/60000 (93%)] Loss: 0.895382
Test set: Average loss: 0.3607, Accuracy: 9052/10000 (91%)
Train Epoch: 0 [0/60000 (0%)] Loss: 2.349131
Train Epoch: 0 [4096/60000 (7%)] Loss: 7.946014
Train Epoch: 0 [8192/60000 (13%)] Loss: 3.232583
Train Epoch: 0 [12288/60000 (20%)] Loss: 2.597900
Train Epoch: 0 [16384/60000 (27%)] Loss: 1.940698
Train Epoch: 0 [20480/60000 (33%)] Loss: 2.448335
Train Epoch: 0 [24576/60000 (40%)] Loss: 2.038943
Train Epoch: 0 [28672/60000 (47%)] Loss: 1.657389
Train Epoch: 0 [32768/60000 (53%)] Loss: 1.328866
Train Epoch: 0 [36864/60000 (60%)] Loss: 1.187172
Train Epoch: 0 [40960/60000 (67%)] Loss: 1.338868
Train Epoch: 0 [45056/60000 (73%)] Loss: 1.290277
Train Epoch: 0 [49152/60000 (80%)] Loss: 0.928663
Train Epoch: 0 [53248/60000 (87%)] Loss: 0.781791
Train Epoch: 0 [57344/60000 (93%)] Loss: 0.777710
Test set: Average loss: 0.4652, Accuracy: 8673/10000 (87%)
cuDNN version: 92000
Peak memory allocated:
fused: 1.94GB, unfused: 1.50GB
Memory allocated at end of forward pass:
fused: 0.59GB, unfused: 0.96GB
脚本总运行时间：（0 分 22.466 秒）