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使用自定义函数融合卷积和批量归一化
创建于：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[0]。然而，这种技术不适用于训练模型。
在本教程中，我们将展示一种在训练期间可以应用的不同技术来融合这两层。与提高运行时性能不同，此优化的目标是减少内存使用。
这种优化背后的想法是观察到卷积和批量归一化（以及许多其他操作）都需要在正向传播期间保存其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，因此能够避免为每个卷积批量归一化对分配另一个输入张量可以显著减少内存使用。
在本教程中，我们通过将卷积和批量归一化结合到一个单一层（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，我们按原样执行正常的卷积和批量归一化，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，这在反向传播中是必要的，我们在反向传播期间再次重新计算卷积的前向传播。
需要注意的是，这种优化的使用是情境性的。虽然（通过避免保存一个缓冲区）我们总是在前向传递结束时减少分配的内存，但在某些情况下，分配的峰值内存可能实际上并没有减少。更多详情请参见最后一部分。
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，在分母的平方根外添加了epsilon。
[0] https://nenadmarkus.com/p/fusing-batchnorm-and-conv/
卷积的反向公式实现
实现自定义函数需要我们自行实现反向传播。在这种情况下，我们需要Conv2D和BatchNorm2D的反向传播公式。最终，我们会在统一的反向传播函数中将它们链接在一起，但下面我们首先将它们作为各自的自定义函数实现，以便我们可以单独验证它们的正确性。
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)
在使用gradcheck进行测试时，使用双精度非常重要
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，样本统计量是输入的函数。在eval模式下，我们使用保存的运行统计量，这些统计量不是输入的函数。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)
True
融合卷积和批归一化
现在大部分工作已经完成，我们可以将它们组合在一起。请注意，在（1）中我们只保存了一个用于反向传播的缓冲区，但这意味着我们在（5）中重新计算卷积的前向传播。还可以看到，在（2）、（3）、（4）和（6）中，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
下一步是将我们的功能变体包装在一个有状态的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 来验证我们的反向公式的正确性
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))
True
测试我们的新层
使用FusedConvBN来训练一个基础网络
下面的代码是对这里的示例进行了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)
Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz
Failed to download (trying next):
HTTP Error 403: Forbidden
Downloading https://ossci-datasets.s3.amazonaws.com/mnist/train-images-idx3-ubyte.gz
Downloading https://ossci-datasets.s3.amazonaws.com/mnist/train-images-idx3-ubyte.gz to ../data/MNIST/raw/train-images-idx3-ubyte.gz
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Extracting ../data/MNIST/raw/train-images-idx3-ubyte.gz to ../data/MNIST/raw
Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz
Failed to download (trying next):
HTTP Error 403: Forbidden
Downloading https://ossci-datasets.s3.amazonaws.com/mnist/train-labels-idx1-ubyte.gz
Downloading https://ossci-datasets.s3.amazonaws.com/mnist/train-labels-idx1-ubyte.gz to ../data/MNIST/raw/train-labels-idx1-ubyte.gz
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Extracting ../data/MNIST/raw/train-labels-idx1-ubyte.gz to ../data/MNIST/raw
Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz
Failed to download (trying next):
HTTP Error 403: Forbidden
Downloading https://ossci-datasets.s3.amazonaws.com/mnist/t10k-images-idx3-ubyte.gz
Downloading https://ossci-datasets.s3.amazonaws.com/mnist/t10k-images-idx3-ubyte.gz to ../data/MNIST/raw/t10k-images-idx3-ubyte.gz
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Extracting ../data/MNIST/raw/t10k-images-idx3-ubyte.gz to ../data/MNIST/raw
Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz
Failed to download (trying next):
HTTP Error 403: Forbidden
Downloading https://ossci-datasets.s3.amazonaws.com/mnist/t10k-labels-idx1-ubyte.gz
Downloading https://ossci-datasets.s3.amazonaws.com/mnist/t10k-labels-idx1-ubyte.gz to ../data/MNIST/raw/t10k-labels-idx1-ubyte.gz
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Extracting ../data/MNIST/raw/t10k-labels-idx1-ubyte.gz to ../data/MNIST/raw
内存使用比较
如果启用了CUDA，打印出fused=True和fused=False的内存使用情况 例如在NVIDIA GeForce RTX 3070上运行，NVIDIA CUDA® 深度神经网络库（cuDNN）8.0.5：融合峰值内存：1.56GB， 未融合峰值内存：2.68GB
需要注意的是，该模型的峰值内存使用量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分配可能会超过未融合模型！这是因为分配给计算某些cuDNN卷积算法的内存可能足够高，以至于“隐藏”了你通常期望在反向传播开始时出现的典型峰值。
出于这个原因，我们还在前向传播结束时记录并显示分配的内存作为近似值，并证明我们确实为每个融合的conv-bn对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: 2.348735
Train Epoch: 0 [4096/60000 (7%)] Loss: 7.435781
Train Epoch: 0 [8192/60000 (13%)] Loss: 5.540894
Train Epoch: 0 [12288/60000 (20%)] Loss: 2.274223
Train Epoch: 0 [16384/60000 (27%)] Loss: 1.618885
Train Epoch: 0 [20480/60000 (33%)] Loss: 1.515203
Train Epoch: 0 [24576/60000 (40%)] Loss: 1.329276
Train Epoch: 0 [28672/60000 (47%)] Loss: 1.184942
Train Epoch: 0 [32768/60000 (53%)] Loss: 1.140154
Train Epoch: 0 [36864/60000 (60%)] Loss: 1.174118
Train Epoch: 0 [40960/60000 (67%)] Loss: 1.057965
Train Epoch: 0 [45056/60000 (73%)] Loss: 0.976334
Train Epoch: 0 [49152/60000 (80%)] Loss: 0.842555
Train Epoch: 0 [53248/60000 (87%)] Loss: 0.690169
Train Epoch: 0 [57344/60000 (93%)] Loss: 0.656998
Test set: Average loss: 0.4197, Accuracy: 8681/10000 (87%)
Train Epoch: 0 [0/60000 (0%)] Loss: 2.349030
Train Epoch: 0 [4096/60000 (7%)] Loss: 7.435158
Train Epoch: 0 [8192/60000 (13%)] Loss: 5.443529
Train Epoch: 0 [12288/60000 (20%)] Loss: 2.457773
Train Epoch: 0 [16384/60000 (27%)] Loss: 1.739528
Train Epoch: 0 [20480/60000 (33%)] Loss: 1.448555
Train Epoch: 0 [24576/60000 (40%)] Loss: 1.311784
Train Epoch: 0 [28672/60000 (47%)] Loss: 1.149165
Train Epoch: 0 [32768/60000 (53%)] Loss: 1.513479
Train Epoch: 0 [36864/60000 (60%)] Loss: 1.243767
Train Epoch: 0 [40960/60000 (67%)] Loss: 1.079315
Train Epoch: 0 [45056/60000 (73%)] Loss: 0.896300
Train Epoch: 0 [49152/60000 (80%)] Loss: 0.839771
Train Epoch: 0 [53248/60000 (87%)] Loss: 0.729098
Train Epoch: 0 [57344/60000 (93%)] Loss: 0.748637
Test set: Average loss: 0.4340, Accuracy: 8715/10000 (87%)
cuDNN version: 90100
Peak memory allocated:
fused: 2.30GB, unfused: 1.77GB
Memory allocated at end of forward pass:
fused: 0.59GB, unfused: 0.96GB
脚本总运行时间： ( 0 分钟 41.191 秒)
