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使用自定义函数融合卷积和批量归一化¶
融合相邻的卷积和批量归一化层通常是推理时的优化，以提高运行时性能。它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]。但是，这种技术不适用于训练模型。
在本教程中，我们将展示一种不同的技术来融合这两个层，该技术可以在训练期间应用。此优化的目标不是提高运行时性能，而是减少内存使用量。
此优化的想法是，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进行反向传播。对于较大的批次大小，这些保存的输入占用了大部分内存使用量，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，可以显着减少内存使用量。
在本教程中，我们通过将卷积和批量归一化合并到一个单层中（作为一个自定义函数）来避免这种额外的分配。在此组合层的正向传播中，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（这是反向传播所必需的），我们在反向传播期间再次重新计算卷积的正向传播。
需要注意的是，此优化的使用是特定于情况的。虽然（通过避免保存一个缓冲区）我们在正向传播结束时始终减少分配的内存量，但有时分配的峰值内存可能不会真正减少。有关更多详细信息，请参见最后部分。
为了简化，在本教程中，我们对 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 和 track_running_statistics=False。另一个小的区别是，我们在计算批量归一化的分母时，在平方根的外部添加了 epsilon。
[0] https://nenadmarkus.com/p/fusing-batchnorm-and-conv/
卷积的反向公式实现¶
实现自定义函数要求我们自己实现反向传播。在这种情况下，我们需要 Conv2D 和 BatchNorm2D 的反向公式。最终，我们将在统一的反向传播函数中将它们链接在一起，但以下我们首先将它们实现为各自的自定义函数，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)
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变得简单得多。以下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
融合卷积和批量归一化¶
现在已经完成了大部分工作，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，但这意味着我们也在 (5) 中重新计算了卷积前向传播。此外，请注意，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
下一步是将我们的函数变体包装在有状态的 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))
True
测试我们新的层¶
使用 FusedConvBN 训练一个基本网络，以下代码是在这里示例的基础上进行了一些轻微修改之后：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)
内存使用量的比较¶
如果启用了 CUDA，请打印出 fused=True 和 fused=False 的内存使用量。例如，在 NVIDIA GeForce RTX 3070、NVIDIA CUDA® 深度神经网络库 (cuDNN) 8.0.5 上运行：融合峰值内存：1.56GB，未融合峰值内存：2.68GB。
需要注意的是，此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。对于更浅的模型，融合模型分配的峰值内存可能超过未融合模型！这是因为计算某些 cuDNN 卷积算法分配的内存可能足够高，以至于“隐藏”了你在反向传播开始时通常会期望看到的峰值。
出于这个原因，我们还记录并显示了前向传播结束时分配的内存，作为一种近似值，以及为了证明我们确实为每个融合的 conv-bn 对分配了一个更少的缓冲区。
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: 7.435155
Train Epoch: 0 [8192/60000 (13%)] Loss: 5.443542
Train Epoch: 0 [12288/60000 (20%)] Loss: 2.457855
Train Epoch: 0 [16384/60000 (27%)] Loss: 1.739211
Train Epoch: 0 [20480/60000 (33%)] Loss: 1.448270
Train Epoch: 0 [24576/60000 (40%)] Loss: 1.312153
Train Epoch: 0 [28672/60000 (47%)] Loss: 1.145359
Train Epoch: 0 [32768/60000 (53%)] Loss: 1.496009
Train Epoch: 0 [36864/60000 (60%)] Loss: 1.251145
Train Epoch: 0 [40960/60000 (67%)] Loss: 1.077391
Train Epoch: 0 [45056/60000 (73%)] Loss: 0.890155
Train Epoch: 0 [49152/60000 (80%)] Loss: 0.840175
Train Epoch: 0 [53248/60000 (87%)] Loss: 0.726032
Train Epoch: 0 [57344/60000 (93%)] Loss: 0.788943
Test set: Average loss: 0.4195, Accuracy: 8843/10000 (88%)
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
脚本的总运行时间： ( 0 分钟 37.781 秒)
