使用自定义函数融合卷积和批归一化
将相邻的卷积层和批归一化层融合在一起通常是一种推理时的优化技术，旨在提高运行效率。这种方法通常通过完全消除批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，这种技术并不适用于模型训练。
在本教程中，我们将展示一种可以在训练过程中应用的融合这两层的不同技术。与优化运行时间不同，这种优化的目标是减少内存使用。
这种优化的核心思想是，卷积和批归一化（以及许多其他操作）在前向传播过程中都需要保存输入的副本以供反向传播使用。对于大批量数据，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-批归一化对分配额外的输入张量将显著减少内存使用。
在本教程中，我们通过将卷积和批归一化合并为一个自定义层来避免这种额外的内存分配。在这个合并层的前向传播中，我们正常执行卷积和批归一化操作，唯一的区别是我们只保存卷积的输入。为了获得批归一化的输入（在反向传播中需要用到），我们在反向传播期间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化的。尽管通过避免保存一个缓冲区，我们总是减少前向传播结束时的内存分配，但在某些情况下，峰值内存分配可能并没有实际减少。更多细节请参见最后一节。
为了简化，在本教程中我们硬编码了 Conv2D 的参数：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，我们在批归一化的计算中，将 epsilon 添加在分母的平方根之外。
[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，我们需要为 Conv2D 和 BatchNorm2D 实现反向传播公式。最终，我们会将它们串联在统一的反向传播函数中，但在此之前，我们首先将它们作为独立的自定义函数实现，以便能够分别验证它们的正确性。
importtorch
fromtorch.autograd.functionimport once_differentiable
importtorch.nn.functionalasF
defconvolution_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
classConv2D(torch.autograd.Function):
@staticmethod
defforward(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
defbackward(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
Batch Norm 的反向公式实现
Batch Norm 有两种模式：训练模式和 eval 模式。在训练模式下，样本统计量是输入数据的函数。在 eval 模式下，我们使用保存的运行统计量，这些统计量与输入数据无关。这使得非训练模式的反向传播过程显著简化。下面我们仅实现并测试训练模式的情况。
defunsqueeze_all(t):
# Helper function to ``unsqueeze`` all the dimensions that we reduce over
return t[None, :, None, None]
defbatch_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
classBatchNorm(torch.autograd.Function):
@staticmethod
defforward(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
defbackward(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BatchNorm
现在大部分工作已经完成，我们可以将它们结合在一起。请注意，在 (1) 中我们只保存了一个反向传播的缓冲区，但这也意味着在 (5) 中我们需要重新计算卷积的前向传播。此外，可以看到在 (2)、(3)、(4) 和 (6) 中，代码与上述示例完全相同。
classFusedConvBN2DFunction(torch.autograd.Function):
@staticmethod
defforward(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
defbackward(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到一个有状态的 nn.Module 中。
importtorch.nnasnn
importmath
classFusedConvBN(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()
defforward(self, X):
return FusedConvBN2DFunction.apply(X, self.conv_weight, self.eps)
defreset_parameters(self) -> None:
nn.init.kaiming_uniform_(self.conv_weight, a=math.sqrt(5))
使用 gradcheck 来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
测试我们的新层
使用 FusedConvBN 训练一个基础网络。以下代码是对此示例进行了一些轻微修改后的结果：https://github.com/pytorch/examples/tree/master/mnist
importtorch.optimasoptim
fromtorchvisionimport datasets, transforms
fromtorch.optim.lr_schedulerimport StepLR
# Record memory allocated at the end of the forward pass
memory_allocated = [[],[]]
classNet(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)
defforward(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
deftrain(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()))
deftest(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]
100%|##########| 9.91M/9.91M [00:00<00:00, 130MB/s]
0%| | 0.00/28.9k [00:00<?, ?B/s]
100%|##########| 28.9k/28.9k [00:00<00:00, 61.1MB/s]
0%| | 0.00/1.65M [00:00<?, ?B/s]
100%|##########| 1.65M/1.65M [00:00<00:00, 93.1MB/s]
0%| | 0.00/4.54k [00:00<?, ?B/s]
100%|##########| 4.54k/4.54k [00:00<00:00, 28.6MB/s]
内存使用情况对比
如果启用了 CUDA，打印出 fused=True 和 fused=False 时的内存使用情况。例如，在 NVIDIA GeForce RTX 3070 和 NVIDIA CUDA® 深度神经网络库 (cuDNN) 8.0.5 上运行的结果如下：fused 峰值内存：1.56GB，unfused 峰值内存：2.68GB。
需要注意的是，该模型的峰值内存使用情况可能会因所使用的特定 cuDNN 卷积算法而异。对于较浅的模型，fused 模型的峰值内存分配甚至可能超过 unfused 模型！这是因为为某些 cuDNN 卷积算法分配的内存可能足够高，以至于“掩盖”了通常在反向传播开始时预期的峰值。
出于这个原因，我们还记录并显示前向传播结束时的内存分配情况作为近似值，以证明我们确实为每个融合的 conv-bn 对少分配了一个缓冲区。
fromstatisticsimport 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: 7.906148
Train Epoch: 0 [8192/60000 (13%)] Loss: 3.858159
Train Epoch: 0 [12288/60000 (20%)] Loss: 2.177509
Train Epoch: 0 [16384/60000 (27%)] Loss: 1.875478
Train Epoch: 0 [20480/60000 (33%)] Loss: 1.718086
Train Epoch: 0 [24576/60000 (40%)] Loss: 1.600347
Train Epoch: 0 [28672/60000 (47%)] Loss: 1.746708
Train Epoch: 0 [32768/60000 (53%)] Loss: 1.246303
Train Epoch: 0 [36864/60000 (60%)] Loss: 1.443410
Train Epoch: 0 [40960/60000 (67%)] Loss: 1.204844
Train Epoch: 0 [45056/60000 (73%)] Loss: 1.313077
Train Epoch: 0 [49152/60000 (80%)] Loss: 1.013597
Train Epoch: 0 [53248/60000 (87%)] Loss: 0.796338
Train Epoch: 0 [57344/60000 (93%)] Loss: 0.749519
Test set: Average loss: 0.3547, Accuracy: 8951/10000 (90%)
Train Epoch: 0 [0/60000 (0%)] Loss: 2.349130
Train Epoch: 0 [4096/60000 (7%)] Loss: 7.946110
Train Epoch: 0 [8192/60000 (13%)] Loss: 3.232401
Train Epoch: 0 [12288/60000 (20%)] Loss: 2.597488
Train Epoch: 0 [16384/60000 (27%)] Loss: 1.941510
Train Epoch: 0 [20480/60000 (33%)] Loss: 2.460332
Train Epoch: 0 [24576/60000 (40%)] Loss: 2.004580
Train Epoch: 0 [28672/60000 (47%)] Loss: 1.616858
Train Epoch: 0 [32768/60000 (53%)] Loss: 1.276979
Train Epoch: 0 [36864/60000 (60%)] Loss: 1.083581
Train Epoch: 0 [40960/60000 (67%)] Loss: 1.386545
Train Epoch: 0 [45056/60000 (73%)] Loss: 1.108090
Train Epoch: 0 [49152/60000 (80%)] Loss: 0.863600
Train Epoch: 0 [53248/60000 (87%)] Loss: 0.740245
Train Epoch: 0 [57344/60000 (93%)] Loss: 0.816747
Test set: Average loss: 0.3749, Accuracy: 9023/10000 (90%)
cuDNN version: 90100
Peak memory allocated:
fused: 1.94GB, unfused: 1.50GB
Memory allocated at end of forward pass:
fused: 0.59GB, unfused: 0.96GB