使用自定義函式融合卷積和批次歸一化

建立日期：2021 年 7 月 22 日 | 最後更新：2023 年 4 月 18 日 | 最後驗證：2024 年 11 月 5 日

將相鄰的卷積層和批次歸一化層融合在一起通常是一種推理時最佳化，以提高執行時間。這通常是透過完全消除批次歸一化層並更新前一個卷積層的權重和偏置來實現的 [0]。然而，這種技術不適用於模型訓練。

在本教程中，我們將展示一種不同的層融合技術，該技術可以在訓練期間應用。這種最佳化的目標不是提高執行時間，而是減少記憶體使用。

這種最佳化背後的想法是認識到卷積和批次歸一化（以及許多其他運算元）在前向傳播期間都需要儲存輸入的副本以供反向傳播使用。對於大批次大小，這些儲存的輸入佔用了大部分記憶體，因此能夠避免為每一對卷積和批次歸一化分配另一個輸入張量可以顯著減少記憶體消耗。

在本教程中，我們透過將卷積和批次歸一化組合成一個單一的層（作為自定義函式）來避免這種額外的分配。在這個組合層的前向傳播中，我們像往常一樣執行卷積和批次歸一化，唯一的區別是我們只儲存卷積的輸入。為了獲得批次歸一化的輸入（這是透過它進行反向傳播所必需的），我們在反向傳播過程中再次重新計算卷積的前向傳播。

需要注意的是，這種最佳化的使用是具有情境性的。雖然（透過避免儲存一個緩衝區）我們在前向傳播結束時總是減少了記憶體分配，但在某些情況下，分配的峰值記憶體可能實際上並沒有減少。詳情請參閱最後一節。

為了簡化，在本教程中，我們硬編碼了 Conv2D 的 bias=False、stride=1、padding=0、dilation=1 和 groups=1。對於 BatchNorm2D，我們硬編碼了 eps=1e-3、momentum=0.1、affine=False 和 track_running_statistics=False。另一個小區別是，我們在計算批次歸一化時，在平方根之外的分母中添加了 epsilon。

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

卷積的反向傳播公式實現

實現自定義函式需要我們自己實現反向傳播。在這種情況下，我們需要 Conv2D 和 BatchNorm2D 的反向傳播公式。最終我們將它們連結到我們統一的反向函式中，但在下面我們首先將它們實現為自己的自定義函式，以便我們可以分別驗證它們的正確性

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 進行測試時，重要的是使用雙精度浮點數

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

批次歸一化的反向傳播公式實現

批次歸一化有兩種模式：訓練模式和 eval 模式。在訓練模式下，樣本統計資訊是輸入的函式。在 eval 模式下，我們使用儲存的執行統計資訊，這些統計資訊不是輸入的函式。這使得非訓練模式的反向傳播顯著簡化。下面我們只實現和測試訓練模式的情況。

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 進行測試

a = torch.rand(1, 2, 3, 4, requires_grad=True, dtype=torch.double)
torch.autograd.gradcheck(BatchNorm.apply, (a,), fast_mode=False)

True

融合卷積和批次歸一化

現在大部分工作已經完成，我們可以將它們組合起來。請注意，在 (1) 中，我們只為反向傳播儲存了一個緩衝區，但這也意味著我們在 (5) 中重新計算卷積的前向傳播。此外，請看 (2)、(3)、(4) 和 (6) 中的程式碼與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

下一步是將我們的函式式變體封裝在一個有狀態的 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 驗證我們的反向傳播公式的正確性

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

測試我們的新層

使用 FusedConvBN 訓練一個基本網路 下面的程式碼是對此處示例進行一些輕微修改後的結果：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)

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記憶體使用比較

如果啟用了 CUDA，則打印出 fused=True 和 fused=False 的記憶體使用情況 在 NVIDIA GeForce RTX 3070、NVIDIA CUDA® 深度神經網路庫 (cuDNN) 8.0.5 上的示例執行結果：融合後的峰值記憶體：1.56GB，未融合的峰值記憶體：2.68GB

需要注意的是，此模型的峰值記憶體使用情況可能因所使用的具體 cuDNN 卷積演算法而異。對於較淺層的模型，融合模型的峰值記憶體分配甚至可能超過未融合模型！這是因為計算某些 cuDNN 卷積演算法所需的記憶體可能足夠高，以至於“隱藏”了你在反向傳播開始時通常預期的峰值。

因此，我們也記錄並顯示了前向傳播結束時的記憶體分配作為近似值，並以此表明對於每個融合的 conv-bn 對，我們確實少分配了一個緩衝區。

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: 7.906041
Train Epoch: 0 [8192/60000 (13%)]       Loss: 3.852560
Train Epoch: 0 [12288/60000 (20%)]      Loss: 2.176885
Train Epoch: 0 [16384/60000 (27%)]      Loss: 1.876234
Train Epoch: 0 [20480/60000 (33%)]      Loss: 1.706322
Train Epoch: 0 [24576/60000 (40%)]      Loss: 1.607102
Train Epoch: 0 [28672/60000 (47%)]      Loss: 1.706126
Train Epoch: 0 [32768/60000 (53%)]      Loss: 1.481350
Train Epoch: 0 [36864/60000 (60%)]      Loss: 1.342697
Train Epoch: 0 [40960/60000 (67%)]      Loss: 1.154232
Train Epoch: 0 [45056/60000 (73%)]      Loss: 1.001995
Train Epoch: 0 [49152/60000 (80%)]      Loss: 1.001608
Train Epoch: 0 [53248/60000 (87%)]      Loss: 0.860608
Train Epoch: 0 [57344/60000 (93%)]      Loss: 0.692767

Test set: Average loss: 0.4204, Accuracy: 8901/10000 (89%)

Train Epoch: 0 [0/60000 (0%)]   Loss: 2.349130
Train Epoch: 0 [4096/60000 (7%)]        Loss: 7.946248
Train Epoch: 0 [8192/60000 (13%)]       Loss: 3.230653
Train Epoch: 0 [12288/60000 (20%)]      Loss: 2.591974
Train Epoch: 0 [16384/60000 (27%)]      Loss: 1.949312
Train Epoch: 0 [20480/60000 (33%)]      Loss: 2.424960
Train Epoch: 0 [24576/60000 (40%)]      Loss: 2.075612
Train Epoch: 0 [28672/60000 (47%)]      Loss: 1.709257
Train Epoch: 0 [32768/60000 (53%)]      Loss: 1.384610
Train Epoch: 0 [36864/60000 (60%)]      Loss: 1.277133
Train Epoch: 0 [40960/60000 (67%)]      Loss: 1.244485
Train Epoch: 0 [45056/60000 (73%)]      Loss: 0.953217
Train Epoch: 0 [49152/60000 (80%)]      Loss: 0.987237
Train Epoch: 0 [53248/60000 (87%)]      Loss: 0.953964
Train Epoch: 0 [57344/60000 (93%)]      Loss: 1.040246

Test set: Average loss: 0.4897, Accuracy: 8488/10000 (85%)

cuDNN version: 90501

Peak memory allocated:
fused: 1.94GB, unfused: 1.50GB
Memory allocated at end of forward pass:
fused: 0.59GB, unfused: 0.96GB