batch_norm_manual gradient inconsistent

[ken012git]

Hi Ptrblk,

I am playing with PyTorch batchnorm2d and your implementation. I tried to use your implementation in mobilenetv3 and the performance seems similar. However, I found the gradient values are not the same, but I am not sure why. Below is my test code:

"""
Comparison of manual BatchNorm2d layer implementation in Python and
nn.BatchNorm2d
@author: ptrblck
"""

import torch
import torch.nn as nn


def compare_bn(bn1, bn2):
    err = False
    if not torch.allclose(bn1.running_mean, bn2.running_mean):
        print('Diff in running_mean: {} vs {}'.format(
            bn1.running_mean, bn2.running_mean))
        err = True

    if not torch.allclose(bn1.running_var, bn2.running_var):
        print('Diff in running_var: {} vs {}'.format(
            bn1.running_var, bn2.running_var))
        err = True

    if bn1.affine and bn2.affine:
        if not torch.allclose(bn1.weight, bn2.weight):
            print('Diff in weight: {} vs {}'.format(
                bn1.weight, bn2.weight))
            err = True
        # compare weight gradient here
        if not torch.allclose(bn1.weight.grad, bn2.weight.grad):
            print('Diff in weight gradient: {} vs {}'.format(
                bn1.weight.grad, bn2.weight.grad))
            err = True

        if not torch.allclose(bn1.bias, bn2.bias):
            print('Diff in bias: {} vs {}'.format(
                bn1.bias, bn2.bias))
            err = True
        # compare bias gradient here
        if not torch.allclose(bn1.bias.grad, bn2.bias.grad):
            print('Diff in bias gradient: {} vs {}'.format(
                bn1.bias.grad, bn2.bias.grad))
            err = True

    if not err:
        print('All parameters are equal!')


class MyBatchNorm2d(nn.BatchNorm2d):
    def __init__(self, num_features, eps=1e-5, momentum=0.1,
                 affine=True, track_running_stats=True):
        super(MyBatchNorm2d, self).__init__(
            num_features, eps, momentum, affine, track_running_stats)

    def forward(self, input):
        self._check_input_dim(input)

        exponential_average_factor = 0.0

        if self.training and self.track_running_stats:
            if self.num_batches_tracked is not None:
                self.num_batches_tracked += 1
                if self.momentum is None:  # use cumulative moving average
                    exponential_average_factor = 1.0 / float(self.num_batches_tracked)
                else:  # use exponential moving average
                    exponential_average_factor = self.momentum

        # calculate running estimates
        if self.training:
            mean = input.mean([0, 2, 3])
            # use biased var in train
            var = input.var([0, 2, 3], unbiased=False)
            n = input.numel() / input.size(1)
            with torch.no_grad():
                self.running_mean = exponential_average_factor * mean\
                    + (1 - exponential_average_factor) * self.running_mean
                # update running_var with unbiased var
                self.running_var = exponential_average_factor * var * n / (n - 1)\
                    + (1 - exponential_average_factor) * self.running_var
        else:
            mean = self.running_mean
            var = self.running_var

        input = (input - mean[None, :, None, None]) / (torch.sqrt(var[None, :, None, None] + self.eps))
        if self.affine:
            input = input * self.weight[None, :, None, None] + self.bias[None, :, None, None]

        return input


# Init BatchNorm layers
my_bn = MyBatchNorm2d(3, affine=True)
bn = nn.BatchNorm2d(3, affine=True)
# Load weight and bias
my_bn.load_state_dict(bn.state_dict())

# Run train
for _ in range(10):
    scale = torch.randint(1, 10, (1,)).float()
    bias = torch.randint(-10, 10, (1,)).float()
    x = torch.randn(10, 3, 100, 100) * scale + bias
    out1 = my_bn(x)
    out2 = bn(x)
    #  calculate gradient for leaf
    out1.sum().backward()
    out2.sum().backward()
    compare_bn(my_bn, bn)

    torch.allclose(out1, out2)
    print('Max diff: ', (out1 - out2).abs().max())

# Run eval
my_bn.eval()
bn.eval()
for _ in range(10):
    scale = torch.randint(1, 10, (1,)).float()
    bias = torch.randint(-10, 10, (1,)).float()
    x = torch.randn(10, 3, 100, 100) * scale + bias
    out1 = my_bn(x)
    out2 = bn(x)
    #  calculate gradient for leaf
    out1.sum().backward()
    out2.sum().backward()
    compare_bn(my_bn, bn)

    torch.allclose(out1, out2)
    print('Max diff: ', (out1 - out2).abs().max())

Thanks in advance.

[ptrblck]

I guess you are running into the expected numerical precision errors due to the usage of sum as I've described here:
pytorch/pytorch#82493 (comment)

TL;DR: small expected numerical mismatches of 1e-7 or 1e-6 will be accumulated num_elements times, if you are summing the output. My post in the upstream issue describes it in more details.

If I'm using out.mean().backward() I'm seeing the expected small differences as ~1e-8; closing.