double backward always returns nan when dtype is float16 and cudnn is enabled.

When a pair of F.reshape and F.batch_normalization is used under the condition that dtype is fload16 and use_cudnn=‘always’, double backward of the pair goes so unstable that it returns nan with high probability.

One use-case of the pair is F.group_normalization: https://github.com/chainer/chainer/blob/afe903389d822583a5355e9d46e6766d048ebeb5/chainer/functions/normalization/group_normalization.py#L61-L72

• Conditions

Platform: Linux-4.4.0-98-generic-x86_64-with-debian-stretch-sid
Chainer: 6.0.0b2
NumPy: 1.15.4
CuPy:
  CuPy Version          : 6.0.0b2
  CUDA Root             : /usr/local/cuda
  CUDA Build Version    : 9020
  CUDA Driver Version   : 9020
  CUDA Runtime Version  : 9020
  cuDNN Build Version   : 7201
  cuDNN Version         : 7201
  NCCL Build Version    : None
iDeep: 2.0.0.post3

• Code to reproduce

import cupy as cp
from chainer import gradient_check
import chainer.functions as F
import numpy


def reshape_and_bn(x, gamma, beta):
    x_shape = x.shape
    expander = [None, Ellipsis, None, None]
    x_ = F.reshape(x, (1, x_shape[0] * x_shape[1], -1, 1))
    dummy_g = cp.ones(x_.shape[1], dtype=x_.dtype)
    dummy_b = cp.zeros(x_.shape[1], dtype=x_.dtype)
    x_normalized = F.batch_normalization(x_, dummy_g, dummy_b)
    x_normalized = F.reshape(x_normalized, x_shape)
    gamma = gamma[expander]
    beta = beta[expander]
    return x_normalized * gamma + beta


def run():
    x = cp.random.uniform(-1, 1, (5, 3, 4, 4)).astype(cp.float16)
    gy = cp.random.uniform(-1, 1, (5, 3, 4, 4)).astype(cp.float16)
    ggx = cp.random.uniform(-1, 1, (5, 3, 4, 4)).astype(cp.float16)
    gamma = cp.random.uniform(-1, 1, 3).astype(cp.float16)
    beta = cp.random.uniform(-1, 1, 3).astype(cp.float16)
    ggamma = cp.random.uniform(-1, 1, 3).astype(cp.float16)
    gbeta = cp.random.uniform(-1, 1, 3).astype(cp.float16)

    print('Backward')
    gradient_check.check_backward(
        reshape_and_bn, (x, gamma, beta,), (gy,), dtype=numpy.float64,
        atol=1e-2, rtol=1e-3
    )

    print('Double Backward')
    gradient_check.check_double_backward(
        reshape_and_bn, (x, gamma, beta), (gy,),
        (ggx, ggamma, gbeta), dtype=numpy.float64,
        atol=1e-2, rtol=1e-3
    )


if __name__ == '__main__':
    run()

• Error messages, stack traces, or logs

For backward,

gradients (numeric):  0.6409951020032167
gradients (backward): -0.5768083848859537


Not equal to tolerance rtol=0.001, atol=0.01

Mismatch: 100%
Max absolute difference: 1.21780349
Max relative difference: 2.1112791
 x: array(0.640995)
 y: array(-0.576808)

assert_allclose failed:
  shape: () ()
  dtype: float64 float64
  i: (0,)
  x[i]: 0.6409951020032167
  y[i]: -0.5768083848859537
  relative error[i]: 2.1112790985691965
  absolute error[i]: 1.2178034868891703
x: 0.6409951
y: -0.57680838

For double backward,

gradients (numeric):  1.773324329406023
gradients (backward): nan


Not equal to tolerance rtol=0.001, atol=0.01

x and y nan location mismatch:
 x: array(1.773324)
 y: array(nan)

assert_allclose failed:
  shape: () ()
  dtype: float64 float64
  i: (0,)
  x[i]: 1.773324329406023
  y[i]: nan
  relative error[i]: nan
  absolute error[i]: nan
x: 1.77332433
y: nan

[crcrpar]

@grafi-tt I tried the snippet with current master, and it worked.

[takagi]

I will check if this issue is related to #6323 .