[BUGFIX] fix ELU function will appear nan when calculating the gradient

[fierceX]

Description

fix ELU function will appear nan when calculating the gradient

e.g:

elu = nn.ELU()
elu.initialize()
x = nd.ones((2, 3))
x.attach_grad()
x[0] = 100
x[1] = -1
with autograd.record():
    y = elu(x)

y.backward()
print(y)
print(x.grad)

output is

[[100.         100.         100.        ]
 [ -0.63212055  -0.63212055  -0.63212055]]
<NDArray 2x3 @cpu(0)>

[[       nan        nan        nan]
 [0.36787945 0.36787945 0.36787945]]
<NDArray 2x3 @cpu(0)>

After experiments, it was found that the where and the exp were used together and that this bug would occur

e.g:

x = nd.ones((2, 3))
x.attach_grad()
x[0] = 100
x[1] = 5

with autograd.record():
    y = nd.where(x > 0, x, nd.exp(x))
y.backward()
print(y)
print(x.grad)

output:

[[100. 100. 100.]
 [  5.   5.   5.]]
<NDArray 2x3 @cpu(0)>

[[nan nan nan]
 [ 1.  1.  1.]]
<NDArray 2x3 @cpu(0)>

When the exp calculation appears inf, even if where does not select the value, but the gradient will still be nan,so this PR does not completely fix the problem, but based on this, modified the ELU calculation method so that it does not appear nan

[haojin2]

Thanks for your contribution!
Actually we do have ELU implemented in the backend so you can call it directly
Please use:

return F.LeakyReLU(x, act_type='elu', slope=self._alpha)

here instead and also you want to change: https://github.com/apache/incubator-mxnet/blob/master/tests/python/unittest/test_gluon.py#L1183 to:

return mx.nd.expm1(x) if x <= 0.0 else x

so that the test would still pass after this change.

[fierceX]

This bug does not affect the forward calculation, but occurs when the gradient is calculated backwards.

[haojin2]

@fierceX Yes I understand, and I'm presenting the recommended way to fix this issue to you in the above comment.

[haojin2]

@fierceX You also need to change tests/python/unittest/test_gluon.py Line 1183 to:

return mx.nd.expm1(x) if x <= 0.0 else x

so that the test could pass, thanks!

[haojin2]

Seems like you have an extra whitespace here, please get rid of that and this is good to go.

[fierceX]

Sorry, less return.

[haojin2]

Nit: The extra space before return

[haojin2]

LGTM. Will merge once the test passes.

[fierceX]

Note: There should still be a bug in the where operator.

[haojin2]

@fierceX We'll surely investigate that.

[haojin2]

@fierceX Can you rebase and do a force push?

[haojin2]

@fierceX Merged, thanks for your contribution!