[GitHub] [incubator-mxnet] apeforest commented on issue #15288: [MXNET-978] Higher order gradient for sigmoid

[GitBox]

apeforest commented on issue #15288: [MXNET-978] Higher order gradient for 
sigmoid
URL: https://github.com/apache/incubator-mxnet/pull/15288#issuecomment-507516653
 
 
   I verified the result is the same as pytorch
   
   ```
   import torch
   import numpy as np
   import math
   
   op = lambda x: torch.sigmoid(x)
   grad_op = lambda x: op(x) * (1 - op(x))
   grad_grad_op = lambda x: grad_op(x) * (1 - 2 * op(x))
   grad_grad_grad_op = lambda x: grad_grad_op(x) - 2 * ( grad_op(x)**2 + 
grad_grad_op(x) * op(x))
   
   x = torch.tensor(np.array([1, 2, 3]), dtype=torch.float32)
   head_grads = torch.tensor(np.array([1, 1, 1]), dtype=torch.float32) * 0.5
   head_grad_grads = torch.tensor(np.array([1, 1, 1]), dtype=torch.float32) * 
0.6
   head_grad_grad_grads = torch.tensor(np.array([1, 1, 1]), 
dtype=torch.float32) * 0.7
   x.requires_grad = True
   head_grads.requires_grad = True
   
   y = op(x)
   x_grad = torch.autograd.grad(y, x, grad_outputs= head_grads, 
create_graph=True, retain_graph=True)[0]
   expected_grad_x = (grad_op(x) * head_grads).detach().numpy()
   print('expected_grad_x = {}'.format(expected_grad_x))
   print('grad_x          = {}'.format(x_grad.detach().numpy()))
   x_grad_grad = torch.autograd.grad(x_grad, x, grad_outputs= head_grad_grads, 
create_graph=True, retain_graph=True)[0]
   x_grad_grad.backward(head_grad_grad_grads)
   
   expected_grad_grad_x = (grad_grad_op(x) * head_grads * 
head_grad_grads).detach().numpy()
   expected_head_grad = (grad_op(x) * head_grad_grads).detach().numpy()
   expected_grad_grad_grad_x = (grad_grad_grad_op(x) * head_grads * 
head_grad_grads * head_grad_grad_grads).detach().numpy()
   
   print('expected_grad_grad_x = {}'.format(expected_grad_grad_x))
   print('grad_grad_x          = {}'.format(x_grad_grad.detach().numpy()))
   print('expected_grad_grad_grad_x = {}'.format(expected_grad_grad_grad_x))
   print('grad_grad_grad_x          = {}'.format(x.grad.detach().numpy()))
   ```

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