Derivative of neural network with respect to input

Question

I trained a neural network to do a regression on the sine function and would like to compute the first and second derivative with respect to the input. I tried using the tf.

Answer 1

What you learned was the sinus function and not its derivative : during the training process, you are controlling the error with your cost function that takes into account only the values, but it does not control the slope at all : you could have learned a very noisy function but matching the data points exactly.

If you are just using the data point in your cost function, you have no guarantee about the derivative you've learned. However, with some advanced training technics, you could also learn such a derivative : https://arxiv.org/abs/1706.04859

So as a summary, it is not a code issue but only a theoritical issue