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I'm trying to convert my neural network implementation with ReLU to ELU.

I have visualisations of the ReLU decision bounaries and they look sensible. When I convert to ELU however, the bondaries look totally wrong.

The following are the only changes I'm making:

  1. alpha = 1

  2. In forward propagation, substitute:

    A1 = np.maximum(0, Z1) # ReLU
    A1 = np.where(Z1 > 0, Z1, alpha * (np.exp(Z1)-1)) # ELU
    
  3. In backward propagation, substitute:

    dgz = np.where(Z1 > 0, 1, 0) # ReLU
    dgz = np.where(Z1 > 0, 1, alpha * (np.exp(Z1)-1) + alpha) # ELU
    

What am I missing?

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  • $\begingroup$ Could you post a pic of the boundaries. Are you sure the ELU approach converged? $\endgroup$ – Jim Mar 15 '18 at 16:19
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The ICLR conference paper that you cite (Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs), 2016, Clevert et al.), provides the derivative in section 3:

$$ f'(x) = \begin{cases} 1 & \text{if } x > 0 \\ \alpha\exp(x) & \text{if } x \le 0. \\ \end{cases} $$

It appears that your implementation (simplified)

  dgz = np.where(Z1 > 0, 1, alpha*np.exp(Z1))

is correct.

However, other factors could explain the difference with $\text{ReLU}$. For example, it could be that the $\text{ELU}$-network requires more iterations to converge. Therefore, have a look at both learning curves (plotted by epoch or iteration).

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