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I'm wondering about the benefits of advanced activation layers such as LeakyReLU, Parametric ReLU, and Exponential Linear Unit (ELU). What are the differences between them and how do they benefit training?

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    $\begingroup$ Partially helpful answer $\endgroup$ – Dawny33 Aug 23 '17 at 17:53
  • $\begingroup$ Would you please explain the exact meaning of 'noise in deactivation results in different levels of absence'?, what is levels of absence? $\endgroup$ – Nina Jan 18 '18 at 11:05
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ReLU

Simply rectifies the input, meaning positive inputs are retained but negatives give an output of zero. (Hahnloser et al. 2010)

$$ f(x) = max(0,x) $$ Pros:

  • Eliminates the vanishing/exploding gradient problem. (true for all following as well)
  • Sparse activation. (true for all following as well)
  • Noise-robust deactivation state (i.e. does not attempt to encode the degree of absence).

Cons:

  • Dying ReLU problem (many neurons end up in a state where they are inactive for most or all inputs).
  • Not differentiable. (true for all following as well)
  • No negative values means mean unit activation is often far from zero. This slows down learning.

Leaky ReLUs

Adds a small coefficient ($<1$) for negative values. (Maas, Hannun, & Ng 2013)

$$ f(x) = \begin{cases} x & \text{if } x \geq 0 \\ 0.1 x & \text{otherwise} \end{cases} $$

Pros:

  • Alleviates dying ReLU problem. (true for all following)
  • Negative activations push mean unit activation closer to zero and thus speeds up learning. (true for all following)

Cons:

  • Deactivation state is not noise-robust (i.e. noise in deactivation results in different levels of absence).

PReLUs

Just like Leaky ReLUs but with a learnable coefficient. (Note that in the below equation a different $a$ can be learned for different channels.) (He et al. 2015)

$$ f(x) = \begin{cases} x & \text{if } x \geq 0 \\ a x & \text{otherwise} \end{cases} $$

Pros:

  • Improved performance (lower error rate on benchmark tasks) compared to Leaky ReLUs.

Cons:

  • Deactivation state is not noise-robust (i.e. noise in deactivation results in different levels of absence).

ELUs

$$ f(x) = \begin{cases} x & \text{if } x \geq 0 \\ \alpha(exp(x)-1) & \text{otherwise} \end{cases} $$

Replaces the small linear gradient of Leaky ReLUs and PReLUs with a vanishing gradient. (Clevert, Unterthiner, Hochreiter 2016)

Pros:

  • Improved performance (lower error and faster learning) compared to ReLUs.
  • Deactivation state is noise-robust.
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    $\begingroup$ Thanks what do you mean by "Noise-robust deactivation state (i.e. does not attempt to encode the degree of absence)" ? $\endgroup$ – nsaura Aug 7 '20 at 0:10

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