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Custom activation function in Neural Network?

Posted 10 months ago
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Hello! Is it possible to set user defined activation function for a layer in neural network?

If this feature is not yet part of WL, are there any plans for such an addition as it would be very helpful.

8 Replies
Posted 10 months ago

ElementwiseLayer[f] allows you to define a layer with a custom activation function f applied to each element of the input:

http://reference.wolfram.com/language/ref/ElementwiseLayer.html.

@narendra : out of curiosity, is there are particular activation you are trying to implement yourself?

Posted 10 months ago

@Sebastian Bodenstein Yes, I am currently writing a paper on activation functions based on fractional calculus. I am currently implementing it in python, however Wolfram would be much better fit for it due to it having inbuilt functions from fractional calculus from which I derive my specific function.

However when I try to use it with ElementwiseLayer, it gives an error of ElementwiseLayer::invscf: my_func could not be symbolically evaluated as a unary scalar function.

(Interestingly, it is a unary scalar function because it can be plotted using only one variable and gives out scalar values when individually applied over scalar values)

@narendra it is always helpful to post a complete code resulting in the error: http://wolfr.am/READ-1ST

Posted 9 months ago

@S├ębastien Guillet While I can not disclose the exact details as I am currently not finished writing the paper yet, ElementWiseLayer does not do well with many functions beyond the normal commonly used ones.

Example: The recently popular Swish Activation Function which performs better than ReLU in most cases. It is defined as x*sigmoid(x)

elem = ElementwiseLayer[x*LogisticSigmoid[x]]

gives an error

ElementwiseLayer::invscf: x LogisticSigmoid[x] could not be symbolically evaluated as a unary scalar function.

This is the same error I am receiving whenever the complexity of function is a little more than exponential or tanh.

Posted 9 months ago

@narendra Replace x with # (Slot) which represent a pure function.

ElementwiseLayer[#*LogisticSigmoid[#] &]

True! @narendra I recommend reading tutorial on Pure Functions:

http://reference.wolfram.com/language/tutorial/PureFunctions.html

Here's an example how to implement somewhat more complex like differential equations: ODEs, SDEs, etc. into ElementwiseLayer[...]: DiffEq in Neural Net

(Open picture into new tab to see it in full size!)

Depending on the result representation with or without Normal[...] to get the value(s).

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