What is the maximum number of sides that a n-unit sigmoid-relu function can produce?

27 Views Asked by At

A $n$-unit sigmoid-relu function is defined as sigmoid of summation of $n$ relu functions where each relu function takes a linear expression in two variables as an input. The contour plot of such function yields a set of concentric $m$-gons sometimes. For a given $n$, what is the maximum $m$?

Find more about Sigmoid function and ReLU function.

It's a fun little experiment based on a question I was asked by one of my juniors in the realm of neural networks. Based on just the experiments, I could say $m = nC2$. I could be way way off. Please enlighten me on this topic.

Feel free to experiment yourselves at this url :

https://colab.research.google.com/drive/1DNvKdzVbSCpK0hxZFzMD7P0VKo4igBVU