On the Beauty of a Neuron Expressivity Matrix

  1. First, let’s count the number of functions with fixed weights but a varying threshold. We select weights w with exactly q ones (picture below) and enumerate all thresholds (t=0,1,2,…,N). We receive q+2 functions. Plus 2 because we get two additional functions: for t>q the neuron is not active (y=0), and for t=0 the neuron is always active y=1.

Motivation

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Viacheslav Osaulenko

Viacheslav Osaulenko

Scientist from Ukraine. Author of a blog about artificial intelligence @AITerritory