McCulloch-Pitts brains and pseudorandom functions

TL;DR

This paper demonstrates that McCulloch-Pitts neural models cannot generate weak pseudorandom functions, highlighting limitations in their capacity to produce unpredictable trajectories.

Contribution

It provides a theoretical proof that McCulloch-Pitts neural networks cannot be used to construct weak pseudorandom functions, addressing a question about their computational capabilities.

Findings

McCulloch-Pitts models cannot produce weak pseudorandom functions.

The study connects neural models with pseudorandomness theory.

It clarifies limitations of early neural network models in generating complex, unpredictable behavior.

Abstract

In a pioneering classic, Warren McCulloch and Walter Pitts proposed a model of the central nervous system. Motivated by EEG recordings of normal brain activity, Chv\'atal and Goldsmith asked whether or not these dynamical systems can be engineered to produce trajectories which are irregular, disorderly, apparently unpredictable. We show that they cannot build weak pseudorandom functions.