Freeness in cognitive science

TL;DR

This paper reviews the potential of free random variables calculus as a novel probabilistic framework for cognitive science, illustrating its applications in neural data analysis, neuronal modeling, and deep learning.

Contribution

It introduces free random variables calculus as a new probabilistic tool for cognitive science and demonstrates its applications in neural data inference, neuronal non-normality, and deep learning.

Findings

Effective inference of noisy brain signals using FRV calculus

Highlighting the importance of non-normality in neuronal models

Applications of FRV in deep learning neural networks

Abstract

In this mini-review, dedicated to the Jubilee of Professor Tadeusz Marek, we highlight in a popular way the power of so-called free random variables (hereafter FRV) calculus, viewed as a potential probability calculus for the XXI century, in applications to the broad area of cognitive sciences. We provide three examples: (i) inference of noisy signals from multivariate correlation data from the brain; (ii) distinguished role of non-normality in real neuronal models; (iii) applications to the field of deep learning in artificial neural networks.