Papers for

cognitive scientists

Papers whose findings have a practical use for this group, as judged from the abstract. Open a paper to read what it means in practice.

MaxEnt probability distributions on spheres inform models of cognition

Maximum Entropy Probability Distributions on Spheres with Fixed Mean Busemann Function and Holomorphic-Information-Geometric Model of Cognition

Abstract: In the first half of the paper we revisit the question regarding MaxEnt probability distributions on spheres. We derive families of MaxEnt distributions on spheres in real and complex vector spaces with fixed expected Busemann function (energy). As a particular case, we deduce sub-families on canonical energy levels where inverse temperature equals the dimension of the sphere. In the second part we focus on the information manifold of canonical MaxEnt distributions on the sphere in the complex vector space. This manifold is isomorphic to the Bergman ball. We introduce the reproducing kernel on this manifold and use the RKHS theory to elaborate the model of cognition. In particular, we state the principle of minimal cognitive effort in RKHS and demonstrate its dual relationship with the MaxEnt principle for probability distributions on the boundary sphere.

Thu 17 SeptInformation Theory

The gist

The paper studies the best ways to spread probabilities on spheres when we fix certain energy-like values. The authors find special families of these distributions in both real and complex spaces. Then they link these distributions to a geometric space called the Bergman ball, using advanced math tools called reproducing kernels. They propose a new way to think about cognition as minimizing effort in this geometric space, showing how it relates to the idea of maximum entropy for probabilities on the sphere.

Open → 2609.20410v1