Dynamics of An Information Theoretic Analog of Two Masses on a Spring

TL;DR

This paper develops an information theoretic model inspired by classical mechanics to analyze belief dynamics among agents, revealing complex behaviors like chaos and insights into stable persuasion strategies.

Contribution

It introduces a novel information theoretic analogue of a physical spring system using Fisher metric and Jeffrey's divergence, connecting mechanics with belief dynamics.

Findings

Dynamics resemble flows on tori with chaotic behavior near boundaries

Manipulating peer pressure is more stable than gradual belief change

The model links classical mechanics concepts with belief update processes

Abstract

In this short communication we investigate an information theoretic analogue of the classic two masses on spring system, arising from a physical interpretation of Friston's free energy principle in the theory of learning in a system of agents. Using methods from classical mechanics on manifolds, we define a kinetic energy term using the Fisher metric on distributions and a potential energy function defined in terms of stress on the agents' beliefs. The resulting Lagrangian (Hamiltonian) produces a variation of the classic DeGroot dynamics. In the two agent case, the potential function is defined using the Jeffrey's divergence and the resulting dynamics are characterized by a non-linear spring. These dynamics produce trajectories that resemble flows on tori but are shown numerically to produce chaos near the boundary of the space. We then investigate persuasion as an information theoretic control problem where analysis indicates that manipulating peer pressure with a fixed target is a more stable approach to altering an agent's belief than providing a slowly changing belief state that approaches the target.