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arXiv · 2609.33896

Harmonic Theory of Behavior

Mohammad Salahshour·Iain D. Couzin
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Abstract

Traditional models of collective behavior rely on prescribed interaction rules, leaving unresolved the question of how behavior arises from neural representations of space. Here, we develop a first-principles theory in which movement, decision-making, and collective organization emerge by coarse-graining fast neural dynamics on a topological representation of directional space. For a ring manifold encoding heading, this reduction yields a macroscopic theory of behavior: a decision landscape over directions that admits a harmonic decomposition. In this framework, behavior is governed by a spectral organization of directional information rather than ad hoc rules. We demonstrate that target-seeking, avoidance, choice, spatial decision-making, and diverse forms of collective motion arise as distinct organizations of the underlying harmonic landscape. The theory unifies neural representations, behavioral decisions, and collective dynamics in a single mathematical description.

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Mohammad Salahshour, Iain D. Couzin. 2026-09-27. Harmonic Theory of Behavior. https://arxiv.org/abs/2609.33896

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