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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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Cite

BibTeXRIS
BibTeX
@misc{salahshour2026harmonic,
  title = {{Harmonic Theory of Behavior}},
  author = {Mohammad Salahshour and Iain D. Couzin},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.33896},
  eprint = {2609.33896},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.33896},
}
RIS
TY  - UNPB
TI  - Harmonic Theory of Behavior
AU  - Mohammad Salahshour
AU  - Iain D. Couzin
PY  - 2026
DA  - 2026/09/27
PB  - arXiv
DO  - 10.48550/arxiv.2609.33896
UR  - https://arxiv.org/abs/2609.33896
AB  - 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.
ER  -