Paper shows algebraic emergence in neural circuits: composed motifs yield group structure absent in primitives
neurovium · x · 2026-10-30
Nima Dehghani's arXiv paper represents canonical neural circuit motifs (divisive normalization, winner-take-all) as finite transformation systems and analyzes their transition monoids.
Key findings:
- Aperiodic updates alone can generate non-aperiodic monoids through composition;
- In WTA, every frozen-drive generator collapses to fixed points, yet short input sequences create winner-dependent inhibitory gating cycles — globally dissipative dynamics with a reversible action;
- The strongest result is WTA-to-DN composition: the composed monoid contains a genuinely composite local cycle coupling normalization state and winner gating, although every primitive generator is aperiodic. Holonomy analysis certifies it as a group component of the Krohn-Rhodes cascade.
The author frames this as a path to interpretability via algebraic decomposition — teasing big networks apart into operational motifs, Lego-style.
Related event: Paper Uses Algebra to Show Emergent Structure in Combined Neural Circuits(2 posts)→
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