Metriplector: From Field Theory to Neural Architecture

• URL: http://arxiv.org/abs/2603.29496v2
• Date: Mon, 06 Apr 2026 09:07:56 GMT
• Title: Metriplector: From Field Theory to Neural Architecture
• Abstract summary: We present Metriplector, a neural architecture primitive in which the input configures an abstract physical system.<n>Multiple fields evolve via coupled metriplectic dynamics, and the stress-energy tensor T, derived from Noether's theorem, provides the readout.<n>We evaluate Metriplector across five domains, each using a task-specific architecture built from this shared primitive with progressively richer physics.
• Score: 0.25168553347063854
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present Metriplector, a neural architecture primitive in which the input configures an abstract physical system -- fields, sources, and operators -- and the dynamics of that system is the computation. Multiple fields evolve via coupled metriplectic dynamics, and the stress-energy tensor T^{μν}, derived from Noether's theorem, provides the readout. The metriplectic formulation admits a natural spectrum of instantiations: the dissipative branch alone yields a screened Poisson equation solved exactly via conjugate gradient; activating the full structure -- including the antisymmetric Poisson bracket -- gives field dynamics for image recognition, language modeling, and robotic control. We evaluate Metriplector across five domains, each using a task-specific architecture built from this shared primitive with progressively richer physics: 81.03% on CIFAR-100 with 2.26M parameters; 88% CEM success on Reacher robotic control with under 1M parameters; 97.2% exact Sudoku solve rate with zero structural injection; 1.182 bits/byte on language modeling with 3.6x fewer training tokens than a GPT baseline; and F1=1.0 on maze pathfinding, generalizing from 15x15 training grids to unseen 39x39 grids.

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