mlsanityData to 7 Oct 2026

Metriplector: From Field Theory to Neural Architecture

arXiv 2603.29496 ↗First posted 31 Mar 2026cs.AI cs.LGcited by 1

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Abstract (arXiv)

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 Tμnu, 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.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 91 of its 143 references that are in the map. First posted on arXiv 31 Mar 2026.

Builds on

91 of 143 references.

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  1. 2026GENERIC-FNO: Embedding Energy Conservation and Entropy Production into Fourier Neural Operatorscited by 0