Metriplector: From Field Theory to Neural Architecture
arXiv:2603.29496v1 Announce Type: new 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^{{\mu}{\nu}}, 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 and language modeling. We evaluate Metriplector across four domains, each using a task-specific arc
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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^{{\mu}{\nu}}, 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 and language modeling. We evaluate Metriplector across four domains, each using a task-specific architecture built from this shared primitive with progressively richer physics: F1=1.0 on maze pathfinding, generalizing from 15x15 training grids to unseen 39x39 grids; 97.2% exact Sudoku solve rate with zero structural injection; 81.03% on CIFAR-100 with 2.26M parameters; and 1.182 bits/byte on language modeling with 3.6x fewer training tokens than a GPT baseline.
Comments: 30 pages, 7 figures
Subjects:
Artificial Intelligence (cs.AI); Machine Learning (cs.LG)
MSC classes: 68T07, 37K05, 70H33
ACM classes: I.2.6; F.2.2
Cite as: arXiv:2603.29496 [cs.AI]
(or arXiv:2603.29496v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2603.29496
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Peter Toth [view email] [v1] Tue, 31 Mar 2026 09:40:26 UTC (210 KB)
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