Metriplector: From Field Theory to Neural Architecture

Computer Science > Artificial Intelligence [Submitted on 31 Mar 2026] Metriplector: From Field Theory to Neural Architecture Dan Oprisa, Peter Toth 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 Focus to learn more Submission history From: Peter Toth [view email] [v1] Tue, 31 Mar 2026 09:40:26 UTC (210 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-03 Change to browse by: cs cs.LG References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)