Metriplector: From Field Theory to Neural Architecture
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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Viability of perturbative expansion for quantum field theories on neurons
Neural Network (NN) architectures that break statistical independence of parameters have been proposed as a new approach for simulating local quantum field theories (QFTs). In the infinite neuron number limit, single-lay…
Neural Network Field Theories: Non-Gaussianity, Actions, and Locality
Both the path integral measure in field theory and ensembles of neural networks describe distributions over functions. When the central limit theorem can be applied in the infinite-width (infinite-$N$) limit, the ensembl…
The Neural Networks with Tensor Weights and the Corresponding Fermionic Quantum Field Theory
In this paper, we establish a theoretical connection between complex-valued neural networks (CVNNs) and fermionic quantum field theory (QFT), bridging a fundamental gap in the emerging framework of neural network quantum…
Quantum field-theoretic machine learning
We derive machine learning algorithms from discretized Euclidean field theories, making inference and learning possible within dynamics described by quantum field theory. Specifically, we demonstrate that the $\phi^{4}$ …
BIG-bench Machine LearningUnified field theoretical approach to deep and recurrent neuronal networks
Understanding capabilities and limitations of different network architectures is of fundamental importance to machine learning. Bayesian inference on Gaussian processes has proven to be a viable approach for studying rec…
Bayesian InferenceGaussian Processes