Metriplector: From Field Theory to Neural Architecture
Summary: 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 Tμν, derived from Noether’s theorem, provides the readout.
The Metriplector framework introduces a groundbreaking approach to neural architectures by connecting physical principles with computational processes. This innovative system leverages advanced mathematical constructs to enhance the performance of machine learning models.
Key Features of Metriplector
The Metriplector formulation offers several distinctive features:
- Coupled Metriplectic Dynamics: The system evolves through multiple interacting fields governed by metriplectic dynamics, which allows for complex interactions akin to physical systems.
- Stress-Energy Tensor Readout: The architecture utilizes the stress-energy tensor Tμν derived from Noether’s theorem, providing a robust mechanism for output generation and interpretation.
- Dissipative Branch: The dissipative branch enables the exact solution of a screened Poisson equation via conjugate gradient methods, enhancing computational efficiency.
- Antisymmetric Poisson Bracket: Activating the full structure, including the antisymmetric Poisson bracket, allows for advanced field dynamics applicable in various domains such as image recognition and language modeling.
Evaluation Across Domains
Metriplector has been evaluated across four distinct domains, each utilizing a task-specific architecture derived from the shared primitive, progressively incorporating more intricate physics:
- Maze Pathfinding: Achieved an F1 score of 1.0, demonstrating remarkable generalization capabilities from 15×15 training grids to unseen 39×39 grids.
- Sudoku Solving: Attained a 97.2% exact solve rate with zero structural injection, showcasing its effectiveness in combinatorial problem-solving.
- CIFAR-100 Image Recognition: Recorded an impressive 81.03% accuracy with only 2.26 million parameters, highlighting the efficiency of the architecture.
- Language Modeling: Achieved 1.182 bits/byte with 3.6 times fewer training tokens than a GPT baseline, demonstrating significant improvements in data efficiency.
Conclusion
The introduction of Metriplector marks a significant advancement in the intersection of physics and machine learning. By leveraging the principles of field theory and transforming them into a neural architecture, Metriplector not only enhances computational dynamics but also sets a new benchmark for performance across diverse applications. Future research may explore deeper integrations of physical principles into AI, potentially paving the way for more sophisticated and efficient models.