arxiv_ml 60% Match Research Paper Theoretical Physicists,Machine Learning Researchers,Computational Scientists 2 weeks ago

Emergent field theories from neural networks

generative-ai › diffusion

📄 Abstract

Abstract: We establish a duality relation between Hamiltonian systems and neural network-based learning systems. We show that the Hamilton's equations for position and momentum variables correspond to the equations governing the activation dynamics of non-trainable variables and the learning dynamics of trainable variables. The duality is then applied to model various field theories using the activation and learning dynamics of neural networks. For Klein-Gordon fields, the corresponding weight tensor is symmetric, while for Dirac fields, the weight tensor must contain an anti-symmetric tensor factor. The dynamical components of the weight and bias tensors correspond, respectively, to the temporal and spatial components of the gauge field.

Authors (1)

Vitaly Vanchurin

Submitted

November 12, 2024

arXiv Category

hep-th

arXiv PDF

Key Contributions

This paper establishes a novel duality relation between Hamiltonian systems and neural network-based learning systems, showing that Hamilton's equations correspond to activation and learning dynamics. This duality is then applied to model various field theories (Klein-Gordon, Dirac) using neural networks, offering a new perspective on simulating physical phenomena.

Business Value

Could lead to new computational tools for physics research and simulation, potentially accelerating discovery in fundamental science and enabling new approaches to complex system modeling.

Paper Metadata

Innovation Type

Theoretical/Algorithmic

Deployment Feasibility

Low, highly theoretical and requires significant expertise in both physics and machine learning.

Limitations Addressed

Difficulty in directly simulating complex field theories,Lack of theoretical connections between dynamical systems and neural network learning

Technical Tags

Hamiltonian systemsneural networksfield theoriesduality relationactivation dynamicslearning dynamicsKlein-Gordon fieldsDirac fieldsgauge fieldphysics-informed neural networks

Research Topics

Theoretical PhysicsMachine Learning TheoryNeural Network DynamicsComputational PhysicsGenerative Models

Methods & Architectures

Duality RelationNeural Network ModelingActivation Dynamics AnalysisLearning Dynamics Analysis Neural NetworksTransformers

Applications & Tasks

Theoretical Physics Computational Science Scientific Machine Learning Modeling Physical SystemsSimulating Field TheoriesUnderstanding Neural Network Dynamics Modeling field theories using neural networksEstablishing duality between Hamiltonian systems and neural networks

Related Fields

Theoretical PhysicsComputational PhysicsMachine LearningDynamical Systems

Keywords

Hamiltonian systemsneural networksfield theorydualityactivation dynamicslearning dynamicsKlein-GordonDiracgauge fieldphysics-informedcomputational physics

Academic Context

#Theoretical Physics#Machine Learning Theory#Neural Network Dynamics#Computational Physics#Generative Models

Commercial Potential

Potential Products

Simulation software for theoretical physicsNew frameworks for physics-informed machine learning

Target Industries

Research & DevelopmentAcademiaHigh-Performance Computing

Use Case Examples

Simulating quantum field theories using neural network dynamics.Developing novel computational approaches for particle physics.

Competitive Edge

Presents a novel theoretical framework connecting two distinct fields, offering a new paradigm for modeling physical systems.

Market Opportunity

Niche but significant within scientific research communities.

Revenue Models

Software licensing for specialized simulation toolsresearch grants.

Resource Requirements

Compute Needs

Potentially high, for training complex neural networks to simulate field theories.

Data Requirements

Theoretical framework, may not require specific datasets for initial development but would for empirical validation.

Deployment Constraints

Requires deep expertise in both physics and ML; practical implementation for complex theories is challenging.

Scalability

Scalability depends on the neural network architecture and the complexity of the field theory being modeled.

Production Readiness

Maturity Level

Theoretical/Research

Time to Market

Very Long

Patent Potential

Low

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