By name: hamiltonian-autonomous-emergent-dgm description: "Autonomous emergence of Hamiltonian parameters in deep generative models via Riemannian diffusion score fields. Extracting implicit physical laws from trained neural networks using algebraic framework. Activation: Hamiltonian, deep generative model, Riemannian diffusion, score field, spin glass, equivariant attention, physical law discovery, force estimator, emergent physics."
Autonomous Emergence of Hamiltonian in Deep Generative Models
Deep generative models autonomously discover and internalize underlying physical laws — achieving 99.7% cosine similarity in recovering microscopic Hamiltonian parameters without any energetic priors.
Metadata
- Source: arXiv:2604.20821
- Authors: Wenjie Xi, Wei-Qiang Chen
- Published: 2026-04-22
- Categories: cond-mat.dis-nn, cond-mat.stat-mech
Core Methodology
Key Innovation
Establishes a rigorous algebraic framework to extract implicit physical interactions learned by generative models. The zero-noise limit of a Riemannian diffusion score field is proven exactly equivalent to the thermodynamic restoring force, enabling the trained neural network to serve as a direct force estimator.
Technical Framework
- Riemannian Diffusion Score Field: Map the score field of a diffusion model to thermodynamic forces
- Force Estimator: Use trained neural network directly as a physical force estimator
- Linear Inversion: Apply overdetermined linear inversion to recover Hamiltonian parameters
- O(3)-Equivariant Architecture: Train attention model on thermal equilibrium snapshots of 1D frustrated spin glass
Key Results
- 99.7% cosine similarity with ground-truth interaction parameters
- 87% variance explained in continuous force field
- No energetic priors needed — physical rules emerge autonomously
Implementation Guide
Prerequisites
- Diffusion model training framework (PyTorch)
- O(3)-equivariant attention architecture
- Spin glass simulation environment
Step-by-Step
- Train O(3)-equivariant attention model on equilibrium configurations
- Extract score field from trained diffusion model
- Map zero-noise score field to restoring forces
- Apply linear inversion to recover Hamiltonian parameters
- Validate against ground-truth parameters
Applications
- Discovering physical laws from simulation data
- Validating that generative models learn rules, not just patterns
- Extracting interaction parameters in many-body systems
- Protein structure analysis (AlphaFold-like applications)
Pitfalls
- Requires high-quality equilibrium training data
- Linear inversion assumes correct functional form
- Computational cost of training equivariant architectures
Related Skills
- energy-based-neurocomputation
- lattice-field-theory-neurons
- neural-emulator-theory