Weight-Space Physics: Interpretable Hypernetworks for Lattice Quantum Field Theories

Research Overview

Lattice field theory (LFT) is a standard approach for simulating non-perturbative physics, but extracting physical insights from these simulations is computationally expensive. While normalizing flows have become effective tools for sampling these distributions, the internal representations learned by these networks are typically opaque. This paper investigates whether the weights of these flow networks can be treated as physical observables, potentially revealing the underlying physics of the theory directly from the network parameters.

The JEPAWG Architecture

The authors propose JEPAWG (Joint-Embedding Predictive Architecture-based Weight Generator), a hypernetwork that maps bare coupling constants to flow weights via a learned latent space. Unlike traditional autoencoders that focus on input reconstruction, JEPAWG uses a joint-embedding objective to align the latent representations of couplings and weights. This approach forces the latent space to capture the physical structure of the theory rather than just the raw parameter values. The model consists of four components: a weight encoder, a coupling encoder, a predictor that maps between them, and a decoder that generates the final flow parameters.

Key Findings

JEPAWG demonstrates significant advantages in both interpretability and generation. First, the model successfully recovers the intrinsic dimensionality of the coupling manifold, matching the expected 2D structure of the theory, whereas standard baselines like VAEs and AEs significantly inflate this dimension. Second, the geometry of the latent space naturally identifies the phase transition of the scalar theory, with the pullback metric on the weights tracking the critical line. Finally, as a generator, JEPAWG outperforms traditional baselines in interpolating and extrapolating to unseen couplings, maintaining high effective sample sizes even when training data contains structural discontinuities from multi-seed initialization.

This work suggests that neural network weights can serve as a new, interpretable diagnostic tool for physical systems. By treating weights as physical observables, researchers can use the geometry of the weight space to verify if a model has learned the correct physical symmetries and scaling laws. This provides a bridge between deep learning and theoretical physics, offering a way to validate machine learning models against known physical ground truths.