JEPAWG: Interpretable Hypernetworks for Weight-Space Physics

Lattice field theory is the workhorse of non-perturbative physics, used to simulate phenomena from the strong nuclear force to critical phenomena in materials. Its Boltzmann distributions are parametrized analytically by \emph{coupling constants}, but these bare parameters are weak predictors of physical observables---extracting physics typically requires extensive simulation. While machine learning tools such as normalizing flows have emerged as effective samplers at fixed couplings, it remains difficult to interpret what the underlying neural networks have learned. This raises a natural question: can the flow \emph{parameters themselves} be generated for new theories, and can their physics be read off directly from the network weights? We propose lattice field theory as a testbed for neural network interpretability: because the target physics is qualitatively well-understood and smoothly varying, it provides ideal synthetic data against which network behavior can be checked against known ground truth. To this end we introduce \textbf{JEPAWG}, a Joint-Embedding Predictive Architecture--based Weight Generator that maps couplings directly to flow weights via a learned latent space. On a scalar theory at lattice sizes $6^2$ and $8^2$, the JEPAWG latent space recovers the correct intrinsic dimension of the underlying manifold, identifies the region of phase transition, encodes a finite-size shift aligned with the 2D Ising exponent $\nu \approx 1$, allowing us to uncover physical structure by studying the network weights alone. As a generator, JEPAWG also interpolates and extrapolates to unseen couplings effectively and remains robust to weight-space incongruences deliberately introduced by combining multi-seed training data, outperforming PCA, AE, and VAE baselines.