JEPAWG reveals dynamics from networks trained on physical parameters
Bifurcations from Weight Space: JEPAWG on Parametric Dynamical Systems
Machine LearningArtificial Intelligence
Summary
Understanding how trained neural networks change when underlying physical conditions shift is hard because there is no clear reference for what their weights should represent. The authors used JEPAWG, a special method that links physical parameters to neural network weights, to study several known dynamical systems. This method accurately forecasts system behavior and spots important changes called bifurcations, including those invisible to traditional techniques. Their work shows JEPAWG can read meaningful physical insights from collections of trained networks.
What this means in practice
- •For forecasting system developers: Use JEPAWG to build models that track qualitative changes in system behavior by analyzing parameter-weight relationships instead of direct forecasting.
- •For control system engineers: Detect hard-to-find dynamical transitions like global bifurcations in physical systems by interpreting changes in trained network weights with JEPAWG.
Authors
Tobias Göbel, Miranda C. N. Cheng
Abstract
Trained network weights are increasingly treated as data, but there is rarely ground truth about what a population of models should encode, which hampers systematic validation of weight-space methods. This makes parametric dynamical systems a natural test-bed: the dynamics change qualitatively at submanifolds of parameter space that are, in well-studied families, known analytically or numerically. Fine-tuning a forecasting network at each point of a parameter grid yields a model zoo indexed by a physical parameter, against which weight-space diagnostics can be checked. We build such model zoos for four dynamical systems and analyse them with JEPAWG, a recently proposed joint-embedding hypernetwork built around a learned parameter--weight representation. It was first introduced for neural samplers for lattice field theories, where its latent geometry located the phase transition and estimated the 2D Ising critical exponent. Applied to dynamical systems, JEPAWG is competitive on forecasting with a hypernetwork trained directly for that task, despite being supervised on the parameter--weight correspondence rather than on forecasts. Beyond forecasting, the norm of the parameter-derivative of the decoded weights locates Hopf points and curves, tracks a period-doubling cascade closely enough to give a qualitative estimate of the Feigenbaum constant, and detects a global bifurcation, which has no eigenvalue signature and is therefore invisible to linearisation. As such, JEPAWG provides interpretable insight into the dynamics that is not available from other hypernetworks. Together, these results indicate that JEPAWG is a workable instrument for reading physical structure off a population of trained networks.