Reproduce “DFORM: Diffeomorphic vector field alignment for assessing dynamics across learned models” on OpenResearch

About this paper

Ruiqi Chen, Giacomo Vedovati, Todd Braver, ShiNung Ching

Researchers at Washington University in St. Louis developed DFORM, a framework to assess the similarity of underlying dynamics across learned models by learning a nonlinear coordinate transformation to align their vector fields. This approach revealed common computational mechanisms in diverse recurrent neural networks solving a spatial memory task, even when other methods showed distinctions.

Key insights

• DFORM operationalizes and generalizes the theoretical concept of smooth orbital equivalence into a continuous, quantifiable similarity metric for complex nonlinear dynamical systems.
• By directly aligning vector fields in their full nonlinear state spaces, DFORM overcomes limitations of methods relying on linear approximations or solely on asymptotic behavior.
• The framework can uncover functionally common underlying dynamical mechanisms across models with diverse architectures or superficial state-space representations, providing deeper insights into learned computational principles.

Summary by alphaXiv.