[R] Detecting invariant manifolds in ReLU-based RNNs

A new research paper accepted to the International Conference on Learning Representations (ICLR) 2026 introduces a significant advance in understanding the internal mechanics of AI models. The work provides a novel, semi-analytic algorithm for constructing the stable and unstable manifolds—key geometric structures—of fixed points and cycles within ReLU-based Recurrent Neural Networks (RNNs). This is a critical development for explainable AI (XAI) and scientific machine learning, where RNNs are frequently trained as formal surrogates to approximate the complex dynamical systems underlying observed data, such as neural activity. The ability to map these manifolds offers a principled window into why a trained network produces specific behaviors, moving beyond black-box interpretations.

The technical contribution allows researchers to dissect an RNN's state space into distinct basins of attraction, which are separated by these manifold structures. The intersections of stable and unstable manifolds are known to lead to chaotic dynamics, and the manifolds themselves form a type of dynamical 'skeleton,' including structures like separatrix cycles. This framework transforms trained RNNs from opaque function approximators into analyzable dynamical systems. For fields like computational neuroscience, where RNNs model brain dynamics, this tool enables rigorous hypothesis testing about the system being modeled. The next step involves applying this analytical lens to RNNs trained on real-world scientific data to extract novel mechanistic insights.