Set-Oriented Approach to the Analysis of Chaotic Itinerancy

What the math gives to ML

The paper provides a constructive coarse-graining of a nonlinear map into a finite directed weighted graph, where grid cells are vertices and possible cell transitions are edges. Strongly connected components identify invariant or metastable regions, while the associated row-stochastic transition matrix supplies stationary occupation probabilities and local transition entropy. This machinery transfers naturally to recurrent networks, state-space models, and learned world models: discretize latent trajectories, detect metastable latent attractors and chaotic itinerant transitions, and use the resulting graph as a diagnostic or regularizer for long-horizon behavior. The main falsifiable prediction is that long-horizon latent statistics should follow the graph's stationary distribution and that convergence rates should be controlled by the subdominant eigenvalue of the coarse transition matrix.