From Redundancy to Minimality: Fixed-Point-Guided Hierarchical Reduction of Learned Piecewise-Linear Dynamics

Excerpt

arXiv:2610.01369v1 Announce Type: new Abstract: Understanding a nonlinear dynamical system from time series requires not only reproducing its trajectories, but also identifying a simple representation that preserves its essential dynamical structure. Almost-linear recurrent neural networks (AL-RNNs) are piecewise-linear RNNs in which only a subset of units use ReLU nonlinearities, so that nonlinear capacity is explicitly controlled by the number of ReLU units. Their activation patterns define li