Koopman Operators for Training Dynamics & RL

Training a neural network traces a trajectory through weight space. Koopman operator theory offers a classical tool for such nonlinear dynamical systems: lift the dynamics into a space where they evolve linearly, and prediction becomes tractable.

The lab has turned this observation into practical machinery. Predictive Differential Training (PDT, ICLR 2026) models the training process itself, using Koopman-based prediction to jump the optimizer several epochs ahead — bypassing SGD iterations — with a differential-learning correction that keeps large-scale training stable.

KIPPO (IJCAI 2025) applies the same lens to reinforcement learning: Koopman-inspired regularization of proximal policy optimization that smooths policy updates and improves stability across control benchmarks.

A third study (arXiv 2026) steps back to ask the underlying scientific question: when is training predictable at all? By measuring structured predictability across optimization regimes, it maps where dynamical-systems tools can be trusted — and where the trajectory is too chaotic to forecast.