Beyond Invariant Dictionary: Data-Driven Koopman Spectral Recovery with Filtered Extended Dynamic Mode Decomposition

What the math gives to ML

The paper provides a constructive way to remove spectral pollution before eigendecomposition rather than filtering eigenvalues after the fact. Its central transferable asset is the forward-intersection chain, which progressively restricts a representation to directions that are both present in the chosen feature space and reachable under the learned dynamics. This can turn latent linear state-space models, neural ODE discretizations, or Koopman-inspired world models into spectrally cleaner systems without requiring an exactly invariant dictionary. The most practical adaptation is to periodically compute a numerically stable compatible subspace with SVD, project the latent transition operator onto it, and compare filtered versus unfiltered rollouts and long-horizon stability.