Online learning of neural state-space models

What the math gives to ML

The paper offers a constructive mechanism for adapting nonlinear neural state-space models online: process non-overlapping input-output batches, infer the latent state at each batch boundary with a subspace encoder, and recursively update the dynamics and observation parameters. The transferable asset is a separation between state initialization from recent observations and parameter adaptation, avoiding replay of the entire history during online learning. A practical neural-network transfer is an online world-model learner with encoder-based state resets and recursive updates, monitored using one-step and multi-step prediction errors. The main falsifiable signatures are bounded per-batch computation independent of stream length, decay of state-estimation perturbations under a contraction condition, and decreasing batch-to-batch prediction error under persistent excitation.