Nonstationary latent dynamics

Real neural recordings are not stationary: electrodes drift and fail, impedances change, the represented behavior and internal state shift, and neural tuning itself reorganizes across days (representational drift). A latent dynamical model estimated on one session is therefore not guaranteed to hold on the next, which is the central obstacle to BCIs that work for years without daily recalibration. The frontier question is how much of the latent dynamics is a stable, session-invariant law and how much is a changing observation map from that law onto the recorded channels.

The most successful current answer separates a stable latent manifold and its dynamics from a nonstationary read-out, and then re-aligns new data to the old latent space — by distribution alignment, adversarial or contrastive session-invariance, manifold/subspace alignment, or test-time adaptation — so the decoder built on the latent dynamics can be reused. Related strands treat the parameters themselves as slowly time-varying (online / adaptive identification) or model drift explicitly as a hyper-dynamics on top of the fast dynamics. The open, honest question is whether an underlying invariant dynamical law truly exists or whether apparent stability is an artefact of the alignment objective; distinguishing genuine invariance from imposed invariance is unresolved.