Stable Neural Flows Can Hide Stochastic Computational Drift

Longitudinal neural recordings can change substantially across sessions even when behavior is stable. Recent methods increasingly address this problem by aligning neural manifolds and comparing their latent trajectories or vector fields. We point out a complementary failure mode: two aligned neural representations can have nearly identical conditional mean motion while their state-conditioned transition variability differs. We call this \emph{stochastic computational drift}. Given a correspondence between session manifolds, we compare finite-lag transition laws in matched tangent spaces. Under a local Gaussian approximation, the squared 2-Wasserstein distance separates exactly into a mean-flow term and a covariance (Bures-Wasserstein) term, yielding interpretable scores for deterministic and stochastic drift without fitting an SDE. On a controlled ring-manifold experiment with nonlinear re-embedding, representation-only drift produces negligible scores after alignment, a diffusion-only perturbation produces a large covariance score with essentially unchanged mean-flow score, and a drift-field perturbation produces the reverse pattern. The effect remains visible across a broad range of finite lags. These preliminary results suggest that claims of cross-session dynamical stability should distinguish stability of mean flow from stability of the full local stochastic transition law.