Pub-AI: AI in Science

Latent Dynamics · 2026-09-30

Correct then Forecast: Observer State-Space Models for Time Series Forecasting

Alexis-Raja Brachet, Guillaume Clavier--Fr\'emond, Abdelhakim Ziani, Pierre-Yves Richard, C\'eline Hudelot

arXiv:2609.33566PDF

Auto-summarized: this summary was generated by a language model from the paper’s text and has not been reviewed by an editor. Check the paper before relying on it. Benchmark numbers appear only after a human has verified them.

TL;DR

The authors introduce Observer State-Space Models (OSSMs) for time-series forecasting. OSSMs treat the observed input sequence as measurements correcting an internal latent state via an observer, while the latent transition is autonomous and shared across context and forecasting intervals. They claim OSSM improves forecasting versus corresponding SSMs under the same parameter count and training setup.

Why it matters

Standard recurrent SSM forecasting can suffer a context–forecast regime change because observations are used as inputs during context but are absent during forecasting. By separating latent-state propagation from measurement assimilation, OSSM aims to keep the same latent dynamics across regimes while letting observations only correct state estimates when available, with a control-theoretic view (observability/convergence) of the resulting estimation error.

Method

  • Formulate forecasting with an observer: update a latent-state estimate using a correction term when observations are available, then propagate with the same latent transition during the forecasting interval without correction.
  • Recover conventional SSMs and SpaceTime as special/particular instances of the OSSM framework, and argue that conventional/SpaceTime entangle autonomous propagation with measurement/readout parameters, causing modeling mismatches.
  • Compare OSSM vs corresponding SSM variants using matched parameter counts and training protocols on multiple forecasting benchmarks.

Limitation

The authors report that some training runs diverged; the results tables mark 'div.' as runs where a head diverged (normalized MSE above 10) or produced no metric at all, and divergence counts as a loss.

Abstract (from arXiv)

Time series forecasting requires extrapolating the dynamics of an observed process beyond the last available measurement. Yet recurrent forecasting models typically treat observations as inputs that directly control their latent dynamics. It leads to a regime change when these observations become unavailable at prediction time. Following a state-estimation perspective, we introduce Observer State-Space Models (OSSMs), a class of recurrent models that interprets the observed input time series as measurements of an underlying autonomous dynamical system. OSSMs explicitly separate latent-state propagation from measurement assimilation: a single transition governs the dynamics across both context and forecasting intervals, while available observations correct the estimated state through an observer. This formulation naturally exposes classical control-theoretic properties, including observability and convergence of the state estimation error. We further show that conventional and recent SSMs can be recovered as particular instances of our OSSM framework, thereby providing a unified interpretation of their recurrent dynamics and revealing modeling inconsistencies. We perform experiments across several benchmarks showing that OSSM achieves substantial improvements while maintaining the same parameter count and training setup as the corresponding SSM baseline. These results support a simple principle for recurrent forecasting: observations should correct the estimated latent state, rather than control the dynamics used to propagate it.

Related papers