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

arXiv: https://arxiv.org/abs/2609.33566 · HTML: https://mlsanity.com/paper/2609.33566/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 48 references that are in the map.
- First posted on arXiv 27 Sep 2026.

## Builds on (most cited first, 30 of 34)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [Time-LLM: Time Series Forecasting by Reprogramming Large Language Models](https://mlsanity.com/paper/2310.01728/) (2023)
- [TFB: Towards Comprehensive and Fair Benchmarking of Time Series Forecasting Methods](https://mlsanity.com/paper/2403.20150/) (2024)
- [Professor Forcing: A New Algorithm for Training Recurrent Networks](https://mlsanity.com/paper/1610.09038/) (2016)
- [Recurrent Neural Networks for Time Series Forecasting: Current Status and Future Directions](https://mlsanity.com/paper/1909.00590/) (2019)
- [Are Language Models Actually Useful for Time Series Forecasting?](https://mlsanity.com/paper/2406.16964/) (2024)
- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictors](https://mlsanity.com/paper/2305.18803/) (2023)
- [DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting](https://mlsanity.com/paper/2306.01984/) (2023)
- [DUET: Dual Clustering Enhanced Multivariate Time Series Forecasting](https://mlsanity.com/paper/2412.10859/) (2024)
- [On the difficulty of learning chaotic dynamics with RNNs](https://mlsanity.com/paper/2110.07238/) (2021)
- [Effectively Modeling Time Series with Simple Discrete State Spaces](https://mlsanity.com/paper/2303.09489/) (2023)
- [Attractor Memory for Long-Term Time Series Forecasting: A Chaos Perspective](https://mlsanity.com/paper/2402.11463/) (2024)
- [SST: Multi-Scale Hybrid Mamba-Transformer Experts for Time Series Forecasting](https://mlsanity.com/paper/2404.14757/) (2024)
- [Flipped Classroom: Effective Teaching for Time Series Forecasting](https://mlsanity.com/paper/2210.08959/) (2022)
- [Mori-Zwanzig latent space Koopman closure for nonlinear autoencoder](https://mlsanity.com/paper/2310.10745/) (2023)
- [Learning-based Design of Luenberger Observers for Autonomous Nonlinear Systems](https://mlsanity.com/paper/2210.01476/) (2022)
- [Time-SSM: Simplifying and Unifying State Space Models for Time Series Forecasting](https://mlsanity.com/paper/2405.16312/) (2024)
- [Dynamical Diffusion: Learning Temporal Dynamics with Diffusion Models](https://mlsanity.com/paper/2503.00951/) (2025)
- [K2VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2505.23017/) (2025)
- [LETS Forecast: Learning Embedology for Time Series Forecasting](https://mlsanity.com/paper/2506.06454/) (2025)

## Abstract (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.