Test-Time Forecasting: Recurrent Depth Enables In-Context Dynamics Prediction
Foundation models for dynamical systems can forecast unseen partial differential equations (PDEs), ordinary differential equations (ODEs), and time series during inference. However, it remains an open question whether these foundation models truly learn generalizable in-context forecasting strategies. We show that looped transformers are capable of emulating propagators for dynamical systems in-context by first establishing a link between linear attention and (extended) dynamic mode decomposition. We then generalize this insight into the $\textit{Test-Time Forecasting}$ (TTF) framework in which a one-step forecaster leverages iterations of gradient descent as recurrent depth. We demonstra...
| Authors | Jeffrey B. Lai, John Quinn, Anthony Bao et al. |
|---|---|
| Primary category | cs.LG |
| Published | 14 October 2026 |
| Last updated at source | 14 October 2026 |
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