Beyond Single-Step Likelihood: Gibbs Variational Last Layers for Long-Horizon Dynamics Learning

Accurate long-horizon probabilistic predictions of dynamical systems are a prerequisite for model-based decision-making. Variational Bayesian last layers (VBLLs) are an attractive model class for this setting, offering tractable uncertainty at near-deterministic cost, yet they are trained exclusively with single-step likelihood objectives that may be insufficient for reliable multi-step rollouts. We revisit VBLLs through the lens of Gibbs variational inference, which decouples posterior inference from the choice of training loss. Building on this perspective, we introduce a family of multi-step training losses that progressively incorporate long-horizon structure, robustness via continuous ranked probability scores (CRPS), and training on full autoregressive rollouts. Our approach retains the simplicity of VBLLs while directly optimizing for multi-step predictive quality. Across illustrative synthetic environments, a diverse suite of chaotic dynamical systems, and real-world data, we show that multi-step, CRPS-based objectives substantially improve long-horizon accuracy and distributional fit, consistently outperforming single-step likelihood training.