揭示教师强制与贝叶斯更新的几何错配，改进混沌系统建模稳定性。
Teacher Forcing as Generalized Bayes: Optimization Geometry Mismatch in Switching Surrogates for Chaotic Dynamics
- 将教师强制视为广义贝叶斯更新，分析其与模型真实似然的几何差异
- 在洛伦兹-63系统中，窗口证据微调虽提升预测精度，却损害关键动力学量
- 提出基于多重切换解释的缺失信息修正，改善模型长期行为可靠性
身份教师强制（ITF）使确定性递归代理在混沌动力系统重建中实现稳定训练，已广泛应用于基于递归神经网络（RNN）的可解释近线性RNN（AL-RNNs）。然而，作为干预式预测损失（即广义贝叶斯更新），教师强制无需匹配自由运行模型的边际似然几何结构。本文在概率切换增强的AL-RNN框架下，比较了ITF与边际似然的目标诱导曲率，通过Louis恒等式估计模糊感知的观测信息。在研究的切换设置中，仅条件于单一强制路径（如ITF所做）会放大曲率，而当存在多个可能的切换解释时，边际似然曲率因缺失信息修正而降低。在洛伦兹-63实验中，窗口化证据微调提升了保留证据表现，但相较ITF预训练模型，反而降低了关注的动力学量（QoIs）。
原文摘要 · Abstract (English)
Identity teacher forcing (ITF) enables stable training of deterministic recurrent surrogates for chaotic dynamical systems and has been highly effective for dynamical systems reconstruction (DSR) with recurrent neural networks (RNNs), including interpretable almost-linear RNNs (AL-RNNs). However, as an intervention-based prediction loss (and thus a generalized Bayes update), teacher forcing need not match the free-running model's marginal likelihood geometry. We compare the objective-induced curvatures of ITF and marginal likelihood in a probabilistic switching augmentation of AL-RNNs, estimating ambiguity-aware observed information via Louis' identity. In the switching setting studied here, conditioning on a single forced regime path (as ITF does) inflates curvature, while marginal likelihood curvature is reduced by a missing-information correction when multiple switching explanations remain plausible. In Lorenz-63 experiments, windowed evidence fine-tuning improves held-out evidence but can degrade dynamical quantities of interest (QoIs) relative to ITF-pretrained models.
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