Teacher Forcing as Generalized Bayes: Optimization Geometry Mismatch in Dynamical Systems Reconstruction

Forum topic · 小凯 · 2026-04-30

Summary

This arXiv paper (2504.21060) by Andre Herz, Daniel Durstewitz, Georgia Koppe and colleagues examines why identity teacher forcing (ITF), while effective for training recurrent neural network surrogates of chaotic dynamical systems, can mismatch the geometry of the free-running model's likelihood. The authors frame teacher forcing as an intervention-based prediction loss, i.e., a generalized Bayes update, and compare objective-induced curvatures of ITF and marginal likelihood within a probabilistic switching augmentation of almost-linear RNNs (AL-RNNs). Using Louis' identity, they estimate ambiguity-aware observed information and show that conditioning on a single forced regime path (as ITF does) inflates curvature, whereas marginal likelihood reduces curvature through a missing-information correction when multiple switching explanations remain plausible. In Lorenz-63 experiments, window-evidence fine-tuning improves held-out evidence but can degrade dynamics quantities of interest relative to ITF-pretrained models.

Overview

Field: Machine Learning Authors: Andre Herz, Daniel Durstewitz, Georgia Koppe, et al. arXiv: 2504.21060

Abstract

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.

The authors 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 through a missing-information correction when multiple switching explanations remain plausible.

In Lorenz-63 experiments, window-evidence fine-tuning improves held-out evidence but may degrade dynamical quantities of interest (QoIs) relative to ITF-pretrained models.

Key Takeaways

ITF is a generalized Bayes update, not equivalent to maximum marginal likelihood for the free-running model.
Forced regime conditioning inflates local curvature; marginal likelihood applies a missing-information correction across switching hypotheses.
Better held-out evidence after fine-tuning does not guarantee better reconstruction of dynamical quantities of interest (Lorenz-63 case).