制御された世界モデルの識別可能性について
On the Identifiability of Controlled World Models
この論文は、ガウス潜在状態を持つ制御された世界モデルが非線形観測から復元可能かどうかを理論的に解析し、識別可能性の条件を提案しています。
著者: Xiangteng Zhang, Yang Guan, Bo Zhang, Hongyang Li, Ya-Qin Zhang, Shengbo Eben Li
分類: cs.LG
原文アブストラクト
World model serves as a promising tool to infer environment dynamics under high-dimensional observations and candidate actions. Recently, LeCun's JEPA provides a compelling framework for learning such models in representation space. Its action-conditioned extension plays a central role in visual control and latent-space planning, but leaves a fundamental question: can it recover the controlled dynamics from nonlinear observations? This paper presents a joint identifiability condition for controlled world models with Gaussian latent states, which consists of two coupled components: (1) representation identifiability and (2) transition identifiability. The former depends on the spectral separation property while the latter is related to non-degenerate variation of conditional action. We prove that when this condition holds, minimizing the LeJEPA-style predictive objective can recover both latent states and controlled dynamics in the sense of orthogonal transformation. We further prove that the upper bound of transition prediction error is inversely proportional to the spectral separation margin. We also characterize an attainable amplification of counterfactual prediction error that scales inversely with the weakest conditional action-excitation margin. The theoretical predictions are empirically supported across four nonlinear observation settings.