[2603.20103] Spectral Alignment in Forward-Backward Representations via Temporal Abstraction

Computer Science > Machine Learning arXiv:2603.20103 (cs) [Submitted on 20 Mar 2026] Title:Spectral Alignment in Forward-Backward Representations via Temporal Abstraction Authors:Seyed Mahdi B. Azad, Jasper Hoffmann, Iman Nematollahi, Hao Zhu, Abhinav Valada, Joschka Boedecker View a PDF of the paper titled Spectral Alignment in Forward-Backward Representations via Temporal Abstraction, by Seyed Mahdi B. Azad and 5 other authors View PDF HTML (experimental) Abstract:Forward-backward (FB) representations provide a powerful framework for learning the successor representation (SR) in continuous spaces by enforcing a low-rank factorization. However, a fundamental spectral mismatch often exists between the high-rank transition dynamics of continuous environments and the low-rank bottleneck of the FB architecture, making accurate low-rank representation learning difficult. In this work, we analyze temporal abstraction as a mechanism to mitigate this mismatch. By characterizing the spectral properties of the transition operator, we show that temporal abstraction acts as a low-pass filter that suppresses high-frequency spectral components. This suppression reduces the effective rank of the induced SR while preserving a formal bound on the resulting value function error. Empirically, we show that this alignment is a key factor for stable FB learning, particularly at high discount factors where bootstrapping becomes error-prone. Our results identify temporal abstraction as a princip...