Spectral Alignment in Forward-Backward Representations via Temporal Abstraction

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 analogously to 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 principled mechanism for shaping the spectral structure of the underlying MDP and enabling effective long-horizon representations in continuous control.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Robotics (cs.RO)

arXiv:2603.20103 [cs.LG]

(or arXiv:2603.20103v4 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2603.20103 Focus to learn more arXiv-issued DOI via DataCite

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