Spectral Alignment in Forward-Backward Representations via Temporal Abstraction

• URL: http://arxiv.org/abs/2603.20103v2
• Date: Mon, 23 Mar 2026 14:27:29 GMT
• Title: Spectral Alignment in Forward-Backward Representations via Temporal Abstraction
• Abstract summary: Forward-backward representations provide a powerful framework for learning the successor representation (SR) in continuous spaces.<n>A fundamental spectral mismatch often exists between the high-rank transition dynamics of continuous environments and the low-rank bottleneck of the FB architecture.<n>We show that temporal abstraction acts as a low-pass filter that suppresses high-frequency spectral components.
• Score: 18.90573294229263
• License: http://creativecommons.org/licenses/by-sa/4.0/
• 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 principled mechanism for shaping the spectral structure of the underlying MDP and enabling effective long-horizon representations in continuous control.

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