Spectral Alignment in Forward-Backward Representations via Temporal Abstraction
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917467489566720 |
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| author | Azad, Seyed Mahdi B. Hoffmann, Jasper Nematollahi, Iman Zhu, Hao Valada, Abhinav Boedecker, Joschka |
| author_facet | Azad, Seyed Mahdi B. Hoffmann, Jasper Nematollahi, Iman Zhu, Hao Valada, Abhinav Boedecker, Joschka |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20103 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral Alignment in Forward-Backward Representations via Temporal Abstraction Azad, Seyed Mahdi B. Hoffmann, Jasper Nematollahi, Iman Zhu, Hao Valada, Abhinav Boedecker, Joschka Machine Learning Artificial Intelligence Robotics 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. |
| title | Spectral Alignment in Forward-Backward Representations via Temporal Abstraction |
| topic | Machine Learning Artificial Intelligence Robotics |
| url | https://arxiv.org/abs/2603.20103 |