# Spectral Alignment in Forward-Backward Representations via Temporal Abstraction

arXiv: https://arxiv.org/abs/2603.20103 · HTML: https://mlsanity.com/paper/2603.20103/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 34 references that are in the map.
- First posted on arXiv 20 Mar 2026.

## Builds on (most cited first, 19 of 19)

- [Successor Features for Transfer in Reinforcement Learning](https://mlsanity.com/paper/1606.05312/) (2016)
- [OGBench: Benchmarking Offline Goal-Conditioned RL](https://mlsanity.com/paper/2410.20092/) (2024)
- [Learning One Representation to Optimize All Rewards](https://mlsanity.com/paper/2103.07945/) (2021)
- [A Laplacian Framework for Option Discovery in Reinforcement Learning](https://mlsanity.com/paper/1703.00956/) (2017)
- [Reinforcement Learning with Action Chunking](https://mlsanity.com/paper/2507.07969/) (2025)
- [Eigenoption Discovery through the Deep Successor Representation](https://mlsanity.com/paper/1710.11089/) (2017)
- [Does Zero-Shot Reinforcement Learning Exist?](https://mlsanity.com/paper/2209.14935/) (2022)
- [Deep Successor Reinforcement Learning](https://mlsanity.com/paper/1606.02396/) (2016)
- [Learning Successor States and Goal-Dependent Values: A Mathematical Viewpoint](https://mlsanity.com/paper/2101.07123/) (2021)
- [Zero-Shot Whole-Body Humanoid Control via Behavioral Foundation Models](https://mlsanity.com/paper/2504.11054/) (2025)
- [Deep Reinforcement Learning with Successor Features for Navigation across Similar Environments](https://mlsanity.com/paper/1612.05533/) (2016)
- [TempoRL: Learning When to Act](https://mlsanity.com/paper/2106.05262/) (2021)
- [Fast Adaptation with Behavioral Foundation Models](https://mlsanity.com/paper/2504.07896/) (2025)
- [Epistemically-guided forward-backward exploration](https://mlsanity.com/paper/2507.05477/) (2025)
- [Laplacian Representations for Decision-Time Planning](https://mlsanity.com/paper/2602.05031/) (2026)
- [Shift Before You Learn: Enabling Low-Rank Representations in Reinforcement Learning](https://mlsanity.com/paper/2509.05193/) (2025)
- [SR-Reward: Taking The Path More Traveled](https://mlsanity.com/paper/2501.02330/) (2025)
- [On Double Descent in Reinforcement Learning with LSTD and Random Features](https://mlsanity.com/paper/2310.05518/) (2023)
- [Temporally Extended Successor Representations](https://mlsanity.com/paper/2209.12331/) (2022)

## Abstract (arXiv)

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.