Spectral Alignment of Forward-Backward Representations: Mitigating Spectral Mismatch via Temporal Abstraction

The paper analyzes the spectral mismatch between the high-rank transition dynamics of continuous environments and the low-rank bottleneck in forward-backward (FB) representations, and proposes temporal abstraction to mitigate this problem. Starting from the spectral properties of the transition operator, the authors show that temporal abstraction acts like a low-pass filter: it suppresses high-frequency components and reduces the effective rank of the successor representation, while preserving a formal bound on the value function error. Experiments show that this alignment is a key factor for stable FB learning at high discount factors. The work has been accepted to NeurIPS 2026.