Beyond the Training Horizon: Mechanisms and Limits of Length Generalization in Looped Transformers

Abstract:Looped Transformers can generalize to reasoning chains longer than those encountered during training, but the computations enabling this behavior and limiting its extent remain unclear. We mechanistically compare two looped-Transformer configurations, which we call the Matched-Recurrence Looped Transformer (MR-Loop) and Decoupled-Recurrence Looped Transformer (DR-Loop), reflecting their respective recurrence-training schemes. We evaluate polynomial iteration, finite-state composition, and knowledge-graph traversal using detailed mechanistic analysis. Attention analysis, intermediate-state decoding, and causal interventions reveal distinct mechanisms learned under final-answer supervision. MR-Loop updates an intermediate state at a fixed readout while advancing relation selection through adjacent-token interactions and a transferable progress cue. DR-Loop instead propagates intermediate states across relation positions, forming an advancing computational frontier. However, both mechanisms become unreliable at greater depths: MR-Loop exhibits degradation of its readout state and progress cues, while DR-Loop exhibits declining reliability of state propagation. Limited self-correction allows local errors to persist and compound. Across both models, we uncover a common representational principle: recurrent states encode not only task-relevant content but also its computational status, whether that content remains in a form that can support subsequent computation. Transferable live-consumed and fresh-aged residual directions causally control whether represented information can participate in subsequent computation, including beyond the training horizon. We further show that length generalization need not rely on faithful step-by-step reasoning, as Looped Transformers can exploit task structure without explicitly representing every intermediate state.

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

arXiv:2609.33144 [cs.LG]

(or arXiv:2609.33144v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.33144 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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