PAR: Progress-Aligned Recurrence for Length Generalization in State Tracking
Looped language models can run more iterations at test time, but additional iterations need not help them solve longer problems. For sequential state tracking, final-answer supervision does not specify how far each iteration should advance, and repeated updates can change the scale of the recurrent state. We introduce \textbf{Progress-Aligned Recurrence (PAR)}, which trains the prediction at iteration $k$ to match the state after the first $k$ operations and rescales recurrent states to their first-iteration norms. On swap-$S_5$, a Qwen2.5-0.5B model trained on at most 32 moves achieves 95.5\% mean full-state accuracy at 512 moves, or $16\times$ the training length, compared with 55.7\% r...
| Authors | Pan Wang, Yihao Hu, Guangyuan Dong et al. |
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| Primary category | cs.CL |
| Published | 20 October 2026 |
| Last updated at source | 20 October 2026 |
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