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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2606.00305 |
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| _version_ | 1866914619583365120 |
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| author | Jiang, Yuxuan Ferraro, Francis |
| author_facet | Jiang, Yuxuan Ferraro, Francis |
| contents | On-Policy Distillation (OPD) improves large language model reasoning by training a student model on trajectories sampled from its own policy under teacher supervision. Although OPD operates on trajectories, its learning signal remains token-level: it identifies deviations through high-loss tokens and repairs them through local reverse-KL correction. We show that this "trajectory-sampled but token-learned" mechanism cannot reliably bridge student trajectories toward teacher trajectories. About 30% of high-loss tokens fall into the low-divergence regime, indicating that many are surface-form mismatches rather than real reasoning forks. Moreover, even truly divergent tokens are difficult to repair with isolated token-level supervision, since reasoning failures often unfold as short-horizon distributional drift. We propose Trajectory-aware OPD (TOPD), which uses near-future trajectory information to identify real divergent states and distribute guidance across multiple future tokens. Experiments show that suppressing non-divergent high-loss tokens improves standard OPD from 47.8% to 48.2% average accuracy, while TOPD further improves performance to 52.2%, with gains on AIME24 from 60.0% to 63.3% and AIME25 from 46.7% to 53.3%. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00305 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bridging Reasoning Trajectories in On-Policy Distillation via Near-Future Guidance Jiang, Yuxuan Ferraro, Francis Computation and Language Artificial Intelligence On-Policy Distillation (OPD) improves large language model reasoning by training a student model on trajectories sampled from its own policy under teacher supervision. Although OPD operates on trajectories, its learning signal remains token-level: it identifies deviations through high-loss tokens and repairs them through local reverse-KL correction. We show that this "trajectory-sampled but token-learned" mechanism cannot reliably bridge student trajectories toward teacher trajectories. About 30% of high-loss tokens fall into the low-divergence regime, indicating that many are surface-form mismatches rather than real reasoning forks. Moreover, even truly divergent tokens are difficult to repair with isolated token-level supervision, since reasoning failures often unfold as short-horizon distributional drift. We propose Trajectory-aware OPD (TOPD), which uses near-future trajectory information to identify real divergent states and distribute guidance across multiple future tokens. Experiments show that suppressing non-divergent high-loss tokens improves standard OPD from 47.8% to 48.2% average accuracy, while TOPD further improves performance to 52.2%, with gains on AIME24 from 60.0% to 63.3% and AIME25 from 46.7% to 53.3%. |
| title | Bridging Reasoning Trajectories in On-Policy Distillation via Near-Future Guidance |
| topic | Computation and Language Artificial Intelligence |
| url | https://arxiv.org/abs/2606.00305 |