CausalOPD: First-Wrong-Step Supervision for Distilling Causal Chain Reasoning
Authors: Jian Zhang, Bingyi Wang, Yizhi Liu
Organizations: Zhejiang University
Abstract
Many critical reasoning tasks, including clinical diagnosis, legal judgment, and industrial fault diagnosis, require step-dependent causal chains in which early errors propagate and correct conclusions can mask invalid reasoning. Although large language models perform well on such tasks, privacy, latency, and controllability motivate distillation into locally deployable models. Standard trajectory imitation does not correct process errors on the student's own rollout distribution. We propose CausalOPD, a curriculum online process distillation framework. A knowledge-augmented teacher first provides trajectories grounded in domain-specific causal rules, entity relations, and structural constraints. The student then generates on-policy trajectories, and the teacher identifies the first wrong step, defined as the earliest transition that verifiably violates available constraints. Starting from the verified prefix, short-horizon reinforcement learning repairs this localized failure. A causal-stage curriculum advances from evidence-level to mechanism-level and conclusion-level errors, following their propagation order. Across three domains, CausalOPD improves average path correctness by 23.4 percentage points over sequence-level online process distillation and reduces the right-label-wrong-reasoning rate from 15.7% to 4.4%. The domain-specific 8B students also surpass both evaluated proprietary references in path correctness across all domains.
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%.
On-policy distillation (OPD) has become a central post-training tool for large language models (LLMs), providing dense per-token teacher supervision along the student's own rollouts. In this work, we identify a common structural cause underlying OPD, which we call prefix failure. Under prefix failure, dense per-token supervision induces a bimodal teacher mixture and fragmented gradients that token-level loss truncation or reweighting fail to address. This observation motivates us to move beyond token-level loss interventions toward trajectory-level output corrections. We thus propose Trajectory-Refined Distillation (TRD), a trajectory-level correction method that revises the student's rollout under the teacher guidance while within on-policy support. By correcting problematic prefixes before distillation, TRD mitigates prefix failure at its source. Moreover, TRD improves the exploration by exposing the student to alternative valid derivations under teacher guidance, even when the original rolls are already correct. TRD can also be applied to on-policy self-distillation (OPSD), a parameter-sharing variant that uses the student model conditioned on privileged informations as the teacher. Across a wide range of benchmarks and base models at multiple scales, TRD consistently outperforms prior baselines, improving single-attempt accuracy and broadening reasoning coverage. Code is available at https://github.com/louieworth/trd
Distilling reasoning traces from strong large language models into smaller ones is a promising route to improve intelligence in resource-constrained settings. Existing approaches face a fundamental trade-off: offline distillation from teacher-generated traces provides high-quality, sample-efficient supervision but suffers from distributional drift: during training, the student model conditions on teacher-generated prefixes, whereas during inference the student autoregresses on self-generated prefixes, leading to compounding errors over long reasoning trajectories. Meanwhile, on-policy or self-distillation methods better match the student's inference-time distribution, but require costly online sampling and often produce low-quality traces in early training. We propose a principled offline reasoning distillation framework that preserves the efficiency and supervision quality of offline teacher-generated data while correcting teacher-student distribution drift. It adaptively emphasizes teacher supervision that is better aligned with the student's on-policy distribution. Evaluations on mathematical reasoning benchmarks of GSM8K, MATH, MATH500, and harder held-out competition-style tasks, including AMC, AIME, and OlympiadBench, show that our method improves reasoning accuracy over prior offline distillation algorithms and yields more stable reasoning traces while preserving instruction-following capabilities. Our work shows that lightweight, distribution-correction-aware training can substantially strengthen offline reasoning distillation without online rollouts.