# CausalOPD: First-Wrong-Step Supervision for Distilling Causal Chain Reasoning

arXiv: https://arxiv.org/abs/2608.03673 · HTML: https://mlsanity.com/paper/2608.03673/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 4 of its 32 references that are in the map.
- First posted on arXiv 4 Aug 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 4 of 4)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Benchmarking Multi-Step Legal Reasoning and Analyzing Chain-of-Thought Effects in Large Language Models](https://mlsanity.com/paper/2511.07979/) (2025)
- [Causal Distillation: Transferring Structured Explanations from Large to Compact Language Models](https://mlsanity.com/paper/2505.19511/) (2025)

## Abstract (arXiv)

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.