# Boosting Process-Correct CoT Reasoning by Modeling Solvability of Multiple-Choice QA

arXiv: https://arxiv.org/abs/2509.25941 · HTML: https://mlsanity.com/paper/2509.25941/

## 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 41 of its 47 references that are in the map.
- First posted on arXiv 30 Sep 2025.

## 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, 30 of 41)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [MedMCQA : A Large-scale Multi-Subject Multi-Choice Dataset for Medical domain Question Answering](https://mlsanity.com/paper/2203.14371/) (2022)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [Dataset Cartography: Mapping and Diagnosing Datasets with Training Dynamics](https://mlsanity.com/paper/2009.10795/) (2020)
- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (2025)
- [Faithful Chain-of-Thought Reasoning](https://mlsanity.com/paper/2301.13379/) (2023)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [LLMs instead of Human Judges? A Large Scale Empirical Study across 20 NLP Evaluation Tasks](https://mlsanity.com/paper/2406.18403/) (2024)
- [Towards Understanding Chain-of-Thought Prompting: An Empirical Study of What Matters](https://mlsanity.com/paper/2212.10001/) (2022)
- [Why Language Models Hallucinate](https://mlsanity.com/paper/2509.04664/) (2025)
- [Evaluating the Logical Reasoning Ability of ChatGPT and GPT-4](https://mlsanity.com/paper/2304.03439/) (2023)
- [ROSCOE: A Suite of Metrics for Scoring Step-by-Step Reasoning](https://mlsanity.com/paper/2212.07919/) (2022)
- [Free Process Rewards without Process Labels](https://mlsanity.com/paper/2412.01981/) (2024)
- [MathDial: A Dialogue Tutoring Dataset with Rich Pedagogical Properties Grounded in Math Reasoning Problems](https://mlsanity.com/paper/2305.14536/) (2023)
- [Calibrated Language Models Must Hallucinate](https://mlsanity.com/paper/2311.14648/) (2023)
- [Making Reasoning Matter: Measuring and Improving Faithfulness of Chain-of-Thought Reasoning](https://mlsanity.com/paper/2402.13950/) (2024)
- [Chain-of-Thought Hub: A Continuous Effort to Measure Large Language Models' Reasoning Performance](https://mlsanity.com/paper/2305.17306/) (2023)
- [Faithful Logical Reasoning via Symbolic Chain-of-Thought](https://mlsanity.com/paper/2405.18357/) (2024)

## Abstract (arXiv)

Reasoning quality in large language models depends not only on producing correct answers but also on generating valid intermediate steps. We study this through multiple-choice question answering (MCQA), which provides a controlled setting with fixed answer options. Our analysis shows that when questions are effectively unsolvable for a model, spurious chains of thought (CoTs) are more likely to appear, leading to false positives. By estimating the solvability of each question, we uncover an intermediate regime where learning is most effective. Building on this insight, we adapt outcome-supervised reward models and reinforcement learning with group-relative advantage to incorporate solvability into their objectives. Across experiments on math and multimodal datasets, these modifications consistently yield higher rates of process-correct reasoning and, in reinforcement learning, improved answer accuracy as well. Our results highlight solvability as a key factor for reducing hallucinations and increasing reliability in CoT reasoning.