# Finding the Cracks: Improving LLMs Reasoning with Paraphrastic Probing and Consistency Verification

arXiv: https://arxiv.org/abs/2602.11361 · HTML: https://mlsanity.com/paper/2602.11361/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 50 of its 56 references that are in the map.
- First posted on arXiv 11 Feb 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 50)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [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)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Large Language Models Are Human-Level Prompt Engineers](https://mlsanity.com/paper/2211.01910/) (2022)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Reasoning with Language Model is Planning with World Model](https://mlsanity.com/paper/2305.14992/) (2023)
- [Automatic Chain of Thought Prompting in Large Language Models](https://mlsanity.com/paper/2210.03493/) (2022)
- [ReST-MCTS*: LLM Self-Training via Process Reward Guided Tree Search](https://mlsanity.com/paper/2406.03816/) (2024)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024)
- [To CoT or not to CoT? Chain-of-thought helps mainly on math and symbolic reasoning](https://mlsanity.com/paper/2409.12183/) (2024)
- [Self-Evaluation Guided Beam Search for Reasoning](https://mlsanity.com/paper/2305.00633/) (2023)
- [Free Process Rewards without Process Labels](https://mlsanity.com/paper/2412.01981/) (2024)

## Built on by (most cited first, 2 of 2)

- [Controlled Reformulation Testing for Logical Consistency in Large Language Models](https://mlsanity.com/paper/2607.14528/) (2026)
- [Detecting Hidden Chain-of-Thought in Large Language Models with Linguistic, Behavioral, and Mechanistic Indicators](https://mlsanity.com/paper/2608.29956/) (2026)

## Abstract (arXiv)

Large language models have demonstrated impressive performance across a variety of reasoning tasks. However, their problem-solving ability often declines on more complex tasks due to hallucinations and the accumulation of errors within these intermediate steps. Recent work has introduced the notion of critical tokens--tokens in the reasoning process that exert significant influence on subsequent steps. Prior studies suggest that replacing critical tokens can refine reasoning trajectories. Nonetheless, reliably identifying and exploiting critical tokens remains challenging. To address this, we propose the Paraphrastic Probing and Consistency Verification~(PPCV) framework. PPCV operates in two stages. In the first stage, we roll out an initial reasoning path from the original question and then concatenate paraphrased versions of the question with this reasoning path. And we identify critical tokens based on mismatches between the predicted top-1 token and the expected token in the reasoning path. A criterion is employed to confirm the final critical token. In the second stage, we substitute critical tokens with candidate alternatives and roll out new reasoning paths for both the original and paraphrased questions. The final answer is determined by checking the consistency of outputs across these parallel reasoning processes. We evaluate PPCV on mainstream LLMs across multiple benchmarks. Extensive experiments demonstrate PPCV substantially enhances the reasoning performance of LLMs compared to baselines.