# Premise-Augmented Reasoning Chains Improve Error Identification in Math reasoning with LLMs

arXiv: https://arxiv.org/abs/2502.02362 · HTML: https://mlsanity.com/paper/2502.02362/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 30 of its 45 references that are in the map.
- First posted on arXiv 4 Feb 2025.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

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

- [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)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [A Survey on Large Language Models for Code Generation](https://mlsanity.com/paper/2406.00515/) (2024)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [ProcessBench: Identifying Process Errors in Mathematical Reasoning](https://mlsanity.com/paper/2412.06559/) (2024)
- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [Evaluation of Text Generation: A Survey](https://mlsanity.com/paper/2006.14799/) (2020)
- [Autoformalization with Large Language Models](https://mlsanity.com/paper/2205.12615/) (2022)
- [FOLIO: Natural Language Reasoning with First-Order Logic](https://mlsanity.com/paper/2209.00840/) (2022)
- [ROSCOE: A Suite of Metrics for Scoring Step-by-Step Reasoning](https://mlsanity.com/paper/2212.07919/) (2022)
- [Orca-Math: Unlocking the potential of SLMs in Grade School Math](https://mlsanity.com/paper/2402.14830/) (2024)
- [On the Self-Verification Limitations of Large Language Models on Reasoning and Planning Tasks](https://mlsanity.com/paper/2402.08115/) (2024)
- [Deductive Verification of Chain-of-Thought Reasoning](https://mlsanity.com/paper/2306.03872/) (2023)
- [Formal Mathematical Reasoning: A New Frontier in AI](https://mlsanity.com/paper/2412.16075/) (2024)
- [ReCEval: Evaluating Reasoning Chains via Correctness and Informativeness](https://mlsanity.com/paper/2304.10703/) (2023)
- [Stepwise Verification and Remediation of Student Reasoning Errors with Large Language Model Tutors](https://mlsanity.com/paper/2407.09136/) (2024)
- [SocREval: Large Language Models with the Socratic Method for Reference-Free Reasoning Evaluation](https://mlsanity.com/paper/2310.00074/) (2023)
- [Autoformalizing Euclidean Geometry](https://mlsanity.com/paper/2405.17216/) (2024)
- [Deductive Beam Search: Decoding Deducible Rationale for Chain-of-Thought Reasoning](https://mlsanity.com/paper/2401.17686/) (2024)
- [Simulating User Agents for Embodied Conversational-AI](https://mlsanity.com/paper/2410.23535/) (2024)

## Built on by (most cited first, 22 of 22)

- [AgentArk: Distilling Multi-Agent Intelligence into a Single LLM Agent](https://mlsanity.com/paper/2602.03955/) (2026)
- [ReasoningFlow: Semantic Structure of Complex Reasoning Traces](https://mlsanity.com/paper/2506.02532/) (2025)
- [Unlocking the Power of Multi-Agent LLM for Reasoning: From Lazy Agents to Deliberation](https://mlsanity.com/paper/2511.02303/) (2025)
- [Process or Result? Manipulated Ending Tokens Can Mislead Reasoning LLMs to Ignore the Correct Reasoning Steps](https://mlsanity.com/paper/2503.19326/) (2025)
- [Guided by Gut: Efficient Test-Time Scaling with Reinforced Intrinsic Confidence](https://mlsanity.com/paper/2505.20325/) (2025)
- [Graph of Verification: Structured Verification of LLM Reasoning with Directed Acyclic Graphs](https://mlsanity.com/paper/2506.12509/) (2025)
- [Do LLM Agents Know How to Ground, Recover, and Assess? A Benchmark for Epistemic Competence in Information-Seeking Agents](https://mlsanity.com/paper/2509.22391/) (2025)
- [SSR: Socratic Self-Refine for Large Language Model Reasoning](https://mlsanity.com/paper/2511.10621/) (2025)
- [ErrorMap and ErrorAtlas: Charting the Failure Landscape of Large Language Models](https://mlsanity.com/paper/2601.15812/) (2026)
- [Stop Before You Fail: Operational Capability Boundaries for Mitigating Unproductive Reasoning in Large Reasoning Models](https://mlsanity.com/paper/2509.24711/) (2025)
- [Hop, Skip, and Overthink: Diagnosing Why Reasoning Models Fumble during Multi-Hop Analysis](https://mlsanity.com/paper/2508.04699/) (2025)
- [Do We Need Frontier Models to Verify Mathematical Proofs?](https://mlsanity.com/paper/2604.02450/) (2026)
- [KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?](https://mlsanity.com/paper/2507.11408/) (2025)
- [Extracting Search Trees from LLM Reasoning Traces Reveals Myopic Planning](https://mlsanity.com/paper/2605.06840/) (2026)
- [Diagnosing Multi-step Reasoning Failures in Black-box LLMs via Stepwise Confidence Attribution](https://mlsanity.com/paper/2605.19228/) (2026)
- [Conformal Certification of Reasoning Trace Prefixes](https://mlsanity.com/paper/2605.30085/) (2026)
- [NCV: A Node-Wise Consistency Verification Approach for Low-Cost Structured Error Localization in LLM Reasoning](https://mlsanity.com/paper/2510.02816/) (2025)
- [Evaluating Large Language Models on Solved and Unsolved Problems in Graph Theory: Implications for Computing Education](https://mlsanity.com/paper/2602.05059/) (2026)
- [Strategy Executability in Mathematical Reasoning: Leveraging Human-Model Differences for Effective Guidance](https://mlsanity.com/paper/2602.22583/) (2026)
- [Two Regimes of Chain-of-Thought Unfaithfulness: Metric-Based Detection Fails Where Models Are Wrong](https://mlsanity.com/paper/2607.23458/) (2026)
- [The Error You See Is Not the Error You Made: Progression-aware Reasoning Origin for Reasoning Error Localization](https://mlsanity.com/paper/2609.33297/) (2026)
- [Is This Evidence Decision-Critical? Learning to Verify Rule-Governed Decisions](https://mlsanity.com/paper/2609.39608/) (2026)

## Abstract (arXiv)

Chain-of-Thought (CoT) prompting enhances mathematical reasoning in large language models (LLMs) by enabling detailed step-by-step solutions. However, due to the verbosity of LLMs, the resulting reasoning chains can be long, making it harder to verify the reasoning steps and trace issues resulting from dependencies between the steps that may be farther away in the sequence of steps. Importantly, mathematical reasoning allows each step to be derived from a small set of premises, which are a subset of the preceding steps in the reasoning chain. In this paper, we present a framework that identifies the premises for each step, to improve the evaluation of reasoning. We restructure conventional linear reasoning chains into Premise Augmented Reasoning Chains (PARC) by introducing premise links, resulting in a directed acyclic graph where the nodes are the steps and the edges are the premise links. Through experiments with a PARC-based dataset that we built, namely PERL (Premises and ERrors identification in LLMs), we demonstrate that LLMs can reliably identify premises within complex reasoning chains. In particular, even open-source LLMs achieve 90% recall in premise identification. We also show that PARC helps to identify errors in reasoning chains more reliably. The accuracy of error identification improves by 6% to 16% absolute when step-by-step verification is carried out in PARC under the premises. Our findings highlight the utility of premise-centric representations in addressing complex problem-solving tasks and open new avenues for improving the reliability of LLM-based reasoning evaluations.