# KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?

arXiv: https://arxiv.org/abs/2507.11408 · HTML: https://mlsanity.com/paper/2507.11408/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 31 of its 48 references that are in the map.
- First posted on arXiv 15 Jul 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 31)

- [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)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [Automatic Chain of Thought Prompting in Large Language Models](https://mlsanity.com/paper/2210.03493/) (2022)
- [Plan-and-Solve Prompting: Improving Zero-Shot Chain-of-Thought Reasoning by Large Language Models](https://mlsanity.com/paper/2305.04091/) (2023)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Faithful Chain-of-Thought Reasoning](https://mlsanity.com/paper/2301.13379/) (2023)
- [Towards Understanding Chain-of-Thought Prompting: An Empirical Study of What Matters](https://mlsanity.com/paper/2212.10001/) (2022)
- [Spurious Rewards: Rethinking Training Signals in RLVR](https://mlsanity.com/paper/2506.10947/) (2025)
- [Implicit Representations of Meaning in Neural Language Models](https://mlsanity.com/paper/2106.00737/) (2021)
- [ROSCOE: A Suite of Metrics for Scoring Step-by-Step Reasoning](https://mlsanity.com/paper/2212.07919/) (2022)
- [LLMs Can Easily Learn to Reason from Demonstrations Structure, not content, is what matters!](https://mlsanity.com/paper/2502.07374/) (2025)
- [Thought Anchors: Which LLM Reasoning Steps Matter?](https://mlsanity.com/paper/2506.19143/) (2025)
- [Making Reasoning Matter: Measuring and Improving Faithfulness of Chain-of-Thought Reasoning](https://mlsanity.com/paper/2402.13950/) (2024)
- [Chain of Thoughtlessness? An Analysis of CoT in Planning](https://mlsanity.com/paper/2405.04776/) (2024)
- [Can Large Language Models Reason and Plan?](https://mlsanity.com/paper/2403.04121/) (2024)
- [A Chain-of-Thought Is as Strong as Its Weakest Link: A Benchmark for Verifiers of Reasoning Chains](https://mlsanity.com/paper/2402.00559/) (2024)
- [Beyond Semantics: The Unreasonable Effectiveness of Reasonless Intermediate Tokens](https://mlsanity.com/paper/2505.13775/) (2025)
- [L2CEval: Evaluating Language-to-Code Generation Capabilities of Large Language Models](https://mlsanity.com/paper/2309.17446/) (2023)
- [Premise-Augmented Reasoning Chains Improve Error Identification in Math reasoning with LLMs](https://mlsanity.com/paper/2502.02362/) (2025)
- [ERA-CoT: Improving Chain-of-Thought through Entity Relationship Analysis](https://mlsanity.com/paper/2403.06932/) (2024)
- [ReasoningFlow: Semantic Structure of Complex Reasoning Traces](https://mlsanity.com/paper/2506.02532/) (2025)
- [Chain and Causal Attention for Efficient Entity Tracking](https://mlsanity.com/paper/2410.05565/) (2024)

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

- [BODHI: Do LLMs Branch Out and Discover Heterogeneous Inferences?](https://mlsanity.com/paper/2608.02867/) (2026)
- [Arithmetic Pedagogy for Language Models](https://mlsanity.com/paper/2606.05106/) (2026)

## Abstract (arXiv)

Chain-of-thought (CoT) traces have been shown to improve performance of large language models on a plethora of reasoning tasks, yet there is no consensus on the mechanism by which this boost is achieved. To shed more light on this, we introduce Causal CoT Graphs (CCGraphs), which are directed acyclic graphs automatically extracted from reasoning traces that model fine-grained causal dependencies in language-model outputs. A collection of 1671 mathematical reasoning problems from MATH500, GSM8K, and AIME, together with their associated CCGraphs, has been compiled into our dataset -- KisMATH. Our detailed empirical analysis with 15 open-weight LLMs shows that (i) reasoning nodes in the CCGraphs are causal contributors to the final answer, which we argue is constitutive of reasoning; and (ii) LLMs emphasize the reasoning paths captured by the CCGraphs, indicating that the models internally realize structures similar to our graphs. KisMATH enables controlled, graph-aligned interventions and opens avenues for further investigation into the role of CoT in LLM reasoning.