# Disentangling Mathematical Reasoning in LLMs: A Methodological Investigation of Internal Mechanisms

arXiv: https://arxiv.org/abs/2604.15842 · HTML: https://mlsanity.com/paper/2604.15842/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 23 of its 41 references that are in the map.
- First posted on arXiv 17 Apr 2026.

## Placed in

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

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [GPT-NeoX-20B: An Open-Source Autoregressive Language Model](https://mlsanity.com/paper/2204.06745/) (2022)
- [Function Vectors in Large Language Models](https://mlsanity.com/paper/2310.15213/) (2023)
- [Linearity of Relation Decoding in Transformer Language Models](https://mlsanity.com/paper/2308.09124/) (2023)
- [Chain-of-Thought Hub: A Continuous Effort to Measure Large Language Models' Reasoning Performance](https://mlsanity.com/paper/2305.17306/) (2023)
- [Language Models Implement Simple Word2Vec-style Vector Arithmetic](https://mlsanity.com/paper/2305.16130/) (2023)
- [Arithmetic Without Algorithms: Language Models Solve Math With a Bag of Heuristics](https://mlsanity.com/paper/2410.21272/) (2024)
- [A Mechanistic Interpretation of Arithmetic Reasoning in Language Models using Causal Mediation Analysis](https://mlsanity.com/paper/2305.15054/) (2023)
- [A Causal Framework to Quantify the Robustness of Mathematical Reasoning with Language Models](https://mlsanity.com/paper/2210.12023/) (2022)
- [pyvene: A Library for Understanding and Improving PyTorch Models via Interventions](https://mlsanity.com/paper/2403.07809/) (2024)
- [LM-Debugger: An Interactive Tool for Inspection and Intervention in Transformer-Based Language Models](https://mlsanity.com/paper/2204.12130/) (2022)
- [Evaluating LLMs' Mathematical and Coding Competency through Ontology-guided Interventions](https://mlsanity.com/paper/2401.09395/) (2024)
- [From Insights to Actions: The Impact of Interpretability and Analysis Research on NLP](https://mlsanity.com/paper/2406.12618/) (2024)
- [The Lookahead Limitation: Why Multi-Operand Addition is Hard for LLMs](https://mlsanity.com/paper/2502.19981/) (2025)
- [Cutting Through the Noise: Boosting LLM Performance on Math Word Problems](https://mlsanity.com/paper/2406.15444/) (2024)
- [Language Models are Symbolic Learners in Arithmetic](https://mlsanity.com/paper/2410.15580/) (2024)
- [Modular Arithmetic: Language Models Solve Math Digit by Digit](https://mlsanity.com/paper/2508.02513/) (2025)

## Abstract (arXiv)

Large language models (LLMs) have demonstrated impressive capabilities, yet their internal mechanisms for handling reasoning-intensive tasks remain underexplored. To advance the understanding of model-internal processing mechanisms, we present an investigation of how LLMs perform arithmetic operations by examining internal mechanisms during task execution. Using early decoding, we trace how next-token predictions are constructed across layers. Our experiments reveal that while the models recognize arithmetic tasks early, correct result generation occurs only in the final layers. Notably, models proficient in arithmetic exhibit a clear division of labor between attention and MLP modules, where attention propagates input information and MLP modules aggregate it. This division is absent in less proficient models. Furthermore, successful models appear to process more challenging arithmetic tasks functionally, suggesting reasoning capabilities beyond factual recall.