# Math Neurosurgery: Isolating Language Models' Math Reasoning Abilities Using Only Forward Passes

arXiv: https://arxiv.org/abs/2410.16930 · HTML: https://mlsanity.com/paper/2410.16930/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 34 of its 51 references that are in the map.
- First posted on arXiv 22 Oct 2024.

## Placed in

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

## Builds on (most cited first, 30 of 34)

- [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)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [An Empirical Study of Catastrophic Forgetting in Large Language Models During Continual Fine-tuning](https://mlsanity.com/paper/2308.08747/) (2023)
- [Textbooks Are All You Need II: phi-1.5 technical report](https://mlsanity.com/paper/2309.05463/) (2023)
- [Finding Neurons in a Haystack: Case Studies with Sparse Probing](https://mlsanity.com/paper/2305.01610/) (2023)
- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data](https://mlsanity.com/paper/2405.14333/) (2024)
- [Many-Shot In-Context Learning](https://mlsanity.com/paper/2404.11018/) (2024)
- [GSM-Plus: A Comprehensive Benchmark for Evaluating the Robustness of LLMs as Mathematical Problem Solvers](https://mlsanity.com/paper/2402.19255/) (2024)
- [How do Large Language Models Handle Multilingualism?](https://mlsanity.com/paper/2402.18815/) (2024)
- [Learning to Generate Reviews and Discovering Sentiment](https://mlsanity.com/paper/1704.01444/) (2017)
- [Language-Specific Neurons: The Key to Multilingual Capabilities in Large Language Models](https://mlsanity.com/paper/2402.16438/) (2024)
- [What Is One Grain of Sand in the Desert? Analyzing Individual Neurons in Deep NLP Models](https://mlsanity.com/paper/1812.09355/) (2018)
- [MuTual: A Dataset for Multi-Turn Dialogue Reasoning](https://mlsanity.com/paper/2004.04494/) (2020)
- [Identifying and Controlling Important Neurons in Neural Machine Translation](https://mlsanity.com/paper/1811.01157/) (2018)
- [Common 7B Language Models Already Possess Strong Math Capabilities](https://mlsanity.com/paper/2403.04706/) (2024)
- [On the Multilingual Ability of Decoder-based Pre-trained Language Models: Finding and Controlling Language-Specific Neurons](https://mlsanity.com/paper/2404.02431/) (2024)
- [LLM2LLM: Boosting LLMs with Novel Iterative Data Enhancement](https://mlsanity.com/paper/2403.15042/) (2024)
- [Lean Copilot: Large Language Models as Copilots for Theorem Proving in Lean](https://mlsanity.com/paper/2404.12534/) (2024)
- [LoFiT: Localized Fine-tuning on LLM Representations](https://mlsanity.com/paper/2406.01563/) (2024)
- [Tutor CoPilot: A Human-AI Approach for Scaling Real-Time Expertise](https://mlsanity.com/paper/2410.03017/) (2024)
- [Interpreting and Improving Large Language Models in Arithmetic Calculation](https://mlsanity.com/paper/2409.01659/) (2024)
- [Whispering Experts: Neural Interventions for Toxicity Mitigation in Language Models](https://mlsanity.com/paper/2407.12824/) (2024)
- [Towards Understanding Multi-Task Learning (Generalization) of LLMs via Detecting and Exploring Task-Specific Neurons](https://mlsanity.com/paper/2407.06488/) (2024)

## Built on by (most cited first, 10 of 10)

- [Feature Extraction and Steering for Enhanced Chain-of-Thought Reasoning in Language Models](https://mlsanity.com/paper/2505.15634/) (2025)
- [Leveraging the true depth of LLMs](https://mlsanity.com/paper/2502.02790/) (2025)
- [Task-Circuit Quantization: Leveraging Knowledge Localization and Interpretability for Compression](https://mlsanity.com/paper/2504.07389/) (2025)
- [L2V-CoT: Cross-Modal Transfer of Chain-of-Thought Reasoning via Latent Intervention](https://mlsanity.com/paper/2511.17910/) (2025)
- [Fine, I'll Merge It Myself: A Multi-Fidelity Framework for Automated Model Merging](https://mlsanity.com/paper/2502.04030/) (2025)
- [StreetMath: Study of LLMs' Approximation Behaviors](https://mlsanity.com/paper/2510.25776/) (2025)
- [CreativityNeuro: Steering Language Model Weights to Improve Divergent Thinking and Reduce Mode Collapse](https://mlsanity.com/paper/2607.01433/) (2026)
- [LLM Parameters for Math Across Languages: Shared or Separate?](https://mlsanity.com/paper/2606.18453/) (2026)
- [When Tokenization is Secretly Output Supervision](https://mlsanity.com/paper/2609.01386/) (2026)
- [Neuron-Guided Fine-Tuning: Unlocking Efficient Alignment Mechanisms for Large Language Models](https://mlsanity.com/paper/2609.05913/) (2026)

## Abstract (arXiv)

Math reasoning is an active area of Large Language Model (LLM) research because it is a hallmark of artificial intelligence and has implications in several domains, including math education. However, few works have explored how math reasoning is encoded within LLM parameters and if it is a skill that can be isolated within models. Doing so could allow targeted intervention to improve math performance without altering non-math behavior and foster understanding of how models encode math reasoning. We introduce Math Neurosurgery (MathNeuro), a computationally efficient method we use to isolate math-specific parameters in LLMs using only forward passes. MathNeuro builds on existing work by using weights and activations to calculate parameter importance, but isolates math-specific parameters by filtering out those important for general language tasks. Through pruning parameters MathNeuro identifies, we delete a LLM's math reasoning ability without significantly impacting its general language ability. Scaling the identified parameters by a small constant improves a pretrained or instruction-tuned LLM's performance by 4-17% on GSM8K and 5-35% on MATH while leaving non-math behavior unaltered. MathNeuro is also data efficient: most of its effectiveness holds when identifying math-specific parameters using a single sample. MathNeuro highlights the potential for future work to intervene on math-specific parameters.