# Mathematical Transfer in LLMs Follows Reasoning Approach More Than Topic

arXiv: https://arxiv.org/abs/2610.00331 · HTML: https://mlsanity.com/paper/2610.00331/

## 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 18 of its 23 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Placed in

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

## Builds on (most cited first, 18 of 18)

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- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [Analysing Mathematical Reasoning Abilities of Neural Models](https://mlsanity.com/paper/1904.01557/) (2019)
- [Skill-it! A Data-Driven Skills Framework for Understanding and Training Language Models](https://mlsanity.com/paper/2307.14430/) (2023)
- [Metacognitive Capabilities of LLMs: An Exploration in Mathematical Problem Solving](https://mlsanity.com/paper/2405.12205/) (2024)
- [OMEGA: Can LLMs Reason Outside the Box in Math? Evaluating Exploratory, Compositional, and Transformative Generalization](https://mlsanity.com/paper/2506.18880/) (2025)
- [Learning Beyond Pattern Matching? Assaying Mathematical Understanding in LLMs](https://mlsanity.com/paper/2405.15485/) (2024)
- [Skill-Aware Data Selection and Fine-Tuning for Data-Efficient Reasoning Distillation](https://mlsanity.com/paper/2601.10109/) (2026)
- [Are We Measuring Strategy or Phrasing? The Gap Between Surface- and Approach-Level Diversity in LLM Math Reasoning](https://mlsanity.com/paper/2606.29985/) (2026)

## Abstract (arXiv)

When selecting mathematical training data for LLMs, a natural organizing principle is topic: probability examples for probability targets. An alternative is reasoning approach: worked solutions that share a solution method with the target, even when the mathematical domain differs. We ask which relation produces greater transfer after fine-tuning. We evaluate two counterbalanced 2×2 designs: probability and combinatorics crossed with invariant reasoning and double counting (2,000 problems), and number theory and geometry crossed with complement and pigeonhole reasoning (800 problems). In each design, every cell serves as the held-out target in turn: same-approach (SA) sources share the target's method but change the topic, while same-topic (ST) sources share the topic but change the method. Every source appears once in each role, so additive source-quality effects cancel from the equally weighted aggregate contrast. Across five base models and three training seeds per design, SA outperforms ST in all 40 seed-pooled model--target comparisons. Model-level advantages range from 8.2 to 16.2 percentage points in the primary design (mean: 10.8) and from 12.0 to 16.0 in the second design (mean: 14.3); all ten model-level 95% confidence intervals exclude zero. In both designs, ST sources are more similar to targets under embedding and lexical measures, so the SA advantage runs opposite to the measured ordering of statement-level resemblance. These findings identify reasoning approach as a more effective matching criterion than topic for mathematical transfer across the evaluated topic--approach combinations.