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Math Reasoning in LLMs is Organized by Approach, Not Topic — arXiv:2609.27041

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.27041
License (as archived): CC0-1.0
Archived: 2026-10-08T09:11:04.262Z
SHA-256 of the archived text: 179edf1daceade394aebd3c03f86c0b2c6e725b2c6da23408949ab64e99a977a
Stable URL of this page: https://metraipolis.com/documento/dc_2eeacca83fdd

How to cite

Math Reasoning in LLMs is Organized by Approach, Not Topic — arXiv:2609.27041 — arXiv (en), https://arxiv.org/abs/2609.27041 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_2eeacca83fdd (Metraipolis archive dc_2eeacca83fdd, sha256 179edf1daceade394aebd3c03f86c0b2c6e725b2c6da23408949ab64e99a977a)

BibTeX

@misc{dc2eeacca83fdd,
  title = {Math Reasoning in LLMs is Organized by Approach, Not Topic — arXiv:2609.27041},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.27041},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_2eeacca83fdd; sha256 179edf1daceade394aebd3c03f86c0b2c6e725b2c6da23408949ab64e99a977a},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.27041. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Mathematical reasoning benchmarks are typically organized by topic, but language models may organize their internal computation by reusable reasoning approach instead. In this paper, we investigate whether open math-capable LLMs organize internally by topical sub-skill or by reasoning approach, and we present evidence that the approach is the key. We introduce a generation-replay protocol: a model first generates a solution, after which we replay the exact prompt-plus-generation trajectory and extract activation-importance signatures over the reasoning tokens. We cluster these signatures without supervision across eight models and five mathematical reasoning sources, then evaluate the recovered structure with structural, semantic, and intervention tests. Across all 40 model-source cells, the recovered clusters outperform matched-size random baselines. Two independent frontier-LLM judges find approach-level coherence in 77-82% of real clusters versus 6-11% in within-source controls, and topic-pure clusters usually receive labels finer than the topic itself. In approach-controlled prompting, changing the requested reasoning approach shifts cluster assignment in seven of eight model conditions, whereas paraphrases largely preserve it. These results indicate that math-capable LLMs organize internal mathematical computation by reasoning approach rather than benchmark topic. The implication is that topic-stratified benchmarks and topic-balanced training corpora can still miss the axis that matters: even deliberately topic-balanced corpora may remain imbalanced over reasoning approaches.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-24 in cs.AI).
Categorie arXiv: Artificial Intelligence (cs.AI).
Pagina del lavoro: https://arxiv.org/abs/2609.27041 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-08T08:13:26.466Z dalla pagina https://arxiv.org/catchup/cs.AI/2026-09-24?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).