arXiv：cs.LG· Yanli Wang, Suijin Wang, Xiaopeng Yuan, Haohan Wang·· 3 小时前AI 评分52
arXiv 论文：数学 LLM 缺少跨子领域翻译中的假设约束表示
Objects Without Morphisms: What LLMs for Mathematics Do Not Represent
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arXiv 论文（arXiv:2610.03551）研究 LLM 在数学相邻子领域方言间翻译陈述时的表示问题，提出用分离盲队列编码真值、内容与范围的无裁判测量工具，并以植入阳性对照验证其敏感性。
正文
Abstract:Large language models (LLMs) have reached expert-level performance on competition mathematics largely through the volume of search placed around them: candidate solutions are sampled in quantity and retained only when an external criterion accepts them. Such a procedure improves the outcome that survives it while leaving untouched what the model represents. We examine that question where no external criterion exists: translating statements between the dialects of neighbouring subfields, where fidelity turns on the level of generality at which content is asserted. The source leaves that level implicit in its vocabulary, so a faithful translation must recover it from the relation between the theories. We introduce an instrument that codes truth, content and scope in separate blind queues, with a judge-free measure of whether a rewrite states the hypothesis implicit in its source, and establish its sensitivity with a planted-positive control. Across seven models from four families, translating towards the general framing widens the domain of quantification in 60.6% of rewrites and narrows it in none; translating towards the concrete framing narrows it in 28.3% and widens it in 0.3%. The hypothesis that would prevent it is stated in 21.6% of model rewrites and 4.2% of human statements. Capability does not govern the asymmetry: it appears in every model tested, and the most capable widens least. It replicates on the half of the benchmark held out by a pre-registered rule, and on statements written by mathematicians. Instructing a model to state every hypothesis it requires raises that rate but not its sensitivity to direction. We argue that these systems have acquired an object-level correspondence between subfield vocabularies without the constraint under which a translation between theories carries hypotheses to hypotheses.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.03551 [cs.LG] |
| (or arXiv:2610.03551v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.03551 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Yanli Wang [view email]
[v1]
Fri, 2 Oct 2026 16:33:32 UTC (780 KB)
来源：arXiv：cs.LG · arxiv.org