Search papers, labs, and topics across Lattice.
This paper investigates what LLMs for mathematics actually represent by analyzing their ability to translate statements between subfields without external validation, focusing on the implicit level of generality. The authors introduce a novel instrument to code truth, content, and scope, revealing that LLMs consistently translate towards more general framings, widening quantification domains significantly more than narrowing them. This asymmetry, observed across multiple models and benchmarks, suggests LLMs acquire object-level vocabulary correspondences without fully representing the underlying theoretical hypotheses.
LLMs for math translate statements towards generality, widening quantification domains in over 60% of cases, yet fail to explicitly state implicit hypotheses, suggesting a shallow understanding of theoretical relationships.
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.
