arXiv cs.CL· Kwan Soo Shin (ComplexSystems Research)·· 11 小时前AI 评分29
平坦模型中的弯曲知识：大规模构建专家级 AI 的算术约束
Curved Knowledge in Flat Models: Building Expert AI at Scale
AI 导读
一项对已发布双曲视觉语言模型检查点的独立审计发现其层级机制并未生效，研究指出这不仅是几何或目标函数的问题，也是算术问题：定义流形的约束在单位曲率和温度下的未截断映射中，即便双精度也在所测语言模型深层范数处失效。
正文 · 原文
Abstract:Intelligence that must act before outside correction arrives must carry the structure of its expert knowledge, and hyperbolic geometry represents hierarchy with a fidelity no Euclidean space of comparable dimension matches. Yet hyperbolic language models confine that geometry to adapters or rebuild the transformer, and an independent audit of released hyperbolic vision language checkpoints finds their hierarchy mechanisms inactive, which has been read as evidence about the geometry or its objective. Here we show that it is also evidence about arithmetic. The constraint defining the manifold is a difference of two terms that grow together; for the unclamped map at unit curvature and temperature it fails in every format we measured, double precision included, at the deep-layer norms of the language models measured here, beyond the limit previously derived. A common remedy, a norm bound, leaves the executed map no radial sensitivity where it acts. In a prespecified test, a tighter bound cost a Lorentz system more of the held out structure it started with than a flat one. Structural supervision has run in six expert systems whose retained input archives and source pools hold at least 13,787,131 records. In paired runs with a published recipe's objective held fixed, removing its starting scale remedy prevented every update and removing its single precision regions raised the radius reached early in training. Arithmetic bounds the computable region, and within it, alongside the objective, arithmetic and its remedies select which runs leave a record and the states they reach on the way, so a flat surviving checkpoint cannot by itself establish that the geometry is inert.
| Comments: | Corrected version: corpus counts are unique records per system (at least 13,787,131); v2's multiples and largest-corpus claim withdrawn (Supplementary Note M10). 40 pages; Supplementary Information (86 pages) as ancillary file. Data and code: doi:https://doi.org/10.5281/zenodo.21438499 |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computation and Language (cs.CL) |
| Cite as: | arXiv:2607.17513 [cs.LG] |
| (or arXiv:2607.17513v3 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2607.17513 arXiv-issued DOI via DataCite |
Submission history
From: Kwan Soo Shin [view email]
[v1]
Mon, 20 Jul 2026 03:38:17 UTC (1,398 KB)
[v2]
Mon, 19 Oct 2026 08:41:46 UTC (1,149 KB)
[v3]
Fri, 6 Nov 2026 11:06:00 UTC (1,151 KB)
来源：arXiv cs.CL · arxiv.org