有限资源下的表征获取：存储与读取的权衡曲线

View PDF HTML (experimental)

Abstract:A learner's obligation to keep acquired content usable imposes a storage-access tradeoff, with exact endpoints that force different physical organizations. For an exact concept-learning task, we determine the storage-read curve within a constant factor. One-read compound queries force answer-specific cells and exponentially costly updates; one-bit, order-independent updates instead force fact-specific cells. At minimum storage capacity, a robust counterpart holds: when update stretch is averaged uniformly over all semantic cube edges, small excess stretch bounds expected distance from a coordinate encoding under the uniform content distribution. It also bounds the information inaccessible to a one-read consumer. Preservation imposes further constraints. On a common invariant ready-state domain, old content preserved by ordinary zero-read overwrites must factor through the unwritten coordinates. Distributed encodings can require reading every cell to choose a preserving update. For conditional Horn reasoning, we obtain a second pair of exact endpoints: maintaining answers makes use local, while minimum storage and one-change named revision force a rule vector whose optimal query-read cost is determined exactly. These results explain how acquired distinctions, subsequent uses, and update constraints jointly determine the costs and organization of a retained resource.

Comments:	76 pages, 1 figure, 6 tables
Subjects:	Artificial Intelligence (cs.AI); Computation and Language (cs.CL)
MSC classes:	68Q17, 68Q32, 68P05
ACM classes:	F.2.3; I.2.6
Cite as:	arXiv:2603.21736 [cs.AI]
	(or arXiv:2603.21736v3 [cs.AI] for this version)
	https://doi.org/10.48550/arXiv.2603.21736 arXiv-issued DOI via DataCite

Submission history

From: Yiling Wu [view email]
[v1] Mon, 23 Mar 2026 09:25:19 UTC (25 KB)
[v2] Thu, 2 Apr 2026 01:22:08 UTC (25 KB)
[v3] Sun, 1 Nov 2026 07:13:51 UTC (97 KB)