arXiv：cs.LG（机器学习，全量分类）· Xin Li·· 1 天前AI 评分28
Poincaré 遇上 Bellman：变化环境中的可修订记忆、操作商与证据支持学习
Poincar\'e Meets Bellman: Revisable Memory, Operational Quotients, and Evidence-Supported Learning in Changing Environments
AI 导读
该研究在稳定性-证据-修订（SER）框架下提出有限模型综合方法，将操作状态抽象与最优控制结合：定性动力学识别可复用的动作-响应结构，动态规划为获取、保留、复用、合并与遗忘定价。
正文
Abstract:Memory consolidation determines both what a learner can do now and which changes remain implementable later. We develop a finite-model synthesis of operational state abstraction and optimal control under the stability-evidence-revision (SER) framework. ``Poincaré meets Bellman'' names two complementary roles: qualitative dynamics identifies reusable action-response structure, and dynamic programming prices acquisition, retention, reuse, merging, and forgetting. Recurrence enters separately through the timing and value of future demands. We distinguish active quotient merging from historical information erasure, characterize exact repair by zero-error functional coding and causal migration, and derive a Bellman recursion over the joint law of hidden state and complete deployed memory. A first-return model yields an explicit retention rule. Conditional results show how factor sharing avoids enumerating combinations and how independent informative observations improve identification, while leaving some zero-error evidence budgets unchanged. Finite enumerations verify the coding and retention calculations. The synthesis gives an exact benchmark for specified finite models, without claiming universal recurrence, bounded-memory open-ended learning, or tractable global planning.
| Subjects: | Machine Learning (cs.LG); Neurons and Cognition (q-bio.NC) |
| Cite as: | arXiv:2512.05990 [cs.LG] |
| (or arXiv:2512.05990v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2512.05990 arXiv-issued DOI via DataCite |
Submission history
From: Xin Li [view email]
[v1]
Fri, 28 Nov 2025 16:28:24 UTC (25 KB)
[v2]
Thu, 1 Oct 2026 14:02:45 UTC (48 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org