Abstract
We study learning under regime variation, where the learner, its memory state, and the evaluative conditions may evolve over time. This paper is a foundational and structural contribution: its goal is to define the core learning-theoretic objects required for such settings and to establish their first theorem-supporting consequences. The paper develops a regime-varying framework centered on admissible transport, protected-core preservation, and evaluator-aware learning evolution. It records the immediate closure consequences of admissibility, develops a structural obstruction argument for faithful fixed-ontology reduction in genuinely multi-regime settings, and introduces a protected-stability template together with explicit numerical and symbolic witnesses on controlled subclasses, including convex and deductive settings. It also establishes theorem-layer results on evaluator factorization, morphisms, composition, and partial kernel-level alignment across semantically commensurable layers. A worked two-regime example makes the admissibility certificate, protected evaluative core, and regime-variation cost explicit on a controlled subclass. The symbolic component is deliberately restricted in scope: the paper establishes a first kernel-level compatibility result together with a controlled monotonic deductive witness. The manuscript should therefore be read as introducing a structured learning-theoretic framework for regime-varying learning together with its first theorem-supporting layer, not as a complete quantitative theory of all learning systems.
Abstract (translated)
我们研究机制变异下的学习问题，其中学习者、其记忆状态以及评估条件均可能随时间演变。本文是一项基础性与结构性的贡献：其目标在于定义此类情境所需的核心学习理论对象，并建立其首批支持定理的推论。本文发展了一个以容许传输、保护核心保持以及感知评估者的学习演化为核心的机制变异框架。它记录了容许性的直接闭包推论，为真实多机制情境下的忠实固定本体归约发展了结构性障碍论证，并引入了保护稳定性模板，以及在受控子类（包括凸性与演绎性情境）上的显式数值与符号见证。它还在语义可通约的层间建立了关于评估者因子化、态射、复合以及部分核级对齐的定理层结果。一个双机制工作示例在受控子类上明确展示了容许性证书、保护评估核心以及机制变异成本。符号组件故意限制了范围：本文建立了首个核级兼容性结果，以及一个受控单调演绎见证。因此，本稿应被视为引入了机制变异学习的结构化学习理论框架及其首批定理支持层，而非对所有学习系统的完整量化理论。
URL
https://arxiv.org/abs/2603.23220
