General Machine Learning: Theory for Learning Under Variable Regimes

TL;DR

This paper develops a foundational theoretical framework for machine learning in environments where regimes change over time, defining core objects and proving initial theorems about their properties.

Contribution

It introduces a structured regime-varying learning framework with core concepts, theorems, and examples, advancing understanding of learning under regime shifts.

Findings

Established admissibility closure consequences

Developed a structural obstruction argument for fixed-ontology reduction

Proved theorem-layer results on evaluator factorization and layer alignment

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.