# General Machine Learning: Theory for Learning Under Variable Regimes

arXiv: https://arxiv.org/abs/2603.23220 · HTML: https://mlsanity.com/paper/2603.23220/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 68 references that are in the map.
- First posted on arXiv 24 Mar 2026.

## Builds on (most cited first, 11 of 11)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Learning to (Learn at Test Time): RNNs with Expressive Hidden States](https://mlsanity.com/paper/2407.04620/) (2024)
- [On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models](https://mlsanity.com/paper/1810.12715/) (2018)
- [Continual Learning and Catastrophic Forgetting](https://mlsanity.com/paper/2403.05175/) (2024)
- [Beyond Preferences in AI Alignment](https://mlsanity.com/paper/2408.16984/) (2024)
- [Neuro-Symbolic AI in 2024: A Systematic Review](https://mlsanity.com/paper/2501.05435/) (2025)
- [Dual-Phase Continual Learning: Supervised Adaptation Meets Unsupervised Retention](https://mlsanity.com/paper/2406.13653/) (2024)
- [SMGI: A Structural Theory of General Artificial Intelligence](https://mlsanity.com/paper/2603.07896/) (2026)

## Abstract (arXiv)

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.