Artificial Intelligence

    

The Law of Invariant-Preserving Loops: Toward Robust Emergence in Self-Modifying Agents

Authors: Jace Hall

Scaling has produced surprising "emergent" behaviors in modern ML systems, yet the mechanisms behindrobust emergence remain unclear. This paper argues that durable emergence is not a mystery of scale,but a consequence of invariant-preserving feedback loops.

When self-modifying agents update in waysthat maintain internal stability while expanding representational reach, new behaviors crystallize as robustattractors; when loops erode invariants, apparent gains collapse into drift and brittleness.

We formalize astability functional S(M) that gates self-improvement (ΔS(M) > 0), outline practical proxies for invariantpreservation (entailment, paraphrase stability, tool pre/post-conditions), and propose falsifiable protocols fortesting the framework.

Empirical footholds from ARC-AGI, AlphaGeometry, and large proof libraries (Coq,Lean, Isabelle) suggest that systems enforcing invariants already outperform pure stochastic scaling onreasoning-heavy tasks.

We argue that invariants unify capability and

Comments: 16 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org) This paper is Part 4 of a four-part series on invariants, coherence, and stability in AI systems.

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Submission history

[v1] 2025-09-12 16:46:14

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