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

Fuente: Zenodo
Guardado en:
Detalles Bibliográficos
Autor principal: Hall, Jace
Formato: Recurso digital
Lenguaje:inglés
Publicado: Zenodo 2025
Materias:
Acceso en línea:
Etiquetas: Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
_version_ 1866901623894179840
author Hall, Jace
author_facet Hall, Jace
contents <p>Scaling has produced surprising “emergent” behaviors in modern ML systems, <em>yet the mechanisms behind robust emergence remain unclear.</em> <strong>This paper argues that durable emergence is not a mystery of scale but a consequence of invariant-preserving feedback loops.</strong> When self-modifying agents update in ways that maintain internal stability while expanding representational reach, new behaviors crystallize as robust attractors; when loops erode invariants, apparent gains collapse into drift and brittleness.</p> <p>The paper formalizes a stability functional S(M) that gates self-improvement (ΔS(M) > 0), outlines practical proxies for invariant preservation (entailment, paraphrase stability, tool pre/post-conditions), and proposes falsifiable protocols for testing the framework. Empirical footholds from ARC-AGI, AlphaGeometry, and large proof libraries (Coq, Lean, Isabelle) suggest that <em>systems enforcing invariants already outperform pure stochastic scaling on reasoning-heavy tasks.</em></p> <p><strong>The arguement is that invariants unify capability and safety: </strong>the same substrate that yields robust emergence also prevents drift. The implication is a reframing of the bottleneck: not FLOPs, but invariants (the universal substrate of adaptive stability) quantified via an Invariant Data-Processing Inequality and a No-Free-Stability bound on verification work.</p>
format Recurso digital
id zenodo_https___doi_org_10_5281_zenodo_17105709
institution Zenodo
language eng
publishDate 2025
publisher Zenodo
record_format zenodo
spellingShingle The Law of Invariant-Preserving Loops: Toward Robust Emergence in Self-Modifying Agents
Hall, Jace
AI safety
emergence
invariants
stability
self-modification
recursive self-improvement
Lyapunov functions
thermodynamic analogy
alignment
verification cost
<p>Scaling has produced surprising “emergent” behaviors in modern ML systems, <em>yet the mechanisms behind robust emergence remain unclear.</em> <strong>This paper argues that durable emergence is not a mystery of scale but a consequence of invariant-preserving feedback loops.</strong> When self-modifying agents update in ways that maintain internal stability while expanding representational reach, new behaviors crystallize as robust attractors; when loops erode invariants, apparent gains collapse into drift and brittleness.</p> <p>The paper formalizes a stability functional S(M) that gates self-improvement (ΔS(M) > 0), outlines practical proxies for invariant preservation (entailment, paraphrase stability, tool pre/post-conditions), and proposes falsifiable protocols for testing the framework. Empirical footholds from ARC-AGI, AlphaGeometry, and large proof libraries (Coq, Lean, Isabelle) suggest that <em>systems enforcing invariants already outperform pure stochastic scaling on reasoning-heavy tasks.</em></p> <p><strong>The arguement is that invariants unify capability and safety: </strong>the same substrate that yields robust emergence also prevents drift. The implication is a reframing of the bottleneck: not FLOPs, but invariants (the universal substrate of adaptive stability) quantified via an Invariant Data-Processing Inequality and a No-Free-Stability bound on verification work.</p>
title The Law of Invariant-Preserving Loops: Toward Robust Emergence in Self-Modifying Agents
topic AI safety
emergence
invariants
stability
self-modification
recursive self-improvement
Lyapunov functions
thermodynamic analogy
alignment
verification cost
url https://doi.org/10.5281/zenodo.17105709