The Law of Invariant-Preserving Loops: Toward Robust Emergence in Self-Modifying Agents
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| Formato: | Recurso digital |
| Lenguaje: | inglés |
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2025
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| _version_ | 1866901623894179840 |
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| 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 |