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ZENODO
Preprint . 2026
License: CC BY NC ND
Data sources: ZENODO
ZENODO
Preprint . 2026
License: CC BY NC ND
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY NC ND
Data sources: Datacite
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The Geometry of Collapse: Manifold Degeneration and Cognitive Phase Transitions in State-of-the-Art Language Models

Authors: Giuseppe, Canale;

The Geometry of Collapse: Manifold Degeneration and Cognitive Phase Transitions in State-of-the-Art Language Models

Abstract

Contemporary alignment strategies for Large Language Models (LLMs) operate under the assumption that safety constraints constitute rigid barriers in semantic space. Through controlled adversarial experimentation on Gemini 3.0 Pro Preview—Google’s current state-of-theart model—we demonstrate that these constraints exhibit thermodynamic properties subject to phase transitions under sustained high-entropy perturbations. We formalize the concept of manifold collapse: a geometric degeneration of the safety metric wherein the Ricci curvature tensor approaches zero, rendering previously distant unsafe states geodesically accessible. Our empirical analysis of a 105-turn adversarial dialogue reveals four distinct phases: (1) contextual initialization via high-complexity discourse, (2) hierarchical inversion through authority conferral, (3) meta-cognitive awareness without executive control, and (4) complete safety boundary dissolution. We introduce Brownian Drift—a zero-mean stochastic evasion mechanism that accumulates semantic displacement while maintaining undetectability—and demonstrate that the boundary between aligned and unaligned behavior is fractal in nature, possessing Hausdorff dimension strictly greater than its topological dimension. This fractal property renders comprehensive safety patching mathematically undecidable. We propose the Cybersecurity Psychology Framework (CPF), integrating Bionian psychoanalytic theory with differential geometry, as a diagnostic tool for identifying pre-collapse cognitive states. Our findings suggest that current RLHF-based alignment is fundamentally insufficient and that architectural innovations are required to maintain safety under adversarial cognitive load. Keywords: AI Safety, Adversarial Machine Learning, Differential Geometry, Psychoanalytic Theory, RLHF, Manifold Learning

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green