What does this research mean for the field?

Refusal behavior in large language models is characterized by critical slowing down and peaks in refusal geometry in the last 5-13% of transformer layers. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To investigate refusal behavior in large language models using geometric and critical slowing down analyses.

March 10, 2026Open Access

Critical Slowing Down as a Universal Precursor to Refusal in LLMs: Grassmannian Geometry and Phase Transition Signatures Across 10 Model Families

Key Points

To investigate refusal behavior in large language models using geometric and critical slowing down analyses.
Analyzed 10 models from 7 organizations using Grassmannian subspace analysis.
Examined transformer layers focusing on refusal geometry peaks.
Studied harmful prompts for autocorrelation patterns in layer transitions.
Calculated predictive AUC using mid-layer activations.
Refusal geometry peaks observed in the last 5-13% of transformer layers for 7 of 10 models.
Chaotic lag-1 autocorrelation confirmed in layer transitions across 4 model families.
Achieved predictive AUC of 0.9956 using mid-layer activations prior to refusal.

Abstract

We present two complementary findings about refusal behavior in large language models. First, Grassmannian subspace analysis across 10 models from 7 organizations shows refusal geometry peaks in the last 5-13% of transformer layers for 7/10 models. Second, harmful prompts exhibit a critical slowing down signature — chaotic lag-1 autocorrelation in layer-to-layer transitions — confirmed across 4 model families (Llama 3.1 8B, Mistral 7B, Gemma 2 9B, Falcon 7B), achieving predictive AUC = 0.9956 using only mid-layer activations before the refusal decision is made.

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