Manifold of Failure: Behavioral Attraction Basins in Language Models

TL;DR

This paper introduces a novel framework using MAP-Elites to systematically map and understand the failure regions in large language models, revealing their topological signatures and vulnerabilities.

Contribution

It presents a new approach to characterize unsafe regions in LLMs by mapping behavioral attraction basins, offering global safety landscape insights beyond existing attack methods.

Findings

Achieved up to 63% behavioral coverage of failure regions.

Discovered up to 370 distinct vulnerability niches.

Revealed model-specific topological signatures of failure landscapes.

Abstract

While prior work has focused on projecting adversarial examples back onto the manifold of natural data to restore safety, we argue that a comprehensive understanding of AI safety requires characterizing the unsafe regions themselves. This paper introduces a framework for systematically mapping the Manifold of Failure in Large Language Models (LLMs). We reframe the search for vulnerabilities as a quality diversity problem, using MAP-Elites to illuminate the continuous topology of these failure regions, which we term behavioral attraction basins. Our quality metric, Alignment Deviation, guides the search towards areas where the model's behavior diverges most from its intended alignment. Across three LLMs: Llama-3-8B, GPT-OSS-20B, and GPT-5-Mini, we show that MAP-Elites achieves up to 63% behavioral coverage, discovers up to 370 distinct vulnerability niches, and reveals dramatically different model-specific topological signatures: Llama-3-8B exhibits a near-universal vulnerability plateau (mean Alignment Deviation 0.93), GPT-OSS-20B shows a fragmented landscape with spatially concentrated basins (mean 0.73), and GPT-5-Mini demonstrates strong robustness with a ceiling at 0.50. Our approach produces interpretable, global maps of each model's safety landscape that no existing attack method (GCG, PAIR, or TAP) can provide, shifting the paradigm from finding discrete failures to understanding their underlying structure.