The Confidence Manifold: Geometric Structure of Correctness Representations in Language Models

arXiv:2602.08159v2 Announce Type: replace-cross Abstract: When a language model asserts that "the capital of Australia is Sydney," does it know this is wrong? Models assert misconceptions with the same fluency as facts, so the question cannot be answered from output uncertainty. Truth-related signals are known to exist in the residual stream, but not their geometry: how many dimensions carry the signal, how simple a detector can be, and whether it transfers. We characterize this geometry across 11 models (124M-14B) and test it causally with activation steering, concept erasure, and distributed alignment search. The structure is simple: two class centroids in a 2-8 dimensional subspace match a trained linear probe, and 25 labeled examples recover 90% of full-data AUC on GPT-2. Steering shifts hallucination rates by 9.1 points on six models, erasure drops detection to chance, and distributed alignment search, the only method that bounds rank, localizes at most five causal dimensions. The internal advantage is regime-specific: probes far outperform P(True) and semantic entropy on adversarial misconceptions but tie on standard QA. Single-dataset probes transfer near-randomly until joint multi-dataset training restores 0.73-0.91 AUC. That centroid distance matches probe performance indicates class separation is a mean shift, making detection geometric rather than learned.

Abstract:When a language model asserts that "the capital of Australia is Sydney," does it know this is wrong? Models assert misconceptions with the same fluency as facts, so the question cannot be answered from output uncertainty. Truth-related signals are known to exist in the residual stream, but not their geometry: how many dimensions carry the signal, how simple a detector can be, and whether it transfers. We characterize this geometry across 11 models (124M-14B) and test it causally with activation steering, concept erasure, and distributed alignment search. The structure is simple: two class centroids in a 2-8 dimensional subspace match a trained linear probe, and 25 labeled examples recover 90% of full-data AUC on GPT-2. Steering shifts hallucination rates by 9.1 points on six models, erasure drops detection to chance, and distributed alignment search, the only method that bounds rank, localizes at most five causal dimensions. The internal advantage is regime-specific: probes far outperform P(True) and semantic entropy on adversarial misconceptions but tie on standard QA. Single-dataset probes transfer near-randomly until joint multi-dataset training restores 0.73-0.91 AUC. That centroid distance matches probe performance indicates class separation is a mean shift, making detection geometric rather than learned.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computation and Language (cs.CL)

arXiv:2602.08159 [cs.LG]

(or arXiv:2602.08159v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2602.08159 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

aiqbench analysis

The Confidence Manifold: Geometric Structure of Correctness Representations in Language Models

Related coverage