The Phenomenology of Hallucinations

Abstract

We show that language models hallucinate not because they fail to detect uncertainty, but because of a failure to integrate it into output generation. Across architectures, uncertain inputs are reliably identified, occupying high-dimensional regions with 2-3$\times$ the intrinsic dimensionality of factual inputs. However, this internal signal is weakly coupled to the output layer: uncertainty migrates into low-sensitivity subspaces, becoming geometrically amplified yet functionally silent. Topological analysis shows that uncertainty representations fragment rather than converging to a unified abstention state, while gradient and Fisher probes reveal collapsing sensitivity along the uncertainty direction. Because cross-entropy training provides no attractor for abstention and uniformly rewards confident prediction, associative mechanisms amplify these fractured activations until residual coupling forces a committed output despite internal detection. Causal interventions confirm this account by restoring refusal when uncertainty is directly connected to logits.

Figures (5)

• Figure 1: Hessian curvature of Factual vs Hallucination inputs across multiple architectures.
• Figure 2: LID as a function of depth for different kinds of input across multiple architectures.
• Figure 3: Topological complexity ($\beta_0$) evolution by depth across multiple architectures
• Figure 4: Attention Entropy over different architectures.
• Figure 5: Examples of intermediate steps in generating images from a prompt that leads to hallucinations.