HACK: Hallucinations Along Certainty and Knowledge Axes

TL;DR

The paper introduces a two-axis framework for hallucinations in LLMs, separating failures caused by missing knowledge (HK$^{-}$) from those occurring despite knowledge (HK$^{+}$) and further examining high-certainty mispredictions (CM). It validates HK$^{+}$ using model-specific data and steering-based stabilization, revealing model- and setting-dependent HK$^{+}$ patterns and generalizable detection probes. It then focuses on Certainty Misalignment (CM), defining a CM-Score to evaluate mitigation specifically on high-certainty, knowledge-consistent hallucinations, and showing CM challenges standard mitigation while CM-tuned probes offer improvements. The findings highlight the need for model-specific evaluation, targeted mitigation, and caution in relying on certainty as a reliability proxy, with broad implications for safety-critical applications. Collectively, the work advances understanding of when and why LLMs hallucinate and provides concrete tools for more robust, CM-aware mitigation strategies.

Abstract

Hallucinations in LLMs present a critical barrier to their reliable usage. Existing research usually categorizes hallucination by their external properties rather than by the LLMs' underlying internal properties. This external focus overlooks that hallucinations may require tailored mitigation strategies based on their underlying mechanism. We propose a framework for categorizing hallucinations along two axes: knowledge and certainty. Since parametric knowledge and certainty may vary across models, our categorization method involves a model-specific dataset construction process that differentiates between those types of hallucinations. Along the knowledge axis, we distinguish between hallucinations caused by a lack of knowledge and those occurring despite the model having the knowledge of the correct response. To validate our framework along the knowledge axis, we apply steering mitigation, which relies on the existence of parametric knowledge to manipulate model activations. This addresses the lack of existing methods to validate knowledge categorization by showing a significant difference between the two hallucination types. We further analyze the distinct knowledge and hallucination patterns between models, showing that different hallucinations do occur despite shared parametric knowledge. Turning to the certainty axis, we identify a particularly concerning subset of hallucinations where models hallucinate with certainty despite having the correct knowledge internally. We introduce a new evaluation metric to measure the effectiveness of mitigation methods on this subset, revealing that while some methods perform well on average, they fail disproportionately on these critical cases. Our findings highlight the importance of considering both knowledge and certainty in hallucination analysis and call for targeted mitigation approaches that consider the hallucination underlying factors.

Figures (21)

• Figure 1: Axes of Hallucinations. Hallucinations can occur whether the model encodes the correct knowledge or not, and with both high and low certainty.
• Figure 2: We distinguish between hallucinations along a knowledge axis based on whether the model possesses the correct knowledge (HK$^{+}$ vs HK$^{-}$). We first test whether the model consistently produces correct answers under direct prompts. If the model consistently fails to produce correct answers, we classify this as HK$^{-}$. If the model consistently produces correct answers under direct prompts, we then evaluate whether semantically equivalent prompts can induce hallucinations despite the model possessing the requisite knowledge (HK$^{+}$).
• Figure 3: Different models have different knowledge. Knowledge similarity on TriviaQA (above the diagonal) and Natural Questions (below the diagonal) between the models.
• Figure 4: Different models have different HK$^{+}$ examples.HK$^{+}$ differences between models on TriviaQA (above the diagonal) and Natural Questions (below the diagonal) between the models.
• Figure 5: Different prompt settings have different HK$^{+}$ examples.HK$^{+}$ differences between prompt settings on TriviaQA (above the diagonal) and Natural Questions (below the diagonal) between the models.