SCIUR us: Shared Circuits for Interpretable Uncertainty Representations in Language Models (2025)

Abstract: We investigate the mechanistic sources of uncertainty in large language models (LLMs), an area with important implications for language model reliability and trustworthiness. To do so, we conduct a series of experiments designed to identify whether the factuality of generated responses and a model’s uncertainty originate in separate or shared circuits in the model architecture. We approach this question by adapting the well-established mechanistic interpretability techniques of causal tracing and zero-ablation to study the effect of different circuits on LLM generations. Our experiments on eight different models and five datasets, representing tasks predominantly requiring factual recall, provide strong evidence that a model’s uncertainty is produced in the same parts of the network that are responsible for the factuality of generated responses.

## introduction uncertainty quantification (uq) in large language models (llms) for knowledge-intensive tasks @xcite remains a critical yet understudied area. despite achieving human-level performance on various benchmarks, llms often struggle with reliable uncertainty estimation, leading to issues such as overconfidence and hallucination @xcite . this limitation has strong implications for their trustworthiness and safety in high-stakes applications. while recent research has explored verbalized uncertainty in llms @xcite @xcite , significant gaps remain in our understanding of and ability to improve uncertainty quantification. in particular, existing uq techniques typically provide little insight into the factors responsible for an uncertainty estimate, limiting their usefulness both as practical tools for improving trustworthiness and as methods for understanding uncertainty reasoning. we propose leveraging mechanistic in-terpretability, an approach focused on characterizing models' internal reasoning mechanisms, to advance our capabilities for and understanding of uncertainty quantification in large language models. to better understand how llms generate uncertainty estimates, we trained p(ik) (probability that i know) probes that represent the model's uncertainty based on multiple generated answers @xcite . we then used these probes' predicted confidences as target metrics for causal tracing and zero-ablation, two interpretability techniques which identify the components of a model that are relevant for a task by testing the effect of an intervention made on activations in the model during evaluation. we compared the mechanistic signatures of changes in the model's accuracy and the probe's output to evaluate whether the same circuits were responsible for the answer and the predicted confidence. in our empirical evaluation, we performed causal tracing and leave-one-out and coar-style @xcite zero-ablation for a large range of model-dataset combinations. we found that model accuracy and probe behavior largely responded to the same interventions, indicating that circuits responsible for the factuality of responses and for the model's uncertainty are located in the same parts of the model. for a group of knowledge-intensive question answering tasks @xcite , model accuracy and probe confidence are (highly) positively related to one another. we conclude that, at least on recall tasks, a language model's representation of confidence may derive mainly from "uncertainty introspection" on its question-answering process, rather than from separate reasoning specific to its uncertainty. to summarize, the key contributions of this paper are as follows: ## methods probe design we use a p(ik) probing approach in part because of the difficulty of reasoning about uncertainty using token probabilities. token probabilities for open-ended questions are a highly imperfect proxy for a model's confidence, because they conflate semantic uncertainty, or uncertainty about content, with syntactic uncertainty, or uncertainty about form @xcite . furthermore, we are most interested in improving uncertainty quantification for fine-tuned chat models, for which token probabilities do not correspond to an underlying distribution over possible text strings. we construct a dataset on which to train the p(ik) probe according to the following steps. the p(ik) probe is a logistic classifier p : r d @xmath0, 1) which takes these last layer activations as input and returns the proportion of correct answers. for example, if the model answers a question correctly 47% of the time, the probe should we used between 2048 and 8192 examples per task (using fewer than 8192 when we were limited by the size of the dataset), and held out 20% of the data as a test split. experiments were done with examples from the test split. ## uncertainty introspection and the shared circuits hypothesis the aim of this paper is to make progress toward characterizing the mechanistic structures used for uq in language models. to this end, we propose a theoretical hypothesis ("shared circuits") about the locations of these structures, along with operationalizations which we test experimentally. ## see graphs in the supplementary materials online (see appendix a). the uq/qa relationship. in the cases studied, the model is more resilient than the probe: that is, interventions generally have a greater effect on the probe than the model (creating the convex shape in figure 4 , left); this depends to some extent on the model architecture. in some cases, when the probe is confidently wrong (see figure 2 , right), the probe may be following the path for the model's (incorrect) highest-probability token. as in @xcite , highly important locations generally fall into two clusters: one in earlier layers at the token positions in the subject, and one at later layers at the last token position. we note that uncertainty information and answer information are often transferred to the last position by attention heads in different layers (fig. 2 . 8 these small differences suggest that our p(ik) probes are using the model's question-answering circuitry directly, rather than by performing separate or posthoc uncertainty calculations. gemma 2 9b inst. ## discussion and conclusion the results of the causal tracing and zero-ablation analyses presented in the previous section broadly support the shared circuits hypothesis, implying that-across the setups we considered-the sets of model components used for question-answering and uncertainty quantification were largely, albeit not entirely, the same. this suggests that p(ik) probing may be a viable way of eliciting introspective, interpretable uncertainty estimates. based on these findings, further research could analyze the mechanisms responsible for p(ik) estimates in greater detail, or apply p(ik) probing as an interpretability tool to study phenomena such as hallucination in llms. similar analyses of other methods of uncertainty quantification (e.g., verbalized uncertainty) may provide insight further insight into the role of uncertainty introspection in uncertainty quantification. more broadly, we see interpretable uncertainty quantification as a potentially useful approach for understanding and improving llm reasoning, in order to improve trustworthiness and reliability and inform technical ai governance.