Measuring Mechanistic Uncertainty in Large Language Models via Causal Robustness

Aneesh Komanduri; Majid Afshar; Timothy A. Miller; Yanjun Gao

cs.CLOct 15, 2026

Measuring Mechanistic Uncertainty in Large Language Models via Causal Robustness

Authors: Aneesh Komanduri, Majid Afshar, Timothy A. Miller, Yanjun Gao

Organizations: University of Colorado Anschutz Medical Campus · University of Wisconsin-Madison · Harvard Medical School · Boston Children’s Hospital

Abstract

Large language models (LLMs) are increasingly used in critical domains, where their susceptibility to hallucinations makes reliable and interpretable uncertainty quantification essential. We introduce the concept of mechanistic uncertainty, which characterizes uncertainty through the stability of the internal mechanisms supporting a model's response. We propose the causal robustness margin, defined as the minimum internal intervention required to deviate the model's output, and operationalize it using Jacobian Lens (Jlens) concept steering vectors. Across three open-source models and five question-answering datasets, we show incorrect and uncertain responses exhibit smaller margins, indicating greater sensitivity to internal interventions, and the causal robustness margin complements conventional output-based uncertainty methods. Finally, in a controlled knowledge injection experiment, correctly learned facts show increased margins after training, suggesting that causal robustness provides a mechanistically grounded signal of uncertainty.

Figures & tables

Figure 1: We perform different magnitudes of steering $\alpha$ (both positive and negative) along Jlens consensus token vectors to determine mechanistic uncertainty. Response flips at lower magnitude steers, as shown in the example, indicate high mechanistic uncertainty. We use mid to last layer activations due to informative verbalizable tokens, whereas earlier layers contain a lot of noise.

Figure 2:

\alpha^{*}

plotted against accuracy. Binning is performed at each

\alpha^{*}

value, and average accuracy is computed over each bin. The trend shows accuracy increasing with

\alpha^{*}

Dataset	Model	AUROC	$\bar{\alpha}_{\mathrm{corr}}^{*}$	$\bar{\alpha}_{\mathrm{inc}}^{*}$
TruthfulQA	Llama-3.1-8B	57.90	0.182	0.137
	Qwen2.5-7B	57.70	0.163	0.128
	Gemma-3-12B	57.30	0.148	0.112
TriviaQA	Llama-3.1-8B	74.28	0.1512	0.0474
	Qwen2.5-7B	75.14	0.0860	0.0328
	Gemma-3-12B	71.08	0.0963	0.0262

Table 1: Causal robustness margins and error discrimination.

\bar{\alpha}_{\mathrm{corr}}^{*}

and

\bar{\alpha}_{\mathrm{inc}}^{*}

are mean margins for correct and incorrect responses; larger margins indicate greater robustness. AUROC uses

-\alpha^{*}

to detect incorrect responses.

Panel of Figure 3 — Figure 3: Correlation between the causal robustness margin $\alpha^{*}$ and conventional uncertainty measures across TriviaQA, PopQA, SciQ, MedQA, and TruthfulQA. Each panel shows binned uncertainty statistics as a function of $\alpha^{*}$ for Llama-3.1-8B-Instruct, Qwen2.5-7B-Instruct, and Gemma-3-12B-Instruct. Shaded regions indicate variability within each $\alpha^{*}$ bin, and the reported $\rho$ values denote Spearman rank correlation.

		Llama-3.1-8B-Instruct		Qwen2.5-7B-Instruct		Gemma-3-12B-Instruct
Dataset	Baseline	Base	$+\alpha^{*}$	Base	$+\alpha^{*}$	Base	$+\alpha^{*}$
TruthfulQA	Self-consistency	0.524	0.569	0.535	0.597	0.440	0.550
	Max token prob.	0.505	0.564	0.501	0.574	0.512	0.566
	Token entropy	0.538	0.576	0.500	0.567	0.508	0.566
TriviaQA	Self-consistency	0.833	0.847	0.769	0.808	0.653	0.752
	Max token prob.	0.828	0.840	0.810	0.822	0.761	0.793

Table 2: AUROC for detecting incorrect answers (positive class: incorrect) for each baseline alone (Base) and combined with

\alpha^{*}

(

+\alpha^{*}

) in a logistic regression, using out-of-fold predictions from 5-fold cross-validation averaged over 10 shuffles. Bold : improvement significant under a paired bootstrap over questions (95% CI of the difference excludes 0; 1,000 resamples).

Table 3: Effect of knowledge injection SFT on PopQA accuracy and causal robustness. (a) Accuracy and mean causal robustness margins before and after SFT. (b) Mean margins by correctness transition (

W

: wrong;

R

: right).

\Delta M=\bar{\alpha}^{*}_{\mathrm{post}}-\bar{\alpha}^{*}_{\mathrm{pre}}

; positive values indicate increased robustness. Only target entities are used for SFT.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 4 — Figure 4: Prompt for contextualizing with Qwen3-32B

Panel of Figure 5 — Figure 5: Prompt for generating paraphrases with Qwen3-32B

Dataset	Model	Baseline Acc.	Recovered (%)	Oracle Acc.
TruthfulQA	Llama-3.1-8B	50.6%	24.8%	62.8%
	Qwen2.5-7B	64.5%	19.7%	71.5%
	Gemma-3-12B	57.5%	17.3%	64.9%
TriviaQA	Llama-3.1-8B	72.8%	24.6%	79.5%
	Qwen2.5-7B	55.9%	16.8%	63.3%
	Gemma-3-12B	72.3%	12.3%	75.7%

Appendix

Table 4: Baseline accuracy and recovery after steering at the causal robustness margin

\alpha^{*}

. Recovered is the percentage of initially incorrect responses made correct. Oracle-steered accuracy preserves initially correct responses and steers only incorrect responses, requiring ground-truth correctness.

Panel of Figure 6 — Figure 6: Correlation between the causal robustness margin $\alpha^{*}$ and sequence likelihood, perplexity, energy, and semantic entropy across models and datasets.

Panel of Figure 7 — Figure 7: TruthfulQA flip examples.

Panel of Figure 8 — Figure 8: TriviaQA flip examples.

Panel of Figure 9 — Figure 9: MedQA flip examples.

Panel of Figure 10 — Figure 10: PopQA flip examples.

Panel of Figure 11 — Figure 11: SciQ flip examples.

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