# Efficient Epistemic Uncertainty Estimation for Large Language Models via Knowledge Distillation

arXiv: https://arxiv.org/abs/2602.01956 · HTML: https://mlsanity.com/paper/2602.01956/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 33 of its 41 references that are in the map.
- First posted on arXiv 2 Feb 2026.

## Placed in

- Knowledge distillation / [Knowledge distillation for LLMs](https://mlsanity.com/distill/knowledge-distillation-for-llms/)

## Builds on (most cited first, 30 of 33)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [How Can We Know When Language Models Know? On the Calibration of Language Models for Question Answering](https://mlsanity.com/paper/2012.00955/) (2020)
- [Blockwise Parallel Decoding for Deep Autoregressive Models](https://mlsanity.com/paper/1811.03115/) (2018)
- [Unlocking Efficiency in Large Language Model Inference: A Comprehensive Survey of Speculative Decoding](https://mlsanity.com/paper/2401.07851/) (2024)
- [Speculative Decoding: Exploiting Speculative Execution for Accelerating Seq2seq Generation](https://mlsanity.com/paper/2203.16487/) (2022)
- [Bayesian Low-rank Adaptation for Large Language Models](https://mlsanity.com/paper/2308.13111/) (2023)
- [SpecDec++: Boosting Speculative Decoding via Adaptive Candidate Lengths](https://mlsanity.com/paper/2405.19715/) (2024)
- [Calibrating Large Language Models with Sample Consistency](https://mlsanity.com/paper/2402.13904/) (2024)
- [A Survey of Uncertainty Estimation Methods on Large Language Models](https://mlsanity.com/paper/2503.00172/) (2025)
- [SPUQ: Perturbation-Based Uncertainty Quantification for Large Language Models](https://mlsanity.com/paper/2403.02509/) (2024)
- [Survey on Knowledge Distillation for Large Language Models: Methods, Evaluation, and Application](https://mlsanity.com/paper/2407.01885/) (2024)
- [BLoB: Bayesian Low-Rank Adaptation by Backpropagation for Large Language Models](https://mlsanity.com/paper/2406.11675/) (2024)
- [Distinguishing the Knowable from the Unknowable with Language Models](https://mlsanity.com/paper/2402.03563/) (2024)
- [AdaEDL: Early Draft Stopping for Speculative Decoding of Large Language Models via an Entropy-based Lower Bound on Token Acceptance Probability](https://mlsanity.com/paper/2410.18351/) (2024)
- [TokUR: Token-Level Uncertainty Estimation for Large Language Model Reasoning](https://mlsanity.com/paper/2505.11737/) (2025)

## Built on by (most cited first, 1 of 1)

- [An Isotropic Approach to Efficient Uncertainty Quantification with Gradient Norms](https://mlsanity.com/paper/2603.29466/) (2026)

## Abstract (arXiv)

Quantifying uncertainty in Large Language Models (LLMs) is essential for mitigating hallucinations and enabling risk-aware deployment in safety-critical tasks. However, estimating Epistemic Uncertainty(EU) via Deep Ensembles is computationally prohibitive at the scale of modern models. We propose a framework that leverages the small draft models to efficiently estimate token-level EU, bypassing the need for full-scale ensembling. Theoretically grounded in a Bias-Variance Decomposition, our approach approximates EU via Jensen-Shannon divergence among drafts (variance proxy) and KL divergence between the draft mixture and the target (bias proxy). To further ensure accuracy without significant overhead, we introduce Online Stochastic Distillation (OSD) to efficiently approximate target aggregation and the Data-Diverse Drafts (DDD) strategy to enhance draft diversity for better target approximation. Extensive experiments on GSM8K demonstrate that our method reduces the estimation error (RMSE) by up to 37% compared to baselines. Crucially, our approach achieves Hallucination Detection performance competitive with heavy perturbation-based methods like TokUR while incurring negligible inference costs, offering a practical solution for uncertainty-aware LLM deployment.