# The Origins of Stochasticity: Comprehensive Investigations on Uncertainty Quantification for Large Language Models

arXiv: https://arxiv.org/abs/2606.22792 · HTML: https://mlsanity.com/paper/2606.22792/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 31 of its 129 references that are in the map.
- First posted on arXiv 22 Jun 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 31)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMs](https://mlsanity.com/paper/2406.15927/) (2024)
- [Conformal Prediction with Large Language Models for Multi-Choice Question Answering](https://mlsanity.com/paper/2305.18404/) (2023)
- [Uncertainty Estimation and Quantification for LLMs: A Simple Supervised Approach](https://mlsanity.com/paper/2404.15993/) (2024)
- [LoRA ensembles for large language model fine-tuning](https://mlsanity.com/paper/2310.00035/) (2023)
- [Evaluating Uncertainty Quantification in End-to-End Autonomous Driving Control](https://mlsanity.com/paper/1811.06817/) (2018)
- [Uncertainty quantification in fine-tuned LLMs using LoRA ensembles](https://mlsanity.com/paper/2402.12264/) (2024)
- [Agents of Chaos](https://mlsanity.com/paper/2602.20021/) (2026)
- [Prover Agent: An Agent-Based Framework for Formal Mathematical Proofs](https://mlsanity.com/paper/2506.19923/) (2025)
- [Cycles of Thought: Measuring LLM Confidence through Stable Explanations](https://mlsanity.com/paper/2406.03441/) (2024)
- [LLM Uncertainty Quantification through Directional Entailment Graph and Claim Level Response Augmentation](https://mlsanity.com/paper/2407.00994/) (2024)
- [Uncertainty-Aware Step-wise Verification with Generative Reward Models](https://mlsanity.com/paper/2502.11250/) (2025)
- [Uncertainty Quantification of Large Language Models through Multi-Dimensional Responses](https://mlsanity.com/paper/2502.16820/) (2025)
- [Efficient Hallucination Detection for LLMs Using Uncertainty-Aware Attention Heads](https://mlsanity.com/paper/2505.20045/) (2025)
- [LACIE: Listener-Aware Finetuning for Confidence Calibration in Large Language Models](https://mlsanity.com/paper/2405.21028/) (2024)
- [Language Model Uncertainty Quantification with Attention Chain](https://mlsanity.com/paper/2503.19168/) (2025)
- [LLM Factoscope: Uncovering LLMs' Factual Discernment through Inner States Analysis](https://mlsanity.com/paper/2312.16374/) (2023)
- [Uncertainty as Feature Gaps: Epistemic Uncertainty Quantification of LLMs in Contextual Question-Answering](https://mlsanity.com/paper/2510.02671/) (2025)
- [CSS: Contrastive Semantic Similarity for Uncertainty Quantification of LLMs](https://mlsanity.com/paper/2406.03158/) (2024)
- [Can Linear Probes Measure LLM Uncertainty?](https://mlsanity.com/paper/2510.04108/) (2025)
- [Divergent Ensemble Networks: Enhancing Uncertainty Estimation with Shared Representations and Independent Branching](https://mlsanity.com/paper/2412.01193/) (2024)

## Built on by (most cited first, 2 of 2)

- [Uncertainty Quantification for LLM Agents: A Taxonomy, an Evaluation Protocol, and an Empirical Study](https://mlsanity.com/paper/2609.07395/) (2026)
- [GRUET: Quantifying Uncertainty of Agentic Reasoning-and-Acting Processes](https://mlsanity.com/paper/2609.24831/) (2026)

## Abstract (arXiv)

Recent advancements in Large Language Models (LLMs) have enabled sophisticated reasoning and content generation, yet their inherent stochasticity poses significant challenges for ensuring predictive credibility. While traditional uncertainty taxonomy paradigms, such as the dichotomy of aleatoric and epistemic uncertainties, provide conceptual foundations, they often fail to capture the multi-component and multi-stage nature of LLM generation and struggle to evaluate the effectiveness of various Uncertainty Quantification (UQ) methods. In this paper, we propose a granular uncertainty taxonomy that systematically attributes LLM uncertainty into input-level, parameter-level, token-level, and decoding-process sources. Correspondingly, we categorize existing UQ methods into Bayesian, ensemble, consensus-based, and single-pass approaches. Furthermore, we introduce a comprehensive evaluation framework covering diverse generation settings and metrics. We empirically evaluate 21 typical UQ methods across three prominent LLM families, including Qwen3, Llama 3.2, and DeepSeek-V3, on benchmarks such as TriviaQA, GSM8K, and HumanEval. Our experimental results demonstrate that (i) the effectiveness of UQ methods is sensitive to task types and generation settings; (ii) consensus-based methods, typed Deg and EigV, consistently outperform other UQ approaches; and (iii) larger model scales correlate with lower uncertainty estimates, suggesting an empirical scaling law for LLM uncertainty. This work bridges the gap between theoretical origins and practical deployment, providing a versatile diagnostic tool for systematically quantifying uncertainty in LLM applications.