# Gradients with Respect to Semantics Preserving Embeddings Tell the Uncertainty of Large Language Models

arXiv: https://arxiv.org/abs/2605.04638 · HTML: https://mlsanity.com/paper/2605.04638/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 37 references that are in the map.
- First posted on arXiv 6 May 2026.

## Builds on (most cited first, 29 of 29)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [A Survey on Large Language Model based Autonomous Agents](https://mlsanity.com/paper/2308.11432/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [FActScore: Fine-grained Atomic Evaluation of Factual Precision in Long Form Text Generation](https://mlsanity.com/paper/2305.14251/) (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)
- [Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback](https://mlsanity.com/paper/2305.14975/) (2023)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [Siren's Song in the AI Ocean: A Survey on Hallucination in Large Language Models](https://mlsanity.com/paper/2309.01219/) (2023)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [A Comprehensive Overview of Large Language Models](https://mlsanity.com/paper/2307.06435/) (2023)
- [INSIDE: LLMs' Internal States Retain the Power of Hallucination Detection](https://mlsanity.com/paper/2402.03744/) (2024)
- [Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models](https://mlsanity.com/paper/2305.19187/) (2023)
- [Shifting Attention to Relevance: Towards the Predictive Uncertainty Quantification of Free-Form Large Language Models](https://mlsanity.com/paper/2307.01379/) (2023)
- [Language Models with Conformal Factuality Guarantees](https://mlsanity.com/paper/2402.10978/) (2024)
- [A Survey on Uncertainty Quantification of Large Language Models: Taxonomy, Open Research Challenges, and Future Directions](https://mlsanity.com/paper/2412.05563/) (2024)
- [To Believe or Not to Believe Your LLM](https://mlsanity.com/paper/2406.02543/) (2024)
- [Evaluating Open-Domain Question Answering in the Era of Large Language Models](https://mlsanity.com/paper/2305.06984/) (2023)
- [Tomayto, Tomahto. Beyond Token-level Answer Equivalence for Question Answering Evaluation](https://mlsanity.com/paper/2202.07654/) (2022)
- [Uncertainty in Natural Language Generation: From Theory to Applications](https://mlsanity.com/paper/2307.15703/) (2023)
- [Gradients as a Measure of Uncertainty in Neural Networks](https://mlsanity.com/paper/2008.08030/) (2020)
- [MARS: Meaning-Aware Response Scoring for Uncertainty Estimation in Generative LLMs](https://mlsanity.com/paper/2402.11756/) (2024)
- [How Useful are Gradients for OOD Detection Really?](https://mlsanity.com/paper/2205.10439/) (2022)
- [Rethinking Uncertainty Estimation in LLMs: A Principled Single-Sequence Measure](https://mlsanity.com/paper/2412.15176/) (2024)
- [Epistemic Uncertainty Quantification For Pre-trained Neural Network](https://mlsanity.com/paper/2404.10124/) (2024)

## Abstract (arXiv)

Uncertainty quantification (UQ) is an important technique for ensuring the trustworthiness of LLMs, given their tendency to hallucinate. Existing state-of-the-art UQ approaches for free-form generation rely heavily on sampling, which incurs high computational cost and variance. In this work, we propose the first gradient-based UQ method for free-form generation, SemGrad, which is sampling-free and computationally efficient. Unlike prior gradient-based methods developed for classification tasks that operates in parameter space, we propose to consider gradients in semantic space. Our method builds on the key intuition that a confident LLM should maintain stable output distributions under semantically equivalent input perturbations. We interpret the stability as the gradients in semantic space and introduce a Semantic Preservation Score (SPS) to identify embeddings that best capture semantics, with respect to which gradients are computed. We further propose HybridGrad, which combines the strengths of SemGrad and parameter gradients. Experiments demonstrate that both of our methods provide efficient and effective uncertainty estimates, achieving superior performance than state-of-the-art methods, particularly in settings with multiple valid responses.