# GrACE: A Generative Approach to Better Confidence Elicitation and Efficient Test-Time Scaling in Large Language Models

arXiv: https://arxiv.org/abs/2509.09438 · HTML: https://mlsanity.com/paper/2509.09438/

## Key facts

- Cited by 3 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 25 of its 58 references that are in the map.
- First posted on arXiv 11 Sep 2025.

## 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, 25 of 25)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMs](https://mlsanity.com/paper/2406.15927/) (2024)
- [Deep Think with Confidence](https://mlsanity.com/paper/2508.15260/) (2025)
- [Hallucination-Free? Assessing the Reliability of Leading AI Legal Research Tools](https://mlsanity.com/paper/2405.20362/) (2024)
- [Confidence Improves Self-Consistency in LLMs](https://mlsanity.com/paper/2502.06233/) (2025)
- [Efficient Test-Time Scaling via Self-Calibration](https://mlsanity.com/paper/2503.00031/) (2025)
- [Calibrating Verbal Uncertainty as a Linear Feature to Reduce Hallucinations](https://mlsanity.com/paper/2503.14477/) (2025)
- [Atomic Calibration of LLMs in Long-Form Generations](https://mlsanity.com/paper/2410.13246/) (2024)
- [LoGU: Long-form Generation with Uncertainty Expressions](https://mlsanity.com/paper/2410.14309/) (2024)
- [Too Consistent to Detect: A Study of Self-Consistent Errors in LLMs](https://mlsanity.com/paper/2505.17656/) (2025)
- [Uncertainty Distillation: Teaching Language Models to Express Semantic Confidence](https://mlsanity.com/paper/2503.14749/) (2025)
- [UNCLE: Benchmarking Uncertainty Expressions in Long-Form Generation](https://mlsanity.com/paper/2505.16922/) (2025)

## Built on by (most cited first, 3 of 3)

- [BrowseConf: Confidence-Guided Test-Time Scaling for Web Agents](https://mlsanity.com/paper/2510.23458/) (2025)
- [All Roads Lead to Rome: Graph-Based Confidence Estimation for Large Language Model Reasoning](https://mlsanity.com/paper/2509.12908/) (2025)
- [Optimizing Chain-of-Thought Confidence via Topological and Dirichlet Risk Analysis](https://mlsanity.com/paper/2511.06437/) (2025)

## Abstract (arXiv)

Assessing the reliability of Large Language Models (LLMs) by confidence elicitation is a prominent approach to AI safety in high-stakes applications, such as healthcare and finance. Existing methods either require expensive computational overhead or suffer from poor calibration, making them impractical and unreliable for real-world deployment. In this work, we propose GrACE, a Generative Approach to Confidence Elicitation that enables scalable and reliable confidence elicitation for LLMs. GrACE adopts a novel mechanism in which the model expresses confidence by the similarity between the last hidden state and the embedding of a special token appended to the vocabulary, in real-time. We fine-tune the model for calibrating the confidence with targets associated with accuracy. Extensive experiments show that the confidence produced by GrACE achieves the best discriminative capacity and calibration on open-ended generation tasks without resorting to additional sampling or an auxiliary model. Moreover, we propose two confidence-based strategies for test-time scaling with GrACE, which not only improve the accuracy of the final decision but also significantly reduce the number of required samples, highlighting its potential as a practical solution for deploying LLMs with reliable, on-the-fly confidence estimation.