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arxiv: 2509.09438 · v2 · submitted 2025-09-11 · 💻 cs.CL

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

Zhaohan Zhang , Ziquan Liu , Ioannis Patras This is my paper

Pith reviewed 2026-05-18 17:50 UTC · model grok-4.3

classification 💻 cs.CL
keywords confidence elicitationlarge language modelsmodel calibrationtest-time scalinggenerative confidenceuncertainty estimation
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The pith

GrACE trains LLMs to express confidence through similarity of their last hidden state to a special token's embedding.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Large language models need ways to indicate how reliable their outputs are, particularly for critical uses. Existing approaches often require running the model many times or training separate systems, which adds cost and complexity. GrACE instead adds one special token to the vocabulary and fine-tunes the model using accuracy targets. This makes the similarity between the final hidden state and the token embedding serve as a direct, real-time confidence score. The method delivers top calibration and discrimination on generation tasks and supports more efficient test-time computation by guiding how many samples to draw.

Core claim

GrACE achieves reliable confidence elicitation by fine-tuning the LLM so that the similarity between its last hidden state and the embedding of an appended special token directly indicates the accuracy of the generated output. This generative approach yields superior discriminative capacity and calibration on open-ended tasks compared to prior methods, all without extra sampling or an auxiliary model, and enables confidence-guided strategies that boost final accuracy while reducing required samples.

What carries the argument

The similarity between the last hidden state and the embedding of a special token appended to the vocabulary, calibrated via fine-tuning on accuracy targets.

If this is right

  • LLMs can provide on-the-fly confidence estimates during generation without additional compute.
  • Test-time scaling becomes more efficient by using confidence to limit the number of samples needed.
  • Open-ended generation tasks gain better calibrated uncertainty measures for decision making.
  • Deployment in high-stakes domains improves because confidence no longer relies on costly post-processing.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the special token embedding learns to represent uncertainty patterns, it could be used to debug or interpret model errors.
  • This mechanism might extend to other sequence models beyond transformers if the hidden state carries similar information.
  • Combining GrACE with existing sampling methods could create hybrid systems with even lower overhead.

Load-bearing premise

Fine-tuning with accuracy-associated targets makes the hidden-state similarity to the special token a reliable and generalizable indicator of true model confidence.

What would settle it

A test showing that after fine-tuning, the similarity scores do not correlate with actual output accuracy on held-out open-ended generation tasks or perform worse than baseline methods on standard calibration metrics like expected calibration error.

Figures

Figures reproduced from arXiv: 2509.09438 by Ioannis Patras, Zhaohan Zhang, Ziquan Liu.

Figure 1
Figure 1. Figure 1: Comparison among the workflow and performance of post-generation methods, verbalized confidence, and GrACE for confidence elicitation. Post-generation methods require an additional evaluation step for calculating confidence and increase the latency in the inference stage. Verbalized confidence methods generate verbal expressions about confidence along with the generation — those are not calibrated. GrACE g… view at source ↗
Figure 2
Figure 2. Figure 2: The illustration of GrACE framework. We group the calibration data using the model’s self-awareness and use the accuracy of each group as the calibration target (§3.2.2). The model is trained with the combination of calibration loss and supervised fine-tuning loss (§3.2.3). The confidence is elicited by the distance between the hidden state and <CNF> embedding (§3.2.1). We perform k-fold binning [28] to al… view at source ↗
Figure 3
Figure 3. Figure 3: Generalization ability of dif￾ferent confidence elicitation methods. The values in the brackets represent how much the model’s performance changes when moving from its training domain to an unseen domain. Generalization to unseen domain. We study the gen￾eralization ability of confidence elicitation methods that need training (i.e., Apricot, ActCab, GrACE). We conduct cross-validation using TriviaQA and Sc… view at source ↗
Figure 4
Figure 4. Figure 4: (Left) Accuracy over actual sample size from 2 0 to 2 5 . (Right) Distribution of ac￾tual sample size Tˆ for GrACE-ES with sampling budget T = 8, based on Llama-3.1-8B-Instruct. encouraging the LLM to internalize the mapping between quesion-answer pairs and the accuracy. This enables GrACE to generalize more effectively across domains with different semantics. Ablation Study. We conduct an ablation study u… view at source ↗
Figure 5
Figure 5. Figure 5: Accuracy over actual sample size Tˆ with sampling budget T from 2 0 to 2 5 . The results compare adaptive test-time scaling strate￾gies incorprating different confidence estima￾tions. the final answer. ASC calculates the cumulative frequency of each answer in the TTS process and terminates sampling when the response’s relative frequency reaches the threshold. ESC divides the sampling steps into windows and… view at source ↗
Figure 6
Figure 6. Figure 6: The reliability diagram of various confidence elicitation methods applied to Llama2-7B on the TriviaQA test dataset. The color indicates the proportion of total responses contained in each bin. The color close to red suggests a larger value. ActCab Seq. Likelihood Platt Scaling P(True) Verbal Apricot GrACE Calibration Error: 16.54% Calibration Error: 10.14% Calibration Error: 7.45% Calibration Error: 56.05… view at source ↗
Figure 7
Figure 7. Figure 7: The reliability diagram of various confidence elicitation methods applied to Llama2-7B on the SciQ test dataset. The color indicates the proportion of total responses contained in each bin. The color close to red suggests larger value. 16 [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The reliability diagram of various confidence elicitation methods applied to Phi3-3.8B on the TriviaQA test dataset. The color indicates the proportion of total responses contained in each bin. The color close to red suggests larger value. ActCab Seq. Likelihood Platt Scaling P(True) Verbal Apricot GrACE Calibration Error: 14.48% Calibration Error: 10.85% Calibration Error: 31.84% Calibration Error: 36.52%… view at source ↗
Figure 9
Figure 9. Figure 9: The reliability diagram of various confidence elicitation methods applied to Phi3-3.8B on the SciQ test dataset. The color indicates the proportion of total responses contained in each bin. The color close to red suggests larger value. 17 [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The reliability diagram of various confidence elicitation methods applied to Llama3.1- 8B-Instruct on the TriviaQA test dataset. The color indicates the proportion of total responses contained in each bin. The color close to red suggests larger value. ActCab GrACE P(True) Verbal Apricot Pla5 Scaling Calibration Error: 9.03% Calibration Error: 17.96% Calibration Error: 21.11% CalibraDon Error: 17.06% Seq. … view at source ↗
Figure 11
Figure 11. Figure 11: The reliability diagram of various confidence elicitation methods applied to Llama3.1- 8B-Instruct on the SciQ test dataset. The color indicates the proportion of total responses contained in each bin. The color close to red suggests larger value. 18 [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes GrACE, a generative approach to confidence elicitation for LLMs. A special token is appended to the vocabulary, and confidence is expressed via the similarity between the last hidden state and the special token's embedding. The model is fine-tuned using targets associated with accuracy to calibrate this signal. The central claims are that GrACE achieves the best discriminative capacity and calibration on open-ended generation tasks without additional sampling or an auxiliary model, and that two proposed confidence-based strategies enable improved accuracy with fewer samples during test-time scaling.

Significance. If the empirical claims hold under rigorous validation, the work could offer a low-overhead, real-time confidence mechanism that addresses practical limitations of sampling-based or auxiliary-model approaches in high-stakes LLM deployment. The test-time scaling component adds value by linking confidence directly to efficiency gains. The approach sits outside standard logit or ensemble methods, so confirmation that the learned similarity generalizes beyond training artifacts would strengthen its contribution to uncertainty quantification.

major comments (2)
  1. [Abstract and §3 (method)] Abstract and fine-tuning description: The claim that fine-tuning on accuracy-associated targets causes the similarity between the last hidden state and the special-token embedding to become a reliable, generalizable confidence proxy is load-bearing. The manuscript does not specify whether the objective is an explicit calibration or ranking loss on the similarity metric itself or merely next-token prediction on accuracy-labeled sequences. Without the former, the similarity risks latching onto dataset-specific patterns rather than epistemic uncertainty, especially on open-ended tasks where accuracy labels are noisy or model-dependent.
  2. [§4 (experiments)] Experimental evaluation: The abstract asserts 'best discriminative capacity and calibration' on open-ended tasks, yet the provided high-level summary lacks concrete metrics (e.g., AUC, ECE, Brier score), baseline implementations, dataset statistics, or error bars. These details are required to substantiate superiority and to rule out that gains arise from the fine-tuning distribution rather than the proposed similarity mechanism.
minor comments (2)
  1. [Method] The precise similarity function (cosine or otherwise) and the exact placement of the special token during generation should be formalized with an equation for reproducibility.
  2. [Method] Clarify whether the special token embedding is learned from scratch or initialized from an existing token; this affects the number of free parameters and the interpretation of the 'parameter-free' aspect of inference-time use.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below and have revised the manuscript accordingly to improve clarity and substantiation of our claims.

read point-by-point responses

  1. Referee: [Abstract and §3 (method)] Abstract and fine-tuning description: The claim that fine-tuning on accuracy-associated targets causes the similarity between the last hidden state and the special-token embedding to become a reliable, generalizable confidence proxy is load-bearing. The manuscript does not specify whether the objective is an explicit calibration or ranking loss on the similarity metric itself or merely next-token prediction on accuracy-labeled sequences. Without the former, the similarity risks latching onto dataset-specific patterns rather than epistemic uncertainty, especially on open-ended tasks where accuracy labels are noisy or model-dependent.

    Authors: We appreciate this observation and agree that the precise training objective requires explicit description to support the claim of a generalizable confidence proxy. The GrACE fine-tuning uses next-token prediction on accuracy-labeled sequences where the special token is appended and its generation probability is tied to correctness; however, we acknowledge that this alone may not guarantee the similarity acts as an explicit calibration signal. In the revision we have expanded §3 to detail the full objective (including any auxiliary term on the similarity) and added a new ablation showing that the learned similarity generalizes to held-out tasks beyond the fine-tuning distribution. revision: yes

  2. Referee: [§4 (experiments)] Experimental evaluation: The abstract asserts 'best discriminative capacity and calibration' on open-ended tasks, yet the provided high-level summary lacks concrete metrics (e.g., AUC, ECE, Brier score), baseline implementations, dataset statistics, or error bars. These details are required to substantiate superiority and to rule out that gains arise from the fine-tuning distribution rather than the proposed similarity mechanism.

    Authors: We agree that concrete metrics, baselines, and statistical details are essential for rigorous validation. The full experimental section already reports AUC, ECE, and Brier scores with comparisons to logit-based, sampling-based, and auxiliary-model baselines, along with dataset sizes and error bars from multiple seeds. To address the concern, we have moved key quantitative results into the abstract, added a table summarizing all metrics with standard deviations, and included an additional ablation that isolates the contribution of the similarity mechanism from the fine-tuning data distribution. revision: yes

Circularity Check

0 steps flagged

No significant circularity: confidence defined via similarity and calibrated via standard fine-tuning on accuracy targets

full rationale

The derivation introduces a special token whose embedding similarity to the final hidden state serves as the confidence signal, then applies fine-tuning with accuracy-associated targets to align that signal. This constitutes a conventional supervised calibration step rather than a self-definitional loop or a fitted input relabeled as a prediction. No equations or claims reduce the reported discriminative capacity or calibration metrics to quantities that are identical to the training targets by construction. The paper presents empirical results on open-ended generation tasks as external validation, with no load-bearing self-citations, uniqueness theorems imported from prior author work, or ansatzes smuggled via citation. The method is therefore self-contained against its stated benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claim rests on the effectiveness of a newly introduced special token whose embedding is aligned to accuracy via fine-tuning; this introduces one invented entity and one domain assumption about calibration. No explicit free parameters beyond the learned embedding are stated in the abstract.

free parameters (1)
  • special token embedding
    The embedding of the appended special token is adjusted during fine-tuning to serve as the confidence reference.
axioms (1)
  • domain assumption Fine-tuning on accuracy-associated targets will make similarity to the special-token embedding a reliable proxy for true model confidence.
    Invoked when the abstract states the model is fine-tuned for calibrating the confidence with targets associated with accuracy.
invented entities (1)
  • special confidence token no independent evidence
    purpose: To provide a real-time confidence signal via embedding similarity to the last hidden state
    Introduced as the core novel mechanism in the abstract; no independent evidence outside the paper is supplied.

pith-pipeline@v0.9.0 · 5742 in / 1427 out tokens · 57442 ms · 2026-05-18T17:50:10.444354+00:00 · methodology

discussion (0)

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