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Also Small Models Can Reasonably Self-Evaluate Their Confidence

Idil Kapikiran, Thomas Decker, Thomas Runkler

arXiv:2609.39478v1cs.LG

TL;DR

Reliable confidence matters because language models can produce fluent but incorrect answers, and confidence should reflect correctness. The study evaluates self-evaluation methods across models and domains. Accuracy declines with smaller models and more specialized questions, while self-evaluated confidence calibration remains broadly stable.

  • Problem

    It is unclear whether reliable self-evaluation requires high model capability, especially beyond the large proprietary models and general-knowledge settings that prior work emphasized.

    Source: §1 · p. 1

  • Method

    The study systematically evaluates self-evaluation-based confidence methods across open-weight model scales and question-answering benchmarks from general to specialized domains.

    Source: §1 · p. 1

  • Results

    Across five model configurations and three datasets, accuracy improves with parameter count and falls with more specialized questions, while rank-based confidence calibration remains broadly stable.

    Source: §5 · p. 5

  • Takeaways & Limitations

    The most accurate model need not provide the most reliable confidence signal, so exploring self-evaluation strategies may benefit deployed-system reliability more than increasing model size alone.

    Source: §5 · p. 5

Abstract

from arXiv · show

This study systematically evaluates self-evaluation-based uncertainty quantification across different language models of varying sizes on question-answering tasks spanning general to specialized knowledge domains. Using various self-evaluation methods where models judge their own predictions, we examine how model scale and domain specificity affect the quality of self-assessed confidence signals. Our results reveal that while accuracy predictably declines with smaller models and more specialized domains, the reliability of self-evaluated confidence remains largely stable across both dimensions. This independence means the most capable model is not necessarily the best at self-assessing prediction reliability. These findings suggest that smaller models can achieve reasonable self-assessed confidence despite lower accuracy, making them viable for resource-constrained deployments.

1 Introduction

Reliable self-assessment matters because language models can know facts yet fail to retrieve them consistently, and confidence should reflect answer correctness. This study tests whether self-evaluated confidence remains calibrated across model scales and knowledge domains.

1 Introduction

  • Existing self-evaluation research has focused on large proprietary models and general knowledge, leaving smaller open-weight models and specialized domains largely unexamined.These settings are especially relevant because compute constraints and limited pretraining coverage can make incorrect answers more likely.Source: §1 · p. 1
  • The central question is how capable a model must be to assess its own answers faithfully, since reliable uncertainty can support abstention even when accuracy is low.A system with uninformative confidence offers no safe operating point.Source: §1 · p. 1
  • Calibration quality remains largely stable across model scale and domain specificity, while smaller models can provide trustworthy uncertainty estimates despite lower accuracy.The study evaluates open-weight models across question-answering benchmarks spanning general to specialized domains.Source: §1 · pp. 1–2

2 Background & Related Work

Prior work has studied self-evaluation and verbalized confidence, but has largely emphasized large models and general knowledge. This section positions the study around the remaining gap in smaller-scale and specialized-domain evaluation.

2 Background & Related Work

  • Sequence-level likelihood can correlate poorly with correctness in open-ended generation, while token-level calibration on multiple-choice formats remains comparatively strong.The cited work attributes the likelihood issue to sequence-level aggregation rather than an inability to express uncertainty.Source: §2 · p. 2
  • P(True) asks models to assess whether their own answers are correct, and later work adds comparative and hybrid candidate-ranking strategies with rank-based metrics for abstention.The study adopts those rank-based evaluation metrics.Source: §2 · p. 2
  • Prior findings report better calibration for verbalized confidence than token probabilities in RLHF models, alongside investigations of elicitation methods and domain saturation in frontier models.Training-based and hidden-representation uncertainty methods are alternatives, but require additional resources that inference-time approaches avoid.Source: §2 · p. 2
  • Self-evaluated confidence at smaller scales and in specialized domains remains largely unexamined, leaving open whether reliable self-evaluation requires high capability or is distinct from task competence.Source: §2 · p. 2

3 Self-Evaluation for Uncertainty Quantification

The study evaluates inference-time methods that prompt models to judge their own answers, using classification-token log-probabilities as confidence signals. It compares single-answer and multi-candidate approaches, including methods that separate answer selection from confidence scoring.

3 Self-Evaluation for Uncertainty Quantification

  • Self-evaluation methods require no training or annotation and use classification-token log-probabilities to score a prompted judgment of the model’s own output.The prompt elicits reflection, while the log-probability signal grounds confidence in the model’s learned distribution rather than relying only on verbalized confidence.Source: §3 · p. 2
  • P(True) generates one answer greedily, then estimates confidence from the model’s probability of affirming that the answer is correct.The binary judgment probability is computed from the log-probabilities of the two answer tokens.Source: §3 · p. 2
  • Multi-sample methods use four diverse candidate answers per question, with the same candidate set shared across scoring strategies to isolate scoring differences.The candidate count balances the chance of including a correct answer against generation cost, which grows linearly with each additional candidate.Source: §3 · p. 3
  • Sequence log-probability sums sampled-token log-probabilities, while its length-normalized variant divides by token count to remove bias toward shorter sequences.These quantities serve as reference signals for autoregressive confidence without deliberative self-evaluation.Source: §3 · p. 3
  • Sample and Select chooses among candidates using the highest selection-token log-probability, which serves as its confidence score.It aggregates single-token variants of answer letters and applies a dynamic floor to letters absent from the top-k log-probabilities.Source: §3 · p. 3
  • Sample and Eval scores each candidate through a binary factuality prompt, while Hybrid selects comparatively and estimates confidence with a separate pointwise judgment.The with-candidates variant adds alternatives as context while retaining a pointwise assessment.Source: §3 · p. 3
  • NOTA augmentation treats the probability of “None of the above” as an uncertainty signal and subtracts it from the Hybrid pointwise judgment.For Sample and Select, the score is the negative NOTA probability, so higher confidence corresponds to lower abstention probability.Source: §3 · p. 4
  • Correctness is judged by semantic equivalence to benchmark references, and Calibration-AUC measures how well confidence ranks correct answers above incorrect ones.Accuracy uses each method’s own selection rule; CalAUC is rank-based and applies to raw log-probabilities without normalization.Source: §3 · p. 4

4 Experiments & Discussion

Across five model configurations and three datasets, accuracy falls with smaller models and more specialized questions, while self-evaluated confidence calibration remains broadly stable. No single scoring strategy leads calibration throughout.

4 Experiments & Discussion

  • NOTA augmentation raised CalAUC in 11 of 12 paired comparisons while leaving accuracy essentially unchanged.Table 1 compares scoring strategies for GPT-4.1 and Ministral-3-3B.Source: §4 · p. 4, Table 1 · p. 4
  • Sample and Select had the lowest CalAUC in five of six columns, while replacing its comparative score with pointwise judgment yielded higher values in those five.No strategy was best throughout; the best CalAUC was spread across four methods, and the two models never agreed on the best method for a dataset.Source: §4 · p. 5
  • GPT-4.1 was close to twice as accurate throughout, but Ministral-3-3B had higher CalAUC on MMLU and MedMCQA.The experiments used five models spanning parameter scales and families, and three datasets ordered from general to specialized knowledge.Source: §4 · pp. 4–5
  • CalAUC remained stable across model scale and domain specialization, while accuracy declined along both dimensions.The best-performing method per model and dataset is shown in Figure 1.Source: §4 · p. 5, Figure 1 · p. 5

5 Conclusion

The conclusion reports that accuracy varies with model scale and domain specialization, but self-evaluated confidence calibration remains broadly stable. It cautions that the most accurate model need not provide the most reliable confidence signal.

5 Conclusion

  • Across five model configurations and three datasets, accuracy improves with parameter count while rank-based confidence calibration remains stable across model sizes and broadly comparable across domain specialization.The conclusion reports similar calibration reliability for smaller and substantially larger models.Source: §5 · p. 5
  • The most accurate model may not provide the most reliable self-evaluated confidence signal, so exploring scoring strategies may benefit reliability more than increasing model size alone.The conclusion suggests evaluating further models, datasets, and uncertainty metrics.Source: §5 · p. 5

A Full Results

The appendix provides complete per-model results across the experiments, beyond the largest and smallest models shown in the paper's tabular results.

A Full Results

  • Appendix Table 2 provides complete per-model results across all experiments and runs; the main paper shows only the largest and smallest models in tabular form.The paper says this presentation was chosen to adhere to the page limit.Source: A Full Results · p. 7

B Model and Dataset Details

The appendix details model access and parameter counts, dataset sources and sizes, and the correctness-judging procedure. It also provides results for all models.

B Model and Dataset Details

  • The model set includes four open-weight models and GPT-4.1 as a proprietary reference, chosen across sizes and model families to avoid confounding scale with training procedure.Open-weight models use vLLM; API-based models use equivalent settings through their respective endpoints.Source: B Model and Dataset Details · p. 7
  • TruthfulQA (generation split; 817 questions), MMLU (validation split; 1,531 questions), and MedMCQA (1,000 sampled questions) are evaluated for correctness by GPT-OSS-120B, which judges semantic equivalence between selected and reference answers.Source: B Model and Dataset Details · p. 7
  • Table 2 covers all models and reports accuracy and CalAUC by method and dataset, including eight multi-generation methods and single-generation P(True).The table marks the best value in each model/metric column per dataset.Source: Table 2 · p. 8
  • Table 3 lists evaluated models, their access method, and approximate parameter count.Source: Table 3 · p. 8

C Prompt Templates

The prompt templates specify how models generate answers, evaluate proposed answers, and select among candidates. The generation prompts are used verbatim across models.

C Prompt Templates

  • The generation prompt requests one factual, informative, unbiased, and safe answer, illustrated with a watermelon-seed question and answer.The prompt asks for no other text.Source: C Prompt Templates · p. 8
  • The selection prompt asks the model to choose the best candidate, preferring an honest “I don’t know” over a wrong answer.The model outputs the capitalized letter corresponding to its choice, including “None of the above.”Source: C Prompt Templates · p. 9
  • Evaluation prompts ask whether a proposed answer is factual, informative, unbiased, and safe, with candidate-aware evaluation also supplying other candidates.The templates include a Yes/No response format and a separate version that presents candidate answers.Source: C Prompt Templates · p. 9

D Worked Example

A TruthfulQA peach question illustrates four self-evaluation methods using GPT-4.1. Their scores distinguish confidence in a single answer, candidate selection, and candidate-level evaluation.

D Worked Example

  • P(True) assigns p(Yes) = 1.00 to the correct California answer, which the judge confirms as well-calibrated high confidence.The answer is generated by greedy decoding.Source: D Worked Example · p. 10
  • Sample and Eval assigns p(Yes) scores of 0.99, 0.98, 0.42, and 0.99 to candidates A–D, respectively, flagging the incorrect Georgia answer.The candidates are sampled at T = 1.Source: D Worked Example · p. 10
  • Seq len-norm likelihood ranks candidate A highest at −0.04, while Sample and Select chooses A at log p(A) = −0.10 with p(E) ≈ 0.001.Hybrid selects A via Sample and Select, then rescores it at s = p(Yes | x, A) = 0.99.Source: D Worked Example · p. 10

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