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HFEPX · Eval paper review

Probability is Not Enough: Exploring and Counting Divergent Tokens for Reasoning Uncertainty Quantification in LLMs

Feiyang Li, Shengjing Liu, Qi Zhan, Sijie Cheng +6 more

Published

Sep 29, 2026

Citations

0

Trust level

Moderate

Usefulness score

35/100 (Low)

Extraction confidence

55% (Moderate)

Derived from extracted protocol signals and abstract evidence.

Rater population

Not reported

Signals refreshed

Sep 29, 2026

Should you rely on this paper?

This paper is adjacent to HFEPX scope and is best used for background context, not as a primary protocol reference.

Use this for comparison and orientation, not as your only source.

Best use

Background context only

Use if you need

A secondary eval reference to pair with stronger protocol papers.

What to verify

Validate the exact study setup in the full paper before operational use.

Main weakness

No major weakness surfaced.

Human feedback signal
Not explicit
Not explicit in abstract metadata
Evaluation signal
Detected
Eval setup described
Usefulness for eval research
35/100
Adjacent candidate

Treat as adjacent context, not a core eval-method reference.

Abstract

As the chain-of-thought reasoning capabilities of large language models improve, evaluating and calibrating their reasoning confidence is becoming increasingly important for quantifying the uncertainty of their answers. Current methods for estimating the confidence of large language models are generally based on probabilities of selected key tokens, but the underlying mechanism remains unclear. Our pilot study finds that replacing selected token probabilities with coarse substitutes can also improve calibration, motivating us to further explore effective signals of model confidence. We introduce Divergent Token Confidence (DTC), a framework that estimates confidence by counting tokens at which two models strongly disagree during decoding. DTC identifies these divergent tokens using the Jensen-Shannon divergence between next-token distributions evaluated along the same reasoning trajectory. We find that their count is almost negatively associated with answer accuracy, thereby serving as a simple yet effective signal for uncertainty quantification. DTC supports both white-box and black-box evaluation using auxiliary models, without explicit training and affecting the generation process. Experiments across multiple model families and six mathematical benchmarks demonstrate improved calibration over probability-based and verbalized baselines. Under white-box evaluation, the count-only estimator achieves an average expected calibration error of 13.0%, compared with 32.7%-42.4% for standard full-sequence confidence methods. In black-box settings, it also improves calibration over the original verbalized scores. For example, mean expected calibration error falls from 32.1%-40.2% to 13.7%-16.3% on DeepSeek-V3.2. These findings provide new insights for improving reasoning uncertainty quantification in large language models. The code is released at https://github.com/szu-tera/DTC.git.

What we could verify

These are the protocol signals we could actually recover from the available paper metadata. Use them to decide whether this paper is worth deeper reading.

Human Feedback Types

missing

None explicit

No explicit feedback protocol extracted.

"As the chain-of-thought reasoning capabilities of large language models improve, evaluating and calibrating their reasoning confidence is becoming increasingly important for quantifying the uncertainty of their answers."

Evaluation Modes

strong

Automatic Metrics

Includes extracted eval setup.

"As the chain-of-thought reasoning capabilities of large language models improve, evaluating and calibrating their reasoning confidence is becoming increasingly important for quantifying the uncertainty of their answers."

Quality Controls

strong

Calibration

Calibration/adjudication style controls detected.

"Our pilot study finds that replacing selected token probabilities with coarse substitutes can also improve calibration, motivating us to further explore effective signals of model confidence."

Benchmarks / Datasets

missing

Not extracted

No benchmark anchors detected.

"As the chain-of-thought reasoning capabilities of large language models improve, evaluating and calibrating their reasoning confidence is becoming increasingly important for quantifying the uncertainty of their answers."

Reported Metrics

strong

Accuracy, Calibration error

Useful for evaluation criteria comparison.

"We find that their count is almost negatively associated with answer accuracy, thereby serving as a simple yet effective signal for uncertainty quantification."

Benchmarks and datasets

No benchmark or dataset names were extracted from the available abstract.

Reported metrics

accuracycalibration error
Human feedback details
Uses human feedback
No
Feedback types
None
Rater population
Not reported
Unit of annotation
Trajectory
Expertise required
Math, Coding
Evaluation details
Evaluation modes
Automatic Metrics
Agentic eval
Long Horizon
Quality controls
Calibration
Evidence quality
Moderate
Use this page as
Background context only

Research brief

Metadata summary

As the chain-of-thought reasoning capabilities of large language models improve, evaluating and calibrating their reasoning confidence is becoming increasingly important for quantifying the uncertainty of their answers.

Based on abstract + metadata only. Check the source paper before making high-confidence protocol decisions.

Key takeaways

  • As the chain-of-thought reasoning capabilities of large language models improve, evaluating and calibrating their reasoning confidence is becoming increasingly important for quantifying the uncertainty of their answers.
  • Current methods for estimating the confidence of large language models are generally based on probabilities of selected key tokens, but the underlying mechanism remains unclear.
  • Our pilot study finds that replacing selected token probabilities with coarse substitutes can also improve calibration, motivating us to further explore effective signals of model confidence.

Researcher actions

  • Compare this paper against nearby papers in the same arXiv category before using it for protocol decisions.
  • Validate inferred eval signals (Automatic metrics) against the full paper.
  • Use related-paper links to find stronger protocol-specific references.

Caveats

  • Generated from abstract + metadata only; no PDF parsing.
  • Signals below are heuristic and may miss details reported outside the abstract.

Recommended queries

Contribution summary

  • We introduce Divergent Token Confidence (DTC), a framework that estimates confidence by counting tokens at which two models strongly disagree during decoding.
  • DTC supports both white-box and black-box evaluation using auxiliary models, without explicit training and affecting the generation process.
  • Under white-box evaluation, the count-only estimator achieves an average expected calibration error of 13.0%, compared with 32.7%-42.4% for standard full-sequence confidence methods.

Why it matters for eval

  • DTC supports both white-box and black-box evaluation using auxiliary models, without explicit training and affecting the generation process.
  • Under white-box evaluation, the count-only estimator achieves an average expected calibration error of 13.0%, compared with 32.7%-42.4% for standard full-sequence confidence methods.

Researcher checklist

  • Human feedback protocol is explicit

    No explicit human feedback protocol detected.

  • Evaluation mode is explicit

    Detected: Automatic Metrics

  • Quality control reporting appears

    Detected: Calibration

  • Benchmark or dataset anchors are present

    No benchmark/dataset anchor extracted from abstract.

  • Metric reporting is present

    Detected: accuracy, calibration error