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CER: Confidence Enhanced Reasoning in LLMs

Paper · 2025 · Ali Razghandi, Seyed Mohammad Hadi Hosseini and Mahdieh Soleymani Baghshah

Summary

Large language models often make mistakes on multi-step tasks such as arithmetic word problems and knowledge-heavy question answering. Self-consistency samples several reasoning chains and takes a majority vote, but every chain counts equally, so it fails when most samples agree on a wrong answer. The authors propose CER (Confidence Enhanced Reasoning). The model is prompted to reason in explicit steps, each ending with an intermediate answer. CER then reads token probabilities from the logits, but only for these critical outputs: numbers in math problems and proper nouns in open-domain questions. These scores are combined into one confidence value per chain, with later steps weighted more heavily. Instead of a simple vote, each candidate answer receives the summed confidence of the chains that reach it. The method needs no fine-tuning or special demonstrations. Across four LLMs and five benchmarks, it beats the baselines by up to 7.4% on math and 5.8% on open-domain QA. This suggests that targeted uncertainty signals are a cheap way to make reasoning more reliable.

Key points

  • The benchmarks cover three math datasets (GSM8K, MATH, MathQA) and two open-domain QA datasets (TriviaQA, HotpotQA).
  • The tested models are Llama 3.1, Llama 3.2, OLMo 2 and Mistral 7B v0.3, plus an extra test on DeepSeek-R1-Distill-Qwen-7B.
  • Word confidence is built from token probabilities using a function f, such as multiplication. Path confidence uses a function g, chosen as a weighted mean. Alternatives such as the product or the minimum gave similar results.
  • In the ablation, scoring all intermediate answers (CER-ALL) consistently beat using only the final answer's confidence (CER-LAST).
  • CER requires access to output logits, so it does not directly apply to black-box models. Code is available at github.com/sharif-ml-lab/CER.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Fields, topics and concepts

📚 Shelves 4The field of science this work belongs to (OpenAlex fields).Computer Science · 16,667 worksArtificial Intelligence · 16,194 worksArts and Humanities · 16,039 worksLanguage and Linguistics · 15,891 works

🧭 Topics 2Research subjects and languages the work is about.Language models & pretraining · 3,320 worksReasoning · 1,426 works

Cite

Cite as Ali Razghandi, Seyed Mohammad Hadi Hosseini and Mahdieh Soleymani Baghshah. 2025. CER: Confidence Enhanced Reasoning in LLMs. Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers).

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.18653/v1/2025.acl-long.390

@inproceedings{razghandi2025cer,
  title = {{CER: Confidence Enhanced Reasoning in LLMs}},
  author = {Ali Razghandi, Seyed Mohammad Hadi Hosseini and Mahdieh Soleymani Baghshah},
  booktitle = {Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)},
  year = {2025},
  doi = {10.18653/v1/2025.acl-long.390},
  url = {https://doi.org/10.18653/v1/2025.acl-long.390}
}

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