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home / papers / 2026 / C2-Faith: Benchmarking LLM Judges for Causal and Coverage Faithfulness in Chain-of-Thought Reasoning

C2-Faith: Benchmarking LLM Judges for Causal and Coverage Faithfulness in Chain-of-Thought Reasoning

Paper · 2026 · Avni Mittal and Rauno Arike

Summary

LLMs are increasingly used to grade chain-of-thought reasoning. This paper asks whether such judges can verify that a reasoning process is faithful, not just that its answer looks right. The authors split faithfulness into two axes. Causality asks whether each step is entailed by what came before. Coverage asks whether the necessary intermediate inferences are actually present.

They build C2-Faith from fully correct PRM800K solutions and edit only the middle portion of each chain. For causality, a single step is swapped for an LLM-written, plausible but logically broken rewrite at a known position. For coverage, a controlled share of steps is removed.

Three frontier judges were tested on three tasks: flagging an error, pinpointing the faulty step, and rating completeness on a 0–4 scale. No model won every task. Judges usually noticed that something was wrong but often misidentified where. All of them rated truncated chains as more complete than they were.

The work cautions against relying on uncalibrated LLM judges for process-level supervision, such as training process reward models.

Key points

  • Benchmark construction: source chains are PRM800K (MATH) solutions with at least 5 steps, all labeled +1. Edits are confined to positions between 30% and 90% of chain length. Coverage deletion rates are 10%, 30%, 50% and 70%.
  • Binary detection: DeepSeek-V3.1 scored highest (94.7%), but it also had a 29.6% false-positive rate on intact chains. o4-mini reached 92.0% detection with 10.4% FPR, and GPT-4.1 reached 82.7% with 11.4% FPR.
  • Step localization: exact-match accuracy was 68.0% for o4-mini, 57.6% for GPT-4.1 and 55.8% for DeepSeek-V3.1. Allowing a two-step tolerance raises this to 76–81%. Every judge tended to point to a step earlier than the true one, by −0.44 to −1.20 steps on average.
  • Coverage scoring: at 10% deletion, DeepSeek-V3.1 gave the top score 95.1% of the time, yielding essentially zero correlation with the reference (ρ ≈ −0.006). GPT-4.1 and o4-mini both reached ρ = 0.331 at 70% deletion. o4-mini is recommended as the best overall judge.
  • Error analysis: 79.8% of injected errors were caught by all three judges. Failures cluster in natural-language steps with few math symbols. Because the judges' misses overlap little, combining them could push detection above 98%.

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 · 18,614 worksArtificial Intelligence · 17,965 worksArts and Humanities · 17,450 worksLanguage and Linguistics · 17,296 works

🧭 Topics 1Research subjects and languages the work is about.Reasoning · 1,685 works

Cite

Cite as Avni Mittal and Rauno Arike. 2026. C2-Faith: Benchmarking LLM Judges for Causal and Coverage Faithfulness in Chain-of-Thought Reasoning. Proceedings of the Fifth Workshop on Generation, Evaluation and Metrics (GEM).

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.18653/v1/2026.gem-main.62

@inproceedings{mittal2026c2,
  title = {{C2-Faith: Benchmarking LLM Judges for Causal and Coverage Faithfulness in Chain-of-Thought Reasoning}},
  author = {Avni Mittal and Rauno Arike},
  booktitle = {Proceedings of the Fifth Workshop on Generation, Evaluation and Metrics (GEM)},
  year = {2026},
  doi = {10.18653/v1/2026.gem-main.62},
  url = {https://doi.org/10.18653/v1/2026.gem-main.62}
}

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