@inproceedings{wu-etal-2026-must,
title = "When Must Faithful Chain-of-Thought Fail? An Information-Theoretic Bound and Its Empirical Limits",
author = "Wu, Jikun and
Guo, Dongxin and
Yiu, SM",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.emnlp-main.1823/",
pages = "41537--41555",
ISBN = "979-8-89176-459-0",
abstract = "Frontier reasoning systems generate chain-of-thought (CoT) traces meant to reveal how they reach answers, yet these traces systematically misrepresent the underlying computation. A tempting explanation is bandwidth: each token carries few bits while the residual stream encodes many, so sufficiently complex tasks would make faithful verbalization impossible in principle. We formalize this intuition and locate its limits. A capacity bound rules out faithful CoT whenever the information the model uses exceeds the trace{'}s token capacity; this condition requires the answer to be longer than the trace, so standard CoT settings do not reach it. A per-step information-loss conjecture is empirically falsified on six of seven benchmarks. A constructive result shows faithful traces remain achievable for polynomial-size circuit families, and an information-bottleneck experiment supports a faithfulness{--}accuracy tradeoff. Measuring critic-score gaps on seven benchmarks for three open-weight models, complemented by perturbation sensitivity, we find no benchmark provably in the above-capacity regime. The capacity bound is architecture-independent, but at evaluated trace lengths it does not bind: observed unfaithfulness is attributable to training rather than to the token interface, and is therefore potentially correctable."
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<abstract>Frontier reasoning systems generate chain-of-thought (CoT) traces meant to reveal how they reach answers, yet these traces systematically misrepresent the underlying computation. A tempting explanation is bandwidth: each token carries few bits while the residual stream encodes many, so sufficiently complex tasks would make faithful verbalization impossible in principle. We formalize this intuition and locate its limits. A capacity bound rules out faithful CoT whenever the information the model uses exceeds the trace’s token capacity; this condition requires the answer to be longer than the trace, so standard CoT settings do not reach it. A per-step information-loss conjecture is empirically falsified on six of seven benchmarks. A constructive result shows faithful traces remain achievable for polynomial-size circuit families, and an information-bottleneck experiment supports a faithfulness–accuracy tradeoff. Measuring critic-score gaps on seven benchmarks for three open-weight models, complemented by perturbation sensitivity, we find no benchmark provably in the above-capacity regime. The capacity bound is architecture-independent, but at evaluated trace lengths it does not bind: observed unfaithfulness is attributable to training rather than to the token interface, and is therefore potentially correctable.</abstract>
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%0 Conference Proceedings
%T When Must Faithful Chain-of-Thought Fail? An Information-Theoretic Bound and Its Empirical Limits
%A Wu, Jikun
%A Guo, Dongxin
%A Yiu, S. M.
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F wu-etal-2026-must
%X Frontier reasoning systems generate chain-of-thought (CoT) traces meant to reveal how they reach answers, yet these traces systematically misrepresent the underlying computation. A tempting explanation is bandwidth: each token carries few bits while the residual stream encodes many, so sufficiently complex tasks would make faithful verbalization impossible in principle. We formalize this intuition and locate its limits. A capacity bound rules out faithful CoT whenever the information the model uses exceeds the trace’s token capacity; this condition requires the answer to be longer than the trace, so standard CoT settings do not reach it. A per-step information-loss conjecture is empirically falsified on six of seven benchmarks. A constructive result shows faithful traces remain achievable for polynomial-size circuit families, and an information-bottleneck experiment supports a faithfulness–accuracy tradeoff. Measuring critic-score gaps on seven benchmarks for three open-weight models, complemented by perturbation sensitivity, we find no benchmark provably in the above-capacity regime. The capacity bound is architecture-independent, but at evaluated trace lengths it does not bind: observed unfaithfulness is attributable to training rather than to the token interface, and is therefore potentially correctable.
%U https://aclanthology.org/2026.emnlp-main.1823/
%P 41537-41555
Markdown (Informal)
[When Must Faithful Chain-of-Thought Fail? An Information-Theoretic Bound and Its Empirical Limits](https://aclanthology.org/2026.emnlp-main.1823/) (Wu et al., EMNLP 2026)
ACL