@inproceedings{ma-etal-2026-beyond-wrong,
title = "Beyond the Wrong Bit: Failure States and the Supervision Unit in Verifiable Reasoning",
author = "Ma, Zihan and
Lin, Zhuoyi and
Luo, Minnan and
Guo, Xiaoxuan and
Wang, Wenya",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {EMNLP} 2026",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.findings-emnlp.269/",
pages = "5645--5665",
ISBN = "979-8-89176-462-0",
abstract = "Verifiable reasoning training compresses an entire response to a binary pass-or-fail label, yet a fail label alone does not reveal whether the corresponding trajectory should be discarded, penalized, or repaired. Many failed trajectories remain close to the correct solution through substantial portions of their intermediate reasoning and deviate only at a later branching point, whereas others contain no reliable prefix that can support a correct suffix. Treating both failure types as uniformly negative supervision suppresses useful reasoning states while reinforcing erroneous ones. To address this limitation, we propose prima, which decomposes failed trajectories into inheritable prefixes and divergent suffixes, and rewrites repairable failures into shared-prefix preference pairs for localized reasoning optimization. We formalize the optimization cost of mixing the two failure types and show that treating them as a uniform negative class shrinks effective gradient magnitude, providing a principled justification for separating repairable from irrecoverable failures before training. Experiments show that prima converts failed trajectories from coarse-grained negative supervision into cleaner suffix-level supervision signals, leading to consistent gains on code and mathematical reasoning tasks."
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<abstract>Verifiable reasoning training compresses an entire response to a binary pass-or-fail label, yet a fail label alone does not reveal whether the corresponding trajectory should be discarded, penalized, or repaired. Many failed trajectories remain close to the correct solution through substantial portions of their intermediate reasoning and deviate only at a later branching point, whereas others contain no reliable prefix that can support a correct suffix. Treating both failure types as uniformly negative supervision suppresses useful reasoning states while reinforcing erroneous ones. To address this limitation, we propose prima, which decomposes failed trajectories into inheritable prefixes and divergent suffixes, and rewrites repairable failures into shared-prefix preference pairs for localized reasoning optimization. We formalize the optimization cost of mixing the two failure types and show that treating them as a uniform negative class shrinks effective gradient magnitude, providing a principled justification for separating repairable from irrecoverable failures before training. Experiments show that prima converts failed trajectories from coarse-grained negative supervision into cleaner suffix-level supervision signals, leading to consistent gains on code and mathematical reasoning tasks.</abstract>
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%0 Conference Proceedings
%T Beyond the Wrong Bit: Failure States and the Supervision Unit in Verifiable Reasoning
%A Ma, Zihan
%A Lin, Zhuoyi
%A Luo, Minnan
%A Guo, Xiaoxuan
%A Wang, Wenya
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Findings of the Association for Computational Linguistics: EMNLP 2026
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-462-0
%F ma-etal-2026-beyond-wrong
%X Verifiable reasoning training compresses an entire response to a binary pass-or-fail label, yet a fail label alone does not reveal whether the corresponding trajectory should be discarded, penalized, or repaired. Many failed trajectories remain close to the correct solution through substantial portions of their intermediate reasoning and deviate only at a later branching point, whereas others contain no reliable prefix that can support a correct suffix. Treating both failure types as uniformly negative supervision suppresses useful reasoning states while reinforcing erroneous ones. To address this limitation, we propose prima, which decomposes failed trajectories into inheritable prefixes and divergent suffixes, and rewrites repairable failures into shared-prefix preference pairs for localized reasoning optimization. We formalize the optimization cost of mixing the two failure types and show that treating them as a uniform negative class shrinks effective gradient magnitude, providing a principled justification for separating repairable from irrecoverable failures before training. Experiments show that prima converts failed trajectories from coarse-grained negative supervision into cleaner suffix-level supervision signals, leading to consistent gains on code and mathematical reasoning tasks.
%U https://aclanthology.org/2026.findings-emnlp.269/
%P 5645-5665
Markdown (Informal)
[Beyond the Wrong Bit: Failure States and the Supervision Unit in Verifiable Reasoning](https://aclanthology.org/2026.findings-emnlp.269/) (Ma et al., Findings 2026)
ACL