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    <abstract>Supervised fine-tuning (SFT) on long chain-of-thought (CoT) trajectories has emerged as a crucial technique for enhancing the reasoning abilities of large language models (LLMs). However, the standard cross-entropy loss treats all tokens equally, ignoring their heterogeneous contributions across a reasoning trajectory. This uniform treatment leads to misallocated supervision and weak generalization, especially in complex, long-form reasoning tasks. To address this, we introduce **V**ariance-**C**ontrolled **O**ptimization-based **RE**weighting (VCORE), a principled framework that reformulates CoT supervision as a constrained optimization problem. By adopting an optimization-theoretic perspective, VCORE enables a principled and adaptive allocation of supervision across tokens, thereby aligning the training objective more closely with the goal of robust reasoning generalization. Empirical evaluations demonstrate that VCORE achieves the strongest overall average performance, with especially clear gains on lower-capacity models. Across both in-domain and out-of-domain settings, VCORE achieves substantial performance gains on mathematical and coding benchmarks, using models from the Qwen3 series (4B, 8B, 32B) and LLaMA-3.1-8B-Instruct. Moreover, we show that VCORE serves as a more effective initialization for subsequent reinforcement learning, establishing a stronger foundation for advancing the reasoning capabilities of LLMs.</abstract>
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%0 Conference Proceedings
%T VCORE: Variance-Controlled Optimization-based Reweighting for Chain-of-Thought Supervision
%A Gong, Xuan
%A Wang, Senmiao
%A Huang, Hanbo
%A Sun, Ruoyu
%A Liang, Shiyu
%Y Liakata, Maria
%Y Moreira, Viviane P.
%Y Zhang, Jiajun
%Y Jurgens, David
%S Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)
%D 2026
%8 July
%I Association for Computational Linguistics
%C San Diego, California, United States
%@ 979-8-89176-390-6
%F gong-etal-2026-vcore
%X Supervised fine-tuning (SFT) on long chain-of-thought (CoT) trajectories has emerged as a crucial technique for enhancing the reasoning abilities of large language models (LLMs). However, the standard cross-entropy loss treats all tokens equally, ignoring their heterogeneous contributions across a reasoning trajectory. This uniform treatment leads to misallocated supervision and weak generalization, especially in complex, long-form reasoning tasks. To address this, we introduce **V**ariance-**C**ontrolled **O**ptimization-based **RE**weighting (VCORE), a principled framework that reformulates CoT supervision as a constrained optimization problem. By adopting an optimization-theoretic perspective, VCORE enables a principled and adaptive allocation of supervision across tokens, thereby aligning the training objective more closely with the goal of robust reasoning generalization. Empirical evaluations demonstrate that VCORE achieves the strongest overall average performance, with especially clear gains on lower-capacity models. Across both in-domain and out-of-domain settings, VCORE achieves substantial performance gains on mathematical and coding benchmarks, using models from the Qwen3 series (4B, 8B, 32B) and LLaMA-3.1-8B-Instruct. Moreover, we show that VCORE serves as a more effective initialization for subsequent reinforcement learning, establishing a stronger foundation for advancing the reasoning capabilities of LLMs.
%U https://aclanthology.org/2026.acl-long.1298/
%P 28161-28180

Markdown (Informal)

[VCORE: Variance-Controlled Optimization-based Reweighting for Chain-of-Thought Supervision](https://aclanthology.org/2026.acl-long.1298/) (Gong et al., ACL 2026)

• VCORE: Variance-Controlled Optimization-based Reweighting for Chain-of-Thought Supervision (Gong et al., ACL 2026)

ACL

• Xuan Gong, Senmiao Wang, Hanbo Huang, Ruoyu Sun, and Shiyu Liang. 2026. VCORE: Variance-Controlled Optimization-based Reweighting for Chain-of-Thought Supervision. In Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 28161–28180, San Diego, California, United States. Association for Computational Linguistics.