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    <abstract>Inference-time optimization scales computation to derive deliberate reasoning steps for effective performance. While previous search-based strategies address the short-sightedness of auto-regressive generation, the vast search space leads to excessive exploration and insufficient exploitation. To strike an efficient balance to derive the optimal step, we frame the decoding strategy as foresight sampling, leveraging simulated future steps to obtain globally optimal step estimation. Built on it, we propose a novel decoding strategy, named φ-Decoding. To provide a precise and expressive estimation of step value, φ-Decoding approximates two distributions via foresight and clustering. Sampling from the joint distribution, the optimal steps can be selected for exploitation. To support adaptive computation allocation, we propose in-width and in-depth pruning strategies, featuring a light-weight solution to achieve inference efficiency. Extensive experiments across seven benchmarks show φ-Decoding outperforms strong baselines in both performance and efficiency. Additional analysis demonstrates its generalization across various LLMs and scalability across a wide range of computing budgets.</abstract>
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%0 Conference Proceedings
%T φ-Decoding: Adaptive Foresight Sampling for Balanced Inference-Time Exploration and Exploitation
%A Xu, Fangzhi
%A Yan, Hang
%A Ma, Chang
%A Zhao, Haiteng
%A Liu, Jun
%A Lin, Qika
%A Wu, Zhiyong
%Y Che, Wanxiang
%Y Nabende, Joyce
%Y Shutova, Ekaterina
%Y Pilehvar, Mohammad Taher
%S Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)
%D 2025
%8 July
%I Association for Computational Linguistics
%C Vienna, Austria
%@ 979-8-89176-251-0
%F xu-etal-2025-ph
%X Inference-time optimization scales computation to derive deliberate reasoning steps for effective performance. While previous search-based strategies address the short-sightedness of auto-regressive generation, the vast search space leads to excessive exploration and insufficient exploitation. To strike an efficient balance to derive the optimal step, we frame the decoding strategy as foresight sampling, leveraging simulated future steps to obtain globally optimal step estimation. Built on it, we propose a novel decoding strategy, named φ-Decoding. To provide a precise and expressive estimation of step value, φ-Decoding approximates two distributions via foresight and clustering. Sampling from the joint distribution, the optimal steps can be selected for exploitation. To support adaptive computation allocation, we propose in-width and in-depth pruning strategies, featuring a light-weight solution to achieve inference efficiency. Extensive experiments across seven benchmarks show φ-Decoding outperforms strong baselines in both performance and efficiency. Additional analysis demonstrates its generalization across various LLMs and scalability across a wide range of computing budgets.
%R 10.18653/v1/2025.acl-long.647
%U https://aclanthology.org/2025.acl-long.647/
%U https://doi.org/10.18653/v1/2025.acl-long.647
%P 13214-13227

Markdown (Informal)

[𝜙-Decoding: Adaptive Foresight Sampling for Balanced Inference-Time Exploration and Exploitation](https://aclanthology.org/2025.acl-long.647/) (Xu et al., ACL 2025)

• 𝜙-Decoding: Adaptive Foresight Sampling for Balanced Inference-Time Exploration and Exploitation (Xu et al., ACL 2025)

ACL

• Fangzhi Xu, Hang Yan, Chang Ma, Haiteng Zhao, Jun Liu, Qika Lin, and Zhiyong Wu. 2025. 𝜙-Decoding: Adaptive Foresight Sampling for Balanced Inference-Time Exploration and Exploitation. In Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 13214–13227, Vienna, Austria. Association for Computational Linguistics.