φ-Decoding: Adaptive Foresight Sampling for Balanced Inference-Time
  Exploration and Exploitation
Authors: name: Fangzhi Xu; name: Hang Yan; name: Chang Ma; name: Haiteng Zhao; name: Jun Liu; name: Qika Lin; name: Zhiyong Wu
Published: 2025-03-17 15:38:33

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 phi-Decoding. To provide a precise and expressive estimation of step
value, phi-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 phi-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.
The code will be released at https://github.com/xufangzhi/phi-Decoding, and the
open-source PyPI package is coming soon.