Verification is a key bottleneck in improving inference speed while maintaining distribution fidelity in Speculative Decoding. Recent work has shown that sequence-level verification leads to a higher number of accepted tokens compared to token-wise verification. However, existing solutions often rely on surrogate approximations or are constrained by partial information, struggling with joint intractability. In this work, we propose Hierarchical Speculative Decoding (HSD), a provably lossless verification method that significantly boosts the expected number of accepted tokens and overcomes joint intractability by balancing excess and deficient probability mass across accessible branches. Our extensive large-scale experiments demonstrate that HSD yields consistent improvements in acceptance rates across diverse model families and benchmarks. Moreover, its strong explainability and generality make it readily integrable into a wide range of speculative decoding frameworks. Notably, integrating HSD into EAGLE-3 yields over a 12% performance gain, establishing state-of-the-art decoding efficiency without compromising distribution fidelity. Code is available at https://github.com/ZhouYuxuanYX/Hierarchical-Speculative-Decoding.
@article{arxiv.2601.05724,
title = {Overcoming Joint Intractability with Lossless Hierarchical Speculative Decoding},
author = {Yuxuan Zhou and Fei Huang and Heng Li and Fengyi Wu and Tianyu Wang and Jianwei Zhang and Junyang Lin and Zhi-Qi Cheng},
journal= {arXiv preprint arXiv:2601.05724},
year = {2026}
}