aiqbench analysis
ExpBoN introduces a novel exponential-noise mechanism for Best-of-$n$ sampling that achieves exponentially fast convergence in total variation and KL divergence compared to prior soft maximization methods. By integrating this approach into the guided speculative inference framework, the resulting ExpGSI method significantly reduces computational costs—by up to 45% at $n=16$—while maintaining high accuracy on math-heavy benchmarks like MATH500 and Minerva Math. This work provides a rigorous theoretical foundation for optimizing test-time alignment in large language models without sacrificing performance.
ExpBoN: Exponential-Noise Best-of-$n$ for Efficient Test-Time LLM Alignment
arXiv:2609.21899v1 Announce Type: new Abstract: Best-of-$n$ (BoN) sampling is a simple yet effective inference-time alignment method, but hard maximization provides only coarse control over the trade-off between reward and distribution shift. Soft Best-of-$n$ (Verdun et al. 2025) provides smoother control and converges to the optimal distribution associated with KL-regularized reward maximization. In this paper, we introduce ExpBoN, an alternative soft BoN method based on the exponential-noise report-noisy-max mechanism. It admits an exact finite-$n$ decomposition, which yields exponentially fast convergence in total variation, expected reward, and both directions of KL divergence. We provide comprehensive theoretical analyses of its convergence and regret behavior. We further integrate ExpBoN into the guided speculative inference (GSI) framework (Geuter, Mroueh, and AlvarezMelis 2025), resulting in ExpGSI, for efficient reward-guided LLM alignment. ExpGSI yields substantial reductions in computational cost while maintaining comparable accuracy. Experiments on MATH500, MMLU-STEM, and Minerva Math with the Qwen2.5-Math and Qwen3 model families show that ExpGSI reduces estimated computation by $14\%$-$39\%$ across candidate budgets for Qwen2.5-Math and by up to $45\%$ at $n=16$ for Qwen3. Overall, our results provide a theoretical and algorithmic foundation for exponential-noise BoN and efficient test-time LLM alignment.
Abstract:Best-of-$n$ (BoN) sampling is a simple yet effective inference-time alignment method, but hard maximization provides only coarse control over the trade-off between reward and distribution shift. Soft Best-of-$n$ (Verdun et al. 2025) provides smoother control and converges to the optimal distribution associated with KL-regularized reward maximization. In this paper, we introduce ExpBoN, an alternative soft BoN method based on the exponential-noise report-noisy-max mechanism. It admits an exact finite-$n$ decomposition, which yields exponentially fast convergence in total variation, expected reward, and both directions of KL divergence. We provide comprehensive theoretical analyses of its convergence and regret behavior. We further integrate ExpBoN into the guided speculative inference (GSI) framework (Geuter, Mroueh, and AlvarezMelis 2025), resulting in ExpGSI, for efficient reward-guided LLM alignment. ExpGSI yields substantial reductions in computational cost while maintaining comparable accuracy. Experiments on MATH500, MMLU-STEM, and Minerva Math with the Qwen2.5-Math and Qwen3 model families show that ExpGSI reduces estimated computation by $14\%$-$39\%$ across candidate budgets for Qwen2.5-Math and by up to $45\%$ at $n=16$ for Qwen3. Overall, our results provide a theoretical and algorithmic foundation for exponential-noise BoN and efficient test-time LLM alignment.
Machine Learning (cs.LG); Information Theory (cs.IT)
arXiv:2609.21899 [cs.LG]
(or arXiv:2609.21899v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.21899 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 281 words
Related coverage
Lattice-Based Cryptography Explained
Quantum Zeitgeist · Aug 15, 2026
Synthesis Superintelligence: from Semiconductors to Superconductors — Periodic Labs’ Liam Fedus and Ekin Dogus Cubuk
Latent Space · Oct 8, 2026
Humanity’s Last Invention — Richard Socher of Recursive
Latent Space · Sep 14, 2026
Debating RSI, the US-China Gap, and Jaggedness with JS Denain of Epoch AI
Interconnects · Sep 22, 2026