CarBoN: Calibrated Best-of-N Sampling Improves Test-time Reasoning (2510.15674v1)

Abstract: Allocating more computation during inference time (test-time scaling) improves LLM performance, especially for reasoning tasks. However, popular methods like Best-of-$N$ sampling often show diminishing returns as $N$ increases. To address this inefficiency, we introduce a general test-time calibration framework that adaptively modifies the model toward high-reward reasoning paths, with theoretical guarantees of improving the lower bound of expected reward under finite sampling, all without LLM retraining. Within this framework, we propose CarBoN (Calibrated Best-of-$N$), a two-phase method that first explores the solution space and then learns a calibration of the logits via an input-specific temperature $T$ and additive shift vector $\delta$, guiding generation toward more reliable reasoning. Experiments on MATH-500 and AIME-2024 show that CarBoN improves efficiency, with up to $4\times$ fewer rollouts to reach the same accuracy, while often achieving higher accuracy under fixed budgets. We also analyze the complementary roles of $T$ and $\delta$ in balancing output diversity and correctness, and demonstrate that the framework also generalizes to step-level sampling strategies such as beam search. For more information, please refer to our project page at huggingface.co/spaces/TrustSafeAI/Test-Time-Calibration.