On the Limits of Test-Time Compute: Sequential Reward Filtering for Better Inference

Test-time compute (TTC) has become an increasingly prominent paradigm for enhancing large language models (LLMs). Despite the empirical success of methods such as best-of-$n$ (BoN) sampling and sequential revision, their fundamental limits remain unclear. We address this gap by analyzing a mixture-of-reference policy model and proving that standard BoN is inherently suboptimal. To move closer to the optimal frontier, we study reward-filtered sequential inference, a simple procedure that selectively incorporates only high-reward generations into the context. This mechanism concentrates computation on superior policy candidates and suppresses inferior ones. On the theoretical side, we show that reward-filtered sequential inference yields strictly stronger guarantees than standard TTC paradigms. On the empirical side, we evaluate such an inference strategy across diverse benchmarks and observe consistent improvements over widely used approaches, demonstrating the practical effectiveness of our framework.

Large language models can often improve their answers when they are allowed to spend more computation at the time of solving a problem. A common strategy is to generate many independent answers and select the best one, but this paper shows that this is not always the most effective use of extra computation. We study a simple alternative in which the model generates answers sequentially, keeps only the high-scoring ones, and uses them to guide later attempts. By discarding low-quality answers and reusing only promising ones, the model can focus on better reasoning paths. Our theoretical analysis and experiments show that this reward-filtered sequential strategy uses computation more efficiently than standard approaches and consistently improves accuracy across reasoning benchmarks and language models, especially on harder problems.