What If We Allocate Test-Time Compute Adaptively?

Test-time compute scaling allocates inference computation uniformly, uses fixed sampling strategies, and applies verification only for reranking. In contrast, we propose a verifier-guided adaptive framework treating reasoning as iterative trajectory generation and selection. For each problem, the agent runs multiple inference iterations. In each iteration, it optionally produces a high-level plan, selects a set of reasoning tools and a compute strategy together with an exploration parameter, and then generates a candidate reasoning trajectory. A process reward model (PRM) serves as a unified control signal: within each iteration, step-level PRM scores are aggregated to guide pruning and expansion during generation, and across iterations, aggregated trajectory rewards are used to select the final response. Across datasets, our dynamic, PRM-guided approach consistently outperforms direct test-time scaling, yielding large gains on MATH-500 and several-fold improvements on harder benchmarks such as AIME24 and AMO-Bench. We characterize efficiency using theoretical FLOPs and a compute intensity metric penalizing wasted generation and tool overhead, demonstrating that verification-guided allocation concentrates computation on high-utility reasoning paths.

When an AI solves math problems, it typically applies the same computational effort to every question, wasting resources on easy ones while having nothing left for genuinely hard ones. We built a system that fixes this by thinking before it acts: for each problem, it first chooses which reasoning tools to use and how hard to try, then a step-by-step judge watches the reasoning as it unfolds, catching errors before they compound. The system generates several solution attempts and picks the best one based on these ongoing quality checks. Tested on standard math benchmarks as well as olympiad-level competition problems, our approach substantially outperforms systems that use a fixed strategy, accuracy on competition problems more than doubled in some cases. Crucially, these gains come not from simply throwing more computation at every problem, but from concentrating effort where it actually matters, showing that AI systems can reason more reliably by being strategically flexible rather than uniformly exhaustive.