Efficiently Scaling LLM Reasoning Programs with Certaindex

Hao Zhang (NVIDIA) · Yian Ma (UC San Diego) · Ion Stoica (UC Berkeley) · Yichao Fu (University of California, San Diego) · Aurick Qiao (Snowflake) · Yonghao Zhuang (CMU, Carnegie Mellon University) · Junda Chen (Harbin Institute of Technology) · Siqi Zhu (UIUC) · Fu · Zhongdongming Dai (University of California, San Diego) · Tajana S Rosing (UCSD)

algorithm-agnostic metricanswer stabilizationcertaindexchain-of-thoughtcompute savingsdynamic token allocationearly exit strategygang schedulingllm serving systemsmonte carlo tree search (mcts)real-world workloadsreasoning program inferenceself-consistencytest-time reasoningthroughput optimization

Test-time reasoning algorithms such as chain-of-thought, self-consistency, and MCTS enhance LLM problem-solving but can wastefully generate many tokens without improving accuracy. At the same time, we observe that these algorithms exhibit answer stabilization: their intermediate solutions often cease to change after a certain point, and further investment of compute does not change their final answer. To quantify this phenomenon, we introduce Certaindex, an algorithm-agnostic metric measuring this evolving stability, signaling when further computation is unlikely to alter the final result. Certaindex is lightweight, can accelerate reasoning program inference via early exit, and further enables dynamic token allocation, gang scheduling, and many opportunities when integrated with real-world LLM serving systems. To quantify real-world benefits, we built Certaindex as a scheduler into Dynasor, our reasoning-aware LLM serving system, and demonstrate up to 50\% compute savings and 3.3$\times$ higher throughput in real workloads with no accuracy drop. Our code is available at https://github.com/hao-ai-lab/Dynasor.git