GLOBE: Geometry-Led Online Behavioral Early Exit via Unit-Sphere Trajectories

Chain-of-thought (CoT) reasoning can improve problem solving, but models often keep generating after the correct answer is already reachable; the extra steps raise serving costs and may replace a correct intermediate result with an incorrect one. We propose GLOBE (Geometry-Led Online Behavioral Early Exit), an online, training-free algorithm that terminates the model's CoT process early. GLOBE embeds each completed reasoning segment as a point on a unit sphere and reads the shape of the resulting semantic trajectory. GLOBE first applies a trial phase that generates short trial answers in a separate branch, stopping the main stream on an accepted trial after checking confidence against a threshold. If generation continues, a trajectory phase stops the stream once this path repeatedly reverses direction with little net progress. On five benchmarks including mathematical reasoning, tool calling, and agent memory, GLOBE cuts output tokens by 49.7% and active end-to-end wall time (E2E) by 51.0% across two models, and achieves a five-task average of 80.58%, comparable to Full CoT.