AlphaOne: Reasoning Models Thinking Slow and Fast at Test Time

This paper presents AlphaOne (alpha1), a universal framework formodulating reasoning progress in large reasoning models (LRMs) at test time.alpha1 first introduces alpha moment, which represents the scaledthinking phase with a universal parameter alpha. Within this scaledpre-alpha moment phase, it dynamically schedules slow thinking transitionsby modeling the insertion of reasoning transition tokens as a Bernoullistochastic process. After the alpha moment, alpha1 deterministicallyterminates slow thinking with the end-of-thinking token, thereby fostering fastreasoning and efficient answer generation. This approach unifies andgeneralizes existing monotonic scaling methods by enabling flexible and denseslow-to-fast reasoning modulation. Extensive empirical studies on variouschallenging benchmarks across mathematical, coding, and scientific domainsdemonstrate alpha1's superior reasoning capability and efficiency. Projectpage: https://alphaone-project.github.io/