We present AlphaOne (𝛼1), a universal framework for modulating reasoning progress in large reasoning models (LRMs) at test time. 𝛼1 first introduces 𝛼 moment, which represents the scaled thinking phase with a universal parameter 𝛼. Within this scaled pre-𝛼 moment phase, it dynamically schedules slow thinking transitions by modeling the insertion of reasoning transition tokens as a Bernoulli stochastic process. After the 𝛼 moment, 𝛼1 deterministically terminates slow thinking with the end-of-thinking token, thereby fostering fast reasoning and efficient answer generation.

This approach unifies and generalizes existing monotonic scaling methods by enabling flexible and dense slow-to-fast reasoning modulation, while offering critical insights into the joint optimization of reasoning capabilities and computational efficiency.