AlphaOne: Reasoning Models Thinking Slow and Fast at Test Time

This paper presents 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. Extensive empirical studies on various challenging benchmarks across mathematical, coding, and scientific domains demonstrate α1's superior reasoning capability and efficiency. Project page: https://alphaone-project.github.io/ Let 𝐾 be the number of sequences 𝐴 ! , 𝐴 " , … , 𝐴 # . … What is the remainder when 𝐾 is divided by 10? Question Vanilla Wait Frequency: 23 Okay, so I need to figure out … First, let me parse the problem. … Then, … Wait, but that can't be, because… </think> … So, the remainder when K is divided by 10 is 0.