# AlphaOne: Reasoning Models Thinking Slow and Fast at Test Time

arXiv: https://arxiv.org/abs/2505.24863 · HTML: https://mlsanity.com/paper/2505.24863/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 39 of its 84 references that are in the map.
- First posted on arXiv 30 May 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 39)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Chameleon: Mixed-Modal Early-Fusion Foundation Models](https://mlsanity.com/paper/2405.09818/) (2024)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Phi-4 Technical Report](https://mlsanity.com/paper/2412.08905/) (2024)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.16419/) (2025)
- [Chain of Draft: Thinking Faster by Writing Less](https://mlsanity.com/paper/2502.18600/) (2025)
- [TTRL: Test-Time Reinforcement Learning](https://mlsanity.com/paper/2504.16084/) (2025)
- [EmbodiedBench: Comprehensive Benchmarking Multi-modal Large Language Models for Vision-Driven Embodied Agents](https://mlsanity.com/paper/2502.09560/) (2025)
- [Dynamic Early Exit in Reasoning Models](https://mlsanity.com/paper/2504.15895/) (2025)
- [Scalable Best-of-N Selection for Large Language Models via Self-Certainty](https://mlsanity.com/paper/2502.18581/) (2025)
- [Reasoning Models Can Be Effective Without Thinking](https://mlsanity.com/paper/2504.09858/) (2025)
- [T2I-R1: Reinforcing Image Generation with Collaborative Semantic-level and Token-level CoT](https://mlsanity.com/paper/2505.00703/) (2025)
- [Thoughts Are All Over the Place: On the Underthinking of o1-Like LLMs](https://mlsanity.com/paper/2501.18585/) (2025)
- [LLaVA-Critic: Learning to Evaluate Multimodal Models](https://mlsanity.com/paper/2410.02712/) (2024)
- [Optimizing Test-Time Compute via Meta Reinforcement Fine-Tuning](https://mlsanity.com/paper/2503.07572/) (2025)
- [Perception-R1: Pioneering Perception Policy with Reinforcement Learning](https://mlsanity.com/paper/2504.07954/) (2025)
- [Towards Thinking-Optimal Scaling of Test-Time Compute for LLM Reasoning](https://mlsanity.com/paper/2502.18080/) (2025)
- [Between Underthinking and Overthinking: An Empirical Study of Reasoning Length and correctness in LLMs](https://mlsanity.com/paper/2505.00127/) (2025)
- [S*: Test Time Scaling for Code Generation](https://mlsanity.com/paper/2502.14382/) (2025)
- [O1 Replication Journey -- Part 2: Surpassing O1-preview through Simple Distillation, Big Progress or Bitter Lesson?](https://mlsanity.com/paper/2411.16489/) (2024)
- [Revisiting the Test-Time Scaling of o1-like Models: Do they Truly Possess Test-Time Scaling Capabilities?](https://mlsanity.com/paper/2502.12215/) (2025)
- [Interpretable Contrastive Monte Carlo Tree Search Reasoning](https://mlsanity.com/paper/2410.01707/) (2024)

## Built on by (most cited first, 29 of 29)

- [OmniSpatial: Towards Comprehensive Spatial Reasoning Benchmark for Vision Language Models](https://mlsanity.com/paper/2506.03135/) (2025)
- [Reinforcement Learning Meets Large Language Models: A Survey of Advancements and Applications Across the LLM Lifecycle](https://mlsanity.com/paper/2509.16679/) (2025)
- [Open Vision Reasoner: Transferring Linguistic Cognitive Behavior for Visual Reasoning](https://mlsanity.com/paper/2507.05255/) (2025)
- [LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signals](https://mlsanity.com/paper/2604.05655/) (2026)
- [Towards Concise and Adaptive Thinking in Large Reasoning Models: A Survey](https://mlsanity.com/paper/2507.09662/) (2025)
- [Stop When Enough: Adaptive Early-Stopping for Chain-of-Thought Reasoning](https://mlsanity.com/paper/2510.10103/) (2025)
- [Parallel-Probe: Towards Efficient Parallel Thinking via 2D Probing](https://mlsanity.com/paper/2602.03845/) (2026)
- [Xolver: Multi-Agent Reasoning with Holistic Experience Learning Just Like an Olympiad Team](https://mlsanity.com/paper/2506.14234/) (2025)
- [Retrieval-of-Thought: Efficient Reasoning via Reusing Thoughts](https://mlsanity.com/paper/2509.21743/) (2025)
- [From Efficiency to Adaptivity: A Deeper Look at Adaptive Reasoning in Large Language Models](https://mlsanity.com/paper/2511.10788/) (2025)
- [DiffAdapt: Difficulty-Adaptive Reasoning for Token-Efficient LLM Inference](https://mlsanity.com/paper/2510.19669/) (2025)
- [LLMs Improving LLMs: Agentic Discovery for Test-Time Scaling](https://mlsanity.com/paper/2605.08083/) (2026)
- [On The Fragility of Benchmark Contamination Detection in Reasoning Models](https://mlsanity.com/paper/2510.02386/) (2025)
- [Neural Chain-of-Thought Search: Searching the Optimal Reasoning Path to Enhance Large Language Models](https://mlsanity.com/paper/2601.11340/) (2026)
- [FoE: Forest of Errors Makes the First Solution the Best in Large Reasoning Models](https://mlsanity.com/paper/2604.02967/) (2026)
- [CyclicReflex: Improving Reasoning Models via Cyclical Reflection Token Scheduling](https://mlsanity.com/paper/2506.11077/) (2025)
- [Steering Large Reasoning Models towards Concise Reasoning via Flow Matching](https://mlsanity.com/paper/2602.05539/) (2026)
- [Learning to Reason with Mixture of Tokens](https://mlsanity.com/paper/2509.21482/) (2025)
- [DecepChain: Inducing Deceptive Reasoning in Large Language Models](https://mlsanity.com/paper/2510.00319/) (2025)
- [MixReasoning: Switching Modes to Think](https://mlsanity.com/paper/2510.06052/) (2025)
- [When Reasoning Meets Its Laws](https://mlsanity.com/paper/2512.17901/) (2025)
- [To Think or Not To Think, That is The Question for Large Reasoning Models in Theory of Mind Tasks](https://mlsanity.com/paper/2602.10625/) (2026)
- [TRiMS: Real-Time Tracking of Minimal Sufficient Length for Efficient Reasoning via RL](https://mlsanity.com/paper/2603.17449/) (2026)
- [Small RL Controller, Large Language Model: RL-Guided Adaptive Sampling for Test-Time Scaling](https://mlsanity.com/paper/2606.03102/) (2026)
- [Oops, Wait: Discourse Tokens Matter in Reasoning Model](https://mlsanity.com/paper/2601.17421/) (2026)
- [Think Longer to Explore Deeper: Learn to Explore In-Context via Length-Incentivized Reinforcement Learning](https://mlsanity.com/paper/2602.11748/) (2026)
- [Risky Business: Measuring The Faithfulness-Safety Tension](https://mlsanity.com/paper/2608.03745/) (2026)
- [Token-Disentangled Latent Test-Time Scaling for Vision-Language Reasoning](https://mlsanity.com/paper/2609.35228/) (2026)
- [Inject a Turn, Not a Token: Learning Where to Redirect LLM Reasoning for Self-Correction](https://mlsanity.com/paper/2610.13672/) (2026)

## Abstract (arXiv)

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/