# Can 1B LLM Surpass 405B LLM? Rethinking Compute-Optimal Test-Time Scaling

arXiv: https://arxiv.org/abs/2502.06703 · HTML: https://mlsanity.com/paper/2502.06703/

## Key facts

- Cited by 136 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 40 of its 77 references that are in the map.
- First posted on arXiv 10 Feb 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 40)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [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)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [Reinforced Self-Training (ReST) for Language Modeling](https://mlsanity.com/paper/2308.08998/) (2023)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [ProcessBench: Identifying Process Errors in Mathematical Reasoning](https://mlsanity.com/paper/2412.06559/) (2024)
- [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024)
- [Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning](https://mlsanity.com/paper/2410.08146/) (2024)
- [V-STaR: Training Verifiers for Self-Taught Reasoners](https://mlsanity.com/paper/2402.06457/) (2024)
- [Free Process Rewards without Process Labels](https://mlsanity.com/paper/2412.01981/) (2024)
- [Marco-o1: Towards Open Reasoning Models for Open-Ended Solutions](https://mlsanity.com/paper/2411.14405/) (2024)
- [O1 Replication Journey: A Strategic Progress Report -- Part 1](https://mlsanity.com/paper/2410.18982/) (2024)
- [RL on Incorrect Synthetic Data Scales the Efficiency of LLM Math Reasoning by Eight-Fold](https://mlsanity.com/paper/2406.14532/) (2024)
- [PRMBench: A Fine-grained and Challenging Benchmark for Process-Level Reward Models](https://mlsanity.com/paper/2501.03124/) (2025)

## Built on by (most cited first, 30 of 136)

- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.16419/) (2025)
- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [TTRL: Test-Time Reinforcement Learning](https://mlsanity.com/paper/2504.16084/) (2025)
- [A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?](https://mlsanity.com/paper/2503.24235/) (2025)
- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [OpenVLThinker: Complex Vision-Language Reasoning via Iterative SFT-RL Cycles](https://mlsanity.com/paper/2503.17352/) (2025)
- [A Comprehensive Survey in LLM(-Agent) Full Stack Safety: Data, Training and Deployment](https://mlsanity.com/paper/2504.15585/) (2025)
- [GenPRM: Scaling Test-Time Compute of Process Reward Models via Generative Reasoning](https://mlsanity.com/paper/2504.00891/) (2025)
- [Efficient Reasoning Models: A Survey](https://mlsanity.com/paper/2504.10903/) (2025)
- [Quantization Hurts Reasoning? An Empirical Study on Quantized Reasoning Models](https://mlsanity.com/paper/2504.04823/) (2025)
- [Scaling Test-time Compute for LLM Agents](https://mlsanity.com/paper/2506.12928/) (2025)
- [Speculative Thinking: Enhancing Small-Model Reasoning with Large Model Guidance at Inference Time](https://mlsanity.com/paper/2504.12329/) (2025)
- [The Complexity Trap: Simple Observation Masking Is as Efficient as LLM Summarization for Agent Context Management](https://mlsanity.com/paper/2508.21433/) (2025)
- [ReasonFlux-PRM: Trajectory-Aware PRMs for Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2506.18896/) (2025)
- [Seek in the Dark: Reasoning via Test-Time Instance-Level Policy Gradient in Latent Space](https://mlsanity.com/paper/2505.13308/) (2025)
- [Video-T1: Test-Time Scaling for Video Generation](https://mlsanity.com/paper/2503.18942/) (2025)
- [Stabilizing Knowledge, Promoting Reasoning: Dual-Token Constraints for RLVR](https://mlsanity.com/paper/2507.15778/) (2025)
- [ETTRL: Balancing Exploration and Exploitation in LLM Test-Time Reinforcement Learning Via Entropy Mechanism](https://mlsanity.com/paper/2508.11356/) (2025)
- [Meta-Reasoner: Dynamic Guidance for Optimized Inference-time Reasoning in Large Language Models](https://mlsanity.com/paper/2502.19918/) (2025)
- [Reasoning on a Budget: A Survey of Adaptive and Controllable Test-Time Compute in LLMs](https://mlsanity.com/paper/2507.02076/) (2025)
- [Amulet: ReAlignment During Test Time for Personalized Preference Adaptation of LLMs](https://mlsanity.com/paper/2502.19148/) (2025)
- [Two Heads are Better Than One: Test-time Scaling of Multi-agent Collaborative Reasoning](https://mlsanity.com/paper/2504.09772/) (2025)
- [PixelThink: Towards Efficient Chain-of-Pixel Reasoning](https://mlsanity.com/paper/2505.23727/) (2025)
- [Shrinking the Generation-Verification Gap with Weak Verifiers](https://mlsanity.com/paper/2506.18203/) (2025)
- [Entropy-Gated Branching for Efficient Test-Time Reasoning](https://mlsanity.com/paper/2503.21961/) (2025)
- [Know What You Don't Know: Uncertainty Calibration of Process Reward Models](https://mlsanity.com/paper/2506.09338/) (2025)
- [Do We Truly Need So Many Samples? Multi-LLM Repeated Sampling Efficiently Scales Test-Time Compute](https://mlsanity.com/paper/2504.00762/) (2025)
- [A Survey of Slow Thinking-based Reasoning LLMs using Reinforced Learning and Inference-time Scaling Law](https://mlsanity.com/paper/2505.02665/) (2025)
- [Variation in Verification: Understanding Verification Dynamics in Large Language Models](https://mlsanity.com/paper/2509.17995/) (2025)
- [RoVer: Robot Reward Model as Test-Time Verifier for Vision-Language-Action Model](https://mlsanity.com/paper/2510.10975/) (2025)

## Abstract (arXiv)

Test-Time Scaling (TTS) is an important method for improving the performance of Large Language Models (LLMs) by using additional computation during the inference phase. However, current studies do not systematically analyze how policy models, Process Reward Models (PRMs), and problem difficulty influence TTS. This lack of analysis limits the understanding and practical use of TTS methods. In this paper, we focus on two core questions: (1) What is the optimal approach to scale test-time computation across different policy models, PRMs, and problem difficulty levels? (2) To what extent can extended computation improve the performance of LLMs on complex tasks, and can smaller language models outperform larger ones through this approach? Through comprehensive experiments on MATH-500 and challenging AIME24 tasks, we have the following observations: (1) The compute-optimal TTS strategy is highly dependent on the choice of policy model, PRM, and problem difficulty. (2) With our compute-optimal TTS strategy, extremely small policy models can outperform larger models. For example, a 1B LLM can exceed a 405B LLM on MATH-500. Moreover, on both MATH-500 and AIME24, a 0.5B LLM outperforms GPT-4o, a 3B LLM surpasses a 405B LLM, and a 7B LLM beats o1 and DeepSeek-R1, while with higher inference efficiency. These findings show the significance of adapting TTS strategies to the specific characteristics of each task and model and indicate that TTS is a promising approach for enhancing the reasoning abilities of LLMs.