# Scaling over Scaling: Exploring Test-Time Scaling Plateau in Large Reasoning Models

arXiv: https://arxiv.org/abs/2505.20522 · HTML: https://mlsanity.com/paper/2505.20522/

## Key facts

- Cited by 11 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 20 of its 32 references that are in the map.
- First posted on arXiv 26 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, 20 of 20)

- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learning](https://mlsanity.com/paper/2503.04697/) (2025)
- [A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?](https://mlsanity.com/paper/2503.24235/) (2025)
- [Optimizing Test-Time Compute via Meta Reinforcement Fine-Tuning](https://mlsanity.com/paper/2503.07572/) (2025)
- [DeepSeek-R1 Thoughtology: Let's think about LLM Reasoning](https://mlsanity.com/paper/2504.07128/) (2025)
- [Scaling Test-Time Compute Without Verification or RL is Suboptimal](https://mlsanity.com/paper/2502.12118/) (2025)
- [Learning Adaptive Parallel Reasoning with Language Models](https://mlsanity.com/paper/2504.15466/) (2025)
- [SETS: Leveraging Self-Verification and Self-Correction for Improved Test-Time Scaling](https://mlsanity.com/paper/2501.19306/) (2025)
- [InftyThink: Breaking the Length Limits of Long-Context Reasoning in Large Language Models](https://mlsanity.com/paper/2503.06692/) (2025)
- [Think Twice: Enhancing LLM Reasoning by Scaling Multi-round Test-time Thinking](https://mlsanity.com/paper/2503.19855/) (2025)
- [Two Heads are Better Than One: Test-time Scaling of Multi-agent Collaborative Reasoning](https://mlsanity.com/paper/2504.09772/) (2025)
- [Heimdall: test-time scaling on the generative verification](https://mlsanity.com/paper/2504.10337/) (2025)
- [Thinking Slow, Fast: Scaling Inference Compute with Distilled Reasoners](https://mlsanity.com/paper/2502.20339/) (2025)
- [MetaScale: Test-Time Scaling with Evolving Meta-Thoughts](https://mlsanity.com/paper/2503.13447/) (2025)
- [Dancing with Critiques: Enhancing LLM Reasoning with Stepwise Natural Language Self-Critique](https://mlsanity.com/paper/2503.17363/) (2025)
- [a1: Steep Test-time Scaling Law via Environment Augmented Generation](https://mlsanity.com/paper/2504.14597/) (2025)
- [Reasoning-as-Logic-Units: Scaling Test-Time Reasoning in Large Language Models Through Logic Unit Alignment](https://mlsanity.com/paper/2502.07803/) (2025)
- [Adaptive Rectification Sampling for Test-Time Compute Scaling](https://mlsanity.com/paper/2504.01317/) (2025)

## Built on by (most cited first, 11 of 11)

- [Recursive Harness Self-Improvement](https://mlsanity.com/paper/2607.15524/) (2026)
- [Parallel Test-Time Scaling for Latent Reasoning Models](https://mlsanity.com/paper/2510.07745/) (2025)
- [Not All Bits Are Equal: Scale-Dependent Memory Optimization Strategies for Reasoning Models](https://mlsanity.com/paper/2510.10964/) (2025)
- [Understanding Performance Gap Between Parallel and Sequential Sampling in Large Reasoning Models](https://mlsanity.com/paper/2604.05868/) (2026)
- [Mitigating Strategy-Selection Bias in Reasoning for More Effective Test-Time Scaling](https://mlsanity.com/paper/2509.17905/) (2025)
- [Limited Reasoning Space: The cage of long-horizon reasoning in LLMs](https://mlsanity.com/paper/2602.19281/) (2026)
- [ARISE: An Adaptive Resolution-Aware Metric for Test-Time Scaling Evaluation in Large Reasoning Models](https://mlsanity.com/paper/2510.06014/) (2025)
- [MarkovScale: Towards Optimal Sequential Scaling at Inference Time](https://mlsanity.com/paper/2602.01120/) (2026)
- [An Asymptotic Theory of Chain-of-Thought in In-Context Learning](https://mlsanity.com/paper/2606.03217/) (2026)
- [AdaTurn: Budget-Aware Test-Time Scaling for Active Visual Perception Agents](https://mlsanity.com/paper/2607.14547/) (2026)
- [Towards Better Exploration in Sequential Test-Time Scaling](https://mlsanity.com/paper/2609.39632/) (2026)

## Abstract (arXiv)

Large reasoning models (LRMs) have exhibited the capacity of enhancing reasoning performance via internal test-time scaling. Building upon this, a promising direction is to further scale test-time compute to unlock even greater reasoning capabilities. However, as we push these scaling boundaries, systematically understanding the practical limits and achieving optimal resource allocation becomes a critical challenge. In this paper, we investigate the scaling plateau of test-time scaling and introduce the Test-Time Scaling Performance Model (TTSPM). We theoretically analyze two fundamental paradigms for such extended scaling, parallel scaling and sequential scaling, from a probabilistic modeling perspective. Our primary contribution is the derivation of the saturation point on the scaling budget for both strategies, identifying thresholds beyond which additional computation yields diminishing returns. Remarkably, despite their distinct mechanisms, both paradigms converge to a unified mathematical structure in their upper bounds. We empirically validate our theoretical findings on challenging reasoning benchmarks, including AIME, MATH-500, and GPQA, demonstrating the practical utility of these bounds for test-time resource allocation. We hope that this work provides insights into the cost-benefit trade-offs of test-time scaling, guiding the development of more resource-efficient inference strategies for large reasoning models.