# Test-time Scaling Techniques in Theoretical Physics -- A Comparison of Methods on the TPBench Dataset

arXiv: https://arxiv.org/abs/2506.20729 · HTML: https://mlsanity.com/paper/2506.20729/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 22 of its 24 references that are in the map.
- First posted on arXiv 25 Jun 2025.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)

## Builds on (most cited first, 22 of 22)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024)
- [FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI](https://mlsanity.com/paper/2411.04872/) (2024)
- [Thoughts Are All Over the Place: On the Underthinking of o1-Like LLMs](https://mlsanity.com/paper/2501.18585/) (2025)
- [On the Self-Verification Limitations of Large Language Models on Reasoning and Planning Tasks](https://mlsanity.com/paper/2402.08115/) (2024)
- [Can 1B LLM Surpass 405B LLM? Rethinking Compute-Optimal Test-Time Scaling](https://mlsanity.com/paper/2502.06703/) (2025)
- [T1: Advancing Language Model Reasoning through Reinforcement Learning and Inference Scaling](https://mlsanity.com/paper/2501.11651/) (2025)
- [ReasonFlux: Hierarchical LLM Reasoning via Scaling Thought Templates](https://mlsanity.com/paper/2502.06772/) (2025)
- [Atom of Thoughts for Markov LLM Test-Time Scaling](https://mlsanity.com/paper/2502.12018/) (2025)
- [Sample, Scrutinize and Scale: Effective Inference-Time Search by Scaling Verification](https://mlsanity.com/paper/2502.01839/) (2025)
- [Think Twice: Enhancing LLM Reasoning by Scaling Multi-round Test-time Thinking](https://mlsanity.com/paper/2503.19855/) (2025)
- [Theoretical Physics Benchmark (TPBench) -- a Dataset and Study of AI Reasoning Capabilities in Theoretical Physics](https://mlsanity.com/paper/2502.15815/) (2025)
- [Step Back to Leap Forward: Self-Backtracking for Boosting Reasoning of Language Models](https://mlsanity.com/paper/2502.04404/) (2025)
- [LADDER: Self-Improving LLMs Through Recursive Problem Decomposition](https://mlsanity.com/paper/2503.00735/) (2025)
- [Scaling Inference-Efficient Language Models](https://mlsanity.com/paper/2501.18107/) (2025)
- [CoAT: Chain-of-Associated-Thoughts Framework for Enhancing Large Language Models Reasoning](https://mlsanity.com/paper/2502.02390/) (2025)

## Built on by (most cited first, 8 of 8)

- [A Survey of Scientific Large Language Models: From Data Foundations to Agent Frontiers](https://mlsanity.com/paper/2508.21148/) (2025)
- [MadEvolve: Evolutionary Optimization of Cosmological Algorithms with Large Language Models](https://mlsanity.com/paper/2602.15951/) (2026)
- [gwBenchmarks: Stress-Testing LLM Agents on High-Precision Gravitational Wave Astronomy](https://mlsanity.com/paper/2605.11269/) (2026)
- [LLMs with in-context learning for Algorithmic Theoretical Physics](https://mlsanity.com/paper/2605.08212/) (2026)
- [Competing with AI Scientists: Agent-Driven Approach to Astrophysics Research](https://mlsanity.com/paper/2604.09621/) (2026)
- [Fine-Tuning Small Reasoning Models for Quantum Field Theory](https://mlsanity.com/paper/2604.18936/) (2026)
- [Decoupled Physical Modeling and Execution for Physics Reasoning](https://mlsanity.com/paper/2608.22126/) (2026)
- [The Future of AI-assisted Physics: Discovering, Verifying and Organizing Results via Formalization](https://mlsanity.com/paper/2610.14059/) (2026)

## Abstract (arXiv)

Large language models (LLMs) have shown strong capabilities in complex reasoning, and test-time scaling techniques can enhance their performance with comparably low cost. Many of these methods have been developed and evaluated on mathematical reasoning benchmarks such as AIME. This paper investigates whether the lessons learned from these benchmarks generalize to the domain of advanced theoretical physics. We evaluate a range of common test-time scaling methods on the TPBench physics dataset and compare their effectiveness with results on AIME. To better leverage the structure of physics problems, we develop a novel, symbolic weak-verifier framework to improve parallel scaling results. Our empirical results demonstrate that this method significantly outperforms existing test-time scaling approaches on TPBench. We also evaluate our method on AIME, confirming its effectiveness in solving advanced mathematical problems. Our findings highlight the power of step-wise symbolic verification for tackling complex scientific problems.