Yurii Kvasiuk

Yurii Kvasiuk

PhD student in Physics

Test-time Scaling Techniques in Theoretical Physics

Overview

This project reproduces and summarizes the findings of Test-time Scaling Techniques in Theoretical Physics: A Comparison of Methods on the TPBench Dataset (arXiv:2506.20729).

The study evaluates how different test-time scaling strategies affect large language model (LLM) reasoning on advanced theoretical-physics problems using TPBench, a benchmark containing symbolic, multi-step derivations across cosmology, field theory, and mathematical physics.

Methodology

The paper compares four explicit test-time scaling approaches:

Sequential Multi-round Reasoning

The model performs iterative refinement—each generation revises or critiques previous attempts.
We find that sequential scaling shows limited gains on harder physics problems.

Parallel Majority Voting

Multiple solutions are generated independently, and the most frequent answer is chosen.
This simple parallel baseline improves stability but plateaus quickly.

Parallel Scaling with Weak Verifiers

The key contribution.
Each candidate derivation is decomposed into symbolic steps and evaluated by a weak verifier based on SymPy, which checks algebraic and calculus consistency step-by-step and assigns a soft verification score. The highest-scoring candidate is selected.

Results

Across all TPBench categories, parallel weak-verifier scaling achieves the highest accuracy—up to ≈22 % improvement and approaching the best-of-N upper bound.
Key observations:

  • We don’t immediately see an improvement from the sequential scaling technique discussed, although we think that the concept is underexplored
  • Symbolic parallel verification, on the other hand, substantially improves robustness with limited computational overhead.

Discussion & Conclusion

Parallel scaling methods perform best, especially when combined with step-wise symbolic verification.
Sequential multi-round reasoning does not enhance performance on difficult problems, indicating the need for more sophisticated iterative frameworks.
The results highlight that domain-aware verification is essential for physics reasoning and that future progress will depend on developing stronger symbolic tools capable of handling the wider range of mathematical expressions found in theoretical physics—such as tensor calculus and operator algebra.
Integrating these verifiers directly into the generation process, rather than using them post hoc, represents an important direction for future research.