A Compute-Matched Re-Evaluation of TroVE on MATH
This work provides a critical re-evaluation for researchers in mathematical reasoning with LLMs, showing that a previously proposed method offers only incremental benefits.
The authors re-evaluated the TroVE method on the MATH benchmark and found that its claimed performance gains primarily resulted from higher computational budget rather than toolbox mechanisms, with benefits reducing to a marginal 1% improvement after compute matching.
Reusing established theorems and formulas is central to mathematical problem solving, serving as essential building blocks for tackling increasingly complex challenges. Recent work, TroVE, argues that code-generating Large Language Models (LLMs) can benefit similarly on the MATH benchmark by inducing and reusing higher-level toolboxes. By allocating computational budget across an ensemble of three modes -- directly generating code, creating tools, and reusing tools -- TroVE claims to outperform a PRIMITIVE baseline that only performs direct generation. However, recent analysis (Berlot-Attwell et al., 2024) casts doubt on these gains, noting that the tools created are often trivial or rarely reused, suggesting that improvements may stem from self-consistency or self-correction. In this work, we re-evaluate TroVE on MATH, analyze the impact of each of its modes, and show that its benefit does not come from these mechanisms, but simply from a higher computational budget spent for TroVE compared to PRIMITIVE. To this end, we also perform a small correction in the original implementation of TroVE's selection mechanism, boosting TroVE's performance on MATH by 3\% in accuracy. After matching for compute, the benefit of TroVE reduces to a marginal improvement of 1\%, suggesting that this toolbox approach does not provide a significant benefit on MATH.