ASyMOB: Algebraic Symbolic Mathematical Operations Benchmark

摘要

Large language models (LLMs) are increasingly applied to symbolic mathematics, yet existing evaluations often conflate pattern memorization with genuine reasoning. To address this gap, we present **ASyMOB**, a high-resolution dataset of **35,368** validated symbolic math problems spanning integration, limits, differential equations, series, and hypergeometrics. Unlike prior benchmarks, **ASyMOB** systematically perturbs each seed problem using symbolic, numeric, and equivalence-preserving transformations, enabling a fine-grained assessment of generalization and robustness. Our evaluation reveals three key findings: (1) most models’ performance collapses under minor perturbations, while top systems exhibit an apparent \textit{regime shift} in robustness; (2) integrated code tools stabilize performance, particularly for weaker models; and (3) we identify examples where Computer Algebra Systems (CAS) fail while LLMs succeed, as well as problems solved only via a hybrid LLM-CAS approach, highlighting a promising integration frontier. **ASyMOB** serves as a principled diagnostic tool for measuring and accelerating progress toward building verifiable, trustworthy AI for scientific discovery.