Shalyt/ASyMOB-Algebraic_Symbolic_Mathematical_Operations_Benchmark

ASyMOB: Algebraic Symbolic Mathematical Operations Benchmark

This dataset is associated with the paper "ASyMOB: Algebraic Symbolic Mathematical Operations Benchmark".

Abstract

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.

Our evaluation reveals three key findings:

1. Most models’ performance collapses under minor perturbations, while top systems exhibit an apparent regime shift in robustness
2. Integrated code tools stabilize performance, particularly for weaker models
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.

ASyMOB Dataset Generation

See the ASyMOB code repository for the data generation code.

ASyMOB_Generation.py generates a diverse set of mathematical question variants from a seed CSV file. It leverages the SymPy library for symbolic mathematics to create various perturbations of original questions, including symbolic, numeric, and equivalence-based transformations. The generated questions are then saved to a JSON file.

Usage

1. Prepare your seed data: Ensure you have a CSV file named Seed and Symbolic Questions.csv (the version used to create this public instance of the ASyMOB dataset is also uploaded here) in the same directory as the script. This CSV should contain the seed mathematical questions, their maximal symbolic perturbations, and answers as SymPy expressions.

   The expected fields in Seed and Symbolic Questions.csv are:

   • Challenge: The mathematical question in LaTeX format, including assumptions regarding variables or other mathematical details.
   • Answer in LaTeX (optional): The answer to the question, represented as a LaTeX string.
   • Answer in Sympy: The answer to the question, represented as a SymPy expression string.
   • Variation: "Original" or "Symbolic".
   • Source: Identifies the origin of the question.
   • Category: Question type (e.g. Integrals, Limits, etc.).

2. Run the script:

   python ASyMOB_Generation.py
   

3. Output: The script will generate a JSON file named Full_ASyMOB_Dataset.json in the same directory. This file will contain all the original seed and symbolic questions along with their newly generated symbolic, numeric, and equivalence-based variants.

   The fields in Full_ASyMOB_Dataset.json are:

   • Index: Sequential ID.
   • Challenge: The mathematical question in LaTeX format, including assumptions regarding variables or other mathematical details.
   • Answer in Sympy: The answer to the question, represented as a SymPy expression string.
   • Variation: e.g., Equivalence-All-Hard, Numeric-One-3, etc.
   • Source: Same as the seed question from which this variation originated.
   • Category: Same as the seed question from which this variation originated.

Customization

• Seed and Symbolic Questions.csv: Modify this CSV to add new seed questions or adjust existing ones.
• symnoise_char_list, symnoise_sym_list: Adjust the lists of symbolic characters and their SymPy representations if your questions use different symbols for perturbation (ASyMOB uses 'A', 'B', 'F', 'G', 'H' by default).
• equivalent_forms_easy, equivalent_forms_hard: Add or modify the equivalent forms to introduce different types of mathematical equivalences.
• noise_digits and reps_num: In generate_NA2S, you can change noise_digits to control the range of random numbers used for numeric perturbations and reps_num to control the number of repetitions for each item.

Citation

If you use ASyMOB in your research, please cite the paper:

@misc{ASyMOB,
      title={ASyMOB: Algebraic Symbolic Mathematical Operations Benchmark}, 
      author={Michael Shalyt and Rotem Elimelech and Ido Kaminer},
      year={2025},
      eprint={2505.23851},
      archivePrefix={arXiv},
      primaryClass={cs.CL},
      url={https://arxiv.org/abs/2505.23851}, 
}