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Whether Transformers can learn to apply symbolic rules and generalise toout-of-distribution examples is an open research question. In this paper, wedevise a data generation method for producing intricate mathematicalderivations, and systematically perturb them with respect to syntax, structure,and semantics. Our task-agnostic approach generates equations, annotations, andinter-equation dependencies, employing symbolic algebra for scalable dataproduction and augmentation. We then instantiate a general experimentalframework on next-equation prediction, assessing systematic mathematicalreasoning and generalisation of Transformer encoders on a total of 200Kexamples. The experiments reveal that perturbations heavily affect performanceand can reduce F1 scores of $97\%$ to below $17\%$, suggesting that inferenceis dominated by surface-level patterns unrelated to a deeper understanding ofmathematical operators. These findings underscore the importance of rigorous,large-scale evaluation frameworks for revealing fundamental limitations ofexisting models.

A Symbolic Framework for Systematic Evaluation of Mathematical Reasoning with Transformers