SymbAlign: A Hybrid Symbolic–Neural Alignment Framework for Automated Mathematical Solution Scoring

Automated scoring of mathematical solutions is challenging due to the diversity of solution strategies and the need to assess both correctness and reasoning. We present SymbAlign++, a hybrid framework that combines symbolic computation and neural semantic similarity for stepwise evaluation of solutions. Symbolic similarity is computed using algebraic equivalence metrics, while neural similarity is captured through pre-trained language models. A per-category adaptive weighting mechanism (α) learns the optimal balance between symbolic and neural signals. Experiments were conducted on multiple categories from the Hendrycks MATH dataset, and the proposed SymbAlign++ achieves superior performance compared to symbolic-only and neural-only baselines. Performance was evaluated using various metrics, including R², Quadratic weighted kappa (QWK), MSE and correlation measures. The framework provides a robust, interpretable, and flexible approach for automated mathematical solution scoring supporting both procedural and semantic assessment.