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

School of Computer Science and Engineering, Vellore Institute of Technology, Chennai

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Published online: 29 April 2026

Abstract

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.