Cost-sensitive Structural Loss for Handwritten Mathematical Symbol Classification

This research demonstrates that standard uniform loss functions, such as Categorical Cross-Entropy, are insufficient for the high-stakes domain of Handwritten Mathematical Expression Recognition (HMER). While traditional Convolutional Neural Networks (CNNs) achieve high global accuracy, they remain unaware of the varying semantic costs associated with misclassifications. By introducing a Weighted Structural Loss framework, the network was successfully guided to prioritize the disambiguation of foundational mathematical operators over digits. Experimental results on a 15-class subset of the HASYv2 dataset confirm that: ·        Increasing the penalty weight to α = 3 effectively eliminates Semantic Disasters, ·        achieving 100% operator recognition accuracy. ·        The model maintains stable performance for digit classes, proving that semantic ·        prioritization does not inherently degrade general classification capabilities. ·        While rotation-based data augmentation introduced training instability, the weighted loss alone provided a robust and stable learning trajectory. In summary, this work demonstrates that incorporating semantic importance into loss function design significantly enhances the reliability of educational and automated evaluation tools, moving the field toward more context-aware artificial intelligence systems.  

[1] Y. Lecun, L. Bottou, Y. Bengio, and P. Haffner, “Gradient-based learning applied to document recognition,” Proceedings of the IEEE, vol. 86, no. 11, pp. 2278–2324, 1998.   [2] M. Thoma, “The hasyv2 dataset,” 2017.   [3] X. Li and D. Zhu, “Crcen: A generalized cost-sensitive neural network approach for imbalanced classification,” 2020.   [4] T.-Y. Lin, P. Goyal, R. Girshick, K. He, and P. Doll´ar, “Focal loss for dense object detection,” 2018.   [5] Y. B. Kalpana and S. Benita P, “Handwritten mathematical expression recognition using deep learning techniques,” Journal of Neonatal Surgery, vol. 14, no. 32S, pp. 516–523, 2025.