DDSVM: A Differentiable Framework for Deep Support Vector Machines with Iterative Geometry-Aware Optimization

Modern deep networks optimize features via cross-entropy without explicit margin maximization, while classical Support Vector Machines maximize the margin on a fixed feature space. Hybrid Deep-SVM approaches typically treat the deep feature extractor as a static input to an SVM head, so SVM geometry never flows back to shape representation learning. We propose the **Differentiable Deep Support Vector Machine (DDSVM)**, an iterative framework that alternates between re-fitting a linear SVM on $L_2$-normalized features and updating the backbone to pull each feature along the SVM-defined margin-widening direction, treating the decision boundary as a dynamic teacher for representation learning. Under spherical normalization the resulting feature gradient lies in the tangent space and optimization focuses exclusively on angular separability. DDSVM reduces top-1 error by **5.6--8.3\%** on image classification benchmarks under data scarcity.

Deep learning models often need many labeled images to work well, but in areas such as medical imaging, defect detection, or specialized sensing, labeled data can be limited. With small training sets, standard methods may learn patterns that do not generalize well to new images. This paper introduces DDSVM, a training method that helps a neural network organize images more clearly in its learned feature space. It uses a support vector machine during training as a guide, encouraging images from the same class to move closer together and images from different classes to become easier to separate. On image classification benchmarks with limited data, DDSVM reduces top-1 error by 5.6–8.3% compared with standard training. These results suggest that DDSVM could be useful when collecting more labeled data is costly or unrealistic.