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.