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

Abstract

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.