Affine Spline

Affine splines, continuous piecewise linear functions, offer a powerful framework for understanding and analyzing deep neural networks (DNNs). Current research focuses on efficiently characterizing the complex partitioning of input space induced by DNNs, which are essentially represented as high-dimensional affine spline mappings, developing algorithms for exact enumeration of these regions, and improving approximation techniques for transforming DNNs into this spline representation. This approach bridges the gap between DNNs and approximation theory, facilitating analysis of network behavior, visualization of feature maps, and potentially leading to improved DNN design and optimization.