The paper presents SplineNets that reformulate CNNs as neural decision graph using B-splines. It's comprised of four technical contributions, i.e., embedding trick, general formulation for a neural decision graph, a loss function of utilizing and specializing splines and a differentiable quantization method. The idea is novel and sensible. It integrates the classic splines into convolutional neural networks which might be valuable for both of theoretical and practical aspects. However, the paper is difficult to read and follow.

SplineNets are continuous generalizations of neural decision graphs, and they can dramatically reduce runtime complexity and computation costs of CNNs, while maintaining or even increasing accuracy. Functions of SplineNets are both dynamic (i.e., conditioned on the input) and hierarchical (i.e.,conditioned on the computational path). SplineNets employ a unified loss function with a desired level of smoothness over both the network and decision parameters, while allowing for sparse activation of a subset of nodes for individual samples. Instead of sampling from a categorical distribution to pick a branch, samples choose a continuous position to pick a function weight. We further show that by maximizing the mutual information between spline positions and class labels, the network can be optimally utilized and specialized for classification tasks.