A Framework for Vector-Weighted Deep Neural Networks

The vast majority of advances in deep neural network research operate on the basis of a real-valued weight space. Recent work in alternative spaces have challenged and complemented this idea; for instance, the use of complex- or binary-valued weights have yielded promising and fascinating results. We propose a framework for a novel weight space consisting of vector values which we christen VectorNet. We first develop the theoretical foundations of our proposed approach, including formalizing the requisite theory for forward and backpropagating values in a vector-weighted layer. We also introduce the concept of expansion and aggregation functions for conversion between real and vector values. These contributions enable the seamless integration of vector-weighted layers with conventional layers, resulting in network architectures exhibiting height in addition to width and depth, and consequently models which we might be inclined to call tall learning. As a means of evaluating its effect on model performance, we apply our framework on top of three neural network architectural families—the multilayer perceptron (MLP), convolutional neural network (CNN), and directed acyclic graph neural network (DAG-NN)—trained over multiple classic machine learning and image classification benchmarks. We also consider evolutionary algorithms for performing neural architecture search over the new hyperparameters introduced by our framework. Lastly, we solidify the case for the utility of our contributions by implementing our approach on real-world data in the domains of mental illness diagnosis and static malware detection, achieving state-of-the-art results in both. Our implementations are made publicly available to drive further investigation into the exciting potential of VectorNet