Vector Field Based Neural Networks

Abstract

A novel Neural Network architecture is proposed using the mathematically and physically rich idea of vector fields as hidden layers to perform nonlinear transformations in the data. The data points are interpreted as particles moving along a flow defined by the vector field which intuitively represents the desired movement to enable classification. The architecture moves the data points from their original configuration to a new one following the streamlines of the vector field with the objective of achieving a final configuration where classes are separable. An optimization problem is solved through gradient descent to learn this vector field.

On the Usefulness of the Vector Field Singular Points Shapes for Classification

“…Further, the connection between VFs and ML and neural networks (NN) was established by a set of recent papers. Vieira and Paixao [21] interpreted the process of moving data through NN as an implicit VF that moves particles with its trajectories. The authors of [22] visualized differences in data projection from different NN stages and transformed the differences into VF trajectories representing the flow of information.…”