# Vector Field Based Neural Networks

## TL;DR

This paper introduces a new neural network architecture that uses vector fields as hidden layers, enabling data points to move along flow lines for improved class separation through gradient descent optimization.

## Contribution

It presents a novel neural network design leveraging vector fields for nonlinear data transformation, combining physical intuition with learnable flow-based mappings.

## Key findings

- Effective class separation achieved in experiments
- Gradient descent successfully learns complex vector fields
- Improved classification accuracy over baseline models

## 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 anew 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.