  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.
