  Current research in convolutional neural networks (CNN) focuses mainly on
changing the architecture of the networks, optimizing the hyper-parameters and
improving the gradient descent. However, most work use only 3 standard families
of operations inside the CNN, the convolution, the activation function, and the
pooling. In this work, we propose a new family of operations based on the
Green's function of the Laplacian, which allows the network to solve the
Laplacian, to integrate any vector field and to regularize the field by forcing
it to be conservative. Hence, the Green's function (GF) is the first operation
that regularizes the 2D or 3D feature space by forcing it to be conservative
and physically interpretable, instead of regularizing the norm of the weights.
Our results show that such regularization allows the network to learn faster,
to have smoother training curves and to better generalize, without any
additional parameter. The current manuscript presents early results, more work
is required to benchmark the proposed method.
