Tropical geometry is a relatively recent field in mathematics and computer science,
combining elements of algebraic geometry and polyhedral geometry. The scalar arithmetic …

Mathematical morphology provides powerful nonlinear operators for a variety of image
processing tasks such as filtering, segmentation, and edge detection. In this paper, we …

Approximation ability is one of the most important topics in the field of neural networks
(NNs). Feedforward NNs, activated by rectified linear units and some of their specific …

We show that a neural network whose output is obtained as the difference of the outputs of
two feedforward networks with exponential activation function in the hidden layer and …

Abstract Deep Neural Networks (DNNs) are generated by sequentially performing linear and
non-linear processes. The combination of linear and non-linear procedures is critical for …

Integrating mathematical morphology operations within deep neural networks has been
subject to increasing attention lately. However, replacing standard convolution layers with …

The integration of mathematical morphology operations within convolutional neural network
architectures has received an increasing attention lately. However, replacing standard …

Empirical mode decomposition (EMD) is a fully data driven method for multiscale
decomposing signals into a set of components known as intrinsic mode functions. EMD is …

In this work, we further the link between neural networks with piecewise linear activations
and tropical algebra. To that end, we introduce the process of Maxpolynomial Division, a …

Morphological neural networks, or layers, can be a powerful tool to boost the progress in
mathematical morphology, either on theoretical aspects such as the representation of …