As a powerful modelling method, piecewise linear neural networks (PWLNNs) have proven
successful in various fields, most recently in deep learning. To apply PWLNN methods, both …

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

This brief proposes a truncated ℓ 1 distance (TL1) kernel, which results in a classifier that is
nonlinear in the global region but is linear in each subregion. With this kernel, the subregion …

The problem of constructing a canonical representation for an arbitrary continuous
piecewise-linear (PWL) function in any dimension is considered in this paper. We solve the …

Digital architectures for the circuit realization of multivariate piecewise‐linear (PWL)
functions are reviewed and compared. The output of the circuits is a digital word …

Global, explicit representations of nonlinearities are desirable when implementing nonlinear
Wave Digital (WD) structures, as they free us from the burden of managing look-up tables …

The problem of constructing a general continuous piecewise-linear neural network is
considered in this paper. It is shown that every projection domain of an arbitrary continuous …

Tropical Geometry and Mathematical Morphology share the same max-plus and min-plus
semiring arithmetic and matrix algebra. In this chapter we summarize some of their main …

In this paper we propose a digital architecture suited for fast, low-power and small-size
electronic implementation of PieceWise Affine (PWA) functions defined over n-dimensional …

This brief proposes a digital circuit architecture implementing a class of continuous
piecewise-affine (PWA) functions. The work rests on a previous architecture realizing PWA …