Improved bounds on neural complexity for representing piecewise linear functions
A deep neural network using rectified linear units represents a continuous piecewise linear
(CPWL) function and vice versa. Recent results in the literature estimated that the number of …
(CPWL) function and vice versa. Recent results in the literature estimated that the number of …
Approximation of Lipschitz functions using deep spline neural networks
Although Lipschitz-constrained neural networks have many applications in machine
learning, the design and training of expressive Lipschitz-constrained networks is very …
learning, the design and training of expressive Lipschitz-constrained networks is very …
[HTML][HTML] On the number of regions of piecewise linear neural networks
Many feedforward neural networks (NNs) generate continuous and piecewise-linear
(CPWL) mappings. Specifically, they partition the input domain into regions on which the …
(CPWL) mappings. Specifically, they partition the input domain into regions on which the …
Region configurations for realizability of lattice piecewise-linear models
JM Tarela, MV Martinez - Mathematical and Computer Modelling, 1999 - Elsevier
Continuous Piecewise-Linear (PWL) functions can be represented by a scheme that selects
adequately the linear components of the function without considering explicitly the …
adequately the linear components of the function without considering explicitly the …
Analytical expression of explicit MPC solution via lattice piecewise-affine function
C Wen, X Ma, BE Ydstie - Automatica, 2009 - Elsevier
An analytical expression of the explicit solution to linear model predictive control (MPC) is
proposed by the introduction of a lattice piecewise-affine (PWA) function. A systematic …
proposed by the introduction of a lattice piecewise-affine (PWA) function. A systematic …
Mathematical theory of deep learning
P Petersen, J Zech - arXiv preprint arXiv:2407.18384, 2024 - arxiv.org
This book provides an introduction to the mathematical analysis of deep learning. It covers
fundamental results in approximation theory, optimization theory, and statistical learning …
fundamental results in approximation theory, optimization theory, and statistical learning …
Universal lipschitz approximation in bounded depth neural networks
Adversarial attacks against machine learning models are a rather hefty obstacle to our
increasing reliance on these models. Due to this, provably robust (certified) machine …
increasing reliance on these models. Due to this, provably robust (certified) machine …
Adaptive hinging hyperplanes and its applications in dynamic system identification
The model of adaptive hinging hyperplanes (AHH) is proposed in this paper. It is based on
multivariate adaptive regression splines (MARS) and generalized hinging hyperplanes …
multivariate adaptive regression splines (MARS) and generalized hinging hyperplanes …
General constructive representations for continuous piecewise-linear functions
S Wang - IEEE Transactions on Circuits and Systems I: Regular …, 2004 - ieeexplore.ieee.org
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 …
piecewise-linear (PWL) function in any dimension is considered in this paper. We solve the …
Advances in the training, pruning and enforcement of shape constraints of morphological neural networks using tropical algebra
N Dimitriadis, P Maragos - arXiv preprint arXiv:2011.07643, 2020 - arxiv.org
In this paper we study an emerging class of neural networks based on the morphological
operators of dilation and erosion. We explore these networks mathematically from a tropical …
operators of dilation and erosion. We explore these networks mathematically from a tropical …