Results 31 to 40 of about 102 (86)

Instability in deep learning – when algorithms cannot compute uncertainty quantifications for neural networks

European Journal of Applied Mathematics
In deep learning, interval neural networks are used to quantify the uncertainty of a pre-trained neural network. Suppose we are given a computational problem $P$ and a pre-trained neural network $\Phi _P$ that aims to solve $P$ .
Luca Eva Gazdag, Vegard Antun, Anders C. Hansen   +2 more
doaj   +1 more source

An MBO method for modularity optimisation based on total variation and signless total variation

European Journal of Applied Mathematics
In network science, one of the significant and challenging subjects is the detection of communities. Modularity [1] is a measure of community structure that compares connectivity in the network with the expected connectivity in a graph sampled from a ...
Zijun Li, Yves van Gennip, Volker John
doaj   +1 more source

A smoothing-type algorithm for solving inequalities under the order induced by a symmetric cone

Journal of Inequalities and Applications, 2011
In this article, we consider the numerical method for solving the system of inequalities under the order induced by a symmetric cone with the function involved being monotone. Based on a perturbed smoothing function, the underlying system of inequalities
Zhang Ying, Lu Nan
doaj  

Consensus-based optimisation with truncated noise

European Journal of Applied Mathematics
Consensus-based optimisation (CBO) is a versatile multi-particle metaheuristic optimisation method suitable for performing non-convex and non-smooth global optimisations in high dimensions.
Massimo Fornasier, Peter Richtárik, Konstantin Riedl, Lukang Sun   +3 more
doaj   +1 more source

The mathematics of adversarial attacks in AI – why deep learning is unstable despite the existence of stable neural networks

European Journal of Applied Mathematics
The unprecedented success of deep learning (DL) makes it unchallenged when it comes to classification problems. However, it is well established that the current DL methodology produces universally unstable neural networks (NNs).
Alexander Bastounis, Anders Hansen, Verner Vlačić   +2 more
doaj   +1 more source

Optimization applications of Goldbach's conjecture. [PDF]

Heliyon, 2023
Lin BMT, Lin SM, Shyu SJ.
europepmc   +1 more source

Enforcing Dirichlet boundary conditions in physics-informed neural networks and variational physics-informed neural networks. [PDF]

Heliyon, 2023
Berrone S, Canuto C, Pintore M, Sukumar N.   +3 more
europepmc   +1 more source

A Simplified Convex Optimization Model for Image Restoration with Multiplicative Noise. [PDF]

J Imaging, 2023
Che H, Tang Y.
europepmc   +1 more source

A fast continuous time approach with time scaling for nonsmooth convex optimization. [PDF]

Adv Contin Discret Model, 2022
Boţ RI, Karapetyants MA.
europepmc   +1 more source

Time Rescaling of a Primal-Dual Dynamical System with Asymptotically Vanishing Damping. [PDF]

Appl Math Optim, 2023
Hulett DA, Nguyen DK.
europepmc   +1 more source