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We consider the design of fast and reliable neural network (NN)-based approximations of traditional stabilizing controllers for linear systems with polytopic uncertainty, including control laws with variable structure and those based on a…

Despite their empirical success, neural networks remain vulnerable to small, adversarial perturbations. A longstanding hypothesis suggests that flat minima, regions of low curvature in the loss landscape, offer increased robustness. While…

Solitons are typically stable objects in 1D models, but their straightforward extensions to 2D and 3D settings tend to be unstable. In particular, the ubiquitous nonlinear Schroedinger (NLS) equation with the cubic self-focusing, creates…

We consider the Shallow-Light Steiner Network problem from a fixed-parameter perspective. Given a graph $G$, a distance bound $L$, and $p$ pairs of vertices $(s_1,t_1),\cdots,(s_p,t_p)$, the objective is to find a minimum-cost subgraph $G'$…

Consider the continuum of points along the edges of a network, i.e., a connected, undirected graph with positive edge weights. We measure the distance between these points in terms of the weighted shortest path distance, called the network…

It turned out that the set of the fixed points is not necessarily the same as the set of the local minima of the energy functional. It depends on the diagonal elements of the connection matrix. The simple method which allows to cut off…

Implicit-depth neural networks have grown as powerful alternatives to traditional networks in various applications in recent years. However, these models often lack guarantees of existence and uniqueness, raising stability, performance, and…

In this article we present new results on neural networks with linear threshold activation functions. We precisely characterize the class of functions that are representable by such neural networks and show that 2 hidden layers are…

While the optimization problem behind deep neural networks is highly non-convex, it is frequently observed in practice that training deep networks seems possible without getting stuck in suboptimal points. It has been argued that this is…

We study the type of solutions to which stochastic gradient descent converges when used to train a single hidden-layer multivariate ReLU network with the quadratic loss. Our results are based on a dynamical stability analysis. In the…

Spiking neural networks (SNNs) are a promising paradigm for energy-efficient computation, yet their theoretical foundations-especially regarding stability and robustness-remain limited compared to artificial neural networks. In this work,…

We introduce the concept of non-uniform input-to-state stability for networks. It combines the uniform global stability with the uniform attractivity of any subnetwork, while it allows for non-uniform convergence of all components. For an…

A novel convolution neural network model, abbreviated NL-CNN is proposed, where nonlinear convolution is emulated in a cascade of convolution + nonlinearity layers. The code for its implementation and some trained models are made publicly…

Feedforward neural networks have wide applicability in various disciplines of science due to their universal approximation property. Some authors have shown that single hidden layer feedforward neural networks (SLFNs) with fixed weights…

Linear network coding transmits data through networks by letting the intermediate nodes combine the messages they receive and forward the combinations towards their destinations. The solvability problem asks whether the demands of all the…

We construct a minimum tree for some boundary symmetric tetrahedra R^3, which has two nodes (interior points) with equal weights (positive numbers) having the property that the common perpendicular of some two opposite edges passes through…

We present a constructive proof of Brouwer's fixed point theorem for uniformly continuous and sequentially locally non-constant functions based on the existence of approximate fixed points. And we will show that Brouwer's fixed point…

We analyze the stability of standing pulse solutions of a neural network integro-differential equation. The network consists of a coarse-grained layer of neurons synaptically connected by lateral inhibition with a non-saturating nonlinear…

Training a large multilayer neural network can present many difficulties due to the large number of useless stationary points. These points usually attract the minimization algorithm used during the training phase, which therefore results…

The information that a pattern of firing in the output layer of a feedforward network of threshold-linear neurons conveys about the network's inputs is considered. A replica-symmetric solution is found to be stable for all but small amounts…