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We introduce a new class of neural networks designed to be convex functions of their inputs, leveraging the principle that any convex function can be represented as the supremum of the affine functions it dominates. These neural networks,…
We propose semi-random features for nonlinear function approximation. The flexibility of semi-random feature lies between the fully adjustable units in deep learning and the random features used in kernel methods. For one hidden layer…
This paper deals with the approximation of the spectrum of linear and nonautonomous delay differential equations through the reduction of the relevant evolution semigroup from infinite to finite dimension. The focus is placed on classic…
Landmark universal function approximation results for neural networks with trained weights and biases provided the impetus for the ubiquitous use of neural networks as learning models in neuroscience and Artificial Intelligence (AI). Recent…
In this paper, we study the asymptotic behavior of solution to a non-autonomous diffusion equations with delay containing some hereditary characteristics and nonlocal diffusion in time-dependent space $C_{\mathcal{H}_{t}(\Omega)}$. When the…
Highly expressive directed latent variable models, such as sigmoid belief networks, are difficult to train on large datasets because exact inference in them is intractable and none of the approximate inference methods that have been applied…
The framework of this article is cell motility modeling. Approximating cells as rigid spheres we take into account for both non-penetration and adhesions forces. Adhesions are modeled as a memory-like microscopic elastic forces. This leads…
This paper is concerned with convergence estimates for fully discrete tree tensor network approximations of high-dimensional functions from several model classes. For functions having standard or mixed Sobolev regularity, new estimates…
The inclusion of a macroscopic adaptive threshold is studied for the retrieval dynamics of layered feedforward neural network models with synaptic noise. It is shown that if the threshold is chosen appropriately as a function of the…
Delayed neural field models can be viewed as a dynamical system in an appropriate functional analytic setting. On two dimensional rectangular space domains, and for a special class of connectivity and delay functions, we describe the…
Continuous neural field models with inhomogeneous synaptic connectivities are known to support traveling fronts as well as stable bumps of localized activity. We analyze stationary localized structures in a neural field model with periodic…
This paper investigates a discontinuous neural network which is used as a model of the mammalian olfactory system and can more generally be applied to solve non-negative sparse approximation problems. By inherently limiting the systems…
We introduce a geometrically transparent strict saddle property for nonsmooth functions. This property guarantees that simple proximal algorithms on weakly convex problems converge only to local minimizers, when randomly initialized. We…
We present an analytically solvable random graph model in which the connections between the nodes can evolve in time, adiabatically slowly compared to the dynamics of the nodes. We apply the formalism to finite connectivity attractor neural…
Debiased machine learning (DML) offers an attractive way to estimate treatment effects in observational settings, where identification of causal parameters requires a conditional independence or unconfoundedness assumption, since it allows…
The parameter space for any fixed architecture of feedforward ReLU neural networks serves as a proxy during training for the associated class of functions - but how faithful is this representation? It is known that many different parameter…
In this work, we present the first stability results for approximate predictors in multi-input non-linear systems with distinct actuation delays. We show that if the predictor approximation satisfies a uniform (in time) error bound,…
In this work, we establish two global attractivity criteria for a multidimensional discrete-time non-autonomous Hopfield neural network model with infinite delays and delays in the leakage terms. The first criterion, which applies when the…
The aim of this paper is to prove the existence and qualitative property of random attractors for a stochastic nonlocal delayed reaction-diffusion equation (SNDRDE) on a semi-infinite interval with a Dirichlet boundary condition on the…
Reversibility in artificial neural networks allows us to retrieve the input given an output. We present feature alignment, a method for approximating reversibility in arbitrary neural networks. We train a network by minimizing the distance…