Related papers: Exponential Synchronization of 2D Cellular Neural …

We discuss synchronization in networks of neuronal oscillators which are interconnected via diffusive coupling, i.e. linearly coupled via gap junctions. In particular, we present sufficient conditions for synchronization in these networks…

We study two-layer neural networks in the mean field limit, where the number of neurons tends to infinity. In this regime, the optimization over the neuron parameters becomes the optimization over the probability measures, and by adding an…

Photonic computing is a computing paradigm which have great potential to overcome the energy bottlenecks of electronic von Neumann architecture. Throughput and power consumption are fundamental limitations of…

Brain-inspired spiking neural networks (SNNs) are recognized as a promising avenue for achieving efficient, low-energy neuromorphic computing. Direct training of SNNs typically relies on surrogate gradient (SG) learning to estimate…

This paper studies the critical behavior of the 3d classical $\mathrm{O}(N)$ model with a boundary. Recently, one of us established that upon treating $N$ as a continuous variable, there exists a critical value $N_c > 2$ such that for $2…

In a previous paper, we have shown that a recurrent neural network (RNN) can be used to detect cellular network radio signal degradations accurately. We unexpectedly found, though, that accuracy gains diminished as we added layers to the…

This paper deals with synchronization of a class of infinite-dimensional systems. The considered network is described by a collection of semilinear Lipschitz boundary-actuated infinite-dimensional dynamics. For undirected connected graphs,…

The nonlinear Shannon capacity limit has been identified as the fundamental barrier to the maximum rate of transmitted information in optical communications. In long-haul high-bandwidth optical networks, this limit is mainly attributed to…

We study the critical features of coupling parameter in the synchronization of neural networks with diluted synapses. Based on simulations, the exponential decay form is observed in the extreme case of global coupling among subsystems and…

We apply the framework of optimal nonlinear control to steer the dynamics of a whole-brain network of FitzHugh-Nagumo oscillators. Its nodes correspond to the cortical areas of an atlas-based segmentation of the human cerebral cortex, and…

Recurrent neural networks (RNNs) are a class of neural networks that have emerged from the paradigm of artificial intelligence and has enabled lots of interesting advances in the field of natural language processing. Interestingly, these…

Convolutional neural networks (CNNs) are commonly used for image classification tasks, raising the challenge of their application on data flows. During their training, adaptation is often performed by tuning the learning rate. Usual…

Large language models (LLMs) are increasingly used as generators in iterative neural architecture search (NAS), yet no formal convergence theory exists for this class of algorithms. We model iterative LLM-NAS as a parametric Cross-Entropy…

We derive the fast convergence rates of a deep neural network (DNN) classifier with the rectified linear unit (ReLU) activation function learned using the hinge loss. We consider three cases for a true model: (1) a smooth decision boundary,…

In the mean field regime, neural networks are appropriately scaled so that as the width tends to infinity, the learning dynamics tends to a nonlinear and nontrivial dynamical limit, known as the mean field limit. This lends a way to study…

This paper studies the problem of real-time fault recovery control for nonlinear control-affine systems subject to actuator loss of effectiveness faults and external disturbances. We derive a two-stage framework that combines causal…

Neural networks (NNs) have emerged as a state-of-the-art method for modeling nonlinear systems in model predictive control (MPC). However, the robustness of NNs, in terms of sensitivity to small input perturbations, remains a critical…

We explore the use of FCNNs (Fully Connected Neural Networks) for designing end-to-end communication systems without taking any inspiration from existing classical communications models or error control coding. This work relies solely on…

Motivated by the gap between theoretical optimal approximation rates of deep neural networks (DNNs) and the accuracy realized in practice, we seek to improve the training of DNNs. The adoption of an adaptive basis viewpoint of DNNs leads to…

Studying physics-informed neural networks (PINNs) for modeling partial differential equations to solve the acoustic wave field has produced promising results for simple geometries in two-dimensional domains. One option is to compute the…