Related papers: Pad\'e Neurons for Efficient Neural Models

This paper presents an implementation of multilayer feed forward neural networks (NN) to optimize CMOS analog circuits. For modeling and design recently neural network computational modules have got acceptance as an unorthodox and useful…

This article is concerned with the approximation and expressive powers of deep neural networks. This is an active research area currently producing many interesting papers. The results most commonly found in the literature prove that neural…

Graph neural networks (GNNs) are typically applied to static graphs that are assumed to be known upfront. This static input structure is often informed purely by insight of the machine learning practitioner, and might not be optimal for the…

Traditional neural networks (multi-layer perceptrons) have become an important tool in data science due to their success across a wide range of tasks. However, their performance is sometimes unsatisfactory, and they often require a large…

Artificial neural networks which are inspired from the learning mechanism of brain have achieved great successes in many problems, especially those with deep layers. In this paper, we propose a nucleus neural network (NNN) and corresponding…

Physics-Informed Neural Networks (PINNs) have enabled significant improvements in modelling physical processes described by partial differential equations (PDEs). PINNs are based on simple architectures, and learn the behavior of complex…

Convolutional neural network (CNN) is widely used in computer vision applications. In the networks that deal with images, CNNs are the most time-consuming layer of the networks. Usually, the solution to address the computation cost is to…

Recent advances in solving ordinary differential equations (ODEs) with neural networks have been remarkable. Neural networks excel at serving as trial functions and approximating solutions within functional spaces, aided by gradient…

Recurrent neural networks (RNNs) have recently achieved remarkable successes in a number of applications. However, the huge sizes and computational burden of these models make it difficult for their deployment on edge devices. A practically…

The coincidence similarity index, based on a combination of the Jaccard and overlap similarity indices, has noticeable properties in comparing and classifying data, including enhanced selectivity and sensitivity, intrinsic normalization,…

Solving nonlinear partial differential equations (PDEs) with multiple solutions using neural networks has found widespread applications in various fields such as physics, biology, and engineering. However, classical neural network methods…

Standard neural network architectures employ fixed activation functions (ReLU, tanh, sigmoid) that are poorly suited for approximating functions with singular or fractional power behavior, a structure that arises ubiquitously in physics,…

We propose a nonlinear reduced basis method for the efficient approximation of parametrized partial differential equations (PDEs), exploiting kernel proper orthogonal decomposition (KPOD) for the generation of a reduced-order space and…

Topological solitons, which are stable, localized solutions of nonlinear differential equations, are crucial in various fields of physics and mathematics, including particle physics and cosmology. However, solving these solitons presents…

A burgeoning line of research leverages deep neural networks to approximate the solutions to high dimensional PDEs, opening lines of theoretical inquiry focused on explaining how it is that these models appear to evade the curse of…

The Convolutional Neural Networks (CNNs) have been the dominant and effective approach for general computer vision tasks. Recently, Kolmogorov-Arnold neural networks (KANs), based on the Kolmogorov-Arnold representation theorem, have shown…

We study a modular neuron alternative to the McCulloch-Pitts neuron that arises naturally in analog devices in which the neuron inputs are represented as coherent oscillatory wave signals. Although the modular neuron can compute $XOR$ at…

A novel neural network inspired by Cauchy's integral formula, is proposed for function approximation tasks that include time series forecasting, missing data imputation, etc. Hence, the novel neural network is named CauchyNet. By embedding…

Leading experts from both communities have suggested the need to (re)connect research in neuroscience and artificial intelligence (AI) to accelerate the development of next-generation AI innovations. They term this convergence as NeuroAI.…

Deep neural networks (DNNs) have been widely applied to solve real-world regression problems. However, selecting optimal network structures remains a significant challenge. This study addresses this issue by linking neuron selection in DNNs…