相关论文: CauchyNet: Compact and Data-Efficient Learning usi…

We have developed a novel activation function, named the Cauchy Activation Function. This function is derived from the Cauchy Integral Theorem in complex analysis and is specifically tailored for problems requiring high precision. This…

XNet is a single-layer neural network architecture that leverages Cauchy integral-based activation functions for high-order function approximation. Through theoretical analysis, we show that the Cauchy activation functions used in XNet can…

We propose compleX-PINN, a novel physics-informed neural network (PINN) architecture incorporating a learnable activation function inspired by the Cauchy integral theorem. By optimizing the activation parameters, compleX-PINN achieves high…

In the fields of computational mathematics and artificial intelligence, the need for precise data modeling is crucial, especially for predictive machine learning tasks. This paper explores further XNet, a novel algorithm that employs the…

A novel artificial neural network method is proposed for solving Cauchy inverse problems. It allows multiple hidden layers with arbitrary width and depth, which theoretically yields better approximations to the inverse problems. In this…

Saliency computation models aim to imitate the attention mechanism in the human visual system. The application of deep neural networks for saliency prediction has led to a drastic improvement over the last few years. However, deep models…

In recent years there has been a considerable amount of research on local post hoc explanations for neural networks. However, work on building interpretable neural architectures has been relatively sparse. In this paper, we present a novel…

We define a neural network in infinite dimensional spaces for which we can show the universal approximation property. Indeed, we derive approximation results for continuous functions from a Fr\'echet space $\X$ into a Banach space $\Y$. The…

This paper presents a novel framework of neural networks for isotropic hyperelasticity that enforces necessary physical and mathematical constraints while simultaneously satisfying the universal approximation theorem. The two key…

One of the reasons why many neural networks are capable of replicating complicated tasks or functions is their universal property. Though the past few decades have seen tremendous advances in theories of neural networks, a single…

In comparison to classical shallow representation learning techniques, deep neural networks have achieved superior performance in nearly every application benchmark. But despite their clear empirical advantages, it is still not well…

Deep convolutional neural networks, assisted by architectural design strategies, make extensive use of data augmentation techniques and layers with a high number of feature maps to embed object transformations. That is highly inefficient…

Modern deep neural networks are powerful and widely applicable models that extract task-relevant information through multi-level abstraction. Their cross-domain success, however, is often achieved at the expense of computational cost, high…

Neural network based approximate computing is a universal architecture promising to gain tremendous energy-efficiency for many error resilient applications. To guarantee the approximation quality, existing works deploy two neural networks…

We present a new approach and a novel architecture, termed WSNet, for learning compact and efficient deep neural networks. Existing approaches conventionally learn full model parameters independently and then compress them via ad hoc…

A Capsule Network (CapsNet) is a relatively new classifier and one of the possible successors of Convolutional Neural Networks (CNNs). CapsNet maintains the spatial hierarchies between the features and outperforms CNNs at classifying images…

We generalize the classical universal approximation theorem for neural networks to the case of complex-valued neural networks. Precisely, we consider feedforward networks with a complex activation function $\sigma : \mathbb{C} \to…

Covariance estimation is ubiquitous in functional data analysis. Yet, the case of functional observations over multidimensional domains introduces computational and statistical challenges, rendering the standard methods effectively…

Complex-valued neural networks have attracted increasing attention in recent years, while it remains open on the advantages of complex-valued neural networks in comparison with real-valued networks. This work takes one step on this…

Convolutional Neural Network (CNN) based Deep Learning (DL) has achieved great progress in many real-life applications. Meanwhile, due to the complex model structures against strict latency and memory restriction, the implementation of CNN…