Related papers: Power Series Expansion Neural Network
Designing an optimal deep neural network for a given task is important and challenging in many machine learning applications. To address this issue, we introduce a self-adaptive algorithm: the adaptive network enhancement (ANE) method,…
This paper investigates the approximation power of three types of random neural networks: (a) infinite width networks, with weights following an arbitrary distribution; (b) finite width networks obtained by subsampling the preceding…
In this paper, we propose a novel image process scheme called class-based expansion learning for image classification, which aims at improving the supervision-stimulation frequency for the samples of the confusing classes. Class-based…
Power series representations for special functions are computationally satisfactory only in the vicinity of the expansion point. Thus, it is an obvious idea to use instead Pad\'{e} approximants or other rational functions constructed from…
Time series analysis is relevant in various disciplines such as physics, biology, chemistry, and finance. In this paper, we present a novel neural network architecture that integrates elements from ResNet structures, while introducing the…
Artificial Neural Networks (ANN) are already heavily involved in methods and applications for frequent tasks in the field of computational chemistry such as representation of potential energy surfaces (PES) and spectroscopic predictions.…
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…
Partition of unity networks (POU-Nets) have been shown capable of realizing algebraic convergence rates for regression and solution of PDEs, but require empirical tuning of training parameters. We enrich POU-Nets with a Gaussian noise model…
Symbolic regression plays a crucial role in modern scientific research thanks to its capability of discovering concise and interpretable mathematical expressions from data. A key challenge lies in the search for parsimonious and…
We introduce a method for using deep neural networks to amortize the cost of inference in models from the family induced by universal probabilistic programming languages, establishing a framework that combines the strengths of probabilistic…
Computing the Bayesian posterior of a neural network is a challenging task due to the high-dimensionality of the parameter space. Anchored ensembles approximate the posterior by training an ensemble of neural networks on anchored losses…
Deep learning has been widely used for hyperspectral pixel classification due to its ability of generating deep feature representation. However, how to construct an efficient and powerful network suitable for hyperspectral data is still…
Query expansion is a method for alleviating the vocabulary mismatch problem present in information retrieval tasks. Previous works have shown that terms selected for query expansion by traditional methods such as pseudo-relevance feedback…
Despite the growing availability of high-capacity computational platforms, implementation complexity still has been a great concern for the real-world deployment of neural networks. This concern is not exclusively due to the huge costs of…
In this study, we examine the potential of one of the ``superexpressive'' networks in the context of learning neural functions for representing complex signals and performing machine learning downstream tasks. Our focus is on evaluating…
Reaction-diffusion systems represent one of the most fundamental formulations used to describe a wide range of physical, chemical, and biological processes. With the increasing adoption of neural networks, recent research has focused on…
Deep neural networks are an extremely successful and widely used technique for various pattern recognition and machine learning tasks. Due to power and resource constraints, these computationally intensive networks are difficult to…
A three-hidden-layer neural network with super approximation power is introduced. This network is built with the floor function ($\lfloor x\rfloor$), the exponential function ($2^x$), the step function ($1_{x\geq 0}$), or their compositions…
In a previous study [B. Li, S. Tang and H. Yu, Commun. Comput. Phy. 27(2):379-411, 2020], it is shown that deep neural networks built with rectified power units (RePU) as activation functions can give better approximation for sufficient…
Deep neural networks are powerful learning models that achieve state-of-the-art performance on many computer vision, speech, and language processing tasks. In this paper, we study a fundamental question that arises when designing deep…