Related papers: Polynomial Regression As an Alternative to Neural …

We introduce twin neural network (TNN) regression. This method predicts differences between the target values of two different data points rather than the targets themselves. The solution of a traditional regression problem is then obtained…

Neural fields have emerged as a new paradigm for representing signals, thanks to their ability to do it compactly while being easy to optimize. In most applications, however, neural fields are treated like black boxes, which precludes many…

In recent years, neural networks have demonstrated their remarkable ability to discern intricate patterns and relationships from raw data. However, understanding the inner workings of these black box models remains challenging, yet crucial…

Graph neural networks (GNNs) have been extensively developed for graph representation learning in various application domains. However, similar to all other neural networks models, GNNs suffer from the black-box problem as people cannot…

We investigate the concept of Best Approximation for Feedforward Neural Networks (FNN) and explore their convergence properties through the lens of Random Projection (RPNNs). RPNNs have predetermined and fixed, once and for all, internal…

During the last decade, deep neural networks (DNN) have demonstrated impressive performances solving a wide range of problems in various domains such as medicine, finance, law, etc. Despite their great performances, they have long been…

Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…

Traditional deep neural nets (NNs) have shown the state-of-the-art performance in the task of classification in various applications. However, NNs have not considered any types of uncertainty associated with the class probabilities to…

Neural networks are commonly regarded as black boxes performing incomprehensible functions. For classification problems networks provide maps from high dimensional feature space to K-dimensional image space. Images of training vector are…

Neural networks (NNs) whose subnetworks implement reusable functions are expected to offer numerous advantages, including compositionality through efficient recombination of functional building blocks, interpretability, preventing…

Polynomial functions have plenty of useful analytical properties, but they are rarely used as learning models because their function class is considered to be restricted. This work shows that when trained properly polynomial functions can…

The accurate prediction of biological features from genomic data is paramount for precision medicine and sustainable agriculture. For decades, neural network models have been widely popular in fields like computer vision, astrophysics and…

We investigate a series of learning kernel problems with polynomial combinations of base kernels, which will help us solve regression and classification problems. We also perform some numerical experiments of polynomial kernels with…

In this manuscript, we show that any neural network with any activation function can be represented as a decision tree. The representation is equivalence and not an approximation, thus keeping the accuracy of the neural network exactly as…

Deep neural networks (DNNs) have been shown to outperform traditional machine learning algorithms in a broad variety of application domains due to their effectiveness in modeling complex problems and handling high-dimensional datasets. Many…

Random Neural Networks (RNNs) are a class of Neural Networks (NNs) that can also be seen as a specific type of queuing network. They have been successfully used in several domains during the last 25 years, as queuing networks to analyze the…

Deep Neural Network (DNN)-based physical layer techniques are attracting considerable interest due to their potential to enhance communication systems. However, most studies in the physical layer have tended to focus on the application of…

A method for approximating continuous functions $\mathbb{Z}_{p}^{n}\rightarrow\mathbb{Z}_{p}$ by a linear superposition of continuous functions $\mathbb{Z}_{p}\rightarrow\mathbb{Z}_{p}$ is presented and a polynomial regression model is…

Neural networks (NNs) have been successfully applied to solve a variety of application problems involving classification and function approximation. Although backpropagation NNs generally predict better than decision trees do for pattern…

Nonlinear regression has been extensively employed in many computer vision problems (e.g., crowd counting, age estimation, affective computing). Under the umbrella of deep learning, two common solutions exist i) transforming nonlinear…