Related papers: Polyhedrons and Perceptrons Are Functionally Equiv…
Deep Neural Networks (DNNs) have become very popular for prediction in many areas. Their strength is in representation with a high number of parameters that are commonly learned via gradient descent or similar optimization methods. However,…
In this paper we first write a proof of the perceptron convergence algorithm for the complex multivalued neural networks (CMVNNs). Our primary goal is to formulate and prove the perceptron convergence algorithm for the bicomplex multivalued…
Multilayer neural networks set the current state of the art for many technical classification problems. But, these networks are still, essentially, black boxes in terms of analyzing them and predicting their performance. Here, we develop a…
Deep learning has received much attention lately due to the impressive empirical performance achieved by training algorithms. Consequently, a need for a better theoretical understanding of these problems has become more evident in recent…
Simple function classes have emerged as toy problems to better understand in-context-learning in transformer-based architectures used for large language models. But previously proposed simple function classes like linear regression or…
Ubiquitous geometric objects can be precisely and efficiently represented as polyhedra. The transformation of a polyhedron into a vector, known as polyhedra representation learning, is crucial for manipulating these shapes with mathematical…
Neural networks based on metric recognition methods have a strictly determined architecture. Number of neurons, connections, as well as weights and thresholds values are calculated analytically, based on the initial conditions of tasks:…
We introduce a unified theoretical framework for the rigorous analysis and systematic construction of deep neural networks (DNNs). This framework addresses a gap in existing theory by explicitly modeling the structure of tensor operations…
Convolutional neural networks are witnessing wide adoption in computer vision systems with numerous applications across a range of visual recognition tasks. Much of this progress is fueled through advances in convolutional neural network…
In this work, we propose a balanced multi-component and multi-layer neural network (MMNN) structure to accurately and efficiently approximate functions with complex features, in terms of both degrees of freedom and computational cost. The…
The normalized radial basis function neural network emerges in the statistical modeling of natural laws that relate components of multivariate data. The modeling is based on the kernel estimator of the joint probability density function…
Hypercomplex neural networks are gaining increasing interest in the deep learning community. The attention directed towards hypercomplex models originates from several aspects, spanning from purely theoretical and mathematical…
In this paper the Mechanical Neural Network(MNN) is introduced, a physical implementation of a multilayer perceptron(MLP) with ReLU activation functions, two input neurons, four hidden neurons and two output neurons. This physical model of…
Pseudo-Hamiltonian neural networks (PHNN) were recently introduced for learning dynamical systems that can be modelled by ordinary differential equations. In this paper, we extend the method to partial differential equations. The resulting…
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…
Feed-forward, fully-connected Artificial Neural Networks (ANNs) or the so-called Multi-Layer Perceptrons (MLPs) are well-known universal approximators. However, their learning performance varies significantly depending on the function or…
Deep Neural Networks (DNNs) are universal function approximators providing state-of- the-art solutions on wide range of applications. Common perceptual tasks such as speech recognition, image classification, and object tracking are now…
Functions are rich in meaning and can be interpreted in a variety of ways. Neural networks were proven to be capable of approximating a large class of functions[1]. In this paper, we propose a new class of neural networks called "Neural…
Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by…
Graph neural networks (GNN) represent an emerging line of deep learning models that operate on graph structures. It is becoming more and more popular due to its high accuracy achieved in many graph-related tasks. However, GNN is not as well…