Related papers: Semialgebraic Neural Networks: From roots to repre…

Subgraph-based graph representation learning (SGRL) has been recently proposed to deal with some fundamental challenges encountered by canonical graph neural networks (GNNs), and has demonstrated advantages in many important data science…

This paper presents a transformative framework for artificial neural networks over graded vector spaces, tailored to model hierarchical and structured data in fields like algebraic geometry and physics. By exploiting the algebraic…

The classical development of neural networks has been primarily for mappings between a finite-dimensional Euclidean space and a set of classes, or between two finite-dimensional Euclidean spaces. The purpose of this work is to generalize…

Let X be an affine real algebraic set . We investigate on the theory of algebraically constructible functions on X and the description of the semi-algebraic subsets of X when we replace the polynomial functions on X by some rational…

We present a simple neural network model which combines a locally-connected feedforward structure, as is traditionally used to model inter-neuron connectivity, with a layer of undifferentiated connections which model the diffuse projections…

The era of data deluge has sparked the interest in graph-based learning methods in a number of disciplines such as sociology, biology, neuroscience, or engineering. In this paper, we introduce a graph recurrent neural network (GRNN) for…

Solving nonlinear systems is an important problem. Numerical continuation methods efficiently solve certain nonlinear systems. The Asymptotic Numerical Method (ANM) is a powerful continuation method that usually converges faster than…

Graph Representation Learning aims to create effective embeddings for nodes and edges that encapsulate their features and relationships. Graph Neural Networks (GNNs) leverage neural networks to model complex graph structures. Recently, the…

Recent years have witnessed the popularity and success of graph neural networks (GNN) in various scenarios. To obtain data-specific GNN architectures, researchers turn to neural architecture search (NAS), which has made impressive success…

Supervised deep learning algorithms have enabled significant performance gains in medical image classification tasks. But these methods rely on large labeled datasets that require resource-intensive expert annotation. Semi-supervised…

We show that every finite semilattice can be represented as an atomized semilattice, an algebraic structure with additional elements (atoms) that extend the semilattice's partial order. Each atom maps to one subdirectly irreducible…

Discovering hidden partial differential equations (PDEs) and operators from data is an important topic at the frontier between machine learning and numerical analysis. This doctoral thesis introduces theoretical results and deep learning…

It is hard to directly implement Graph Neural Networks (GNNs) on large scaled graphs. Besides of existed neighbor sampling techniques, scalable methods decoupling graph convolutions and other learnable transformations into preprocessing and…

Deep learning's success has been widely recognized in a variety of machine learning tasks, including image classification, audio recognition, and natural language processing. As an extension of deep learning beyond these domains, graph…

All-optical neural networks (AONNs) have emerged as a promising paradigm for ultrafast and energy-efficient computation. These networks typically consist of multiple serially connected layers between input and output layers--a configuration…

The development of Kolmogorov-Arnold networks (KANs) marks a significant shift from traditional multi-layer perceptrons in deep learning. Initially, KANs employed B-spline curves as their primary basis function, but their inherent…

In this paper we introduce a novel Salience Affected Artificial Neural Network (SANN) that models the way neuromodulators such as dopamine and noradrenaline affect neural dynamics in the human brain by being distributed diffusely through…

Semialgebraic graphs are graphs whose vertices are points in $\mathbb{R}^d$, and adjacency between two vertices is determined by the truth value of a semialgebraic predicate of constant complexity. We show how to harness polynomial…

Computing latent representations for graph-structured data is an ubiquitous learning task in many industrial and academic applications ranging from molecule synthetization to social network analysis and recommender systems. Knowledge graphs…

Deep learning usually requires large amounts of labeled training data, but annotating data is costly and tedious. The framework of semi-supervised learning provides the means to use both labeled data and arbitrary amounts of unlabeled data…