VC dimension of Graph Neural Networks with Pfaffian activation functions.

Graph Neural Networks (GNNs) have emerged in recent years as a powerful tool to learn tasks across a wide range of graph domains in a data-driven fashion. Based on a message passing mechanism, GNNs have gained increasing popularity due to their intuitive formulation, closely linked to the Weisfeiler-Lehman (WL) test for graph isomorphism, to which they were demonstrated to be equivalent (Morris et al., 2019 and Xu et al.

A topological description of loss surfaces based on Betti Numbers.

In the context of deep learning models, attention has recently been paid to studying the surface of the loss function in order to better understand training with methods based on gradient descent. This search for an appropriate description, both analytical and topological, has led to numerous efforts in identifying spurious minima and characterize gradient dynamics. Our work aims to contribute to this field by providing a topological measure for evaluating loss complexity in the case of multilayer neural networks.

Composite Graph Neural Networks for Molecular Property Prediction.

Graph Neural Networks have proven to be very valuable models for the solution of a wide variety of problems on molecular graphs, as well as in many other research fields involving graph-structured data. Molecules are heterogeneous graphs composed of atoms of different species. Composite graph neural networks process heterogeneous graphs with multiple-state-updating networks, each one dedicated to a particular node type.

Weisfeiler-Lehman goes dynamic: An analysis of the expressive power of Graph Neural Networks for attributed and dynamic graphs.

Graph Neural Networks (GNNs) are a large class of relational models for graph processing. Recent theoretical studies on the expressive power of GNNs have focused on two issues. On the one hand, it has been proven that GNNs are as powerful as the Weisfeiler-Lehman test (1-WL) in their ability to distinguish graphs.

Modular Multi-Source Prediction of Drug Side-Effects With DruGNN.

Drug Side-Effects (DSEs) have a high impact on public health, care system costs, and drug discovery processes. Predicting the probability of side-effects, before their occurrence, is fundamental to reduce this impact, in particular on drug discovery. Candidate molecules could be screened before undergoing clinical trials, reducing the costs in time, money, and health of the participants.

On Inductive-Transductive Learning With Graph Neural Networks.

Many real-world domains involve information naturally represented by graphs, where nodes denote basic patterns while edges stand for relationships among them. The graph neural network (GNN) is a machine learning model capable of directly managing graph-structured data. In the original framework, GNNs are inductively trained, adapting their parameters based on a supervised learning environment.

Multi-Modal Siamese Network for Diagnostically Similar Lesion Retrieval in Prostate MRI.

Multi-parametric prostate MRI (mpMRI) is a powerful tool to diagnose prostate cancer, though difficult to interpret even for experienced radiologists. A common radiological procedure is to compare a magnetic resonance image with similarly diagnosed cases. To assist the radiological image interpretation process, computerized Content-Based Image Retrieval systems (CBIRs) can therefore be employed to improve the reporting workflow and increase its accuracy.

Image generation by GAN and style transfer for agar plate image segmentation.

Background And Objectives: Deep learning models and specifically Convolutional Neural Networks (CNNs) are becoming the leading approach in many computer vision tasks, including medical image analysis. Nevertheless, the CNN training usually requires large sets of supervised data, which are often difficult and expensive to obtain in the medical field. To address the lack of annotated images, image generation is a promising method, which is becoming increasingly popular in the computer vision community.

The Vapnik-Chervonenkis dimension of graph and recursive neural networks.

The Vapnik-Chervonenkis dimension (VC-dim) characterizes the sample learning complexity of a classification model and it is often used as an indicator for the generalization capability of a learning method. The VC-dim has been studied on common feed-forward neural networks, but it has yet to be studied on Graph Neural Networks (GNNs) and Recursive Neural Networks (RecNNs). This paper provides upper bounds on the order of growth of the VC-dim of GNNs and RecNNs.

On the complexity of neural network classifiers: a comparison between shallow and deep architectures.

Recently, researchers in the artificial neural network field have focused their attention on connectionist models composed by several hidden layers. In fact, experimental results and heuristic considerations suggest that deep architectures are more suitable than shallow ones for modern applications, facing very complex problems, e.g.

Solving graph data issues using a layered architecture approach with applications to web spam detection.

This paper proposes the combination of two state-of-the-art algorithms for processing graph input data, viz., the probabilistic mapping graph self organizing map, an unsupervised learning approach, and the graph neural network, a supervised learning approach. We organize these two algorithms in a cascade architecture containing a probabilistic mapping graph self organizing map, and a graph neural network.

SortNet: learning to rank by a neural preference function.

Relevance ranking consists in sorting a set of objects with respect to a given criterion. However, in personalized retrieval systems, the relevance criteria may usually vary among different users and may not be predefined. In this case, ranking algorithms that adapt their behavior from users' feedbacks must be devised.

Computational capabilities of graph neural networks.

In this paper, we will consider the approximation properties of a recently introduced neural network model called graph neural network (GNN), which can be used to process-structured data inputs, e.g., acyclic graphs, cyclic graphs, and directed or undirected graphs.

The graph neural network model.

Many underlying relationships among data in several areas of science and engineering, e.g., computer vision, molecular chemistry, molecular biology, pattern recognition, and data mining, can be represented in terms of graphs.

Recursive processing of cyclic graphs.

Recursive neural networks are a powerful tool for processing structured data. According to the recursive learning paradigm, the input information consists of directed positional acyclic graphs (DPAGs). In fact, recursive networks are fed following the partial order defined by the links of the graph.

Universal Approximation Using Feedforward Neural Networks: A Survey of Some Existing Methods, and Some New Results.

In this paper, we present a review of some recent works on approximation by feedforward neural networks. A particular emphasis is placed on the computational aspects of the problem, i.e.