Related papers: Nerve theorems for fixed points of neural networks

Network inference has been extensively studied in several fields, such as systems biology and social sciences. Learning network topology and internal dynamics is essential to understand mechanisms of complex systems. In particular, sparse…

We study how neural networks trained by gradient descent extrapolate, i.e., what they learn outside the support of the training distribution. Previous works report mixed empirical results when extrapolating with neural networks: while…

Network embedding is a very important method for network data. However, most of the algorithms can only deal with static networks. In this paper, we propose an algorithm Recurrent Neural Network Embedding (RNNE) to deal with dynamic…

Various Graph Neural Networks (GNNs) have been successful in analyzing data in non-Euclidean spaces, however, they have limitations such as oversmoothing, i.e., information becomes excessively averaged as the number of hidden layers…

Graph representation learning is a fundamental task in various applications that strives to learn low-dimensional embeddings for nodes that can preserve graph topology information. However, many existing methods focus on static graphs while…

A recent publication provides the network graph for a neocortical microcircuit comprising 8 million connections between 31,000 neurons (H. Markram, et al., Reconstruction and simulation of neocortical microcircuitry, Cell, 163 (2015) no. 2,…

We introduce a family of multilayer graph kernels and establish new links between graph convolutional neural networks and kernel methods. Our approach generalizes convolutional kernel networks to graph-structured data, by representing…

Graph classification is an important learning task for graph-structured data. Graph neural networks (GNNs) have recently gained growing attention in graph learning and have shown significant improvements in many important graph problems.…

Deep Learning methods, specifically convolutional neural networks (CNNs), have seen a lot of success in the domain of image-based data, where the data offers a clearly structured topology in the regular lattice of pixels. This…

Deep neural network architectures often consist of repetitive structural elements. We introduce an approach that reveals these patterns and can be broadly applied to the study of deep learning. Similarly to how a power strip helps untangle…

Recently, graph-based models designed for downstream tasks have significantly advanced research on graph neural networks (GNNs). GNN baselines based on neural message-passing mechanisms such as GCN and GAT perform worse as the network…

Mathematical modeling has broad applications in neuroscience whether modeling the dynamics of a single synapse or an entire network of neurons. In Part I, we model vesicle replenishment and release at the photoreceptor synapse to better…

At the intersection of computation and cognitive science, graph theory is utilized as a formalized description of complex relationships and structures. Traditional graph models are often static, lacking dynamic and autonomous behavioral…

Convolutional neural networks (CNN's) are powerful and widely used tools. However, their interpretability is far from ideal. One such shortcoming is the difficulty of deducing a network's ability to generalize to unseen data. We use…

The dominant paradigm for learning on graph-structured data is message passing. Despite being a strong inductive bias, the local message passing mechanism suffers from pathological issues such as over-smoothing, over-squashing, and limited…

Graph neural networks (GNNs) are powerful graph-based deep-learning models that have gained significant attention and demonstrated remarkable performance in various domains, including natural language processing, drug discovery, and…

Convolutional neural networks typically consist of many convolutional layers followed by one or more fully connected layers. While convolutional layers map between high-order activation tensors, the fully connected layers operate on…

Traditional convolutional neural networks are limited to handling Euclidean space data, overlooking the vast realm of real-life scenarios represented as graph data, including transportation networks, social networks, and reference networks.…

Networks are fundamental to the study of complex systems, ranging from social contacts, message transactions, to biological regulations and economical networks. In many realistic applications, these networks may vary over time. Modeling and…

Graph convolutional neural networks (GCNNs) are nonlinear processing tools to learn representations from network data. A key property of GCNNs is their stability to graph perturbations. Current analysis considers deterministic perturbations…