Related papers: Geographical Coarsegraining of Complex Networks

Diffusion over networks has recently been used to define spatiotemporal scales and extend Kadanoff block spins of Euclidean space to supernodes of networks in the Laplacian renormalization group (LRG). Yet, its ad hoc coarse-graining…

Problems in scientific computing, such as distributing large sparse matrix operations, have analogous formulations as hypergraph partitioning problems. A hypergraph is a generalization of a traditional graph wherein "hyperedges" may connect…

We present a rectangle-based segmentation algorithm that sets up a graph and performs a graph cut to separate an object from the background. However, graph-based algorithms distribute the graph's nodes uniformly and equidistantly on the…

This paper provides a least squares formulation for the training of a 2-layer convolutional neural network using quadratic activation functions, a 2-norm loss function, and no regularization term. Using this method, an analytic expression…

Network pruning is widely used to lighten and accelerate neural network models. Structured network pruning discards the whole neuron or filter, leading to accuracy loss. In this work, we propose a novel concept of neuron merging applicable…

Graph-theoretical analyses of complex brain networks is a rapidly evolving field with a strong impact for neuroscientific and related clinical research. Due to a number of confounding variables, however, a reliable and meaningful…

We present a new strategy for contracting tensor networks in arbitrary geometries. This method is designed to follow as strictly as possible the renormalization group philosophy, by first contracting tensors in an exact way and, then,…

We propose a renormalization group treatment of stochastically growing networks. As an example, we study percolation on growing scale-free networks in the framework of a real-space renormalization group approach. As a result, we find that…

We revisit the idea of brain damage, i.e. the pruning of the coefficients of a neural network, and suggest how brain damage can be modified and used to speedup convolutional layers. The approach uses the fact that many efficient…

A complex network is a condensed representation of the relational topological framework of a complex system. A main reason for the existence of such networks is the transmission of items through the entities of these complex systems. Here,…

Graph Convolutional Networks (GCNs) are extensively utilized for deep learning on graphs. The large data sizes of graphs and their vertex features make scalable training algorithms and distributed memory systems necessary. Since the…

Graph Neural Networks (GNNs) have demonstrated significant achievements in processing graph data, yet scalability remains a substantial challenge. To address this, numerous graph coarsening methods have been developed. However, most…

In the wood industry, logs are commonly quality screened by discrete X-ray scans on a moving conveyor belt from a few source positions. Typically, the measurements are obtained in a single two-dimensional (2D) plane (a "slice") by a…

Due to the significant computational challenge of training large-scale graph neural networks (GNNs), various sparse learning techniques have been exploited to reduce memory and storage costs. Examples include \textit{graph sparsification}…

Structured pruning compresses neural networks by reducing channels (filters) for fast inference and low footprint at run-time. To restore accuracy after pruning, fine-tuning is usually applied to pruned networks. However, too few remaining…

We use the k-core decomposition to visualize large scale complex networks in two dimensions. This decomposition, based on a recursive pruning of the least connected vertices, allows to disentangle the hierarchical structure of networks by…

Graph neural networks (GNNs) are known to operate with high accuracy on learning from graph-structured data, but they suffer from high computational and resource costs. Neural network compression methods are used to reduce the model size…

Recent research on pattern discovery has progressed from mining frequent patterns and sequences to mining structured patterns, such as trees and graphs. Graphs as general data structure can model complex relations among data with wide…

Graph coarsening is a technique for solving large-scale graph problems by working on a smaller version of the original graph, and possibly interpolating the results back to the original graph. It has a long history in scientific computing…

In this paper we propose a deep learning approach for segmenting sub-cortical structures of the human brain in Magnetic Resonance (MR) image data. We draw inspiration from a state-of-the-art Fully-Convolutional Neural Network (F-CNN)…