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Found 20 papers, 9 papers with code
Subhomogeneous Deep Equilibrium Models
Implicit-depth neural networks have grown as powerful alternatives to traditional networks in various applications in recent years.
Neural Rank Collapse: Weight Decay and Small Within-Class Variability Yield Low-Rank Bias
Recent work in deep learning has shown strong empirical and theoretical evidence of an implicit low-rank bias: weight matrices in deep networks tend to be approximately low-rank and removing relatively small singular values during training or from available trained models may significantly reduce model size while maintaining or even improving model performance.
Learning the effective order of a hypergraph dynamical system
Dynamical systems on hypergraphs can display a rich set of behaviours not observable for systems with pairwise interactions.
Learning the Right Layers: a Data-Driven Layer-Aggregation Strategy for Semi-Supervised Learning on Multilayer Graphs
Clustering (or community detection) on multilayer graphs poses several additional complications with respect to standard graphs as different layers may be characterized by different structures and types of information.
Rank-adaptive spectral pruning of convolutional layers during training
The computing cost and memory demand of deep learning pipelines have grown fast in recent years and thus a variety of pruning techniques have been developed to reduce model parameters.
Laplacian-based Semi-Supervised Learning in Multilayer Hypergraphs by Coordinate Descent
Graph Semi-Supervised learning is an important data analysis tool, where given a graph and a set of labeled nodes, the aim is to infer the labels to the remaining unlabeled nodes.
Low-rank lottery tickets: finding efficient low-rank neural networks via matrix differential equations
The main idea is to restrict the weight matrices to a low-rank manifold and to update the low-rank factors rather than the full matrix during training.
A nonlinear diffusion method for semi-supervised learning on hypergraphs
Hypergraphs are a common model for multiway relationships in data, and hypergraph semi-supervised learning is the problem of assigning labels to all nodes in a hypergraph, given labels on just a few nodes.
Node and Edge Nonlinear Eigenvector Centrality for Hypergraphs
Network scientists have shown that there is great value in studying pairwise interactions between components in a system.
Social and Information Networks Numerical Analysis Numerical Analysis Data Analysis, Statistics and Probability
Nonlinear Higher-Order Label Spreading
Label spreading is a general technique for semi-supervised learning with point cloud or network data, which can be interpreted as a diffusion of labels on a graph.
Nonlocal PageRank
In this work we introduce and study a nonlocal version of the PageRank.
Social and Information Networks Numerical Analysis Numerical Analysis Physics and Society
Generalized Matrix Means for Semi-Supervised Learning with Multilayer Graphs
We study the task of semi-supervised learning on multilayer graphs by taking into account both labeled and unlabeled observations together with the information encoded by each individual graph layer.
Total variation based community detection using a nonlinear optimization approach
Thus we describe a new nonlinear optimization approach to solve the equivalent problem leading to a community detection strategy based on $TV_Q$.
Social and Information Networks Optimization and Control Physics and Society 49M20, 65K10, 91D30, 91C20
Spectral Clustering of Signed Graphs via Matrix Power Means
Moreover, we prove that the eigenvalues and eigenvector of the signed power mean Laplacian concentrate around their expectation under reasonable conditions in the general Stochastic Block Model.
Multi-Dimensional, Multilayer, Nonlinear and Dynamic HITS
We introduce a ranking model for temporal multi-dimensional weighted and directed networks based on the Perron eigenvector of a multi-homogeneous order-preserving map.
A Nonlinear Spectral Method for Core--Periphery Detection in Networks
We derive and analyse a new iterative algorithm for detecting network core--periphery structure.
Social and Information Networks Numerical Analysis Data Analysis, Statistics and Probability
The Power Mean Laplacian for Multilayer Graph Clustering
Multilayer graphs encode different kind of interactions between the same set of entities.
Community detection in networks via nonlinear modularity eigenvectors
In this work we propose a nonlinear relaxation which is instead based on the spectrum of a nonlinear modularity operator $\mathcal M$.
Clustering Signed Networks with the Geometric Mean of Laplacians
As a solution we propose to use the geometric mean of the Laplacians of positive and negative part and show that it outperforms the existing approaches.
An Efficient Multilinear Optimization Framework for Hypergraph Matching
Hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows to integrate higher-order geometric information.
