A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The study bounds the effective diameter of graphs with positive Ollivier curvature.
New bounds for average graph distance using curvature and centrality.
Uniform diameter bound for reflection group disk patterns.
Proposes Isometric Graph Neural Networks to preserve graph distances.
The paper connects reflection groups to maps with specific dynamical properties.
FinReflectKG builds a comprehensive financial knowledge graph from SEC filings, improving extraction quality.
Hierarchical graph clustering is a common technique to reveal the multi-scale structure of complex networks. We propose a novel metric for assessing the quality of a hierarchical clustering. This metric reflects the ability to reconstruct the graph from the dendrogram, which encodes the hierarchy. The optimal represent…
Develops Aleksandrov reflection for hyperbolic flows, proving convergence to umbilic surfaces.
We give a combinatorial characterization of generic minimally rigid reflection frameworks. The main new idea is to study a pair of direction networks on the same graph such that one admits faithful realizations and the other has only collapsed realizations. In terms of infinitesimal rigidity, realizations of the former…
The transition constant was introduced in our 1981 paper and denoted as N(14). It is equal to the maximal degree of the ground fields of V-arithmetic connected edge graphs with 4 vertices and of the minimality 14. This constant is fundamental since if the degree of the ground field of an arithmetic hyperbolic reflectio…
Method finds motifs in knowledge graphs, revealing their structure.
We study the problem of prediction for evolving graph data. We formulate the problem as the minimization of a convex objective encouraging sparsity and low-rank of the solution, that reflect natural graph properties. The convex formulation allows to obtain oracle inequalities and efficient solvers. We provide empirical…
TechRank ranks companies and technologies based on investor preferences.
New model learns graph neural networks equivariant to various transformations.
For finite reflection groups of types A and B, we determine the diameter of the graph whose vertices are reduced words for the longest element and whose edges are braid relations. This is deduced from a more general theorem that applies to supersolvable hyperplane arrangements.
A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a distance or similarity metric on the points, then look for highly connected subgra…
We consider the two problems of predicting links in a dynamic graph sequence and predicting functions defined at each node of the graph. In many applications, the solution of one problem is useful for solving the other. Indeed, if these functions reflect node features, then they are related through the graph structure.…
A deep learning model organizes RNA graphs to reveal folding patterns and properties.
New method improves graph neural networks by considering different types of relations in sampling.
A novel Gromov-Wasserstein learning framework is proposed to jointly match (align) graphs and learn embedding vectors for the associated graph nodes. Using Gromov-Wasserstein discrepancy, we measure the dissimilarity between two graphs and find their correspondence, according to the learned optimal transport. The node …
The paper shows that relaxing assumptions about causal graphs can lead to exponentially large equivalence classes.
Graph deep learning models, such as graph convolutional networks (GCN) achieve remarkable performance for tasks on graph data. Similar to other types of deep models, graph deep learning models often suffer from adversarial attacks. However, compared with non-graph data, the discrete features, graph connections and diff…
Generative graph models create instances of graphs that mimic the properties of real-world networks. Generative models are successful at retaining pairwise associations in the underlying networks but often fail to capture higher-order connectivity patterns known as network motifs. Different types of graphs contain diff…
A new graph neural network tackles oversmoothing and generalization issues.
Study simplicial volume of manifolds from reflection group trick.
Tree Mover's Distance measures graph attributes and improves GNN performance.
We consider the detection of activations over graphs under Gaussian noise, where signals are piece-wise constant over the graph. Despite the wide applicability of such a detection algorithm, there has been little success in the development of computationally feasible methods with proveable theoretical guarantees for ge…
Proposes a method for coarse graph alignment using sparse partial least squares.
New distances for causal graphs improve evaluation of learned structures.
New trick builds hyperbolic manifolds from compact ones, proving some don't virtually fiber.
New algorithm improves graph-based active learning by identifying unexplored regions.
This paper proposes a simple but effective graph-based agglomerative algorithm, for clustering high-dimensional data. We explore the different roles of two fundamental concepts in graph theory, indegree and outdegree, in the context of clustering. The average indegree reflects the density near a sample, and the average…
We construct a new type of quantum walks on simplicial complexes as a natural extension of the well-known Szegedy walk on graphs. One can numerically observe that our proposing quantum walks possess linear spreading and localization as in the case of the Grover walk on lattices. Moreover, our numerical simulation sugge…
Ancestral graph models, introduced by Richardson and Spirtes (2002), generalize both Markov random fields and Bayesian networks to a class of graphs with a global Markov property that is closed under conditioning and marginalization. By design, ancestral graphs encode precisely the conditional independence structures t…
We present a novel and hierarchical approach for supervised classification of signals spanning over a fixed graph, reflecting shared properties of the dataset. To this end, we introduce a Convolutional Cluster Pooling layer exploiting a multi-scale clustering in order to highlight, at different resolutions, locally con…
The location-based social network, Foursquare, reflects the human activities of a city. The mobility dynamics inferred from Foursquare helps us understanding urban social events like crime In this paper, we propose a directed graph from the aggregated movement between regions using Foursquare data. We derive region ris…
Geometric GNNs improve graph discrimination through GWL.
Method learns graph structure for multi-task learning, revealing interpretable relationships.
Graph cross network improves graph classification accuracy.
Predicting interactions between structured entities lies at the core of numerous tasks such as drug regimen and new material design. In recent years, graph neural networks have become attractive. They represent structured entities as graphs and then extract features from each individual graph using graph convolution op…
Improves GNN prediction sets with conformal prediction for node classification.
The Bratteli diagram is an infinite graph which reflects the structure of projections in a C*-algebra. We prove that every strictly ergodic unimodular Bratteli diagram of rank 2g+m-1 gives rise to a minimal geodesic lamination with the m-component principal region on a surface of genus g greater or equal to 1. The proo…
A-DOGE embeds attributed graphs efficiently using density of states.
A new model learns graph structures from data.
Learning graph-structured data with graph neural networks (GNNs) has been recently emerging as an important field because of its wide applicability in bioinformatics, chemoinformatics, social network analysis and data mining. Recent GNN algorithms are based on neural message passing, which enables GNNs to integrate loc…
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit computationally convenient factorization properties and have long been a valuable tool for t…
Moebius-Kantor graph connects multiple groups and topological properties.
Nonnegative Matrix Factorization (NMF) has been continuously evolving in several areas like pattern recognition and information retrieval methods. It factorizes a matrix into a product of 2 low-rank non-negative matrices that will define parts-based, and linear representation of nonnegative data. Recently, Graph regula…