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.
Graph potentials link to topological QFTs, with computational methods.
FastMap-D embeds directed graphs using potential fields.
We give a closed formula for the multivariable Conway potential function of any graph link in a homology sphere. As corollaries, we answer three questions by Walter Neumann about graph links.
Proves bounds on spanning two-forests and random cut sizes.
The aim of this short note is to draw attention to a method by which the partition function and marginal probabilities for a certain class of random fields on complete graphs can be computed in polynomial time. This class includes Ising models with homogeneous pairwise potentials but arbitrary (inhomogeneous) unary pot…
Paper proves no nontrivial solutions to certain elliptic equations on graphs.
The paper proves optimal smoothness for certain Lagrangian graphs with specific Hölder continuity.
Nonexistence results for semilinear parabolic and hyperbolic inequalities on metric graphs
Efficiently learns DAG structures without cycles.
Diffuse interface methods have recently been introduced for the task of semi-supervised learning. The underlying model is well-known in materials science but was extended to graphs using a Ginzburg--Landau functional and the graph Laplacian. We here generalize the previously proposed model by a non-smooth potential fun…
Graph Interplay (GIP) improves GSSL performance by enhancing graph-level communications.
A new method recovers latent potentials from graph flows, preserving ordering and stability.
Long time existence and convergence to a circle is proved for radial graph solutions to a mean curvature type curve flow in warped product surfaces (under a weak assumption on the warp potential of the surface). This curvature flow preserves the area enclosed by the evolving curve, and this fact is used to prove a gene…
We study recursive-cube-of-rings (RCR), a class of scalable graphs that can potentially provide rich inter-connection network topology for the emerging distributed and parallel computing infrastructure. Through rigorous proof and validating examples, we have corrected previous misunderstandings on the topological prope…
We consider the mean curvature flow of entire Lagrangian graphs with Lipschitz continuous initial data. Assuming only a certain bound on the Lipschitz norm of an initial entire Lagrangian graph in , we show that the parabolic equation \eqref{PMA} for the Lagrangian potential has a longtime solution which is sm…
Root Laplacian Eigenmaps help in spectral embedding of graphs.
Structured prediction can be thought of as a simultaneous prediction of multiple labels. This is often done by maximizing a score function on the space of labels, which decomposes as a sum of pairwise and unary potentials. The above is naturally modeled with a graph, where edges and vertices are related to pairwise and…
New TQFT homologies help color graphs, potentially solving the four color theorem.
Paper explores embedding methods for detecting pseudo-cliques in random graphs, showing limitations and potential.
The paper proposes and discusses semiorthogonal decompositions for moduli spaces of vector bundles.
ChatGPT enhances GNN for stock movement prediction.
We present a simple combinatorial model for quasipositive surfaces and positive braids, based on embedded bipartite graphs. As a first application, we extend the well-known duality on standard diagrams of torus links to twisted torus links. We then introduce a combinatorial notion of adjacency for bipartite graph links…
Chord diagrams on circles and their intersection graphs (also known as circle graphs) have been intensively studied, and have many applications to the study of knots and knot invariants, among others. However, chord diagrams on more general graphs have not been studied, and are potentially equally valuable in the study…
This tutorial introduces causal modeling methods for researchers.
ELD compares graphs by their embedded Laplacian eigenvectors, resolving ambiguities.
A new graph model HMG and neural network HMGNN improve molecule property predictions.
Graph Networks are used to make decisions in potentially complex scenarios but it is usually not obvious how or why they made them. In this work, we study the explainability of Graph Network decisions using two main classes of techniques, gradient-based and decomposition-based, on a toy dataset and a chemistry task. Ou…
This article studies the mean curvature flow of Lagrangian submanifolds. In particular, we prove the following global existence and convergence theorem: if the potential function of a Lagrangian graph in T^{2n} is convex, then the flow exists for all time and converges smoothly to a flat Lagrangian submanifold.
The study constructs optimal tori on Fano manifolds and confirms mirror symmetry.
Research on graph representation learning has received a lot of attention in recent years since many data in real-world applications come in form of graphs. High-dimensional graph data are often in irregular form, which makes them more difficult to analyze than image/video/audio data defined on regular lattices. Variou…
Graph theory criterion for Hodge theory to match linearly.
Graph Neural Networks improve 3D object detection in LiDAR point clouds.
Detects graph topology changes from noisy signals using prior spectral information.
Develops potential theory for WZW equation in Kähler potentials space.
Problems of segmentation, denoising, registration and 3D reconstruction are often addressed with the graph cut algorithm. However, solving an unconstrained graph cut problem is NP-hard. For tractable optimization, pairwise potentials have to fulfill the submodularity inequality. In our learning paradigm, pairwise poten…
Line graph transformation aids graph isomorphism tests by excluding challenging graph properties.
Nowadays Knowledge Graphs constitute a mainstream approach for the representation of relational information on big heterogeneous data, however, they may contain a big amount of imputed noise when constructed automatically. To address this problem, different error detection methodologies have been proposed, mainly focus…
The family of image visibility graphs (IVGs) have been recently introduced as simple algorithms by which scalar fields can be mapped into graphs. Here we explore the usefulness of such operator in the scenario of image processing and image classification. We demonstrate that the link architecture of the image visibilit…
Graph autoencoders (AE) and variational autoencoders (VAE) recently emerged as powerful node embedding methods. In particular, graph AE and VAE were successfully leveraged to tackle the challenging link prediction problem, aiming at figuring out whether some pairs of nodes from a graph are connected by unobserved edges…
Identifies root causes of outliers in unknown cyclic graphs.
The abstract formulates and proves a categorification of Robertson's conjecture.
Estimates smooth graph signals from partial measurements.
New method separates graph structure from node attributes to recover lost signal.
Grale designs graphs for graph learning, improving performance on large datasets.
Graph convolutional neural networks (Graph-CNNs) extend traditional CNNs to handle data that is supported on a graph. Major challenges when working with data on graphs are that the support set (the vertices of the graph) do not typically have a natural ordering, and in general, the topology of the graph is not regular …
This paper analyzes various graph clustering methods and their applications.
Deep learning has been shown to be successful in a number of domains, ranging from acoustics, images, to natural language processing. However, applying deep learning to the ubiquitous graph data is non-trivial because of the unique characteristics of graphs. Recently, substantial research efforts have been devoted to a…
Estimates multiple networks using graphons for non-aligned graphs.