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 paper introduces a method for detecting principal communities and embedding vertices.
The paper identifies saddlepoints in unsupervised auto-encoding neural nets.
We define integral odd Khovanov homology of principally unimodular bipartite graph-links.
DGA and DVGA learn disentangled graph representations to improve graph analysis.
In many physical, statistical, biological and other investigations it is desirable to approximate a system of points by objects of lower dimension and/or complexity. For this purpose, Karl Pearson invented principal component analysis in 1901 and found 'lines and planes of closest fit to system of points'. The famous k…
Extends graph encoder embedding to weighted graphs and matrices.
Auto-encoders have emerged as a successful framework for unsupervised learning. However, conventional auto-encoders are incapable of utilizing explicit relations in structured data. To take advantage of relations in graph-structured data, several graph auto-encoders have recently been proposed, but they neglect to reco…
Directly compute classification by learning features with class scores.
A fast graph embedding method for large graphs.
Principal components analysis (PCA) is the optimal linear auto-encoder of data, and it is often used to construct features. Enforcing sparsity on the principal components can promote better generalization, while improving the interpretability of the features. We study the problem of constructing optimal sparse linear a…
Efficient method for vertex embedding and community detection.
The (variational) graph auto-encoder and its variants have been popularly used for representation learning on graph-structured data. While the encoder is often a powerful graph convolutional network, the decoder reconstructs the graph structure by only considering two nodes at a time, thus ignoring possible interaction…
Transformer adapts to graphs with adaptive attention and auto-regressive decoding.
We introduce the variational graph auto-encoder (VGAE), a framework for unsupervised learning on graph-structured data based on the variational auto-encoder (VAE). This model makes use of latent variables and is capable of learning interpretable latent representations for undirected graphs. We demonstrate this model us…
GraphToken encodes structured data for LLMs, improving graph reasoning tasks.
Novel PCA method for high-dimensional inverse problems.
Over the last few years, machine learning over graph structures has manifested a significant enhancement in text mining applications such as event detection, opinion mining, and news recommendation. One of the primary challenges in this regard is structuring a graph that encodes and encompasses the features of textual …
FVNNs use graph convolutions on fair covariance estimates to improve fairness in machine learning.
Proposes flexible auto-encoders for varying data dimensions.
A method to uniformly sample graph-encoded surfaces of fixed size.
Derives formulae for general permutation equivariant layers and presents a second order graph variational encoder.
Just like Atiyah Lie algebroids encode the infinitesimal symmetries of principal bundles, exact Courant algebroids are believed to encode the infinitesimal symmetries of -gerbes. At the same time, transitive Courant algebroids may be viewed as the higher analogue of Atiyah Lie algebroids, and the non-commutative a…
We construct manifestly superconformal field theories in six dimensions which contain a non-Abelian tensor multiplet. In particular, we show how principal 3-bundles over a suitable twistor space encode solutions to these self-dual tensor field theories via a Penrose-Ward transform. The resulting higher or categorified …
Many scientific datasets are of high dimension, and the analysis usually requires visual manipulation by retaining the most important structures of data. Principal curve is a widely used approach for this purpose. However, many existing methods work only for data with structures that are not self-intersected, which is …
We construct a series of finitely presented semigroups. The centers of these semigroups encode uniquely up to rigid ambient isotopy in 3-space all non-oriented spatial graphs. This encoding is obtained by using three-page embeddings of graphs into the product of the line with the cone on three points. By exploiting thr…
We present two instances, L-GAE and L-VGAE, of the variational graph auto-encoding family (VGAE) based on separating feature propagation operations from graph convolution layers typically found in graph learning methods to a single linear matrix computation made prior to input in standard auto-encoder architectures. Th…
Capacity control, the bias/variance dilemma, and learning unknown functions from data, are all concerned with identifying effective and consistent fits of unknown geometric loci to random data points. A geometric locus is a curve or surface formed by points, all of which possess some uniform property. A geometric locus…
Graph auto-encoder predicts unobserved node features from biological networks and omics data.
Paper proposes LCP for structural encodings, outperforming existing methods.
There has been huge interest in studying human brain connectomes inferred from different imaging modalities and exploring their relationship with human traits, such as cognition. Brain connectomes are usually represented as networks, with nodes corresponding to different regions of interest (ROIs) and edges to connecti…
In this paper, we consider recommender systems with side information in the form of graphs. Existing collaborative filtering algorithms mainly utilize only immediate neighborhood information and have a hard time taking advantage of deeper neighborhoods beyond 1-2 hops. The main caveat of exploiting deeper graph informa…
Graph attention networks improve performance on heterogeneous graphs.
Can neural networks learn to compare graphs without feature engineering? In this paper, we show that it is possible to learn representations for graph similarity with neither domain knowledge nor supervision (i.e.\ feature engineering or labeled graphs). We propose Deep Divergence Graph Kernels, an unsupervised method …
New method uses graph generative models for graph classification.
Semi-implicit graph variational auto-encoder (SIG-VAE) is proposed to expand the flexibility of variational graph auto-encoders (VGAE) to model graph data. SIG-VAE employs a hierarchical variational framework to enable neighboring node sharing for better generative modeling of graph dependency structure, together with …
Graph-based clustering plays an important role in the clustering area. Recent studies about graph convolution neural networks have achieved impressive success on graph type data. However, in general clustering tasks, the graph structure of data does not exist such that the strategy to construct a graph is crucial for p…
Paper explores embedding methods for detecting pseudo-cliques in random graphs, showing limitations and potential.
A novel approach is put forth that utilizes data similarity, quantified on a graph, to improve upon the reconstruction performance of principal component analysis. The tasks of data dimensionality reduction and reconstruction are formulated as graph filtering operations, that enable the exploitation of data node connec…
Improved graph embedding through refined linear transformation and community recovery.
We introduce the Contextual Graph Markov Model, an approach combining ideas from generative models and neural networks for the processing of graph data. It founds on a constructive methodology to build a deep architecture comprising layers of probabilistic models that learn to encode the structured information in an in…
Generative networks have made it possible to generate meaningful signals such as images and texts from simple noise. Recently, generative methods based on GAN and VAE were developed for graphs and graph signals. However, the mathematical properties of these methods are unclear, and training good generative models is di…
Two CSSL-based methods improve graph classification with limited labeled data.
This paper explores GNN functions on random graphs, highlighting the importance of node Positional Encodings.
A checkerboard graph of a special diagram of an oriented link is made a directed, edge-weighted graph in a natural way so that a principal minor of its Laplacian matrix is a Seifert matrix of the link. Doubling and weighting the edges of the graph produces a second Laplacian matrix such that a principal minor is an Ale…
Paper rigorously defines Feynman graph integrals on Kähler manifolds.
New method shows ignoring morphological graph info improves reinforcement learning performance.
Paper connects probability density cuts to graph theory eigenfunctions.
New approach learns graph representations by contrasting first-order neighbors and graph diffusion views.