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.
New algorithms improve multi-task bandit performance by transferring reward samples.
New matrix reveals cluster info in sparse directed graphs.
A graph's winding numbers around two non-adjacent vertices differ by ±1.
Finding a new mathematical representations for graph, which allows direct comparison between different graph structures, is an open-ended research direction. Having such a representation is the first prerequisite for a variety of machine learning algorithms like classification, clustering, etc., over graph datasets. In…
This paper considers *-graphs in which all vertices have degree 4 or 6, and studies the question of calculating the genus of orientable 2-surfaces into which such graphs may be embedded. A *-graph is a graph endowed with a formal adjacency structure on the half-edges around each vertex, and an embedding of a *-graph is…
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…
A new graph kernel uses LCS and Wasserstein distance for better graph comparisons.
A knot K is called Gordian adjacent to a knot L if there exists an unknotting sequence for L containing K. We provide a sufficient condition for Gordian adjacency of torus knots via the study of knots in the thickened torus. We also completely describe Gordian adjacency for torus knots of index 2 and 3 using Levine-Tri…
Paper determines 2-adjacent knots up to 12 crossings.
Adjacency defined for three-manifolds, linking them to the 3-sphere.
A new GCN model learns higher-order neighbors without explicit adjacency matrix computation.
Proposes CAL to learn causal adjacency for better spatiotemporal prediction.
The paper introduces an adjacency constraint to improve goal-conditioned HRL.
Graphs represent knot adjacency for n crossings.
Traditional works on community detection from observations of information cascade assume that a single adjacency matrix parametrizes all the observed cascades. However, in reality the connection structure usually does not stay the same across cascades. For example, different people have different topics of interest, th…
Recently similarity graphs became the leading paradigm for efficient nearest neighbor search, outperforming traditional tree-based and LSH-based methods. Similarity graphs perform the search via greedy routing: a query traverses the graph and in each vertex moves to the adjacent vertex that is the closest to this query…
Reconstruct spacetime from order and number of points.
A knot K is called n-adjacent to the unknot, if K admits a projection containing n generalized crossings such that changing any m (no larger than n) of them yields a projection of the unknot. We show that a non-trivial satellite knot K is n-adjacent to the unknot, for some n>0, if and only if it is n-adjacent to the un…
For graphs generated from stochastic blockmodels, adjacency spectral embedding is asymptotically consistent. Further, adjacency spectral embedding composed with universally consistent classifiers is universally consistent to achieve the Bayes error. However when the graph contains private or sensitive information, trea…
This paper develops the exact linear relationship between the leading eigenvector of the unnormalized modularity matrix and the eigenvectors of the adjacency matrix. We propose a method for approximating the leading eigenvector of the modularity matrix, and we derive the error of the approximation. There is also a comp…
A knot is said to be Gordian adjacent to a knot if is an intermediate knot on an unknotting sequence of . We extend previous results on Gordian adjacency by showing sufficient conditions for Gordian adjacency between classes of positive braid knots through manipulations of braid words. In additio…
The paper examines how well node similarities are preserved by random projections in graph embeddings.
New algorithm improves similarity graph construction for nearest neighbor search.
We study properties of Cartesian products of digital images, using a variety of adjacencies that have appeared in the literature.
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…
In this paper, we investigate the geometry of a general class of gradient flows with multiple local maxima. we decompose the underlying space into disjoint regions of attraction and establish the adjacency criterion. The criterion states a necessary and sufficient condition for two regions of attraction of stable equil…
Two spectral algorithms for community detection in graphs with covariates are compared.
Due to a resource-constrained environment, network compression has become an important part of deep neural networks research. In this paper, we propose a new compression method, \textit{Inter-Layer Weight Prediction} (ILWP) and quantization method which quantize the predicted residuals between the weights in all convol…
Random projections help in representing sparse graphs efficiently.
EPINE enhances network embedding by improving adjacency matrix-based high-order proximity.
Bipartite data is common in data engineering and brings unique challenges, particularly when it comes to clustering tasks that impose on strong structural assumptions. This work presents an unsupervised method for assessing similarity in bipartite data. Similar to some co-clustering methods, the method is based on regu…
Enhances graph neural networks by considering feature similarities in node aggregation.
A U(n)-manifold is multiaxial if the isotropy groups are always conjugate to unitary subgroups. The classification and the concordance of such manifolds have been studied by Davis, Hsiang and Morgan under much more strict conditions. We show that in general, without much extra condition, the homotopy classification of …
Graph Convolutional Networks improved with topological features for better accuracy.
New method for freezing sets in arbitrary dimensions.
A common analytical problem in neuroscience is the interpretation of neural activity with respect to sensory input or behavioral output. This is typically achieved by regressing measured neural activity against known stimuli or behavioral variables to produce a "tuning function" for each neuron. Unfortunately, because …
Optimal task order improves continual learning performance.
New method speeds up diffusion models without sacrificing quality.
A knot K is called n-adjacent to another knot K', if K admits a projection containing n generalized crossings such that changing any 0 < m \leq n of them yields a projection of K'. We apply techniques from the theory of sutured 3-manifolds, Dehn surgery and the theory of geometric structures of 3-manifolds to answer th…
New model for network analysis using functional data.
A scalable method to learn causal graphs from large data.
AutoLL uses neural networks to automatically reorder graph nodes for linear layouts.
The paper discusses a pooling mechanism to induce subsampling in graph structured data and introduces it as a component of a graph convolutional neural network. The pooling mechanism builds on the Non-Negative Matrix Factorization (NMF) of a matrix representing node adjacency and node similarity as adaptively obtained …
Paper learns causal structures from data using gradient-based optimization.
It is known that the Alexander polynomial detects fibered knots and 3-manifolds that fiber over the circle. In this note, we show that when the Alexander polynomial becomes inconclusive, the notion of "knot adjacency", studied in the paper "Knot adjacency, genus and essential tori" by the authors, can be used to obtain…
Improved bipartite link prediction using 2-hop paths.
Active Search has become an increasingly useful tool in information retrieval problems where the goal is to discover as many target elements as possible using only limited label queries. With the advent of big data, there is a growing emphasis on the scalability of such techniques to handle very large and very complex …
Proposes SimPool for graph pooling using structural similarity features.