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.
LOCUS separates brain network connectivity matrices efficiently.
We introduce Clique Matrices as an alternative representation of undirected graphs, being a generalisation of the incidence matrix representation. Here we use clique matrices to decompose a graph into a set of possibly overlapping clusters, de ned as well-connected subsets of vertices. The decomposition is based on a s…
New method proves Jones Polynomial's connect sum property.
Connections between nodes of fully connected neural networks are usually represented by weight matrices. In this article, functional transfer matrices are introduced as alternatives to the weight matrices: Instead of using real weights, a functional transfer matrix uses real functions with trainable parameters to repre…
DiffeoCFM efficiently generates realistic brain connectivity matrices using pullback metrics.
New curvature tensor and matrices for connection graphs derived from Bakry-Émery curvature.
Analyzes Berry phases and connection matrices on Siegel-Jacobi spaces.
We investigate the connections between the differential-geometric properties of the exponential map from the space of real skew symmetric matrices onto the group of real special orthogonal matrices and the manifold of real orthogonal matrices equipped with the Riemannian structure induced by the Frobenius metric.
Researchers develop geodesics for a new metric on correlation matrices.
The purpose of this paper is to establish a connection between various subjects such as dynamical r-matrices, Lie bialgebroids, and Lagrangian subalgebras. Our method relies on the theory of Dirac structures developed in dg-ga/9508013 and dg-ga/9611001. In particular, we give a new method of classifying dynamical r-mat…
Graph connection Laplacian (GCL) is a modern data analysis technique that is starting to be applied for the analysis of high dimensional and massive datasets. Motivated by this technique, we study matrices that are akin to the ones appearing in the null case of GCL, i.e the case where there is no structure in the datas…
R-PLS improves analysis of brain functional connectivity matrices.
Knots and 4-manifolds linked via matrix kinking.
In this paper we show that for the purposes of dimensionality reduction certain class of structured random matrices behave similarly to random Gaussian matrices. This class includes several matrices for which matrix-vector multiply can be computed in log-linear time, providing efficient dimensionality reduction of gene…
New metric tensor field on symmetric matrices simplifies eigenvector computation.
A recent strategy to circumvent the exploding and vanishing gradient problem in RNNs, and to allow the stable propagation of signals over long time scales, is to constrain recurrent connectivity matrices to be orthogonal or unitary. This ensures eigenvalues with unit norm and thus stable dynamics and training. However …
New method connects neural networks to diagrammatic algebra.
New algorithms reduce communication in GNN training.
Inverse metric matrices on Siegel-Jacobi spaces are calculated for Berezin quantization.
Study of twisted Alexander matrices for certain quandles and their invariants.
WISDoM (Wishart Distributed Matrices) is a new framework for the quantification of deviation of symmetric positive-definite matrices associated to experimental samples, like covariance or correlation matrices, from expected ones governed by the Wishart distribution WISDoM can be applied to tasks of supervised learning,…
A new model uses Toeplitz matrices to analyze time-series data transitions.
The space of matrices of positive determinant GL^+_n inherits an extrinsic metric space structure from R^{n^2}. On the other hand, taking the infimum of the lengths of all paths connecting two points in GL^+_n gives an intrinsic metric. We prove bilipschitz equivalence for intrinsic and extrinsic metrics on GL^+_n, exp…
Random feature matrices' singular values concentrate near their full expectation in high dimensions.
A non-Hermitean extension of paradigmatic Wishart random matrices is introduced to set up a theoretical framework for statistical analysis of (real, complex and real quaternion) stochastic time series representing two "remote" complex systems. The first paper in a series provides a detailed spectral theory of non-Hermi…
We investigate some geometric properties of the real algebraic variety of symmetric matrices with repeated eigenvalues. We explicitly compute the volume of its intersection with the sphere and prove a Eckart-Young-Mirsky-type theorem for the distance function from a generic matrix to points in . We exhibit conne…
New algorithm for Coxeter connections with maximally ramified singularities.
Study extends symmetries of sphere points to surface mapping classes.
A connection is made between the Krammer representation and the Birman-Murakami-Wenzl algebra. Inspired by a dimension argument, a basis is found for a certain irrep of the algebra, and relations which generate the matrices are found. Following a rescaling and change of parameters, the matrices are found to be identica…
Paper solves a key problem in learning from high-dimensional covariance matrices.
New bound for neural networks with full-rank weights, independent of network width.
Construction of (colored) knot polynomials for double-fat graphs is further generalized to the case when "fingers" and "propagators" are substituting R-matrices in arbitrary closed braids with m-strands. Original version of arXiv:1504.00371 corresponds to the case m=2, and our generalizations sheds additional light on …
On the manifold of positive definite matrices, we investigate the existence of pairs of flat affine connections, dual with respect to a given monotone metric. The connections are defined either using the -embeddings and finding the duals with respect to the metric, or by means of contrast functionals. We show that i…
Study embeds PC matrices into Grassmannian manifold for geometric interpretation.
Method estimates sparse inverse covariance and partial correlation matrices efficiently.
In this study, a pairwise comparison matrix is generalized to the case when coefficients create Lie group , non necessarily abelian. A necessary and sufficient criterion for pairwise comparisons matrices to be consistent is provided. Basic criteria for finding a nearest consistent pairwise comparisons matrix (extend…
The low displacement rank (LDR) framework for structured matrices represents a matrix through two displacement operators and a low-rank residual. Existing use of LDR matrices in deep learning has applied fixed displacement operators encoding forms of shift invariance akin to convolutions. We introduce a class of LDR ma…
We introduce a class of metrics on gauge theoretic moduli spaces. These metrics are made out of the universal matrix that appears in the universal connection construction of M. S. Narasimhan and S. Ramanan. As an example we construct metrics on the c_{2}=1 SU(2) moduli space of instantons on R^4 for various universal m…
Overview of high-dimensional dynamical systems and their applications to machine learning.
Graph energy helps detect communities in networks better than traditional methods.
We describe new results and algorithms for two different, but related, problems which deal with circulant matrices: learning shift-invariant components from training data and calculating the shift (or alignment) between two given signals. In the first instance, we deal with the shift-invariant dictionary learning probl…
We study the local structure of Lie bialgebroids at regular points. In particular, we classify all transitive Lie bialgebroids. In special cases, they are connected to classical dynamical -matrices and matched pairs induced by Poisson group actions
A necessary condition for a connection in a vector bundle to be locally metric is for its curvature matrix, which consists of forms, to be skew symmetric with respect to some local frame. In this paper we give a simple algorithm that can be used to decide when a matrix of forms is equivalent to a skew symmetric…
Study connects covariance cleaning theory to information theory for heavy-tailed distributions.
The paper studies matrix normalization and graph balancing using a new functional and gradient descent.
The Clifford group for 2 qubits is divided into 20 orbits, each with 4608 matrices.
SGD and weight decay encourage neural networks to learn low-rank weight matrices.
Spinor formalism is the formalism induced by solutions of the Clifford equation (the connecting operators). For the space-time manifold (n = 4), these operators, connecting the tangent and spinor bundle, are operators that are represented by the Dirac matrices in the special basis. Reduced connecting operators are repr…