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.
High-dimensional ConvNets detect patterns in 32+ dimensions for geometric registration.
Graph Neural Networks improve financial time series forecasting accuracy.
Information mapping is a popular application of Multivoxel Pattern Analysis (MVPA) to fMRI. Information maps are constructed using the so called searchlight method, where the spherical multivoxel neighborhood of every voxel (i.e., a searchlight) in the brain is evaluated for the presence of task-relevant response patte…
In real-world, many problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns, especially in the field of computer vision. Recently, the alignment of geometric patterns in high dimension finds several novel applications…
A ``hyperideal circle pattern'' in is a finite family of oriented circles, similar to the ``usual'' circle patterns but such that the closed disks bounded by the circles do not cover the whole sphere. Hyperideal circle patterns are directly related to hyperideal hyperbolic polyhedra, and also to circle packings. …
Formula removes geometric patterns from random hyperbolic surfaces.
QGMS framework detects market endpoints using geometric patterns.
Evaluating data separation in a geometrical space is fundamental for pattern recognition. A plethora of dimensionality reduction (DR) algorithms have been developed in order to reveal the emergence of geometrical patterns in a low dimensional visible representation space, in which high-dimensional samples similarities …
The main objective of this study is to understand how geometric hyper-ideal circle patterns can be constructed from given combinatorial angle data. We design a hybrid method consisting of a topological/deformation approach augmented with a variational principle. In this way, together with the question of characterizati…
In this paper, we are concerned with the 2D and 3D geometric shape generation by prescribing a set of characteristic values of a specific geometric body. One of the major motivations of our study is the 3D human body generation in various applications. We develop a novel method that can generate the desired body with c…
Here are studied pairs of transversal foliations with singularities, defined on the Elliptic region (where the Gaussian curvature is positive) of an oriented surface immersed in . The leaves of the foliations are the lines of geometric mean curvature, along which the normal curvature is given …
New method finds ideal circle patterns on spheres.
Milnor's triple linking numbers of a link in the 3-sphere are interpreted geometrically in terms of the pattern of intersections of the Seifert surfaces of the components of the link. This generalizes the well known formula as an algebraic count of triple points when the pairwise linking numbers vanish.
The paper studies the combinatorial p-th Calabi flow for finite and infinite circle patterns.
Paper explores folding patterns of curved creases preserving their geometric properties.
Study knot groups from disc patterns in 3D space.
In this paper a data analytical approach featuring support vector machines (SVM) is employed to train a predictive model over an experimentaldataset, which consists of the most relevant studies for two-phase flow pattern prediction. The database for this study consists of flow patterns or flow regimes in gas-liquid two…
Unified framework for pattern recovery in penalized and thresholded estimation.
Study uses geometric algebra to analyze credit cycles, revealing dangerous feedback loops.
New geometric theory explains nonuniform origami responses.
Boolean matrix has been used to represent digital information in many fields, including bank transaction, crime records, natural language processing, protein-protein interaction, etc. Boolean matrix factorization (BMF) aims to find an approximation of a binary matrix as the Boolean product of two low rank Boolean matri…
Paper resolves spherical curvature flow problem.
A new associative memory uses Sinkhorn divergence for efficient pattern retrieval.
The paper explores how sinks and diagonal patterns prevent attention oversmoothing.
Study reveals LLM personas have two distinct components: frame-robust aggregated traits and frame-dependent geometric features.
A Delaunay cell decomposition of a surface with constant curvature gives rise to a circle pattern, consisting of the circles which are circumscribed to the facets. We treat the problem whether there exists a Delaunay cell decomposition for a given (topological) cell decomposition and given intersection angles of the ci…
This work improves KG embeddings by integrating hyperbolic and attention mechanisms.
We consider the matrix completion problem with a deterministic pattern of observed entries. In this setting, we aim to answer the question: under what condition there will be (at least locally) unique solution to the matrix completion problem, i.e., the underlying true matrix is identifiable. We answer the question fro…
Motivated by the prediction of cell loads in cellular networks, we formulate the following new, fundamental problem of statistical learning of geometric marks of point processes: An unknown marking function, depending on the geometry of point patterns, produces characteristics (marks) of the points. One aims at learnin…
We consider the problem of inferring the interactions between a set of N binary variables from the knowledge of their frequencies and pairwise correlations. The inference framework is based on the Hopfield model, a special case of the Ising model where the interaction matrix is defined through a set of patterns in the …
A novel geometric algebra-based KG embedding framework improves link prediction.
This paper presents an efficient algorithm for evolving point cloud data on smooth manifolds using B-Splines.
Associated to oriented surfaces immersed in R^3 here are studied pairs of transversal foliations with singularities, defined on the Elliptic region, where the Gaussian curvature K, given by the product of the principal curvatures k_1, k_2 of the immersion, is positive. The leaves of the foliations are the lines of M- m…
This paper provides a general framework to study the effect of sampling properties of training data on the generalization error of the learned machine learning (ML) models. Specifically, we propose a new spectral analysis of the generalization error, expressed in terms of the power spectra of the sampling pattern and t…
Researchers decompose Forman-Ricci curvature for efficient computation in VR complexes.
CEDA analyzes large categorical datasets using tree geometry and binary codes.
Hexagon grid patterns emerge from conformal isometry in grid cell neural networks.
We study local and global approximations of smooth nets of curvature lines and smooth conjugate nets by respective discrete nets (circular nets and planar quadrilateral nets) with infinitesimal quads. It is shown that choosing the points of discrete nets on the smooth surface one can obtain second-order approximation g…
Generative Adversarial Graph Neural Network (Sig-Graph GAN) models financial time series data.
Geo2DR learns graph representations using substructure patterns.
The paper analyzes how grid cells perform path integration and learns hexagon grid patterns.
In this paper, we analyze the fundamental conditions for low-rank tensor completion given the separation or tensor-train (TT) rank, i.e., ranks of unfoldings. We exploit the algebraic structure of the TT decomposition to obtain the deterministic necessary and sufficient conditions on the locations of the samples to ens…
CAG method predicts nonlinear solid mechanics responses in real-time with high accuracy and efficiency.
A deep learning model organizes RNA graphs to reveal folding patterns and properties.
This paper provides a theoretical justification of the superior classification performance of deep rectifier networks over shallow rectifier networks from the geometrical perspective of piecewise linear (PWL) classifier boundaries. We show that, for a given threshold on the approximation error, the required number of b…
In the spirit of Klein's Erlangen Program, we investigate the geometric and algebraic structure of fundamental line complexes and the underlying privileged discrete integrable system for the minors of a matrix which constitute associated Plücker coordinates. Particular emphasis is put on the restriction to Lie circle g…
This research studies affine invariance in continuous-domain convolutional neural networks.
Machine learning methods struggle with geometric data, but shape space analysis provides a framework for studying and analyzing geometric variability.