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.
Solves multi-class imbalanced data problem with geometry-based sampling and synthetic data.
Proposes a VAE for HDLSS data augmentation.
Interpolates mean shift and spectral clustering on graphs.
As a natural application of the {\it theory of geometric averaging} in Finsler geometry and generalized Finsler geometry, a new approach to investigate {\it generalized Finsler geometry}, based on a convex invariance of the average structures, is introduced.
Given a complete and (locally) cartesian closed category U, it is shown that the category of functors from the category of Weil algebras to the category U is (locally, resp.) cartesian closed. The corresponding axiomatization for differential geometry based upon Weil functors is then given.
Novel approach uses quasi-conformal geometry for OSA classification from cephalometry.
In this letter we investigate some aspects of the noncommutative differential geometry based on derivations of the algebra of endomorphisms of an oriented complex hermitian vector bundle. We relate it, in a natural way, to the geometry of the underlying principal bundle and compute the cohomology of its complex of nonc…
We propose a twistor construction of surfaces in Lie sphere geometry based on the linear system which copies equations of Wilczynski's projective frame. In the particular case of Lie-applicable surfaces this linear system describes joint eigenfunctions of a pair of commuting Schrödinger operators with magnetic fields.
New geometry based on Siegel upper half-space with volume formula.
The data deluge comes with high demands for data labeling. Crowdsourcing (or, more generally, ensemble learning) techniques aim to produce accurate labels via integrating noisy, non-expert labeling from annotators. The classic Dawid-Skene estimator and its accompanying expectation maximization (EM) algorithm have been …
Introduces a new geometry based on difference angles, showing unique properties.
These are the lecture notes from the 26th Winter School "Geometry and Physics", Czech Republic, Srni, January 14 - 21, 2006. These lectures are an introduction into the realm of generalized geometry based on the tangent plus the cotangent bundle. In particular we discuss the relation of this geometry to physics, namely…
Study non-convex matrix factorization using Riemannian geometry.
In 1931 Elie Cartan constructed a geometry which was rarely considered. Cartan proposed a way to define an infinitesimal metric starting from a variational problem on hypersurfaces in an -dimensional manifold . This distance depends not only of the point $\textsc{m}\in\mathcal{M}$ but on the orient…
We investigate a class of multi-dimensional two-component systems of Monge-Ampère type that can be viewed as generalisations of heavenly-type equations appearing in self-dual Ricci-flat geometry. Based on the Jordan-Kronecker theory of skew-symmetric matrix pencils, a classification of normal forms of such systems is o…
By introducing a weight function to the Laplace operator, Bakry and Émery defined the "drift Laplacian" to study diffusion processes. Our first main result is that, given a Bakry-Émery manifold, there is a naturally associated family of graphs whose eigenvalues converge to the eigenvalues of the drift Laplacian as the …
New method speeds up Bayesian inverse problem solving with neural operators.
We propose a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive th…
We study a new kind of Courant algebroid on Poisson manifolds, which is a variant of the generalized tangent bundle in the sense that the roles of tangent and the cotangent bundle are exchanged. Its symmetry is a semidirect product of -diffeomorphisms and -transformations. It is a starting point of an alternative…
The article constructs strong Carrollian geometries at infinity for Ricci flat Einstein manifolds.
We construct a tangent bundle exponential map and locally autoparallel coordinates for geometries based on a general connection on the tangent bundle of a manifold. As concrete application we use these new coordinates for Finslerian geometries and obtain Finslerian geodesic coordinates. They generalise normal coordinat…
The Riemannian geometry is one of the main theoretical pieces in Modern Mathematics and Physics. The study of Riemann Geometry in the relevant literature is performed by using a well defined analytical path. Usually it starts from the concept of metric as the primary concept and by using the connections as an intermedi…
Variational Proximal Policy Optimization improves reinforcement learning from human feedback.
New method learns shape correspondences robustly from raw geometry.
We examine how generalised geometries can be associated with a labelled Dynkin diagram built around a gravity line. We present a series of new generalised geometries based on the groups for which the generalised tangent space transforms in a spinor representation of the group. In …
Book teaches how Lagrangian torus fibration base geometry can be read off.
We look at several problems in even dimensional conformal geometry based around the de Rham complex. A leading and motivating problem is to find a conformally invariant replacement for the usual de Rham harmonics. An obviously related problem is to find, for each order of differential form bundle, a ``gauge'' operator …
TRA detects causal direction from bivariate data using geometric shapes.
Natural gradient simplification for deep learning networks.
In category theory, logic and geometry cooperate with each other producing what is known under the name Synthetic Differential Geometry (SDG). The main difference between SDG and standard differential geometry is that the intuitionistic logic of SDG enforces the existence of infinitesimal objects which essentially modi…
New framework uses geometry of embeddings to predict robustness.
Tensor networks improve b-jet classification in high-energy physics.
In this paper, we consider the problem of fast and efficient indexing techniques for sequences evolving in non-Euclidean spaces. This problem has several applications in the areas of human activity analysis, where there is a need to perform fast search, and recognition in very high dimensional spaces. The problem is ma…
Training model to generate data has increasingly attracted research attention and become important in modern world applications. We propose in this paper a new geometry-based optimization approach to address this problem. Orthogonal to current state-of-the-art density-based approaches, most notably VAE and GAN, we pres…
A novel method compresses point cloud attributes by folding them onto a 2D grid.
Meta-BO method clusters and learns from prior tasks to optimize heterogeneous functions.
New SigSwap model for path-dependent financial risk.
This work proves generalization bounds for neural networks without Lipschitz assumptions.
This paper studies the interplay between the N=2 gauge theories in three and four dimensions that have a geometric description in terms of twisted compactification of the six-dimensional (2,0) SCFT. Our main goal is to construct the three-dimensional domain walls associated to any three-dimensional cobordism. We find t…
This paper advocates Riemannian multi-manifold modeling in the context of network-wide non-stationary time-series analysis. Time-series data, collected sequentially over time and across a network, yield features which are viewed as points in or close to a union of multiple submanifolds of a Riemannian manifold, and dis…
Develops k-contact geometry theory for field theories.
New metrics for information geometry and machine learning from Lie groups.
Proposes a new phylogenetic tree space with biologically principled geometry.
Ricci-Filtration enhances retrieval-augmented generation rerankers for query-answer tasks by using discrete Ricci flow on graphs.
NLGS optimizes latent geometry for better model performance.
End-to-end DRNs outperform ConvNets in EEG decoding.
Enhanced Sampling Scheme improves masked generative modeling.
PRS improves rejection sampling by learning better proposals.