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.
We found stronger counterexamples to the topological Tverberg conjecture.
BO optimized for high dimensions using feature space learning.
In this paper, we define lower dimensional volumes of spin manifolds with boundary. We compute the lower dimensional volume for 5-dimensional and 6-dimensional spin manifolds with boundary and we also get the Kastler-Kalau-Walze type theorem in this case.
New model estimates higher-order interactions in stochastic processes using lower-dimensional projections.
In this paper we explain how to define "lower dimensional'' volumes of any compact Riemannian manifold as the integrals of local Riemannian invariants. For instance we give sense to the area and the length of such a manifold in any dimension. Our reasoning is motivated by an idea of Connes and involves in an essential …
Lower-dimensional video discriminators improve GAN performance.
This work reduces the dimensionality of text data using SVD, improving performance and computational efficiency.
In this paper, we define lower dimensional volumes associated to sub-Dirac operators for foliations. In some cases, we compute these lower dimensional volumes. We also prove the Kastler-Kalau-Walze type theorems for foliations with or without boundary. As a corollary, we give an explanation of the gravitational action …
A novel GP architecture, Thin and Deep GP, learns lower-dimensional representations without losing interpretability.
In this paper, we define lower dimensional volumes of spin manifolds with boundary. We compute the lower dimensional volume for 6-dimensional spin manifolds with boundary and the gravity on boundary is derived by the noncommutative residue associated with Dirac operators.For 6-dimensional manifo…
While neural networks are powerful approximators used to classify or embed data into lower dimensional spaces, they are often regarded as black boxes with uninterpretable features. Here we propose Graph Spectral Regularization for making hidden layers more interpretable without significantly impacting performance on th…
Generative Topological Networks (GTNs) simplify latent space generation.
Many features of dimensional reduction schemes are determined by the breaking of higher dimensional general covariance associated with the selection of a particular subset of coordinates. By investigating residual covariance we introduce lower dimensional tensors --generalizing to one side Kaluza-Klein gauge fields and…
Paper studies binary random projections with controllable sparsity patterns for computational and accuracy advantages.
Improved disability insurance model with collective health claims.
The results of this paper are outdated. Finer versions of them will appear elsewhere.
New method for model inversion attacks on deep networks.
RS-HDMR-GPR simplifies complex functions with machine-learned lower-dimensional terms.
We mostly determine which closed smooth oriented 4-manifolds fibering over lower dimensional manifolds are virtually symplectic, i.e. finitely covered by symplectic 4-manifolds.
We explore algebraic characterizations of 2-knots whose associated knot manifolds fibre over lower-dimensional orbifolds, and consider also some issues related to the groups of higher-dimensional fibred knots.
In the present paper, we determine the topologies of three-dimensional closed Alexandrov spaces which converge to lower dimensional spaces in the Gromov-Hausdorff topology.
This paper develops a method to learn lower-dimensional submanifolds of brain connectomes.
We prove that any compact Kähler manifold bearing a holomorphic Cartan geometry contains a rational curve just when the Cartan geometry is inherited from a holomorphic Cartan geometry on a lower dimensional compact Kähler manifold.
Two methods monitor high-dimensional processes via manifold fitting or learning.
In order to avoid the curse of dimensionality, frequently encountered in Big Data analysis, there was a vast development in the field of linear and nonlinear dimension reduction techniques in recent years. These techniques (sometimes referred to as manifold learning) assume that the scattered input data is lying on a l…
Suppose that two large, multi-dimensional data sets are each noisy measurements of the same underlying random process, and principle components analysis is performed separately on the data sets to reduce their dimensionality. In some circumstances it may happen that the two lower-dimensional data sets have an inordinat…
New method improves inference for hierarchical models.
New algorithm balances spatial data approximation and prediction accuracy.
Optimal persuasion involves projecting state vectors onto lower-dimensional 'optimal information manifolds'.
Improved DMs with DP-SGD for generating private images.
In this paper, we define lower dimensional volumes of compact Riemannian manifolds with boundary. For five dimensional spin manifolds with boundary, we prove a Kastler-Kalau-Walze type theorem associated with one-form perturbations of Dirac operators in this case.
A method models nonlinear dynamics from data using barycentric coordinates and memory.
Estimates high-dimensional posterior densities by marginal distributions and neural networks.
LDAdam optimizes large models with low memory by adapting to lower-dimensional subspaces.
New method reconstructs manifolds from data using Gaussian processes.
Study on symmetries in wide neural networks' dynamics without bias.
Superposition in autoencoders leads to loss in simple models.
The decomposability of a Cartesian product of two nondecomposable manifolds into products of lower dimensional manifolds is studied. For 3-manifolds we obtain an analog of a result due to Borsuk for surfaces, and in higher dimensions we show that similar analogs do not exist unless one imposes further restrictions such…
Study geometric properties of loss functions to understand neural network performance.
In statistical dimensionality reduction, it is common to rely on the assumption that high dimensional data tend to concentrate near a lower dimensional manifold. There is a rich literature on approximating the unknown manifold, and on exploiting such approximations in clustering, data compression, and prediction. Most …
A new method improves generative models by learning lower-dimensional representations.
We consider Riemannian 4-manifolds that Gromov-Hausdorff converge to a lower dimensional limit space, with the Ricci tensor going to zero. Among other things, we show that if the limit space is two dimensional then under some mild assumptions, the limiting four dimensional geometry away from the curvature blowup region…
We show that if a co-dimension two knot is deform-spun from a lower-dimensional co-dimension 2 knot, there are constraints on the Alexander polynomials. In particular this shows, for all n, that not all co-dimension 2 knots in S^n are deform-spun from knots in S^{n-1}.
A new matrix factorization method for high-dimensional data.
This paper is the first of a 3-part series that classifies the 5-dimensional Thurston geometries. The present paper (part 1 of 3) summarizes the general classification, giving the full list, an outline of the method, and some illustrative examples. This includes phenomena that have not appeared in lower dimensional geo…
New examples of Calabi-Yau 3-folds with unique properties.
The linking integral is an invariant of the link-type of two manifolds immersed in a Euclidean space. It is shown that the ordinary Gauss integral in three dimensions may be simplified to a winding number integral in two dimensions. This result is then generalized to show that in certain circumstances the linking integ…
This paper has four main parts. In the first part, we construct a noncommutative residue for the hypoelliptic calculus on Heisenberg manifolds, that is, for the class of Heisenberg PsiDOs introduced by Beals-Greiner and Taylor. This noncommutative residue appears as the residual trace on integer order Heisenberg PsiDOs…