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.
A new graphical model for discrete data without parametric restrictions.
A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equatio…
Transforms game optimization dynamics into frequency domain for precise hyperparameter analysis.
The paper constructs and analyzes self-similar blowup solutions for a wave map equation.
Derives EoM for DNNs to describe GD dynamics precisely.
New neural stack and Turing Machine architectures prove stability and computational power.
There is a pressing need to build an architecture that could subsume these networks under a unified framework that achieves both higher performance and less overhead. To this end, two fundamental issues are yet to be addressed. The first one is how to implement the back propagation when neuronal activations are discret…
Notes on continuity of discrete-spectrum Fredholm operators.
Low precision networks in the reinforcement learning (RL) setting are relatively unexplored because of the limitations of binary activations for function approximation. Here, in the discrete action ATARI domain, we demonstrate, for the first time, that low precision policy distillation from a high precision network pro…
Study identifies and analyzes three types of errors in learning Fourier operators.
Discretizes Hodge-Dirac operators on a torus.
We study certain polynomial trace identities in the group $SL(2,\IC)$ and their application in the theory of discrete groups. We obtain canonical representations for two generator groups in §4 and then in §5 we give a new proof for Gehring and Martin's polynomial trace identities for good words, and extend that result …
This work revisits, from a geometric perspective, the notion of discrete connection on a principal bundle, introduced by M. Leok, J. Marsden and A. Weinstein. It provides precise definitions of discrete connection, discrete connection form and discrete horizontal lift and studies some of their basic properties and rela…
Develops a framework for learning nonlinear operators using Mercer kernels.
High-dimensional inference for sparse spectral precision matrices
Discrete exterior calculus shows natural properties of wedge product and averaging.
Random Gaussian fields on 4D Riemannian manifolds with conformal invariance.
We define a discrete Laplace-Beltrami operator for simplicial surfaces. It depends only on the intrinsic geometry of the surface and its edge weights are positive. Our Laplace operator is similar to the well known finite-elements Laplacian (the so called ``cotan formula'') except that it is based on the intrinsic Delau…
This research proves that quadratic regularized optimal transport can approximate the Laplace-Beltrami operator on smooth manifolds.
We analyze convergence of Fermat distances and their application in clustering.
We propose simple conditions equivalent to the discreteness of the spectrum of the Laplace-Beltrami operator on a class of Riemannian manifolds close to warped products. For this class of manifolds we establish a relationship between discreteness of the spectrum and stochastic incompleteness.
State of the art deep learning models have made steady progress in the fields of computer vision and natural language processing, at the expense of growing model sizes and computational complexity. Deploying these models on low power and mobile devices poses a challenge due to their limited compute capabilities and str…
Develops combinatorial theory of vector bundles on simplicial complexes.
Study on Lawson surfaces' first Laplace eigenvalue using symmetry and algebraic methods.
New STH distance finds patterns in event timeseries without resampling.
Approximating Gaussian Whittle-Matern Fields over Well-Centered Triangulations of Riemannian Manifolds
In differential geometry of surfaces the Dirac operator appears intrinsically as a tool to address the immersion problem as well as in an extrinsic flavour (that comes with spin transformations to comformally transfrom immersions) and the two are naturally related. In this paper we consider a corresponding pair of disc…
NOs can learn any finite collection of classes in functional data.
In this work, we consider the hedging error due to discrete trading in models with jumps. Extending an approach developed by Fukasawa [In Stochastic Analysis with Financial Applications (2011) 331-346 Birkhäuser/Springer Basel AG] for continuous processes, we propose a framework enabling us to (asymptotically) optimize…
Extends ONNX for quantized neural networks with new formats and operators.
The purpose of this paper is to describe geometrically discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids. From a variational principle we derive the discrete Euler-Lagrange equations and we introduce a symplectic 2-section, which is preserved by the Lagrange evolution operator. In terms of the discrete Leg…
In this paper higher order mimetic discretizations are introduced which are firmly rooted in the geometry in which the variables are defined. The paper shows how basic constructs in differential geometry have a discrete counterpart in algebraic topology. Generic maps which switch between the continuous differential for…
Transformers can predict new tokens based on any number of context tokens, approximating continuous mappings with fixed resources.
In this paper we propose and study a family of continuous wavelets on general domains, and a corresponding stochastic discretization that we call Monte Carlo wavelets. First, using tools from the theory of reproducing kernel Hilbert spaces and associated integral operators, we define a family of continuous wavelets by …
Generalized Precision Matrix for scalable estimation of nonparametric Markov networks.
Study discrete analog of zeta-determinant maximization on triangulated surfaces.
Physics-informed neural operator learns from coarse to fine discretized data.
We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a black-box differential equation solver. These continuous-depth models have constan…
This work is thought as an operative guide to discrete exterior calculus (DEC), but at the same time with a rigorous exposition. We present a version of (DEC) on cubic cell, defining it for discrete manifolds. An example of how it works, it is done on the discrete torus, where usual Gauss and Stokes theorems are recove…
GLAD improves latent graph generation by quantizing discrete latent space.
Essential self-adjointness and spectrum of CR GJMS operator proved.
Unified approach to discrete and smooth isoperimetric inequalities of arbitrary order.
Low precision operations can provide scalability, memory savings, portability, and energy efficiency. This paper proposes SWALP, an approach to low precision training that averages low-precision SGD iterates with a modified learning rate schedule. SWALP is easy to implement and can match the performance of full-precisi…
Neural networks learn discrete tasks on continuous data via emergent geometry.
Discretizes diffusions and harmonic functions on covering spaces.
Reparameterization of variational auto-encoders with continuous random variables is an effective method for reducing the variance of their gradient estimates. In the discrete case, one can perform reparametrization using the Gumbel-Max trick, but the resulting objective relies on an operation and is non-dif…
We consider Toeplitz operators associated with the renormalized Bochner-Laplacian on high tensor powers of a positive line bundle on a compact symplectic manifold. We study the asymptotic behavior, in the semiclassical limit, of low-lying eigenvalues and the corresponding eigenfunctions of a self-adjoint Toeplitz opera…
Using an integrable discrete Dirac operator, we construct a discrete version of the Weierstrass representation of time-like surfaces parametrized along isotropic directions in , and . The corresponding discrete surfaces have isotropic edges. We show that any discrete surface satisfying a gen…