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.
New method creates minimal submanifolds using complex-valued eigenfunctions.
Unified framework for complex-valued eigenfunctions on Riemannian symmetric spaces.
New complete minimal submanifolds found in specific Riemannian spaces.
New method for minimal submanifolds in spheres using eigenfunctions.
We prove that, given any knot in a compact 3-manifold M, there exists a Riemannian metric on M such that there is a complex-valued eigenfunction u of the Laplacian, corresponding to the first nontrivial eigenvalue, whose nodal set has a connected component given by . Higher dimensional analogs of thi…
New compact minimal submanifolds found in Riemannian symmetric spaces.
Constructs explicit harmonic functions and morphisms on complex and quaternionic Grassmannians.
Harmonic morphisms and p-harmonic functions constructed on symmetric spaces.
Complex-valued neural networks avoid spurious local minima.
A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with complex-valued vectors followed by (2) taking the absolute value of every entry…
Complex-valued (p,q)-harmonic morphisms defined and studied.
The paper uses complex-valued functions to simplify plane differential geometry and kinematics.
In the spirit of Ray and Singer we define a complex valued analytic torsion using non-selfadjoint Laplacians. We establish an anomaly formula which permits to turn this into a topological invariant. Conjecturally this analytically defined invariant computes the complex valued Reidemeister torsion, including its phase. …
Bayesian sparsification improves complex-valued neural networks by 50-100x with minimal performance loss.
Study complex-valued VAEs for radar OOD detection.
The construction of synthetic complex-valued signals from real-valued observations is an important step in many time series analysis techniques. The most widely used approach is based on the Hilbert transform, which maps the real-valued signal into its quadrature component. In this paper, we define a probabilistic gene…
Complex-valued neural networks are not a new concept, however, the use of real-valued models has often been favoured over complex-valued models due to difficulties in training and performance. When comparing real-valued versus complex-valued neural networks, existing literature often ignores the number of parameters, r…
We study the curvature of a manifold on which there can be defined a complex-valued submersive harmonic morphism with either, totally geodesic fibers or that is holomorphic with respect to a complex structure which is compatible with the second fundamental form. We also give a necessary curvature condition for the exis…
Usually, complex-valued RKHS are presented as an straightforward application of the real-valued case. In this paper we prove that this procedure yields a limited solution for regression. We show that another kernel, here denoted as pseudo kernel, is needed to learn any function in complex-valued fields. Accordingly, we…
This paper describes a novel energy-based probabilistic distribution that represents complex-valued data and explains how to apply it to direct feature extraction from complex-valued spectra. The proposed model, the complex-valued restricted Boltzmann machine (CRBM), is designed to deal with complex-valued visible unit…
C-SURE improves complex-valued deep learning models by shrinking estimates, outperforming MLE and SurReal.
Over the last decade, both the neural network and kernel adaptive filter have successfully been used for nonlinear signal processing. However, they suffer from high computational cost caused by their complex/growing network structures. In this paper, we propose two random Euler filters for complex-valued nonlinear filt…
This paper proves a generalization bound for complex-valued neural networks scaling with spectral complexity.
This research explores complex-valued neural networks and their implementation.
We propose a novel adaptive kernel based regression method for complex-valued signals: the generalized complex-valued kernel least-mean-square (gCKLMS). We borrow from the new results on widely linear reproducing kernel Hilbert space (WL-RKHS) for nonlinear regression and complex-valued signals, recently proposed by th…
New submersion proves complex-valued harmonic map existence.
CVNN outperforms RVNN on non-circular data.
We consider an elliptic self-adjoint first order pseudodifferential operator acting on columns of m complex-valued half-densities over a connected compact n-dimensional manifold without boundary. The eigenvalues of the principal symbol are assumed to be simple but no assumptions are made on their sign, so the operator …
We consider an elliptic self-adjoint first order differential operator acting on pairs (2-columns) of complex-valued half-densities over a connected compact 3-dimensional manifold without boundary. The principal symbol of our operator is assumed to be trace-free. We study the spectral function which is the sum of squar…
We extend the complex-valued analytic torsion, introduced by Burghelea and Haller on closed manifolds, to compact Riemannian bordisms. We do so by considering a flat complex vector bundle over a compact Riemannian manifold, endowed with a fiberwise nondegenerate symmetric bilinear form. The Riemmanian metric and the bi…
CVNNs improve performance in tasks with complex-valued inputs.
In this note, we report the back propagation formula for complex valued singular value decompositions (SVD). This formula is an important ingredient for a complete automatic differentiation(AD) infrastructure in terms of complex numbers, and it is also the key to understand and utilize AD in tensor networks.
Complex valued analytic torsion and dynamical zeta function studied on locally symmetric spaces.
Study critical points of Laplace eigenfunctions in polygons.
Establishes log-concavity estimates for convex domains' first Dirichlet eigenfunctions.
The study counts critical points of Steklov eigenfunctions on manifolds.
Study heat profiles and eigenfunctions using Brownian motion.
Eigenfunction gradients on curved spaces imply rigid structure.
We describe the relationship between complex-valued harmonic morphisms from Minkowski 4-space} and the shear-free ray congruences of mathematical physics. Then we show how a horizontally conformal submersion on a domain of Euclidean 3-space gives the boundary values at infinity of a complex-valued harmonic morphism on …
Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process is uncorrelated with its complex conjugate. This assumption is a good model of th…
CAP-BM learns complex-valued data's amplitude and phase distributions.
PolarBM models complex-valued audio signals in polar coordinates, improving over conventional methods.
Complex-valued neural networks can approximate any continuous function with bounded widths and depths.
We study concentration phenomena of eigenfunctions of the Laplacian on closed Riemannian manifolds. We prove that the volume measure of a closed manifold concentrates around nodal sets of eigenfunctions exponentially. Applying the method of Colding and Minicozzi we also prove restricted exponential concentration inequa…
The paper bounds Cheeger ratios of eigenfunctions and their level sets.
Survey of complex-valued neural networks for improved performance.
The study uses heat flow to analyze properties of Laplace eigenfunctions on manifolds and domains.
There are three equivalent ways of representing two jointly observed real-valued signals: as a bivariate vector signal, as a single complex-valued signal, or as two analytic signals known as the rotary components. Each representation has unique advantages depending on the system of interest and the application goals. I…