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.
Complex-valued neural networks avoid spurious local minima.
Bayesian sparsification improves complex-valued neural networks by 50-100x with minimal performance loss.
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…
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…
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.
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…
CVNN outperforms RVNN on non-circular data.
Complex-valued neural networks can approximate any continuous function with bounded widths and depths.
Survey of complex-valued neural networks for improved performance.
CVNNs improve performance in tasks with complex-valued inputs.
Complex-valued neural networks can approximate any continuous function.
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.
C-SURE improves complex-valued deep learning models by shrinking estimates, outperforming MLE and SurReal.
CAP-BM learns complex-valued data's amplitude and phase distributions.
New method creates minimal submanifolds using complex-valued eigenfunctions.
This work improves interpretability and calibration of complex-valued neural networks using Newton-Puiseux analysis.
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…
Complex-valued (p,q)-harmonic morphisms defined and studied.
PolarBM models complex-valued audio signals in polar coordinates, improving over conventional methods.
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. …
A fast method for learning MZI parameters in optical neural networks.
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…
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…
While deep learning has received a surge of interest in a variety of fields in recent years, major deep learning models barely use complex numbers. However, speech, signal and audio data are naturally complex-valued after Fourier Transform, and studies have shown a potentially richer representation of complex nets. In …
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…
Unified framework for complex-valued eigenfunctions on Riemannian symmetric spaces.
Deep learning has become an area of interest in most scientific areas, including physical sciences. Modern networks apply real-valued transformations on the data. Particularly, convolutions in convolutional neural networks discard phase information entirely. Many deterministic signals, such as seismic data or electrica…
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…
FreDN separates trends and periodicities in non-stationary time series forecasts.
Previous studies have found that an adversary attacker can often infer unintended input information from intermediate-layer features. We study the possibility of preventing such adversarial inference, yet without too much accuracy degradation. We propose a generic method to revise the neural network to boost the challe…
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.
A "wireless fingerprint" which exploits hardware imperfections unique to each device is a potentially powerful tool for wireless security. Such a fingerprint should be able to distinguish between devices sending the same message, and should be robust against standard spoofing techniques. Since the information in wirele…
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…
Complex valued analytic torsion and dynamical zeta function studied on locally symmetric spaces.
Deep learning has recently led to great successes in tasks such as image recognition (e.g Krizhevsky et al., 2012). However, deep networks are still outmatched by the power and versatility of the brain, perhaps in part due to the richer neuronal computations available to cortical circuits. The challenge is to identify …
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 …
IGT learns graph representations without supervision.
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…
Risk diversification is one of the dominant concerns for portfolio managers. Various portfolio constructions have been proposed to minimize the risk of the portfolio under some constrains including expected returns. We propose a portfolio construction method that incorporates the complex valued principal component anal…
We construct new complex-valued harmonic morphisms from Euclidean spaces from functions which are holomorphic with respect to Hermitian structures. In particular, we give the first global examples of complex-valued harmonic morphisms from for each which do not arise from a Kähler structure; it is know…
Let S be a closed topological surface. Haupt's theorem provides necessary and sufficient conditions for a complex-valued character of the first integer homology group of S to be realized by integration against a complex-valued 1-form that is holomorphic with respect to some complex structure on S. We prove a refinement…
The paper studies geometric representations of submanifolds using complex-valued functions.
In this paper, we generalize Huber's criterion to multichannel sparse recovery problem of complex-valued measurements where the objective is to find good recovery of jointly sparse unknown signal vectors from the given multiple measurement vectors which are different linear combinations of the same known elementary vec…
New complex-valued maps found on complex geometries.