Complex-valued Gaussian process improves time series analysis of brain oscillations.
problem Improving time series analysis of complex-valued signals, especially brain oscillations.
method Modeling real-valued signals as the real part of a latent complex-valued Gaussian process with new covariance functions.
result Complex-valued Gaussian process provides better estimates of amplitude and frequency than existing methods.
Proposes random Euler filters for efficient complex-valued nonlinear signal processing.
problem Efficiently processing complex-valued nonlinear signals with reduced computational cost.
method Introduces linear and widely-linear random Euler complex-valued filters with fixed network structures.
result Analytical minimum mean square error and optimum step-size derived for transient and steady-state performances.
A new method for complex-valued signals improves convergence and performance.
problem Nonlinear channel equalization and complex-valued signals with different properties.
method Generalized complex kernel least-mean-square (gCKLMS) algorithm.
result The gCKLMS algorithm converges faster and performs better than previous methods.
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…
PolarBM models complex-valued audio signals in polar coordinates, improving over conventional methods.
problem Discarding structural information in complex-valued problems simplifies models but loses important amplitude-phase relationships.
method Proposes PolarBM, a novel Boltzmann machine for complex-valued variables in polar coordinates, and LogPolarBM for logarithmic amplitude.
result PolarBM and LogPolarBM achieve superior modeling accuracy compared to conventional models, including deep neural networks.
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…
Survey of complex-valued neural networks for improved performance.
problem Lack of complex-valued neural networks in machine learning frameworks.
method Literature review of CVNNs.
result Advantages of CVNNs over real-valued neural networks.
Proposes a Complex Transformer for complex-valued sequence modeling.
problem Lack of deep learning models for complex-valued data.
method Develops a Complex Transformer using transformer backbone with specialized attention and encoder-decoder networks.
result Achieves state-of-the-art performance on complex-valued datasets.
Complex-valued neural networks improve seismic data analysis by preserving phase information.
problem Low-frequency aliasing in seismic data due to discarded phase information.
method Developed complex-valued deep convolutional networks to leverage phase information in deterministic physical data.
result Complex-valued networks outperform real-valued networks in training and inference from deterministic physical data.
Proposes a new complex Gaussian distribution for better modeling of complex-valued signals.
problem Limited ability of Gaussian distribution to represent diverse amplitude characteristics.
method Introduces a power-weighted noncentral complex Gaussian distribution on the complex plane.
result Consistently outperforms conventional distributions in log-likelihood for speech power spectra.
Method recovers complex-valued signals from speckle-noised measurements.
problem Recovering complex-valued signals from speckle-noised measurements.
method Bagged Deep Image Priors integrated with projected gradient descent and Newton-Schulz algorithm.
result Achieves state-of-the-art performance in MSE reduction.
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…
Complex-valued neural networks improve wireless fingerprinting robustness.
problem Distinguish between devices sending the same message, robust against spoofing.
method Used complex-valued neural networks for supervised learning of fingerprints from wireless signals.
result Noise augmentation by adding white Gaussian noise leads to significant performance gains.
This paper proves a generalization bound for complex-valued neural networks scaling with spectral complexity.
problem Ensuring the performance of complex-valued neural networks on unseen data.
method Theoretical derivation using Maurey Sparsification Lemma and Dudley Entropy Integral, empirical validation on various datasets.
result The spectral complexity of weight matrices is a significant factor in the generalization ability of complex-valued neural networks.
CRBM extracts speech features from complex spectra directly.
problem Speech coding ignores phase information in complex spectra.
method CRBM learns relationships between visible and hidden units from complex-valued spectra.
result CRBM outperforms conventional methods in speech coding.
CVAE detects weak complex signals in maritime radar, improving detection over classical methods.
problem Detecting weak complex-valued signals in non-Gaussian, range-varying interference.
method Complex-valued Variational AutoEncoder (CVAE) trained on clutter-plus-noise, whitening, ANMF fusion.
result CVAE yields higher detection probability Pd at matched false-alarm rate Pfa, especially with whitening.
This work improves interpretability and calibration of complex-valued neural networks using Newton-Puiseux analysis.
problem Insufficient interpretability and probability calibration of complex-valued neural networks.
method Newton-Puiseux framework to examine local decision geometry, fitting a polynomial surrogate and factorizing it using Newton-Puiseux expansions.
result Enhanced Expected Calibration Error in ECG and wireless modulation datasets compared to uncalibrated softmax and standard post-hoc baselines.
We propose a new algorithm to learn a dictionary for reconstructing and sparsely encoding signals from measurements without phase. Specifically, we consider the task of estimating a two-dimensional image from squared-magnitude measurements of a complex-valued linear transformation of the original image. Several recent …
This paper reconstructs complex graph signals using kernel methods on manifolds.
problem Reconstructing complex graph signals from samples on graph vertices.
method Kernel methods on complex manifolds, embedding vertices into higher-dimensional spaces.
result Effective reconstruction of complex graph signals, outperforming conventional methods.
New method uses image registration to recover complex signals from amplitude data.
problem Recovering complex-valued signals from amplitude measurements.
method Indirect registration using LDDMM formalism with exterior calculus.
result Algorithm performs well under various conditions including noise and topology.
New method creates minimal submanifolds using complex-valued eigenfunctions.
problem Creating minimal submanifolds in compact Riemannian manifolds.
method Employing complex-valued eigenfunctions.
result Manufactured minimal submanifolds in compact Riemannian manifolds.
Complex-valued neural networks avoid spurious local minima.
problem Finding spurious local minima in neural networks.
method Proved no spurious local minima for shallow complex neural networks with quadratic activations.
result Complex-valued weights eliminate spurious local minima in neural networks.
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…
Improved U-Nets with various intermediate blocks enhance singing voice separation.
problem Improving singing voice separation accuracy using U-Net architectures.
method Implemented and compared U-Nets with different intermediate spectrogram transformation blocks.
result A specific block type achieves state-of-the-art SDR by 0.9 dB.
New solutions found using rational exponents in complex-valued geometry.
problem Difficult non-linear problems in differential geometry.
method Generalizing from polynomial solutions to rational exponents.
result Many new solutions found.
Complex-valued (p,q)-harmonic morphisms defined and studied.
problem Defining and studying (p,q)-harmonic morphisms between Riemannian manifolds.
method Introducing and characterizing complex-valued (p,q)-harmonic morphisms.
result Characterization and new non-trivial examples of complex-valued (p,q)-harmonic morphisms.
Paper introduces new complex-valued kernel for improved regression.
problem Limited solution for complex-valued regression using real-valued kernels.
method Derives widely RKHS (WRKHS) and pseudo-kernel to address limitations.
result WRKHS yields better performance in complex-valued regression.
New solutions found for complex-valued harmonic morphisms with rational exponents.
problem Finding new solutions to complex-valued harmonic morphisms.
method Generalizing from polynomial solutions to rational exponents.
result Many new solutions to the problem.
Complex-valued neural networks perform similarly to real-valued models for real-valued classification tasks.
problem Comparing real-valued and complex-valued neural networks for real-valued classification tasks.
method Comparison of neural networks with similar capacity sizes, using various activation functions and weight initialisation strategies.
result Complex-valued neural networks perform equal to or slightly worse than real-valued models for real-valued classification tasks.
Study improves RF sensor robustness for target recognition.
problem Variability in RF target responses makes them vulnerable to attacks.
method Evaluates techniques for building robust classification architectures.
result Improves accuracy in identifying true target characteristics.
The paper uses complex-valued functions to simplify plane differential geometry and kinematics.
problem Simplifying complex problems in plane differential geometry and kinematics.
method Consistent use of complex-valued functions of a real variable.
result Derives results in a particularly simple, uniform, and transparent way.
Deep learning uses WiFi CSI for reliable human presence detection.
problem Reliable human presence detection using ambient RF signals.
method Pre-processing of estimated CSI followed by deep learning.
result Near perfect presence detection during multiple extended periods.
Kähler information manifolds for signal filters in weighted Hardy spaces are explored.
problem Developing a geometric framework for signal processing filters in weighted Hardy spaces.
method Introducing weighted Hardy spaces and smooth transformations of transfer functions, demonstrating the Kähler manifold structure.
result The Riemannian geometry of weighted Hardy norms for transfer functions forms a Kähler manifold.
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.
problem Efficiently compressing complex-valued neural networks for embedded systems.
method Extending Sparse Variational Dropout to complex-valued networks and conducting a numerical study.
result Achieved state-of-the-art performance on MusicNet with 50-100x compression.
Study complex-valued VAEs for radar OOD detection.
problem Detecting out-of-distribution signals in complex radar environments.
method Proposed and compared several detection metrics for CVAE.
result CVAE-MSE and latent-based scores outperform ANMF-Tyler.
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…
Enhances on-policy RL with past reward statistics and hot-wiring.
problem Challenges of sparse reward signals in on-policy methods.
method Multi-critic supervision and hot-wiring mechanism.
result Improves on-policy learning for sparse reward tasks.
Unified framework for complex-valued eigenfunctions on Riemannian symmetric spaces.
problem Finding a unified scheme for complex-valued eigenfunctions on Riemannian symmetric spaces.
method Employing the Cartan embedding for classical compact Riemannian symmetric spaces and quaternionic Grassmannians.
result Construction of new eigenfunctions on quaternionic Grassmannians.
C-SURE improves complex-valued deep learning models by shrinking estimates, outperforming MLE and SurReal.
problem Improving accuracy and robustness of complex-valued deep learning models.
method Proposes a Stein's unbiased risk estimate (SURE) for complex-valued data and integrates it into a prototype CNN classifier.
result C-SURE outperforms SurReal and MLE in accuracy and robustness on complex-valued datasets.
New method constructs complex-valued r-harmonic functions on Riemannian manifolds.
problem Constructing complex-valued r-harmonic functions on Riemannian manifolds.
method Introducing a new method for constructing complex-valued r-harmonic functions on Riemannian manifolds and applying it to specific semisimple Lie groups.
result The method successfully constructs complex-valued r-harmonic functions on various Riemannian manifolds, including specific Lie groups.
This research explores complex-valued neural networks and their implementation.
problem The challenges of implementing complex-valued neural networks and their potential for non-complex data.
method Detailed theory and implementation of CVNN, including Wirtinger calculus, complex backpropagation, and modules like complex layers and activation functions. Python implementation using cvnn toolbox.
result Demonstrates the potential of CVNN for non-complex data through simulations.
New submersion proves complex-valued harmonic map existence.
problem Existence of non-constant harmonic morphisms.
method Constructing harmonic Riemannian submersions from symmetric spaces.
result Existence of non-constant, globally defined complex-valued harmonic morphism.
CVNN outperforms RVNN on non-circular data.
problem Classifying complex-valued data with statistical dependence.
method Comparison of CVNN and RVNN on non-circular data.
result CVNN outperforms RVNN in accuracy and generalization.
In many applications one may acquire a composition of several signals that may be corrupted by noise, and it is a challenging problem to reliably separate the components from one another without sacrificing significant details. Adding to the challenge, in a compressive sensing framework, one is given only an undersampl…
Novel complex RNN improves stability and performance in sequence tasks.
problem Lack of complex representations in deep learning for sequence tasks.
method Developed a complex gated recurrent cell combining complex-valued and norm-preserving state transitions with a gating mechanism.
result Improves stability and convergence properties, performs competitively on various tasks.
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…
In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the relative scarcity of formal tools for SBL in complex-valued models, this paper propo…