Related papers: Non Commutative Convolutional Signal Models in Neu…
Spherical convolutional neural networks (Spherical CNNs) learn nonlinear representations from 3D data by exploiting the data structure and have shown promising performance in shape analysis, object classification, and planning among others.…
A resistive memory network that has no crossover wiring is proposed to overcome the hardware limitations to size and functional complexity that is associated with conventional analogue neural networks. The proposed memory network is based…
Fourier-based wavefront sensors, such as the Pyramid Wavefront Sensor (PWFS), are the current preference for high contrast imaging due to their high sensitivity. However, these wavefront sensors have intrinsic nonlinearities that constrain…
Existing permanental processes often impose constraints on kernel types or stationarity, limiting the model's expressiveness. To overcome these limitations, we propose a novel approach utilizing the sparse spectral representation of…
This paper focuses on spectral graph convolutional neural networks (ConvNets), where filters are defined as elementwise multiplication in the frequency domain of a graph. In machine learning settings where the dataset consists of signals…
A one parameter set of noncommutative complex algebras is given. These may be considered deformation quantisation algebras. The commutative limit of these algebras correspond to the algebra of polynomial functions over a manifold or…
This paper studies the statistical models of the noise-robust normalized subband adaptive filter (NR-NSAF) algorithm in the mean and mean square deviation senses involving transient-state and steady-state behavior by resorting to the method…
This paper reports a breakdown in linear stability theory under conditions of neutral stability that is deduced by an examination of exponential modes of the form $h\approx {{e}^{i(kx-\omega t)}}$, where $h$ is a response to a disturbance,…
Nonstationary Gabor frames were recently introduced in adaptive signal analysis. They represent a natural generalization of classical Gabor frames by allowing for adaptivity of windows and lattice in either time or frequency. In this paper…
The effectiveness of Convolutional Neural Networks (CNNs) has been substantially attributed to their built-in property of translation equivariance. However, CNNs do not have embedded mechanisms to handle other types of transformations. In…
A low-complexity model for signal quality prediction in a nonlinear fiber-optical network is developed. The model, which builds on the Gaussian noise model, takes into account the signal degradation caused by a combination of chromatic…
We consider the problem of recovering of continuous multi-dimensional functions from the noisy observations over the regular grid. Our focus is at the adaptive estimation in the case when the function can be well recovered using a linear…
In spite of their huge success, transformer models remain difficult to scale in depth. In this work, we develop a unified signal propagation theory and provide formulae that govern the moments of the forward and backward signal through the…
The algebraic stability theorem for $\mathbb{R}$-persistence modules is a fundamental result in topological data analysis. We present a stability theorem for $n$-dimensional rectangle decomposable persistence modules up to a constant…
Feature extraction in noisy image datasets presents many challenges in model reliability. In this paper, we use the discrete Fourier transform in conjunction with persistent homology analysis to extract specific frequencies that correspond…
A novel and efficient end-to-end learning model for automatic modulation classification is proposed for wireless spectrum monitoring applications, which automatically learns from the time domain in-phase and quadrature data without…
In this paper we discuss the stability properties of convolutional neural networks. Convolutional neural networks are widely used in machine learning. In classification they are mainly used as feature extractors. Ideally, we expect similar…
The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…
In this paper we study the asymptotic theory for spectral analysis of stationary random fields, including linear and nonlinear fields. Asymptotic properties of Fourier coefficients and periodograms, including limiting distributions of…
Neural networks rely on convolutions to aggregate spatial information. However, spatial convolutions are expensive in terms of model size and computation, both of which grow quadratically with respect to kernel size. In this paper, we…