Related papers: Spectral Convolution Networks
Activation functions are the linchpins of deep learning, profoundly influencing both the representational capacity and training dynamics of neural networks. They shape not only the nature of representations but also optimize convergence…
In this paper, a new variant to fractional signal processing is proposed known as the Reduced Order Fractional Fourier Transform. Various properties satisfied by its transformation kernel is derived. The properties associated with the…
Fourier-encoded implicit neural representations (INRs) have shown strong capability in modeling continuous signals from discrete samples. However, conventional Fourier feature mappings use a fixed set of frequencies over the entire spatial…
The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…
Fourier transform (FT) plays a crucial role in a broad range of applications, from enhancement, restoration and analysis through to security, compression and manipulation. The Fourier transform (FT) is a process that converts a function…
We study concentration operators associated with either the discrete or the continuous Fourier transform, that is, operators that incorporate a spatial cut-off and a subsequent frequency cut-off to the Fourier inversion formula. Their…
The Convolutional Neural Network (CNN) is a state-of-the-art architecture for a wide range of deep learning problems, the quintessential example of which is computer vision. CNNs principally employ the convolution operation, which can be…
We propose a decomposition method for the spectral peaks in an observed frequency spectrum, which is efficiently acquired by utilizing the Fast Fourier Transform. In contrast to the traditional methods of waveform fitting on the spectrum,…
We consider a network of interconnected dynamical systems. Spectral network identification consists in recovering the eigenvalues of the network Laplacian from the measurements of a very limited number (possibly one) of signals. These…
In the study of neural network interpretability, there is growing evidence to suggest that relevant features are encoded across many neurons in a distributed fashion. Making sense of these distributed representations without knowledge of…
Gradient-based neural network training traditionally enforces symmetry between forward and backward propagation, requiring activation functions to be differentiable (or sub-differentiable) and strictly monotonic in certain regions to…
We review neural network architectures which were motivated by Fourier series and integrals and which are referred to as Fourier neural networks. These networks are empirically evaluated in synthetic and real-world tasks. Neither of them…
In this work we analyze strategies for convolutional neural network scaling; that is, the process of scaling a base convolutional network to endow it with greater computational complexity and consequently representational power. Example…
This paper examines the possibility of, and the possible advantages to learning the filters of convolutional neural networks (CNNs) for image analysis in the wavelet domain. We are stimulated by both Mallat's scattering transform and the…
Spectral bias, the tendency of neural networks to learn low-frequency features first, is a well-known issue with many training algorithms for physics-informed neural networks (PINNs). To overcome this issue, we propose IFeF-PINN, an…
We propose neural network layers that explicitly combine frequency and image feature representations and show that they can be used as a versatile building block for reconstruction from frequency space data. Our work is motivated by the…
The search for efficient neural network architectures has gained much focus in recent years, where modern architectures focus not only on accuracy but also on inference time and model size. Here, we present FUN, a family of novel…
We address the problem of decomposing an image into albedo and shading. We propose the Fast Fourier Intrinsic Network, FFI-Net in short, that operates in the spectral domain, splitting the input into several spectral bands. Weights in…
The nonstationary nature of signals and nonlinear systems require the time-frequency representation. In time-domain signal, frequency information is derived from the phase of the Gabor's analytic signal which is practically obtained by the…
Graph convolutional networks(GCNs) have become the most popular approaches for graph data in these days because of their powerful ability to extract features from graph. GCNs approaches are divided into two categories, spectral-based and…