Related papers: Spectral Convolution Networks
Convolution, a cornerstone of signal processing and optical neural networks, has traditionally been implemented by mapping mathematical operations onto complex hardware. Here, we overcome this challenge by revealing that wave dynamics in…
Time-domain surveys such as the Zwicky Transient Facility (ZTF) have opened a new frontier in the discovery and characterization of transients. While photometric light curves provide broad temporal coverage, spectroscopic observations…
Acoustic recognition has emerged as a prominent task in deep learning research, frequently utilizing spectral feature extraction techniques such as the spectrogram from the Short-Time Fourier Transform and the scalogram from the Wavelet…
One of the key challenges in the area of signal processing on graphs is to design dictionaries and transform methods to identify and exploit structure in signals on weighted graphs. To do so, we need to account for the intrinsic geometric…
Deep networks, especially convolutional neural networks (CNNs), have been successfully applied in various areas of machine learning as well as to challenging problems in other scientific and engineering fields. This paper introduces…
It is common in the accelerator community to use the impedance of accelerator components to describe wake interactions in the frequency domain. However, it is often desirable to understand such wake interactions in the time domain in a…
This paper presents a new approach for assembling graph neural networks based on framelet transforms. The latter provides a multi-scale representation for graph-structured data. We decompose an input graph into low-pass and high-pass…
The Fractional Fourier Transform (FRFT) has been playing a unique and increasingly important role in signal and image processing. In this letter, we investigate the property of frequency shift in two-dimensional FRFT (2D-FRFT) domain. It is…
Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being…
Despite being the most popular methods of data analysis, Fourier-based techniques suffer from the problem of static resolution that is currently believed to be a fundamental limitation of the Fourier Transform. Although alternative…
The objective in this paper is to demonstrate that four of the most used techniques in applied mathematics, viz., Fourier series, Fourier transform, Laplace transform and the Fourier-Laplace transform can be introduced using eigenvalue…
Interpreting spectropolarimetric observations of the solar atmosphere takes much longer than the acquiring the data. The most important reason for this is that the model fitting, or "inversion", used to infer physical quantities from the…
Convolution neural networks have achieved remarkable performance in many tasks of computing vision. However, CNN tends to bias to low frequency components. They prioritize capturing low frequency patterns which lead them fail when suffering…
Pseudospectral numerical schemes for solving the Dirac equation in general static curved space are derived using a pseudodifferential representation of the Dirac equation along with a simple Fourier-basis technique. Owing to the presence of…
Spectral analysis is a powerful tool, decomposing any function into simpler parts. In machine learning, Mercer's theorem generalizes this idea, providing for any kernel and input distribution a natural basis of functions of increasing…
Recent work has empirically shown that deep neural networks latch on to the Fourier statistics of training data and show increased sensitivity to Fourier-basis directions in the input. Understanding and modifying this Fourier-sensitivity of…
Deep learning on graphs and in particular, graph convolutional neural networks, have recently attracted significant attention in the machine learning community. Many of such techniques explore the analogy between the graph Laplacian…
Recently, there is increasing interest and research on the interpretability of machine learning models, for example how they transform and internally represent EEG signals in Brain-Computer Interface (BCI) applications. This can help to…
We propose a neural network for both forward and inverse continuous nonlinear Fourier transforms, NFT and INFT respectively. We demonstrate the network's capability to perform NFT and INFT for a random mix of NFDM-QAM signals. The network…
The neural network and quantum computing are both significant and appealing fields, with their interactive disciplines promising for large-scale computing tasks that are untackled by conventional computers. However, both developments are…