Related papers: Linear Time Complexity Deep Fourier Scattering Net…

The singular values of convolutional mappings encode interesting spectral properties, which can be used, e.g., to improve generalization and robustness of convolutional neural networks as well as to facilitate model compression. However,…

Recognition of speech, and in particular the ability to generalize and learn from small sets of labelled examples like humans do, depends on an appropriate representation of the acoustic input. We formulate the problem of finding robust…

In this article, we develop comprehensive frequency domain methods for estimating and inferring the second-order structure of spatial point processes. The main element here is on utilizing the discrete Fourier transform (DFT) of the point…

We introduce a two-layer wavelet scattering network, for object classification. This scattering transform computes a spatial wavelet transform on the first layer and a new joint wavelet transform along spatial, angular and scale variables…

Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep…

The inductive biases of trained neural networks are difficult to understand and, consequently, to adapt to new settings. We study the inductive biases of linearizations of neural networks, which we show to be surprisingly good summaries of…

While numerous forecasters have been proposed using different network architectures, the Transformer-based models have state-of-the-art performance in time series forecasting. However, forecasters based on Transformers are still suffering…

Fast linear transforms are ubiquitous in machine learning, including the discrete Fourier transform, discrete cosine transform, and other structured transformations such as convolutions. All of these transforms can be represented by dense…

Recurrence networks are powerful tools used effectively in the nonlinear analysis of time series data. The analysis in this context is done mostly with unweighted and undirected complex networks constructed with specific criteria from the…

This paper proposes a frequency-time hybrid solver for the time-dependent wave equation in two-dimensional interior spatial domains. The approach relies on four main elements, namely, 1) A multiple scattering strategy that decomposes a…

High-dimensional longitudinal time series data is prevalent across various real-world applications. Many such applications can be modeled as regression problems with high-dimensional time series covariates. Deep learning has been a popular…

Sound event detection systems typically consist of two stages: extracting hand-crafted features from the raw audio waveform, and learning a mapping between these features and the target sound events using a classifier. Recently, the focus…

We investigate the potential of stochastic neural networks for learning effective waveform-based acoustic models. The waveform-based setting, inherent to fully end-to-end speech recognition systems, is motivated by several comparative…

Fourier Neural Operators (FNOs) have emerged as leading surrogates for solver operators for various functional problems, yet their stability, generalization and frequency behavior lack a principled explanation. We present a systematic…

We present a compositional theory of nonlinear audio signal processing based on a categorification of the Volterra series. We begin by augmenting the classical definition of the Volterra series so that it is functorial with respect to a…

A scattering transform defines a signal representation which is invariant to translations and Lipschitz continuous relatively to deformations. It is implemented with a non-linear convolution network that iterates over wavelet and modulus…

In deep time series forecasting, the Fourier Transform (FT) is extensively employed for frequency representation learning. However, it often struggles in capturing multi-scale, time-sensitive patterns. Although the Wavelet Transform (WT)…

Time-frequency scattering is a mathematical transformation of sound waves. Its core purpose is to mimick the way the human auditory system extracts information from its environment. In the context of improving the artificial intelligence of…

Feature selection is an essential problem in computer vision, important for category learning and recognition. Along with the rapid development of a wide variety of visual features and classifiers, there is a growing need for efficient…

This paper proposes a novel algorithm for image phase retrieval, i.e., for recovering complex-valued images from the amplitudes of noisy linear combinations (often the Fourier transform) of the sought complex images. The algorithm is…