arXiv research

New algorithms learn sparse set functions in non-orthogonal Fourier bases.

RNNs solve modular addition tasks using low rank and sparse Fourier structures.

We find a closed-form determinant for a specific sparse covariance matrix model.

We present graph wavelet neural network (GWNN), a novel graph convolutional neural network (CNN), leveraging graph wavelet transform to address the shortcomings of previous spectral graph CNN methods that depend on graph Fourier transform. Different from graph Fourier transform, graph wavelet transform can be obtained …

Neural networks compress and sample WDN contamination dynamics efficiently.

High-dimensional inference for sparse spectral precision matrices

We give a new algorithm for approximating the Discrete Fourier transform of an approximately sparse signal that has been corrupted by worst-case $L_0$ noise, namely a bounded number of coordinates of the signal have been corrupted arbitrarily. Our techniques generalize to a wide range of linear transformations that are…

Nonnegative matrix factorization (NMF) is a popular method for audio spectral unmixing. While NMF is traditionally applied to off-the-shelf time-frequency representations based on the short-time Fourier or Cosine transforms, the ability to learn transforms from raw data attracts increasing attention. However, this adds…

We consider the problem of sparse phase retrieval from Fourier transform magnitudes to recover the $k$-sparse signal vector and its support $\mathcal{T}$. We exploit extended support estimate $\mathcal{E}$ with size larger than $k$ satisfying $\mathcal{E} \supseteq \mathcal{T}$ and obtained by a trained deep neural net…

Paper proves Fourier transform for valuations, simplifying previous work.

EFiGP uses Fourier and eigen-decomposition for efficient ODE parameter estimation.

Improves sparse recovery with non-linear Fourier features.

FEDformer combines Transformer with seasonal-trend decomposition for efficient long-term forecasting.

A new algorithm computes Fourier coefficients for a specified range efficiently.

In this paper, we propose several dictionary learning algorithms for sparse representations that also impose specific structures on the learned dictionaries such that they are numerically efficient to use: reduced number of addition/multiplications and even avoiding multiplications altogether. We base our work on facto…

Structured CNN designed using the prior information of problems potentially improves efficiency over conventional CNNs in various tasks in solving PDEs and inverse problems in signal processing. This paper introduces BNet2, a simplified Butterfly-Net and inline with the conventional CNN. Moreover, a Fourier transform i…

Efficiently scales continuous kernels with sparse Fourier domain learning.

The covariance of a stationary process $X$ is diagonalized by a Fourier transform. It does not take into account the complex Fourier phase and defines Gaussian maximum entropy models. We introduce a general family of phase harmonic covariance moments, which rely on complex phases to capture non-Gaussian properties. The…

Paper computes link determinants using Fourier-Hadamard transforms.

Efficient algorithm learns mixture models of heavy-tailed distributions.

The Fourier transform of Heegaard Floer d-invariants helps classify 3-manifolds.

X-ray transform on H-type groups solved, revealing function injectivity.

Proves conditions for Fourier transforms in rank 1 symmetric spaces.

This work improves Fourier pricing for multi-asset options using RQMC with domain transformation.

Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for the sparse spectrum approximation to avoid both issues. We model the covariance fu…

Algorithm describes Fourier transform of Stokes data at infinity.

The paper studies Fourier-Laplace transforms in polynomial OU volatility models for option pricing.

In this work we propose a method for learning wavelet filters directly from data. We accomplish this by framing the discrete wavelet transform as a modified convolutional neural network. We introduce an autoencoder wavelet transform network that is trained using gradient descent. We show that the model is capable of le…

In this paper, we study robust tensor completion by using transformed tensor singular value decomposition (SVD), which employs unitary transform matrices instead of discrete Fourier transform matrix that is used in the traditional tensor SVD. The main motivation is that a lower tubal rank tensor can be obtained by usin…

Random Fourier features model reconstructs wind fields from sparse measurements.

We prove that the Fourier--Laplace--Nahm transform for connections on the projective line is a hyper-Kähler isometry.

Transformers improve with Fourier integral attentions.

The paper derives statistics of multi-factor functions from their Fourier transforms.

Study spherical Fourier transform on hypergeometric type harmonic manifolds.

Efficient trainable front-end for neural speech enhancement.

In this paper we prove a new inversion theorem and a refinement of an old support theorem for two Radon transforms on a symmetric space. Included are some new identities for the Abel transform and some results about the Fourier transform from a joint work with Rawat, Sengupta and Sitaram.

Let $Φ\in\mathbb{R}^{m\times n}$ be a sparse Johnson-Lindenstrauss transform [KN14] with $s$ non-zeroes per column. For a subset $T$ of the unit sphere, $\varepsilon\in(0,1/2)$ given, we study settings for $m,s$ required to ensure $\mathop{\mathbb{E}}_Φ\sup_{x\in T} \left|\|Φx\|_2^2 - 1 \right| < \varepsilon ,$ i.e…

Given two compact hyperkähler surfaces $X$ and $Y$ and a holomorphic vector bundle $Q$ on $X\times Y$, which is a generalized instanton, one can define a Fourier-Mukai transform, which, under suitable assumptions, maps vector bundles on $X$ to vector bundles on $Y$. If $X$ and $Y$ are dual complex tori, this transform …

This work studies the Tensor Robust Principal Component Analysis (TRPCA) problem, which aims to exactly recover the low-rank and sparse components from their sum. Our model is motivated by the recently proposed linear transforms based tensor-tensor product and tensor SVD. We define a new transforms depended tensor rank…

Enhances Fourier estimator performance for asynchronous event-data.

Many signals on Cartesian product graphs appear in the real world, such as digital images, sensor observation time series, and movie ratings on Netflix. These signals are "multi-dimensional" and have directional characteristics along each factor graph. However, the existing graph Fourier transform does not distinguish …

RP-GFRFT unifies fractional order and rotation control for graph signals.

The paper derives and proves the Helgason Fourier transform for vector bundle-valued differential forms on homogeneous spaces.

Study identifies and analyzes three types of errors in learning Fourier operators.

New method combines spectral and sparse methods for Gaussian processes.

The study establishes uncertainty principles on harmonic manifolds of rank one.

FourNet approximates financial transition densities using Fourier transforms.

The paper connects quantum $6j$-symbols to tetrahedra volumes via discrete Fourier transforms.