arXiv research

Improved sampling strategy reduces Fourier measurements for neural network signals.

Random Fourier features is one of the most popular techniques for scaling up kernel methods, such as kernel ridge regression. However, despite impressive empirical results, the statistical properties of random Fourier features are still not well understood. In this paper we take steps toward filling this gap. Specifica…

This work proves convergence of adaptive resampling for random Fourier features.

Develops Active Fourier Auditor to estimate ML model properties without reconstructing them.

Random Fourier features model reconstructs wind fields from sparse measurements.

A neural network method estimates densities from characteristic functions.

Random Fourier features classification achieves fast learning rates with fewer features.

Enhances Fourier estimator performance for asynchronous event-data.

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

A Lissajous knot is one that can be parameterized by a single cosine function in each coordinate. Lissajous knots are highly symmetric, and for this reason, not all knots are Lissajous. We prove several theorems which allow us to place bounds on the number of Lissajous knot types with given frequencies and to efficient…

This paper proposes a novel framework to regularize the highly ill-posed and non-linear Fourier ptychography problem using generative models. We demonstrate experimentally that our proposed algorithm, Deep Ptych, outperforms the existing Fourier ptychography techniques, in terms of quality of reconstruction and robustn…

This paper optimizes Gaussian mixture model learning with optimal sampling complexity.

The paper proposes a novel method for optimizing bounded functions using Fourier series and Ricci flow.

A new method for nonstationary Gaussian processes using Fourier features.

The computational cost of training with softmax cross entropy loss grows linearly with the number of classes. For the settings where a large number of classes are involved, a common method to speed up training is to sample a subset of classes and utilize an estimate of the loss gradient based on these classes, known as…

Fourier methods have a long and proven track record as an excellent tool in data processing. As memory and computational constraints gain importance in embedded and mobile applications, we propose to combine Fourier methods and recurrent neural network architectures. The short-time Fourier transform allows us to effici…

NFM models time-series data directly in the Fourier domain, achieving state-of-the-art performance.

We show a connection between the Fourier spectrum of Boolean functions and the REINFORCE gradient estimator for binary latent variable models. We show that REINFORCE estimates (up to a factor) the degree-1 Fourier coefficients of a Boolean function. Using this connection we offer a new perspective on variance reduction…

Scalable kernel methods for large datasets using Fourier representations and NUFFT.

Neural networks compress and sample WDN contamination dynamics efficiently.

Online change detection algorithm using random Fourier features.

New method uses tensor decompositions to overcome the curse of dimensionality for large-scale learning.

The stochastic leverage effect, defined as the standardized covariation between the returns and their related volatility, is analyzed in a stochastic volatility model set-up. A novel estimator of the effect is defined using a pre-estimation of the Fourier coefficients of the return and the volatility processes. The con…

FourNet approximates financial transition densities using Fourier transforms.

Improved MMD test for two-sample testing with random Fourier features.

Deep neural networks correct Mie scattering in FTIR spectra of biological samples.

New methods estimate multivariate shortfall risk more efficiently.

New spectral mixture representation for isotropic kernels simplifies random Fourier features.

Score function estimators improve $k$-subset sampling efficiency.

Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability of kernel methods is limited for large scale datasets. Random Fourier Features (R…

We study estimation of (semi-)inner products between two nonparametric probability distributions, given IID samples from each distribution. These products include relatively well-studied classical $\mathcal{L}^2$ and Sobolev inner products, as well as those induced by translation-invariant reproducing kernels, for whic…

FNOs learn solution operators of dissipative equations efficiently via spectral methods.

A new SINC method for fast and accurate option pricing.

Study on estimating volatility of volatility using Fourier methods and provides insights into volatility dynamics.

Improved sampling for Diffusion Models by accounting for covariance.

A new method integrates Fourier basis expansion and mapping for improved time series forecasting.

We compare the CPU effort and pricing biases of seven Fourier-based implementations. Our analyses show that truncation and discretization errors significantly increase as we move away from the Black-Scholes-Merton framework. We rank the speed and accuracy of the competing choices, showing which methods require smaller …

Quantum Fourier Transform aids machine learning inference.

Markov Chain Monte Carlo methods become increasingly popular in applied mathematics as a tool for numerical integration with respect to complex and high-dimensional distributions. However, application of MCMC methods to heavy tailed distributions and distributions with analytically intractable densities turns out to be…

DAFNO learns surrogates for complex systems on irregular geometries.

The paper proposes a method to learn the structure of continuous-action games with non-parametric utilities using a limited number of samples.

New methods improve translation-equivariant neural processes for modeling unknown functions.

Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data implicitly assumes periodicity and bandlimitedness of the signal. In this paper, we…

In this paper, we study the adversarial attack and defence problem in deep learning from the perspective of Fourier analysis. We first explicitly compute the Fourier transform of deep ReLU neural networks and show that there exist decaying but non-zero high frequency components in the Fourier spectrum of neural network…

This paper analyzes GANs using Fourier modes to stabilize training.

Study shows overparameterization helps in generalizing from smooth interpolants.

High-dimensional inference for sparse spectral precision matrices

Random Fourier features is a widely used, simple, and effective technique for scaling up kernel methods. The existing theoretical analysis of the approach, however, remains focused on specific learning tasks and typically gives pessimistic bounds which are at odds with the empirical results. We tackle these problems an…