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Time series analysis is vital for numerous applications, and transformers have become increasingly prominent in this domain. Leading methods customize the transformer architecture from NLP and CV, utilizing a patching technique to convert…

We introduce a quantum algorithm to perform the Laplace transform on quantum computers. Already, the quantum Fourier transform (QFT) is the cornerstone of many quantum algorithms, but the Laplace transform or its discrete version has not…

Sparse variational approximations are popular methods for scaling up inference and learning in Gaussian processes to larger datasets. For $N$ training points, exact inference has $O(N^3)$ cost; with $M \ll N$ features, state of the art…

Diffusion Transformers (DiT) are renowned for their impressive generative performance; however, they are significantly constrained by considerable computational costs due to the quadratic complexity in self-attention and the extensive…

For high dimensional problems, such as approximation and integration, one cannot afford to sample on a grid because of the curse of dimensionality. An attractive alternative is to sample on a low discrepancy set, such as an integration…

To reach the next frontier in multimode nonlinear optics, it is crucial to better understand the classical and quantum phenomena of systems with many interacting degrees of freedom -- both how they emerge and how they can be tailored to…

Non-line-of-Sight (NLOS) imaging systems collect light at a diffuse relay surface and input this measurement into computational algorithms that output a 3D volumetric reconstruction. These algorithms utilize the Fast Fourier Transform (FFT)…

This paper aims to propose and theoretically analyze a new distributed scheme for sparse linear regression and feature selection. The primary goal is to learn the few causal features of a high-dimensional dataset based on noisy observations…

We study the problem of interpolating a noisy Fourier-sparse signal in the time duration $[0, T]$ from noisy samples in the same range, where the ground truth signal can be any $k$-Fourier-sparse signal with band-limit $[-F, F]$. Our main…

Iterative hard thresholding (IHT) is a projected gradient descent algorithm, known to achieve state of the art performance for a wide range of structured estimation problems, such as sparse inference. In this work, we consider IHT as a…

Convolution operations are foundational to classical image processing and modern deep learning architectures, yet their extension into the quantum domain has remained algorithmically and physically costly due to inefficient data encoding…

Transformers are ubiquitous in Natural Language Processing (NLP) tasks, but they are difficult to be deployed on hardware due to the intensive computation. To enable low-latency inference on resource-constrained hardware platforms, we…

Decoded Quantum Interferometry (DQI) is a recently proposed quantum optimization algorithm that exploits sparsity in the Fourier spectrum of objective functions, with the potential for exponential speedups over classical algorithms on…

Natural signals and images are well-known to be approximately sparse in transform domains such as Wavelets and DCT. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing…

In this paper we propose a scalable version of a state-of-the-art deterministic time-invariant feature extraction approach based on consecutive changes of basis and nonlinearities, namely, the scattering network. The first focus of the…

While vision transformers have achieved impressive results, effectively and efficiently accelerating these models can further boost performances. In this work, we propose a dense/sparse training framework to obtain a unified model, enabling…

In this paper modified variants of the sparse Fourier transform algorithms from [14] are presented which improve on the approximation error bounds of the original algorithms. In addition, simple methods for extending the improved sparse…

Quantum kernel methods are promising for near-term quantum ma- chine learning, yet their behavior under data corruption remains insuf- ficiently understood. We analyze how quantum feature constructions degrade under controlled additive…

Computing the convolution $A\star B$ of two length-$n$ vectors $A,B$ is an ubiquitous computational primitive. Applications range from string problems to Knapsack-type problems, and from 3SUM to All-Pairs Shortest Paths. These applications…

Features based on sparse representation, especially using the synthesis dictionary model, have been heavily exploited in signal processing and computer vision. However, synthesis dictionary learning typically involves NP-hard sparse coding…