Related papers: A Survey on Constructing Parseval Fusion Frames vi…
Large pre-trained models, or foundation models, have shown impressive performance when adapted to a variety of downstream tasks, often out-performing specialized models. Hypernetworks, neural networks that generate some or all of the…
Structured sparsity has emerged as a popular model pruning technique, widely adopted in various architectures, including CNNs, Transformer models, and especially large language models (LLMs) in recent years. A promising direction to further…
The paper studies finite extensions of Bessel sequences in infinite-dimensional Hilbert spaces. We provide a characterization of Bessel sequences that can be extended to frames by adding finitely many vectors. We also characterize frames…
Simulated tempering is popular method of allowing MCMC algorithms to move between modes of a multimodal target density {\pi}. One problem with simulated tempering for multimodal targets is that the weights of the various modes change for…
Humans (and many vertebrates) face the problem of fusing together multiple fixations of a scene in order to obtain a representation of the whole, where each fixation uses a high-resolution fovea and decreasing resolution in the periphery.…
In recent years it has turned out that shearlets have the potential to retrieve directional information so that they became interesting for many applications. Moreover the continuous shearlet transform has the outstanding property to stem…
Averaging predictions of a deep ensemble of networks is apopular and effective method to improve predictive performance andcalibration in various benchmarks and Kaggle competitions. However, theruntime and training cost of deep ensembles…
The characteristic feature of inverse problems is their instability with respect to data perturbations. In order to stabilize the inversion process, regularization methods have to be developed and applied. In this work we introduce and…
We introduce fractional integrals on the $n$-dimensional spherical cap, study their boundednes in weighted $L^p$ spaces and obtain explicit inversion formulas. The results are applied to the inversion problem for Riesz potentials on a…
Permutation symmetries of deep networks make basic operations like model merging and similarity estimation challenging. In many cases, aligning the weights of the networks, i.e., finding optimal permutations between their weights, is…
An important and yet difficult problem in fitting multivariate mixture models is determining the mixture complexity. We develop theory and a unified framework for finding the nonparametric maximum likelihood estimator of a multivariate…
We study the construction of exponential frames and Riesz sequences for a class of fractal measures on ${\mathbb R}^d$ generated by infinite convolution of discrete measures using the idea of frame towers and Riesz-sequence towers. The…
In this work, a scalable and modular architecture for massive MIMO base stations with distributed processing is proposed. New antennas can readily be added by adding a new node as each node handles all the additional involved processing.…
One of a key problems in signal reconstruction process with the use of frames is to find a dual frame. Typically, a canonical dual frame is used. However, there are many applications where this choice appears to be unfortunate. Due to that…
Random features (RFs) are a popular technique to scale up kernel methods in machine learning, replacing exact kernel evaluations with stochastic Monte Carlo estimates. They underpin models as diverse as efficient transformers (by…
Imaging devices exploit the Nyquist-Shannon sampling theorem to avoid both aliasing and redundant oversampling by design. Conversely, in medical image resampling, images are considered as continuous functions, are warped by a spatial…
In this paper, we develop new fast and efficient algorithms for designing single/multiple unimodular waveforms/codes with good auto- and cross-correlation or weighted correlation properties, which are highly desired in radar and…
We derive various interesting properties of complex equiangular cyclic frames for many pairs (n, k) using Gauss sums and number theory. We further use these results to study the random and burst errors of some special cases of complex…
We solve the problem of best approximation by Parseval frames to an arbitrary frame in a subspace of an infinite dimensional Hilbert space. We explicitly describe all the solutions and we give a criterion for uniqueness. This best…
The construction of optimal line packings in real or complex Euclidean spaces has shown to be a tantalizingly difficult task, because it includes the problem of finding maximal sets of equiangular lines. In the regime where equiangular…