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Recent studies of the computational power of recurrent neural networks (RNNs) reveal a hierarchy of RNN architectures, given real-time and finite-precision assumptions. Here we study auto-regressive Transformers with linearised attention,…

Fluorescence molecular tomography (FMT) is a sensitive optical imaging technology widely used in biomedical research. However, the ill-posedness of the inverse problem poses a huge challenge to FMT reconstruction. Although end-to-end deep…

Deep learning algorithms provide a new paradigm to study high-dimensional dynamical behaviors, such as those in fusion plasma systems. Development of novel model reduction methods, coupled with detection of abnormal modes with plasma…

Filtered back projection (FBP) is a commonly used technique in tomographic image reconstruction demonstrating acceptable quality. The classical direct implementations of this algorithm require the execution of $\Theta(N^3)$ operations,…

Adapting Foundation Models (FMs) for downstream tasks through Federated Learning (FL) emerges a promising strategy for protecting data privacy and valuable FMs. Existing methods fine-tune FM by allocating sub-FM to clients in FL, however,…

We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…

In the first part of this paper, we define a deep convolutional neural network connected with the fractional Fourier transform (FrFT) using the $\theta$-translation operator, the translation operator associated with the FrFT. Subsequently,…

The Fast Proximal Gradient Method (FPGM) and the Monotone FPGM (MFPGM) for minimization of nonsmooth convex functions are introduced and applied to tomographic image reconstruction. Convergence properties of the sequence of objective…

Recent medical image segmentation methods apply implicit neural representation (INR) to the decoder for achieving a continuous coordinate decoding to tackle the drawback of conventional discrete grid-based data representations. However, the…

Click-through rate (CTR) prediction plays a critical role in recommender systems and online advertising. The data used in these applications are multi-field categorical data, where each feature belongs to one field. Field information is…

Kernel methods are a highly effective and widely used collection of modern machine learning algorithms. A fundamental limitation of virtually all such methods are computations involving the kernel matrix that naively scale quadratically…

In this paper, we develop novel techniques that can be used to alter the architecture of a neural network, while maintaining the function it represents. Such operations are known as function preserving transforms and have proven useful in…

The emergence of extremely large-scale antenna arrays (ELAA) in millimeter-wave (mmWave) communications, particularly in high-mobility scenarios, highlights the importance of near-field beam prediction. Unlike the conventional far-field…

The use of integral equation methods for the efficient numerical solution of PDE boundary value problems requires two main tools: quadrature rules for the evaluation of layer potential integral operators with singular kernels, and fast…

Tucker decomposition is proposed to reduce the memory requirement of the far-fields in the fast multipole method (FMM)-accelerated surface integral equation simulators. It is particularly used to compress the far-fields of FMM groups, which…

We present techniques for speeding up the test-time evaluation of large convolutional networks, designed for object recognition tasks. These models deliver impressive accuracy but each image evaluation requires millions of floating point…

We develop a fast and accurate method for 3D alignment, recovering the rotation and translation that best align a reference volume with a noisy observation. Classical matched filtering evaluates cross-correlation over a large discretized…

Despite recent advances in multi-scale deep representations, their limitations are attributed to expensive parameters and weak fusion modules. Hence, we propose an efficient approach to fuse multi-scale deep representations, called…

The nonlinear Fourier transform (NFT) has recently gained significant attention in fiber optic communications and other engineering fields. Although several numerical algorithms for computing the NFT have been published, the design of…

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)…