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Transformers do not scale very well to long sequence lengths largely because of quadratic self-attention complexity. In the recent months, a wide spectrum of efficient, fast Transformers have been proposed to tackle this problem, more often…
Modern machine learning models use an ever-increasing number of parameters to train (175 billion parameters for GPT-3) with large datasets to obtain better performance. Bigger is better has been the norm. Optical computing has been…
The metaplectic transform (MT), also known as the linear canonical transform, is a unitary integral mapping which is widely used in signal processing and can be viewed as a generalization of the Fourier transform. For a given function…
The analytic signal is a useful mathematical tool. It separates qualitative and quantitative information of a signal in form of the local phase and local amplitude. The Clifford Fourier transform (CFT) plays a vital role in the…
LLMs are becoming increasingly capable and widespread. Consequently, the potential and reality of their misuse is also growing. In this work, we address the problem of detecting LLM-generated text that is not explicitly declared as such. We…
We present Deep Tensor Canonical Correlation Analysis (DTCCA), a method to learn complex nonlinear transformations of multiple views (more than two) of data such that the resulting representations are linearly correlated in high order. The…
Canonical correlation analysis (CCA) is a technique to find statistical dependencies between a pair of multivariate data. However, its application to high dimensional data is limited due to the resulting time complexity. While the…
Canonical Correlation Analysis (CCA) has been widely applied to jointly embed multiple views of data in a maximally correlated latent space. However, the alignment between various data perspectives, which is required by traditional…
Randomized Numerical Linear Algebra (RandNLA) is a powerful class of methods, widely used in High Performance Computing (HPC). RandNLA provides approximate solutions to linear algebra functions applied to large signals, at reduced…
Recent advancements in medical imaging have resulted in more complex and diverse images, with challenges such as high anatomical variability, blurred tissue boundaries, low organ contrast, and noise. Traditional segmentation methods…
Transformer has become ubiquitous in natural language processing (e.g., machine translation, question answering); however, it requires enormous amount of computations to achieve high performance, which makes it not suitable for mobile…
A theory of higher rank multiresolution analysis is given in the setting of abelian multiscalings. This theory enables the construction, from a higher rank MRA, of finite wavelet sets whose multidilations have translates forming an…
The purpose of this paper is to introduce a set of four test images containing features and structures that can facilitate effective examination and comparison of image processing algorithms. More specifically, the images are designed to…
Canonical correlation analysis (CCA) is a multivariate statistical technique for finding the linear relationship between two sets of variables. The kernel generalization of CCA named kernel CCA has been proposed to find nonlinear relations…
The canonical range resolution limit in radar, sonar, and lidar systems is found to be a special case of a more general resolution limit. The general limit indicates that it is possible to surpass the canonical limit in moderate (of order…
he octonion offset linear canonical transform can be defined as a time shifted and frequency modulated version of the octonion linear canonical transform, a more general framework of most existing signal processing tools. In this paper, we…
The growing number of parameters and computational demands of large language models (LLMs) present significant challenges for their efficient deployment. Recently, there is an increasing interest in quantizing weights to extremely low…
We propose a method to solve the electronic Schr\"odinger equation for strongly correlated systems by applying a unitary transformation to reduce the complexity of the physical Hamiltonian. In particular, we seek a transformation that maps…
Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear relationships in data. Although nonlinear variants…
A model, called the linear transform network (LTN), is proposed to analyze the compression and estimation of correlated signals transmitted over directed acyclic graphs (DAGs). An LTN is a DAG network with multiple source and receiver…