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Dynamic metasurface antennas (DMAs) are an emerging hybrid-MIMO technology distinguished by an ultrathin form factor, low cost, and low power consumption. In real-world DMA prototypes, mutual coupling (MC) between meta-elements is generally…
The inner representation of deep neural networks (DNNs) is indecipherable, which makes it difficult to tune DNN models, control their training process, and interpret their outputs. In this paper, we propose a novel approach to investigate…
Monte Carlo sampling techniques have been proposed as a strategy to reduce the computational cost of contractions in tensor network approaches to solving many-body systems. Here we put forward a variational Monte Carlo approach for the…
Computation of the vertices of the convex hull of a set $S$ of $n$ points in $\mathbb{R} ^m$ is a fundamental problem in computational geometry, optimization, machine learning and more. We present "All Vertex Triangle Algorithm" (AVTA), a…
Dimensionality reduction algorithms are standard tools in a researcher's toolbox. Dimensionality reduction algorithms are frequently used to augment downstream tasks such as machine learning, data science, and also are exploratory methods…
Compared to traditional electrodynamic loudspeakers, the parametric array loudspeaker (PAL) offers exceptional directivity for audio applications but suffers from significant nonlinear distortions due to its inherent intricate demodulation…
Tensor Network (TN) Kernel Machines speed up model learning by representing parameters as low-rank TNs, reducing computation and memory use. However, most TN-based Kernel methods are deterministic and ignore parameter uncertainty. Further,…
Automated machine learning (AutoML) usually involves several crucial components, such as Data Augmentation (DA) policy, Hyper-Parameter Optimization (HPO), and Neural Architecture Search (NAS). Although many strategies have been developed…
The low multilinear rank approximation, also known as the truncated Tucker decomposition, has been extensively utilized in many applications that involve higher-order tensors. Popular methods for low multilinear rank approximation usually…
Tsetlin machines (TMs) have been successful in several application domains, operating with high efficiency on Boolean representations of the input data. However, Booleanizing complex data structures such as sequences, graphs, images, signal…
Topological data analysis (TDA) detects geometric structure in biological data. However, many TDA algorithms are memory intensive and impractical for massive datasets. Here, we introduce a statistical protocol that reduces TDA's memory…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
The progressive hedging algorithm (PHA) is a cornerstone among algorithms for large-scale stochastic programming problems. However, its traditional implementation is hindered by some limitations, including the requirement to solve all…
Integral equations are widely used in fields such as applied modeling, medical imaging, and system identification, providing a powerful framework for solving deterministic problems. While parameter identification for differential equations…
Discovering a suitable neural network architecture for modeling complex dynamical systems poses a formidable challenge, often involving extensive trial and error and navigation through a high-dimensional hyper-parameter space. In this…
In this work, we develop an optimization framework for problems whose solutions are well-approximated by Hierarchical Tucker (HT) tensors, an efficient structured tensor format based on recursive subspace factorizations. By exploiting the…
The rising interest in leveraging higher-order interactions present in complex systems has led to a surge in more expressive models exploiting higher-order structures in the data, especially in topological deep learning (TDL), which designs…
Tensor network (TN) representation is a powerful technique for computer vision and machine learning. TN structure search (TN-SS) aims to search for a customized structure to achieve a compact representation, which is a challenging NP-hard…
The proliferation of saddle points, rather than poor local minima, is increasingly understood to be a primary obstacle in large-scale non-convex optimization for machine learning. Variable elimination algorithms, like Variable Projection…