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This article introduces a nonlinear generalized matrix factor model (GMFM) that allows for mixed-type variables, extending the scope of linear matrix factor models (LMFM) that are so far limited to handling continuous variables. We…
Error syndromes for heavy hexagonal code and other topological codes such as surface code have typically been decoded by using Minimum Weight Perfect Matching (MWPM) based methods. Recent advances have shown that topological codes can be…
Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…
Large language models (LLMs) have been applied in various applications due to their astonishing capabilities. With advancements in technologies such as chain-of-thought (CoT) prompting and in-context learning (ICL), the prompts fed to LLMs…
The tensor-structured parametric analysis (TPA) has been recently developed for simulating and analysing stochastic behaviours of gene regulatory networks [Liao et. al., 2015]. The method employs the Fokker-Planck approximation of the…
Large Language Models (LLMs) have pushed the frontier of artificial intelligence but are comprised of hundreds of billions of parameters and operations. For faster inference latency, LLMs are deployed on multiple hardware accelerators…
Global climate models (GCMs), typically run at ~100-km resolution, capture large-scale environmental conditions but cannot resolve convection and cloud processes at kilometer scales. Convection-permitting models offer higher-resolution…
Traditional load analysis is facing challenges with the new electricity usage patterns due to demand response as well as increasing deployment of distributed generations, including photovoltaics (PV), electric vehicles (EV), and energy…
Most machine learning models for structured data encode the structural knowledge of a node by leveraging simple aggregation functions (in neural models, typically a weighted sum) of the information in the node's neighbourhood. Nevertheless,…
The prominence of deep learning, large amount of annotated data and increasingly powerful hardware made it possible to reach remarkable performance for supervised classification tasks, in many cases saturating the training sets. However the…
The convergence of many numerical optimization techniques is highly dependent on the initial guess given to the solver. To address this issue, we propose a novel approach that utilizes tensor methods to initialize existing optimization…
We introduce a new low-dimensional model of high-dimensional numerical simulation data based on low-rank tensor decompositions. Our new model aims to minimize differences between the model data and simulation data as well as functions of…
Tensor regression is an important tool for tensor data analysis, but existing works have not considered the impact of outliers, making them potentially sensitive to such data points. This paper proposes a low tubal rank robust regression…
Performance tuning, software/hardware co-design, and job scheduling are among the many tasks that rely on models to predict application performance. We propose and evaluate low-rank tensor decomposition for modeling application performance.…
Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…
Controllability and observability energy functions play a fundamental role in model order reduction and are inherently connected to optimal control problems. For linear dynamical systems the energy functions are known to be quadratic…
We present a new method for high-dimensional linear regression when a scale parameter of the additive errors is unknown. The proposed estimator is based on a penalized Huber $M$-estimator, for which theoretical results on estimation error…
Latent variable models are an elegant framework for capturing rich probabilistic dependencies in many applications. However, current approaches typically parametrize these models using conditional probability tables, and learning relies…
Although large language models (LLM) have achieved remarkable performance, their enormous parameter counts hinder deployment on resource-constrained hardware. Low-rank compression can reduce both memory usage and computational demand, but…
We propose an empirical method for identifying low damped modes and corresponding mode shapes using frequency measurements from a Wide Area Monitoring System. The method consists of two main steps: Firstly, Complex Principal Component…