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Low Rank Approximation is among most fundamental subjects of numerical linear algebra having important applications to various areas of modern computing and %they range from machine learning theory and %neural networks to data mining and…

Mathematical programming -- the task of expressing operations and decision-making problems in precise mathematical language -- is fundamental across domains, yet remains a skill-intensive process requiring operations research expertise.…

Today's high performance deep learning architectures involve large models with numerous parameters. Low precision numerics has emerged as a popular technique to reduce both the compute and memory requirements of these large models. However,…

This paper investigates approximation-theoretic aspects of the in-context learning capability of the transformers in representing a family of noisy linear dynamical systems. Our first theoretical result establishes an upper bound on the…

Neural Networks (NNs) are the method of choice for building learning algorithms. Their popularity stems from their empirical success on several challenging learning problems. However, most scholars agree that a convincing theoretical…

Log parsing serves as an essential prerequisite for various log analysis tasks. Recent advancements in this field have improved parsing accuracy by leveraging the semantics in logs through fine-tuning large language models (LLMs) or…

This work investigates how using reduced precision data in Convolutional Neural Networks (CNNs) affects network accuracy during classification. More specifically, this study considers networks where each layer may use different precision…

Large Language Models (LLMs) are being applied in a wide array of settings, well beyond the typical language-oriented use cases. In particular, LLMs are increasingly used as a plug-and-play method for fitting data and generating…

Over the past a few years, research and development has made significant progresses on big data analytics. A fundamental issue for big data analytics is the efficiency. If the optimal solution is unable to attain or not required or has a…

We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or…

This paper deals with robust regression and subspace estimation and more precisely with the problem of minimizing a saturated loss function. In particular, we focus on computational complexity issues and show that an exact algorithm with…

The ability of large language models (LLMs) to validate their output and identify potential errors is crucial for ensuring robustness and reliability. However, current research indicates that LLMs struggle with self-correction, encountering…

Artificial Neural Networks are powerful function approximators capable of modelling solutions to a wide variety of problems, both supervised and unsupervised. As their size and expressivity increases, so too does the variance of the model,…

Logs are ubiquitous digital footprints, playing an indispensable role in system diagnostics, security analysis, and performance optimization. The extraction of actionable insights from logs is critically dependent on the log parsing…

Large Language Models (LLMs) have shown remarkable performance in various natural language processing tasks but face challenges in mathematical reasoning, where complex problem-solving requires both linguistic understanding and mathematical…

Deep neural networks (DNNs) have been deployed in myriad machine learning applications. However, advances in their accuracy are often achieved with increasingly complex and deep network architectures. These large, deep models are often…

We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…

We present a method to increase the dynamical range of a Residue Number System (RNS) by adding virtual RNS layers on top of the original RNS, where the required modular arithmetic for a modulus on any non-bottom layer is implemented by…

The distribution of data in the world (eg, internet, etc.) significantly differs from the well-curated datasets and is often over-populated with samples from common categories. The algorithms designed for well-curated datasets perform…