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Longest common subsequence (LCS) is one of the most fundamental problems in combinatorial optimization. Apart from theoretical importance, LCS has enormous applications in bioinformatics, revision control systems, and data comparison…
Long-range tasks demand reasoning over long inputs. However, existing solutions are limited, e.g., long-context models require large compute budgets, parameter-efficient fine-tuning (PEFT) needs training data, and retrieval-augmented…
Support for arithmetic in multiple precisions and number formats is becoming increasingly common in emerging high-performance architectures. From a computational scientist's perspective, our goal is to determine how and where we can safely…
The challenge of mastering computational tasks of enormous size tends to frequently override questioning the quality of the numerical outcome in terms of accuracy. By this we do not mean the accuracy within the discrete setting, which…
Long-range sequence modeling is a crucial aspect of natural language processing and time series analysis. However, traditional models like Recurrent Neural Networks (RNNs) and Transformers suffer from computational and memory…
Multiplication of polynomials is among key operations in computer algebra which plays important roles in developing techniques for other commonly used polynomial operations such as division, evaluation/interpolation, and factorization. In…
Low-rank approximation is a fundamental technique in modern data analysis, widely utilized across various fields such as signal processing, machine learning, and natural language processing. Despite its ubiquity, the mechanics of low-rank…
In this note, we introduce a new finite difference approximation called the Black-Box Logarithmic Expansion Numerical Derivative (BLEND) algorithm, which is based on a formal logarithmic expansion of the differentiation operator. BLEND…
We present a complete algorithm for finding an exact minimal polynomial from its approximate value by using an improved parameterized integer relation construction method. Our result is superior to the existence of error controlling on…
The great advances of learning-based approaches in image processing and computer vision are largely based on deeply nested networks that compose linear transfer functions with suitable non-linearities. Interestingly, the most frequently…
High-dimensional compositional data are commonplace in the modern omics sciences amongst others. Analysis of compositional data requires a proper choice of orthonormal coordinate representation as their relative nature is not compatible…
Large language models (LLMs) have achieved impressive proficiency in basic arithmetic, rivaling human-level performance on standard numerical tasks. However, little attention has been given to how these models perform when numerical…
Many scientific computing problems can be reduced to Matrix-Matrix Multiplications (MMM), making the General Matrix Multiply (GEMM) kernels in the Basic Linear Algebra Subroutine (BLAS) of interest to the high-performance computing…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
Deploying Deep Neural Networks in low-power embedded devices for real time-constrained applications requires optimization of memory and computational complexity of the networks, usually by quantizing the weights. Most of the existing works…
The employment of intelligent reflecting surfaces (IRSs) is a potential and promising solution to increase the spectral and energy efficiency of wireless communication networks. Despite their many advantages, IRS-aided communications have…
Long Short-Term Memory (LSTM) is one of the most widely used recurrent structures in sequence modeling. It aims to use gates to control information flow (e.g., whether to skip some information or not) in the recurrent computations, although…
Variable selection in linear models plays a pivotal role in modern statistics. Hard-thresholding methods such as $l_0$ regularization are theoretically ideal but computationally infeasible. In this paper, we propose a new approach, called…
Description Logics (DLs) are used in knowledge-based systems to represent and reason about terminological knowledge of the application domain in a semantically well-defined manner. In this thesis, we establish a number of novel complexity…
Recently, lattice-reduction-aided detectors have been proposed for multiple-input multiple-output (MIMO) systems to give performance with full diversity like maximum likelihood receiver, and yet with complexity similar to linear receivers.…