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Lipschitz Bound Estimation is an effective method of regularizing deep neural networks to make them robust against adversarial attacks. This is useful in a variety of applications ranging from reinforcement learning to autonomous systems.…

The deployment of deep neural networks (DNNs) in safety-critical edge environments necessitates robustness against hardware-induced bit-flip errors. While empirical studies indicate that reducing numerical precision can improve fault…

Nowadays refinery optimization utilizes sheer amounts of data, which can be handled with modern Linear Programming (LP) software, but the interpreting and applying the results remains challenging. Large petrochemical companies use massive…

Large language models (LLMs) have shown their potential in long-context understanding and mathematical reasoning. In this paper, we study the problem of using LLMs to detect tabular anomalies and show that pre-trained LLMs are zero-shot…

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…

Looped computation shows promise in improving the reasoning-oriented performance of LLMs by scaling test-time compute. However, existing approaches typically require either training recurrent models from scratch or applying disruptive…

The last decade has witnessed the breakthrough of deep neural networks (DNNs) in many fields. With the increasing depth of DNNs, hundreds of millions of multiply-and-accumulate (MAC) operations need to be executed. To accelerate such…

The era of huge data necessitates highly efficient machine learning algorithms. Many common machine learning algorithms, however, rely on computationally intensive subroutines that are prohibitively expensive on large datasets. Oftentimes,…

Variable selection is one of the most important tasks in statistics and machine learning. To incorporate more prior information about the regression coefficients, the constrained Lasso model has been proposed in the literature. In this…

In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide…

Large language models (LLMs) exhibit remarkable capabilities across diverse tasks, yet aligning them efficiently and effectively with human expectations remains a critical challenge. This thesis advances LLM alignment by introducing novel…

Lagrange coded computation (LCC) is essential to solving problems about matrix polynomials in a coded distributed fashion; nevertheless, it can only solve the problems that are representable as matrix polynomials. In this paper, we propose…

The standard approximation of a natural logarithm in statistical analysis interprets a linear change of \(p\) in \(\ln(X)\) as a \((1+p)\) proportional change in \(X\), which is only accurate for small values of \(p\). I suggest…

Black-box Large Language Models (LLMs) provide practical and accessible alternatives to other machine learning methods, as they require minimal labeled data and machine learning expertise to develop solutions for various decision making…

This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problem instances. The paper…

DNNs have been quickly and broadly exploited to improve the data analysis quality in many complex science and engineering applications. Today's DNNs are becoming deeper and wider because of increasing demand on the analysis quality and more…

We apply methods from randomized numerical linear algebra (RandNLA) to develop improved algorithms for the analysis of large-scale time series data. We first develop a new fast algorithm to estimate the leverage scores of an autoregressive…

When a computational task tolerates a relaxation of its specification or when an algorithm tolerates the effects of noise in its execution, hardware, programming languages, and system software can trade deviations from correct behavior for…

Mathematical reasoning in Large Language Models (LLMs) is often evaluated using benchmarks with limited numerical ranges, failing to reflect real-world problem-solving across diverse scales. Furthermore, most existing evaluation methods…

In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…