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Despite tremendous progress, machine learning and deep learning still suffer from incomprehensible predictions. Incomprehensibility, however, is not an option for the use of (deep) reinforcement learning in the real world, as unpredictable…

In the past few years, Large Language Models (LLMs) have exploded in usefulness and popularity for code generation tasks. However, LLMs still struggle with accuracy and are unsuitable for high-risk applications without additional oversight…

Interpreting mathematical expressions at runtime is a standard task in scientific software engineering. There are different approaches to this problem from creating an embedded domain-specific language (eDSL) with its own parser and…

Large Language Models (LLMs), despite extensive pretraining on broad internet corpora, often struggle to adapt effectively to specialized domains. There is growing interest in fine-tuning these models for such domains; however, progress is…

Randomized numerical linear algebra - RandNLA, for short - concerns the use of randomization as a resource to develop improved algorithms for large-scale linear algebra computations. The origins of contemporary RandNLA lay in theoretical…

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…

Many iterative algorithms in optimization, computational geometry, computer algebra, and other areas of computer science require repeated computation of some algebraic expression whose input changes slightly from one iteration to the next.…

Mathematical models are increasingly used in both academia and the pharmaceutical industry to understand how phenotypes emerge from systems of molecular interactions. However, their current construction as monolithic sets of equations…

Many useful tasks in data science and machine learning applications can be written as simple variations of matrix multiplication. However, users have difficulty performing such tasks as existing matrix/vector libraries support only a…

LambdaBeam is a state-of-the-art, execution-guided algorithm for program synthesis that utilizes higher-order functions, lambda functions, and iterative loops within a Domain-Specific Language (DSL). LambdaBeam generates each program from…

Deep knowledge analysis tasks always involve the systematic extraction and association of knowledge from large volumes of data, followed by logical reasoning to discover insights. However, to solve such complex tasks, existing deep research…

LAPACK and ScaLAPACK are arguably the defacto standard libraries among the scientific community for solving linear algebra problems on sequential, shared-memory and distributed-memory architectures. While ease of use was a major design goal…

Problem-solving has been a fundamental driver of human progress in numerous domains. With advancements in artificial intelligence, Large Language Models (LLMs) have emerged as powerful tools capable of tackling complex problems across…

Linear algebra routines are basic building blocks for the statistical software. In this paper we analyzed how can we can improve R performance for matrix computations. We benchmarked few matrix operations using the standard linear algebra…

Large Language Models (LLMs) have demonstrated great promise in generating code, especially when used inside an evolutionary computation framework to iteratively optimize the generated algorithms. However, in some cases they fail to…

Code synthesis, which requires a deep understanding of complex natural language problem descriptions, generation of code instructions for complex algorithms and data structures, and the successful execution of comprehensive unit tests,…

We introduce efficient differentially private (DP) algorithms for several linear algebraic tasks, including solving linear equalities over arbitrary fields, linear inequalities over the reals, and computing affine spans and convex hulls. As…

In many sequence learning tasks, such as program synthesis and document summarization, a key problem is searching over a large space of possible output sequences. We propose to learn representations of the outputs that are specifically…

Consider the collection of all binary matrices having a specific sequence of row and column sums and consider sampling binary matrices uniformly from this collection. Practical algorithms for exact uniform sampling are not known, but there…

The advancement of artificial intelligence algorithms has expanded their application to several fields such as the biomedical domain. Artificial intelligence systems, including Large Language Models (LLMs), can be particularly advantageous…