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The complexity of matrix multiplication (hereafter MM) has been intensively studied since 1969, when Strassen surprisingly decreased the exponent 3 in the cubic cost of the straightforward classical MM to log 2 (7) $\approx$ 2.8074.…
The Smatch metric is a popular method for evaluating graph distances, as is necessary, for instance, to assess the performance of semantic graph parsing systems. However, we observe some issues in the metric that jeopardize meaningful…
Loop compilation for Tightly Coupled Processor Arrays (TCPAs), a class of massively parallel loop accelerators, entails solving NP-hard problems, yet depends on the loop bounds and number of available processing elements (PEs), parameters…
Communication costs, resulting from synchronization requirements during learning, can greatly slow down many parallel machine learning algorithms. In this paper, we present a parallel Markov chain Monte Carlo (MCMC) algorithm in which…
As an important technology in artificial intelligence Granular Computing (GrC) has emerged as a new multi-disciplinary paradigm and received much attention in recent years. Information granules forming an abstract and efficient…
Mixed-integer linear programming (MILP) is widely employed for modeling combinatorial optimization problems. In practice, similar MILP instances with only coefficient variations are routinely solved, and machine learning (ML) algorithms are…
A Gaussian process (GP) is a powerful and widely used regression technique. The main building block of a GP regression is the covariance kernel, which characterizes the relationship between pairs in the random field. The optimization to…
This paper performs the analysis necessary to bound the running time of known, efficient algorithms for generating all longest common subsequences. That is, we bound the running time as a function of input size for algorithms with time…
Markov chain Monte Carlo (MCMC) methods are foundational algorithms for Bayesian inference and probabilistic modeling. However, most MCMC algorithms are inherently sequential and their time complexity scales linearly with the sequence…
The efficient computation of Jacobians represents a fundamental challenge in computational science and engineering. Large-scale modular numerical simulation programs can be regarded as sequences of evaluations of in our case differentiable…
Generalized bicycle (GB) codes have emerged as a promising class of quantum error-correcting codes with practical decoding capabilities. While numerous asymptotically good quantum codes and quantum low-density parity-check code…
Symbolic mathematical computing systems have served as a canary in the coal mine of software systems for more than sixty years. They have introduced or have been early adopters of programming language ideas such ideas as dynamic memory…
Geometric Problem Solving (GPS) remains at the heart of enhancing mathematical reasoning in large language models because it requires the combination of diagrammatic understanding, symbolic manipulation and logical inference. In existing…
The Machine Assisted Generation, Comparison, and Calibration (MAGCC) framework provides machine assistance and automation of recurrent crucial steps and processes in the development, implementation, testing, and use of scientific simulation…
Modern biomedical datasets are increasingly high dimensional and exhibit complex correlation structures. Generalized Linear Mixed Models (GLMMs) have long been employed to account for such dependencies. However, proper specification of the…
While Large Language Models (LLMs) are increasingly used for synthesizing textual PLC programming languages like Structured Text (ST) code, other IEC 61131-3 standard graphical languages like Sequential Function Charts (SFCs) remain…
Markov Chain Monte Carlo (MCMC) is a computational approach to fundamental problems such as inference, integration, optimization, and simulation. The field has developed a broad spectrum of algorithms, varying in the way they are motivated,…
In the problem of $\texttt{Generalised Pattern Matching}\ (\texttt{GPM})$ [STOC'94, Muthukrishnan and Palem], we are given a text $T$ of length $n$ over an alphabet $\Sigma_T$, a pattern $P$ of length $m$ over an alphabet $\Sigma_P$, and a…
Generating high-performance code for diverse hardware and application domains is challenging. Functional array programming languages with patterns like map and reduce have been successfully combined with term rewriting to define and explore…
Today, AI technology is showing its strengths in almost every industry and walks of life. From text generation, text summarization, chatbots, NLP is being used widely. One such paradigm is automatic code generation. An AI could be…