ERI:Fast and Scalable Matrix Computations for Distributed AI

Large-scale matrix computations are fundamental to many technologies that increasingly shape modern society, including machine learning, large language models, scientific computing, healthcare analytics, autonomous systems, and data processing. The rapid growth in model sizes and data volumes requires these computations to be executed across distributed cloud and computing clusters containing many worker nodes. However, such distributed systems are often affected by slow or failed workers, commonly referred to as stragglers, which can significantly delay overall execution and reduce system efficiency. This project advances the mathematical and algorithmic foundations of fast and efficient distributed computing by developing coding-based techniques that improve the resilience and robustness of distributed matrix computations against stragglers in realistic large-scale operating conditions. In addition to enhancing the speed and reliability of a distributed computation process, the project contributes to the broader development of scalable artificial intelligence infrastructures. The project also supports workforce development by training undergraduate and graduate students in distributed computing, cloud computing platforms, coding theory, and machine learning systems. Educational activities include the integration of research outcomes into classroom modules and student research experiences, as well as outreach activities involving mathematics tutoring and computer science learning modules for K-12 students. The project studies the scientific problem of straggler-resilient and numerically reliable distributed matrix multiplication in large computing clusters. The research focuses on three closely connected design questions: how to recover the desired computation from as few worker results as possible, how to keep the encoding and decoding overhead low, and how to ensure that the recovery process remains numerically stable in finite-precision arithmetic. First, the research team studies the recovery threshold, defined as the minimum number of worker results needed to reconstruct the desired matrix product. For a chosen recovery threshold, the project formulates an optimization framework that selects encoding and decoding coefficients to achieve accurate recovery over all possible straggler patterns, subject to storage and computation constraints per worker node. The research develops algorithmic approaches based on different optimization methods to obtain efficient coding designs for a high-quality recovery. The team also examines whether the recovery threshold can be reduced while retaining reliable reconstruction. In this direction, approximate recovery is explicitly considered, since allowing a small reconstruction error can enable recovery from fewer worker responses and improve time-to-completion in straggler-prone systems. Second, the project investigates low-complexity coding schemes that reduce the computational cost of encoding and decoding. Instead of relying on arbitrary coefficients that require multiplication or division operations, the research designs structured codes in which encoding and decoding primarily involve additions and subtractions. This direction prevents preprocessing and recovery costs from becoming bottlenecks in large-scale deployments. Third, the project addresses numerical stability by studying the conditioning of the decoding matrices associated with different straggler patterns. Since poorly conditioned decoding operations can amplify round-off errors, noise, or finite-precision effects, the research incorporates conditioning-aware objectives and constraints into the code-design process. The project studies structured encoding designs, refined coefficient choices, and worst-case conditioning criteria to improve decoding reliability across many worker subsets. Overall, these connected thrusts produce a unified framework for designing coded distributed matrix computation schemes that balance s NSF Award ID: 2553138 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Anindya Bijoy Das | Institution: University of Akron, AKRON, OH | Award Amount: $199,413 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2553138 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2553138.html