Mason Haberle L&S Sciences
Holder-Brascamp-Lieb, Red-Blue Pebbling, and Communication-Optimal Algorithms
Numerical linear algebra underlies much of the modern world. It is essential to a wide variety of situations, and, as such, it is of great interest to analyze and optimize the underlying algorithms. In recent years, there has been an increased interest in optimizing algorithms to reduce communication, which is frequently many orders of magnitude slower than performing calculations. The Hlder-Brascamp-Lieb inequality and the Red-Blue Pebbling Game are two powerful approaches to theoretical analysis of communication, and both are used to derive communication optimal lower bounds. Once these bounds have been derived, the next challenge is to implement an algorithm that attains these minimums, and thus, is communication minimizing. Many currently implemented algorithms do not meet these bounds, and this is a matter of great importance, with large potential time and energy savings. In this way, our project has two broad goals. Our first is to implement a communication optimal algorithm for the implementation of convolutional neural networks, and our second is to develop a theoretical framework that unifies the Hlder-Brascamp-Lieb inequality and the Red-Blue Pebbling Game.
Message To Sponsor
I am deeply grateful to the Sherrill Fund for their donation and the opportunity they afforded me to work closely with three other wonderful students and two brilliant professors on the SURF Math Team this summer. When I look back at how I've grown as a mathematician and a researcher since the beginning of the program in May, I am astounded to see how far I've come. I have pushed myself outside of my comfort zone by exploring the unfamiliar world of numerical linear algebra while presenting new results to accomplished professors in the field. I have interacted and shared ideas with a worldwide community of researchers specializing in communication-avoiding algorithms. Most saliently I have built friendships with my team and bonds with our faculty mentors which give me the confidence and support I need in order to pursue mathematics in graduate school and further. My SURF experience has molded my mathematical pursuits and aspirations, and it is thanks to the Sherrill Fund that I have had the chance to take that journey.