Engineering topics

Raugas, Mark V.

Publications and source records attributed to Raugas, Mark V..

3 records

DOE OSTI2024

Machine Learning meets Algebraic Combinatorics: A Suite of Benchmark Datasets to Accelerate AI for Mathematics Research

The use of benchmark datasets has become an important engine of progress in machine learning (ML) over the past 15 years. Recently there has been growing interest in utilizing machine learning to drive advances in research-level mathematics. However, off-the-shelf solutions often fail to deliver the types of insights required by mathematicians. This suggests the need for new ML methods specifically designed with mathematics in mind. The question then is: what benchmarks should the community use to evaluate these? On the one hand, toy problems such as learning the multiplicative structure of small finite groups have become popular in the mechanistic interpretability community whose perspective on explainability aligns well with the needs of mathematicians. While toy datasets are a useful benchmark for initial work, they lack the scale, complexity, and sophistication of many of the principal objects of study in modern mathematics. To address this, we introduce a new collection of benchmark datasets, Algebraic Combinatorics Benchmarks (ACBench), representing either classic or open problems in algebraic combinatorics, a subfield of mathematics that studies discrete structures arising from abstract algebra. After describing the datasets, we discuss the challenges involved in constructing “good” mathematics benchmarks, describe baseline model performance, and discuss some of the insights these datasets can provide that may be of interest even to those who are not interested in mathematics research itself.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

SpectralFly: Ramanujan Graphs as Flexible and Efficient Interconnection Networks

In recent years, graph theoretic considerations have become increasingly important in the design of HPC interconnection topologies. One approach is to seek optimal or near-optimal families of graphs with respect to a particular graph theoretic property, such as diameter. For example, the SlimFly topology is based on a construction of McKay, Miller, and \v{S}ir\'{a}\v{n} which produces a diameter two graph on a number of nodes approaching the Moore bound, i.e. the largest possible diameter two graph with a fixed radix. Motivated by recent work of Aksoy, Bruillard, Young, and Raugas, we consider topologies which optimize the spectral gap rather than the diameter. In particular, we introduce a novel HPC topology, SpectralFly, designed around the Ramanujan graph construction of Lubotzky, Phillips, and Sarnak (LPS). In this work, we show that the combinatorial properties, such as diameter, bisection bandwidth, average path length, and resilience to link failure, of SpectralFly topologies are better than, or comparable to, similarly constrained DragonFly, SlimFly, and BundleFly topologies. Additionally, we simulate the performance of SpectralFly topologies on a representative sample of physics-inspired HPC workloads using the Structure Simulation Toolkit Macroscale Element Library simulator and demonstrate considerable benefit to using LPS construction as the basis of the SpectralFly topology.

graphs and networks, network topology, interconnec↗

DOE OSTI2022

LC-MEMENTO: A Memory Model for Accelerated Architectures

With the advent of heterogeneous architectures, in particular, with the ubiquity of multi-GPU systems, it is becoming increasingly important to manage device memory efficiently in order to reap the benefits of the additional core count. To date, such responsibility mainly falls on the programmer where device-to-host data communication (and vice versa), if not done properly, may incur costly memory transfer operations and synchronization. The problem may be compounded by additional requirement to maintain system-wide memory consistency that may involve expensive synchronization overhead. In this paper, we present Location Consistency Memory Model for Enhanced Transfer Operations (LC-MEMENTO). This framework considers incorporating runtime techniques for multi-GPU memory management to support relaxed synchronization semantics and memory transfer operations automatically. Specifically, we implement a relaxed form of a memory consistency model based on the Location Consistency (LC) in an Asynchronous Many-Task Runtime (ARTS) and demonstrate that, this memory model enables additional optimization opportunities for the three representative applications encompassing different computational patterns (scientific computation, graphs, data streaming, etc.).

Memory Models, Accelerators, Adaptive Optimization↗