P. Sadayappan

Xintian Yang, Srinivasan Parthasarathy, Ponnuswamy Sadayappan

Scaling up the sparse matrix-vector multiplication kernel on modern Graphics Processing Units (GPU) has been at the heart of numerous studies in both academia and industry. In this article we present a novel non-parametric, self-tunable, approach to data representation for computing this kernel, particularly targeting sparse matrices representing power-law graphs. Using real data, we show how our representation scheme, coupled with a novel tiling algorithm, can yield significant benefits over the current state of the art GPU efforts on a number of core data mining algorithms such as PageRank, HITS and Random Walk with Restart.

Jesun Firoz, Franco Pellegrini, Mario Geiger et al.

Chemistry Foundation Models (CFMs) that leverage Graph Neural Networks (GNNs) operating on 3D molecular graph structures are becoming indispensable tools for computational chemists and materials scientists. These models facilitate the understanding of matter and the discovery of new molecules and materials. In contrast to GNNs operating on a large homogeneous graphs, GNNs used by CFMs process a large number of geometric graphs of varying sizes, requiring different optimization strategies than those developed for large homogeneous GNNs. This paper presents optimizations for two critical phases of CFM training: data distribution and model training, targeting MACE - a state-of-the-art CFM. We address the challenge of load balancing in data distribution by formulating it as a multi-objective bin packing problem. We propose an iterative algorithm that provides a highly effective, fast, and practical solution, ensuring efficient data distribution. For the training phase, we identify symmetric tensor contraction as the key computational kernel in MACE and optimize this kernel to improve the overall performance. Our combined approach of balanced data distribution and kernel optimization significantly enhances the training process of MACE. Experimental results demonstrate a substantial speedup, reducing per-epoch execution time for training from 12 to 2 minutes on 740 GPUs with a 2.6M sample dataset.

Ashim Gupta, Sina Mahdipour Saravani, P. Sadayappan et al.

The increasing size of transformer-based models in NLP makes the question of compressing them important. In this work, we present a comprehensive analysis of factorization based model compression techniques. Specifically, we focus on comparing straightforward low-rank factorization against the recently introduced Monarch factorization, which exhibits impressive performance preservation on the GLUE benchmark. To mitigate stability issues associated with low-rank factorization of the matrices in pre-trained transformers, we introduce a staged factorization approach wherein layers are factorized one by one instead of being factorized simultaneously. Through this strategy we significantly enhance the stability and reliability of the compression process. Further, we introduce a simple block-wise low-rank factorization method, which has a close relationship to Monarch factorization. Our experiments lead to the surprising conclusion that straightforward low-rank factorization consistently outperforms Monarch factorization across both different compression ratios and six different text classification tasks.

Tripti Agarwal, Harvey Dam, Dorra Ben Khalifa et al.

In response to the rapidly escalating costs of computing with large matrices and tensors caused by data movement, several lossy compression methods have been developed to significantly reduce data volumes. Unfortunately, all these methods require the data to be decompressed before further computations are done. In this work, we develop a lossy compressor that allows a dozen fairly fundamental operations directly on compressed data while offering good compression ratios and modest errors. We implement a new compressor PyBlaz based on the familiar GPU-powered PyTorch framework, and evaluate it on three non-trivial applications, choosing different number systems for internal representation. Our results demonstrate that the compressed-domain operations achieve good scalability with problem sizes while incurring errors well within acceptable limits. To our best knowledge, this is the first such lossy compressor that supports compressed-domain operations while achieving acceptable performance as well as error.

Gordon E. Moon, Aravind Sukumaran-Rajam, Srinivasan Parthasarathy et al.

Non-negative Matrix Factorization (NMF) is a key kernel for unsupervised dimension reduction used in a wide range of applications, including topic modeling, recommender systems and bioinformatics. Due to the compute-intensive nature of applications that must perform repeated NMF, several parallel implementations have been developed in the past. However, existing parallel NMF algorithms have not addressed data locality optimizations, which are critical for high performance since data movement costs greatly exceed the cost of arithmetic/logic operations on current computer systems. In this paper, we devise a parallel NMF algorithm based on the HALS (Hierarchical Alternating Least Squares) scheme that incorporates algorithmic transformations to enhance data locality. Efficient realizations of the algorithm on multi-core CPUs and GPUs are developed, demonstrating significant performance improvement over existing state-of-the-art parallel NMF algorithms.

Jiankai Sun, Bortik Bandyopadhyay, Armin Bashizade et al.

Directed graphs have been widely used in Community Question Answering services (CQAs) to model asymmetric relationships among different types of nodes in CQA graphs, e.g., question, answer, user. Asymmetric transitivity is an essential property of directed graphs, since it can play an important role in downstream graph inference and analysis. Question difficulty and user expertise follow the characteristic of asymmetric transitivity. Maintaining such properties, while reducing the graph to a lower dimensional vector embedding space, has been the focus of much recent research. In this paper, we tackle the challenge of directed graph embedding with asymmetric transitivity preservation and then leverage the proposed embedding method to solve a fundamental task in CQAs: how to appropriately route and assign newly posted questions to users with the suitable expertise and interest in CQAs. The technique incorporates graph hierarchy and reachability information naturally by relying on a non-linear transformation that operates on the core reachability and implicit hierarchy within such graphs. Subsequently, the methodology levers a factorization-based approach to generate two embedding vectors for each node within the graph, to capture the asymmetric transitivity. Extensive experiments show that our framework consistently and significantly outperforms the state-of-the-art baselines on two diverse real-world tasks: link prediction, and question difficulty estimation and expert finding in online forums like Stack Exchange. Particularly, our framework can support inductive embedding learning for newly posted questions (unseen nodes during training), and therefore can properly route and assign these kinds of questions to experts in CQAs.