Enabling Massive Deep Neural Networks with the GraphBLAS

Deep Neural Networks (DNNs) have emerged as a core tool for machine learning. The computations performed during DNN training and inference are dominated by operations on the weight matrices describing the DNN. As DNNs incorporate more stages and more nodes per stage, these weight matrices may be required to be sparse because of memory limitations. The GraphBLAS.org math library standard was developed to provide high performance manipulation of sparse weight matrices and input/output vectors. For sufficiently sparse matrices, a sparse matrix library requires significantly less memory than the corresponding dense matrix implementation. This paper provides a brief description of the mathematics underlying the GraphBLAS. In addition, the equations of a typical DNN are rewritten in a form designed to use the GraphBLAS. An implementation of the DNN is given using a preliminary GraphBLAS C library. The performance of the GraphBLAS implementation is measured relative to a standard dense linear algebra library implementation. For various sizes of DNN weight matrices, it is shown that the GraphBLAS sparse implementation outperforms a BLAS dense implementation as the weight matrix becomes sparser.Comment: 10 pages, 7 figures, to appear in the 2017 IEEE High Performance Extreme Computing (HPEC) conferenc

Training Behavior of Sparse Neural Network Topologies

Improvements in the performance of deep neural networks have often come through the design of larger and more complex networks. As a result, fast memory is a significant limiting factor in our ability to improve network performance. One approach to overcoming this limit is the design of sparse neural networks, which can be both very large and efficiently trained. In this paper we experiment training on sparse neural network topologies. We test pruning-based topologies, which are derived from an initially dense network whose connections are pruned, as well as RadiX-Nets, a class of network topologies with proven connectivity and sparsity properties. Results show that sparse networks obtain accuracies comparable to dense networks, but extreme levels of sparsity cause instability in training, which merits further study.Comment: 6 pages. Presented at the 2019 IEEE High Performance Extreme Computing (HPEC) Conference. Received "Best Paper" awar

RadiX-Net: Structured Sparse Matrices for Deep Neural Networks

The sizes of deep neural networks (DNNs) are rapidly outgrowing the capacity of hardware to store and train them. Research over the past few decades has explored the prospect of sparsifying DNNs before, during, and after training by pruning edges from the underlying topology. The resulting neural network is known as a sparse neural network. More recent work has demonstrated the remarkable result that certain sparse DNNs can train to the same precision as dense DNNs at lower runtime and storage cost. An intriguing class of these sparse DNNs is the X-Nets, which are initialized and trained upon a sparse topology with neither reference to a parent dense DNN nor subsequent pruning. We present an algorithm that deterministically generates RadiX-Nets: sparse DNN topologies that, as a whole, are much more diverse than X-Net topologies, while preserving X-Nets' desired characteristics. We further present a functional-analytic conjecture based on the longstanding observation that sparse neural network topologies can attain the same expressive power as dense counterpartsComment: 7 pages, 8 figures, accepted at IEEE IPDPS 2019 GrAPL workshop. arXiv admin note: substantial text overlap with arXiv:1809.0524

Streaming 1.9 Billion Hypersparse Network Updates per Second with D4M

The Dynamic Distributed Dimensional Data Model (D4M) library implements associative arrays in a variety of languages (Python, Julia, and Matlab/Octave) and provides a lightweight in-memory database implementation of hypersparse arrays that are ideal for analyzing many types of network data. D4M relies on associative arrays which combine properties of spreadsheets, databases, matrices, graphs, and networks, while providing rigorous mathematical guarantees, such as linearity. Streaming updates of D4M associative arrays put enormous pressure on the memory hierarchy. This work describes the design and performance optimization of an implementation of hierarchical associative arrays that reduces memory pressure and dramatically increases the update rate into an associative array. The parameters of hierarchical associative arrays rely on controlling the number of entries in each level in the hierarchy before an update is cascaded. The parameters are easily tunable to achieve optimal performance for a variety of applications. Hierarchical arrays achieve over 40,000 updates per second in a single instance. Scaling to 34,000 instances of hierarchical D4M associative arrays on 1,100 server nodes on the MIT SuperCloud achieved a sustained update rate of 1,900,000,000 updates per second. This capability allows the MIT SuperCloud to analyze extremely large streaming network data sets.Comment: 6 pages; 6 figures; accepted to IEEE High Performance Extreme Computing (HPEC) Conference 2019. arXiv admin note: text overlap with arXiv:1807.05308, arXiv:1902.0084

GraphChallenge.org: Raising the Bar on Graph Analytic Performance

The rise of graph analytic systems has created a need for new ways to measure and compare the capabilities of graph processing systems. The MIT/Amazon/IEEE Graph Challenge has been developed to provide a well-defined community venue for stimulating research and highlighting innovations in graph analysis software, hardware, algorithms, and systems. GraphChallenge.org provides a wide range of pre-parsed graph data sets, graph generators, mathematically defined graph algorithms, example serial implementations in a variety of languages, and specific metrics for measuring performance. Graph Challenge 2017 received 22 submissions by 111 authors from 36 organizations. The submissions highlighted graph analytic innovations in hardware, software, algorithms, systems, and visualization. These submissions produced many comparable performance measurements that can be used for assessing the current state of the art of the field. There were numerous submissions that implemented the triangle counting challenge and resulted in over 350 distinct measurements. Analysis of these submissions show that their execution time is a strong function of the number of edges in the graph, $N_e$, and is typically proportional to $N_e^{4/3}$ for large values of $N_e$. Combining the model fits of the submissions presents a picture of the current state of the art of graph analysis, which is typically $10^8$ edges processed per second for graphs with $10^8$ edges. These results are $30$ times faster than serial implementations commonly used by many graph analysts and underscore the importance of making these performance benefits available to the broader community. Graph Challenge provides a clear picture of current graph analysis systems and underscores the need for new innovations to achieve high performance on very large graphs.Comment: 7 pages, 6 figures; submitted to IEEE HPEC Graph Challenge. arXiv admin note: text overlap with arXiv:1708.0686

Fast Mapping onto Census Blocks

Pandemic measures such as social distancing and contact tracing can be enhanced by rapidly integrating dynamic location data and demographic data. Projecting billions of longitude and latitude locations onto hundreds of thousands of highly irregular demographic census block polygons is computationally challenging in both research and deployment contexts. This paper describes two approaches labeled "simple" and "fast". The simple approach can be implemented in any scripting language (Matlab/Octave, Python, Julia, R) and is easily integrated and customized to a variety of research goals. This simple approach uses a novel combination of hierarchy, sparse bounding boxes, polygon crossing-number, vectorization, and parallel processing to achieve 100,000,000+ projections per second on 100 servers. The simple approach is compact, does not increase data storage requirements, and is applicable to any country or region. The fast approach exploits the thread, vector, and memory optimizations that are possible using a low-level language (C++) and achieves similar performance on a single server. This paper details these approaches with the goal of enabling the broader community to quickly integrate location and demographic data.Comment: 8 pages, 7 figures, 55 references; accepted to IEEE HPEC 202