Sparse Allreduce: Efficient Scalable Communication for Power-Law Data

Many large datasets exhibit power-law statistics: The web graph, social networks, text data, click through data etc. Their adjacency graphs are termed natural graphs, and are known to be difficult to partition. As a consequence most distributed algorithms on these graphs are communication intensive. Many algorithms on natural graphs involve an Allreduce: a sum or average of partitioned data which is then shared back to the cluster nodes. Examples include PageRank, spectral partitioning, and many machine learning algorithms including regression, factor (topic) models, and clustering. In this paper we describe an efficient and scalable Allreduce primitive for power-law data. We point out scaling problems with existing butterfly and round-robin networks for Sparse Allreduce, and show that a hybrid approach improves on both. Furthermore, we show that Sparse Allreduce stages should be nested instead of cascaded (as in the dense case). And that the optimum throughput Allreduce network should be a butterfly of heterogeneous degree where degree decreases with depth into the network. Finally, a simple replication scheme is introduced to deal with node failures. We present experiments showing significant improvements over existing systems such as PowerGraph and Hadoop

A Distributed Frank-Wolfe Algorithm for Communication-Efficient Sparse Learning

Learning sparse combinations is a frequent theme in machine learning. In this paper, we study its associated optimization problem in the distributed setting where the elements to be combined are not centrally located but spread over a network. We address the key challenges of balancing communication costs and optimization errors. To this end, we propose a distributed Frank-Wolfe (dFW) algorithm. We obtain theoretical guarantees on the optimization error $\epsilon$ and communication cost that do not depend on the total number of combining elements. We further show that the communication cost of dFW is optimal by deriving a lower-bound on the communication cost required to construct an $\epsilon$-approximate solution. We validate our theoretical analysis with empirical studies on synthetic and real-world data, which demonstrate that dFW outperforms both baselines and competing methods. We also study the performance of dFW when the conditions of our analysis are relaxed, and show that dFW is fairly robust.Comment: Extended version of the SIAM Data Mining 2015 pape

Scalable Graph Convolutional Network Training on Distributed-Memory Systems

Graph Convolutional Networks (GCNs) are extensively utilized for deep learning on graphs. The large data sizes of graphs and their vertex features make scalable training algorithms and distributed memory systems necessary. Since the convolution operation on graphs induces irregular memory access patterns, designing a memory- and communication-efficient parallel algorithm for GCN training poses unique challenges. We propose a highly parallel training algorithm that scales to large processor counts. In our solution, the large adjacency and vertex-feature matrices are partitioned among processors. We exploit the vertex-partitioning of the graph to use non-blocking point-to-point communication operations between processors for better scalability. To further minimize the parallelization overheads, we introduce a sparse matrix partitioning scheme based on a hypergraph partitioning model for full-batch training. We also propose a novel stochastic hypergraph model to encode the expected communication volume in mini-batch training. We show the merits of the hypergraph model, previously unexplored for GCN training, over the standard graph partitioning model which does not accurately encode the communication costs. Experiments performed on real-world graph datasets demonstrate that the proposed algorithms achieve considerable speedups over alternative solutions. The optimizations achieved on communication costs become even more pronounced at high scalability with many processors. The performance benefits are preserved in deeper GCNs having more layers as well as on billion-scale graphs.Comment: To appear in PVLDB'2