Allreduce Operation Research Articles

Collective Communication Performance Evaluation for Distributed Deep Learning Training

In distributed deep learning, the improper use of the collective communication library can lead to a decline in deep learning performance due to increased communication time. Representative collective communication libraries such as MPI, GLOO, and NCCL exhibit varying performance based on server environment and communication architecture. In this study, we investigate three key aspects to evaluate the performance of the collective communication libraries in a distributed deep learning setting in an intra-node environment. First, we conduct a comparison and analysis of collective communication library performance within common distributed deep learning architectures, such as parameter servers and ring all-reduce methods. Second, we evaluate the performance of these libraries in different environments, including various container platforms and bare metal setups, considering the scalability and flexibility advantages offered by cloud virtualization. Last, to ensure practicality, we assess the libraries’ performance in a Linux shell and within the PyTorch framework. In the cross-docker virtualization environment, NCCL shows up to 213% higher latency compared to single docker, while GLOO exhibits 36% lower latency in single docker than in cross docker, and NCCL achieves up to 345% lower execution time in all-reduce operations compared to other libraries (MPI and GLOO). These findings will inform the selection of an appropriate collective communication library for designing effective distributed deep learning environments.

Canary: Congestion-aware in-network allreduce using dynamic trees

The allreduce operation is an essential building block for many distributed applications, ranging from the training of deep learning models to scientific computing. In an allreduce operation, data from multiple hosts is aggregated together and then broadcasted to each host participating in the operation. Allreduce performance can be improved by a factor of two by aggregating the data directly in the network. Switches aggregate data coming from multiple ports before forwarding the partially aggregated result to the next hop. In all existing solutions, each switch needs to know the ports from which it will receive the data to aggregate. However, this forces packets to traverse a predefined set of switches, making these solutions prone to congestion. For this reason, we design Canary, the first congestion-aware in-network allreduce algorithm. Canary uses load balancing algorithms to forward packets on the least congested paths. Because switches do not know from which ports they will receive the data to aggregate, they use timeouts to aggregate the data in a best-effort way. We develop a P4 Canary prototype and evaluate it on a Tofino switch. We then validate Canary through simulations on large networks, showing performance improvements up to 40% compared to the state-of-the-art.

SUARA: A scalable universal allreduce communication algorithm for acceleration of parallel deep learning applications

Parallel and distributed deep learning (PDNN) has become an effective strategy to reduce the long training times of large-scale deep neural networks. Mainstream PDNN software packages based on the message-passing interface (MPI) and employing synchronous stochastic gradient descent rely crucially on the performance of MPI allreduce collective communication routine.In this work, we propose a novel scalable universal allreduce meta-algorithm called SUARA. In general, SUARA consists of L serial steps, where L≥2, executed by all MPI processes involved in the allreduce operation. At each step, SUARA partitions this set of processes into subsets, which execute optimally selected library allreduce algorithms to solve sub-allreduce problems on these subsets in parallel, to accomplish the whole allreduce operation after completing all the L steps. We then design, theoretically study and implement a two-step SUARA (L=2) called SUARA2 on top of the Open MPI library. We prove that the theoretical asymptotic speedup of SUARA2 executed by P processes over the base Open MPI routine is O(P). Our experiments on Shaheen-II supercomputer employing 1024 nodes demonstrate over 2x speedup of SUARA2 over native Open MPI allreduce routine, which translates into the performance improvement of training of ResNet-50 DNN on ImageNet by 9%.

P4SGD: Programmable Switch Enhanced Model-Parallel Training on Generalized Linear Models on Distributed FPGAs

Generalized linear models (GLMs) are a widely utilized family of machine learning models in real-world applications. As data size increases, it is essential to perform efficient distributed training for these models. However, existing systems for distributed training have a high cost for communication and often use large batch sizes to balance computation and communication, which negatively affects convergence. Therefore, we argue for an efficient distributed GLM training system that strives to achieve linear scalability, while keeping batch size reasonably low. As a start, we propose P4SGD, a distributed heterogeneous training system that efficiently trains GLMs through model parallelism between distributed FPGAs and through forward-communication-backward pipeline parallelism within an FPGA. Moreover, we propose a light-weight, latency-centric in-switch aggregation protocol to minimize the latency of the AllReduce operation between distributed FPGAs, powered by a programmable switch. As such, to our knowledge, P4SGD is the first solution that achieves almost linear scalability between distributed accelerators through model parallelism. We implement P4SGD on eight Xilinx U280 FPGAs and a Tofino P4 switch. Our experiments show P4SGD converges up to 6.5X faster than the state-of-the-art GPU counterpart.

FPGA-Based AI Smart NICs for Scalable Distributed AI Training Systems

Training state-of-the-art artificial intelligence (AI) models requires scaling to many compute nodes and relies heavily on collective communication operations, such as all-reduce, to exchange the weight gradients between nodes. The overhead of these operations can bottleneck training performance as the number of nodes increases. In this paper, we first characterize the all-reduce operation overhead. Then, we propose a new smart network interface card (NIC) for distributed AI training using field-programmable gate arrays (FPGAs) to accelerate all-reduce operations and optimize bandwidth utilization via data compression. The AI smart NIC frees up the system's compute resources to perform the more compute-intensive tensor operations and increases the overall node-to-node communication efficiency. We build a prototype 6-node AI training system and show that our proposed FPGA-based AI smart NIC enhances overall training performance by 1.6×, with an estimated 2.5× performance improvement at 32 nodes.

Accelerating distributed deep neural network training with pipelined MPI allreduce

TensorFlow (TF) is usually combined with the Horovod (HVD) workload distribution package to obtain a parallel tool to train deep neural network on clusters of computers. HVD in turn utilizes a blocking Allreduce primitive to share information among processes, combined with a communication thread to overlap communication with computation. In this work, we perform a thorough experimental analysis to expose (1) the importance of selecting the best algorithm in MPI libraries to realize the Allreduce operation; and (2) the performance acceleration that can be attained when replacing a blocking Allreduce with its non-blocking counterpart (while maintaining the blocking behaviour via the appropriate synchronization mechanism). Furthermore, (3) we explore the benefits of applying pipelining to the communication exchange, demonstrating that these improvements carry over to distributed training via TF+HVD. Finally, (4) we show that pipelining can also boost performance for applications that make heavy use of other collectives, such as Broadcast and Reduce-Scatter.

Scalable Unsupervised ML: Latency Hiding in Distributed Sparse Tensor Decomposition

Latency overhead in distributed-memory parallel CPD-ALS scales with the number of processors, limiting the scalability of computing CPD of large irregularly sparse tensors. This overhead comes in the form of sparse reduce and expand operations performed on factor-matrix rows via point-to-point messages. We propose to hide the latency overhead through embedding all of the point-to-point messages incurred by the sparse reduce and expand into dense collective operations which already exist in the CPD-ALS. The conventional parallel CPD-ALS algorithm is not amenable for embedding so we propose a computation/communication rearrangement to enable the embedding. We embed the sparse expand and reduce into a hypercube-based ALL-REDUCE operation to limit the latency overhead to O(log K) for a K-processor system. The embedding comes with the cost of increased bandwidth overhead due to the multi-hop routing of factor-matrix rows during the embedded-ALL-REDUCE. We propose an embedding scheme that takes advantage of the expand/reduce properties to reduce this overhead. Furthermore, we propose a novel recursive bipartitioning framework that enables simultaneous hypergraph partitioning and subhypergraph-to-subhypercube mapping to achieve subtensor-to-processor assignment with the objective of reducing the bandwidth overhead during the embedded-ALL-REDUCE. We also propose a bin-packing-based algorithm for factor-matrix row to processor assignment aiming at reducing processors maximum send and receive volumes during the embedded-ALL-REDUCE. Experiments on up to 4096 processors show that the proposed framework scales significantly better than the state-of-the-art point-to-point method.

Integrating state of the art compute, communication, and autotuning strategies to multiply the performance of ab initio molecular dynamics on massively parallel multi-core supercomputers

The development in today’s supercomputer hardware is that the compute power of the individual nodes grows much faster than the speed of their interconnects. To benefit from this evolution in computer hardware, the challenge in modernization of simulation software is to increase the computational load on the nodes and to reduce simultaneously the inter-node communication. Here, we demonstrate the implementation of such a strategy for plane-wave based electronic structure methods and ab initio molecular dynamics (AIMD) simulations. Our focus is on ultra-soft pseudopotentials (USPP), since they allow to shift workload from fast Fourier transforms (FFTs) to highly node-efficient matrix–matrix multiplications. For communication intensive routines, as the multiple distributed 3-d FFTs of the electronic states and the distributed matrix–matrix multiplications related to the β-projectors of the pseudopotentials, parallel MPI+OpenMP algorithms are revised to make use of overlapping computation and communication. The necessary partitioning of the workload is optimized by auto-tuning algorithms. In addition, the largest global MPI_Allreduce operation is replaced by highly tuned node-local parallelized operations using MPI shared-memory windows to avoid inter-node communication. A batched algorithm for the multiple 3-d FFTs improves the throughput of the MPI_Alltoall communication and, thus, the scalability of the implementation, both for USPP and for frequently used norm-conserving pseudopotentials. The new algorithms have been implemented in the AIMD program CPMD (www.cpmd.org). The enhanced performance and scalability of the code is demonstrated on simulations of liquid water with up to 2048 molecules. It is shown that 100ps simulations with many hundred water molecules can be done now routinely within a few days on a moderate number of nodes.

Breaking (Global) Barriers in Parallel Stochastic Optimization with Wait-Avoiding Group Averaging

Deep learning at scale is dominated by communication time. Distributing samples across nodes usually yields the best performance, but poses scaling challenges due to global information dissemination and load imbalance across uneven sample lengths. State-of-the-art decentralized optimizers mitigate the problem, but require more iterations to achieve the same accuracy as their globally-communicating counterparts. We present Wait-Avoiding Group Model Averaging (WAGMA) SGD, a wait-avoiding stochastic optimizer that reduces global communication via subgroup weight exchange. The key insight is a combination of algorithmic changes to the averaging scheme and the use of a group allreduce operation. We prove the convergence of WAGMA-SGD, and empirically show that it retains convergence rates similar to Allreduce-SGD. For evaluation, we train ResNet-50 on ImageNet; Transformer for machine translation; and deep reinforcement learning for navigation at scale. Compared with state-of-the-art decentralized SGD variants, WAGMA-SGD significantly improves training throughput (e.g., 2.1x on 1,024 GPUs for reinforcement learning), and achieves the fastest time-to-solution (e.g., the highest score using the shortest training time for Transformer).

BlueConnect: Decomposing all-reduce for deep learning on heterogeneous network hierarchy

As deep neural networks get more complex and input datasets get larger, it can take days or even weeks to train a deep neural network to the desired accuracy. Therefore, enabling distributed deep learning at a massive scale is critical since it offers the potential to reduce the training time from weeks to hours. In this article, we present BlueConnect, an efficient communication library for distributed deep learning that is highly optimized for popular GPU-based platforms. BlueConnect decomposes a single all-reduce operation into a large number of parallelizable reduce–scatter and all-gather operations to exploit the tradeoff between latency and bandwidth and adapt to a variety of network configurations. Therefore, each individual operation can be mapped to a different network fabric and take advantage of the best performing implementation for the corresponding fabric. According to our experimental results on two system configurations, BlueConnect can outperform the leading industrial communication library by a wide margin, and the BlueConnect-integrated Caffe2 can significantly reduce synchronization overhead by 87% on 192 GPUs for Resnet-50 training over prior schemes.

A Hybrid MPI/OpenMP Parallelization of $K$ -Means Algorithms Accelerated Using the Triangle Inequality

The standard formulation of the K -means clustering (Lloyd's method) performs many unnecessary distance calculations. In this paper, we focus on four approaches that use the triangle inequality to avoid unnecessary distance calculations. These approaches are Drake's, Elkan's, Annulus, and Yinyang algorithms. We propose a hybrid MPI/OpenMP parallelization of these algorithms in which the dataset and the corresponding data structures storing bounds on distances are evenly divided among MPI processes. Then, in the assignment step of a K -means iteration, each MPI process computes the assignment of its portion of data using OpenMP threads. In the update step of the iteration, the cluster centroids are computed using a hierarchical all-reduce operation. In the computational experiments, we compared the strong scalability of these four algorithms with the scalability of Lloyd's algorithm, parallelized using the same approach. The results indicate that all four algorithms maintain an advantage in computing time over Lloyd's algorithm. A comparison with two software packages, whose sources are publicly available, in the same computing environment, shows that our implementations are more efficient.

Simulation of the performance and scalability of message passing interface (MPI) communications of atmospheric models running on exascale supercomputers

Abstract. In this study, we identify the key message passing interface (MPI) operations required in atmospheric modelling; then, we use a skeleton program and a simulation framework (based on SST/macro simulation package) to simulate these MPI operations (transposition, halo exchange, and allreduce), with the perspective of future exascale machines in mind. The experimental results show that the choice of the collective algorithm has a great impact on the performance of communications; in particular, we find that the generalized ring-k algorithm for the alltoallv operation and the generalized recursive-k algorithm for the allreduce operation perform the best. In addition, we observe that the impacts of interconnect topologies and routing algorithms on the performance and scalability of transpositions, halo exchange, and allreduce operations are significant. However, the routing algorithm has a negligible impact on the performance of allreduce operations because of its small message size. It is impossible to infinitely grow bandwidth and reduce latency due to hardware limitations. Thus, congestion may occur and limit the continuous improvement of the performance of communications. The experiments show that the performance of communications can be improved when congestion is mitigated by a proper configuration of the topology and routing algorithm, which uniformly distribute the congestion over the interconnect network to avoid the hotspots and bottlenecks caused by congestion. It is generally believed that the transpositions seriously limit the scalability of the spectral models. The experiments show that the communication time of the transposition is larger than those of the wide halo exchange for the semi-Lagrangian method and the allreduce in the generalized conjugate residual (GCR) iterative solver for the semi-implicit method below 2×105 MPI processes. The transposition whose communication time decreases quickly with increasing number of MPI processes demonstrates strong scalability in the case of very large grids and moderate latencies. The halo exchange whose communication time decreases more slowly than that of transposition with increasing number of MPI processes reveals its weak scalability. In contrast, the allreduce whose communication time increases with increasing number of MPI processes does not scale well. From this point of view, the scalability of spectral models could still be acceptable. Therefore it seems to be premature to conclude that the scalability of the grid-point models is better than that of spectral models at the exascale, unless innovative methods are exploited to mitigate the problem of the scalability presented in the grid-point models.

Heterogeneous and unconventional cluster architectures and applications

Heterogeneous and unconventional cluster architectures and applications

Improving all-reduce collective operations for imbalanced process arrival patterns

Two new algorithms for the all-reduce operation optimized for imbalanced process arrival patterns (PAPs) are presented: (1) sorted linear tree, (2) pre-reduced ring as well as a new way of online PAP detection, including process arrival time estimations, and their distribution between cooperating processes was introduced. The idea, pseudo-code, implementation details, benchmark for performance evaluation and a real case example for machine learning are provided. The results of the experiments were described and analyzed, showing that the proposed solution has high scalability and improved performance in comparison with the usually used ring and Rabenseifner algorithms.

Hierarchical redesign of classic MPI reduction algorithms

Optimization of MPI collective communication operations has been an active research topic since the advent of MPI in 1990s. Many general and architecture-specific collective algorithms have been proposed and implemented in the state-of-the-art MPI implementations. Hierarchical topology-oblivious transformation of existing communication algorithms has been recently proposed as a new promising approach to optimization of MPI collective communication algorithms and MPI-based applications. This approach has been successfully applied to the most popular parallel matrix multiplication algorithm, SUMMA, and the state-of-the-art MPI broadcast algorithms, demonstrating significant multifold performance gains, especially for large-scale HPC systems. In this paper, we apply this approach to optimization of the MPI Reduce and Allreduce operations. Theoretical analysis and experimental results on a cluster of Grid’5000 platform are presented.

Parallel iterative refinement linear least squares solvers based on all-reduce operations

We present the novel parallel linear least squares solvers ARPLS-MPIR and ARPLS-IR.We provide a careful analysis of their communication cost.We analyze their parallel runtime behavior experimentally.Mixed precision iterative refinement reduces computation and communication cost for well-conditioned problems.ARPLS-IR is also applicable to ill-conditioned problems and especially for narrow problems outperforms DPLASMA and ScaLapack. We present the novel parallel linear least squares solvers ARPLS-IR and ARPLS-MPIR for dense overdetermined linear systems. All internode communication of our ARPLS solvers arises in the context of all-reduce operations across the parallel system and therefore they benefit directly from efficient implementations of such operations. Our approach is based on the semi-normal equations, which are in general not backward stable. However, the method is stabilised by using iterative refinement. We show that performing iterative refinement in mixed precision also increases the parallel performance of the algorithm. We consider different variants of the ARPLS algorithm depending on the conditioning of the problem and in this context also evaluate the method of normal equations with iterative refinement. For ill-conditioned systems, we demonstrate that the semi-normal equations with standard iterative refinement achieve the best accuracy compared to other parallel solvers.We discuss the conceptual advantages of ARPLS-IR and ARPLS-MPIR over alternative parallel approaches based on QR factorisation or the normal equations. Moreover, we analytically compare the communication cost to an approach based on communication-avoiding QR factorisation. Numerical experiments on a high performance cluster illustrate speed-ups up to 3820 on 2048 cores for ill-conditioned tall and skinny matrices over state-of-the-art solvers from DPLASMA or ScaLAPACK.

Bandwidth optimal all-reduce algorithms for clusters of workstations

We consider an efficient realization of the all-reduce operation with large data sizes in cluster environments, under the assumption that the reduce operator is associative and commutative. We derive a tight lower bound of the amount of data that must be communicated in order to complete this operation and propose a ring-based algorithm that only requires tree connectivity to achieve bandwidth optimality. Unlike the widely used butterfly-like all-reduce algorithm that incurs network contention in SMP/multi-core clusters, the proposed algorithm can achieve contention-free communication in almost all contemporary clusters, including SMP/multi-core clusters and Ethernet switched clusters with multiple switches. We demonstrate that the proposed algorithm is more efficient than other algorithms on clusters with different nodal architectures and networking technologies when the data size is sufficiently large.