Asynchronous Parallel Stochastic Gradient Descent - A Numeric Core for Scalable Distributed Machine Learning Algorithms

The implementation of a vast majority of machine learning (ML) algorithms boils down to solving a numerical optimization problem. In this context, Stochastic Gradient Descent (SGD) methods have long proven to provide good results, both in terms of convergence and accuracy. Recently, several parallelization approaches have been proposed in order to scale SGD to solve very large ML problems. At their core, most of these approaches are following a map-reduce scheme. This paper presents a novel parallel updating algorithm for SGD, which utilizes the asynchronous single-sided communication paradigm. Compared to existing methods, Asynchronous Parallel Stochastic Gradient Descent (ASGD) provides faster (or at least equal) convergence, close to linear scaling and stable accuracy

Optimization of Computationally and I/O Intense Patterns in Electronic Structure and Machine Learning Algorithms

Development of scalable High-Performance Computing (HPC) applications is already a challenging task even in the pre-Exascale era. Utilization of the full potential of (near-)future supercomputers will most likely require the mastery of massively parallel heterogeneous architectures with multi-tier persistence systems, ideally in fault tolerant mode. With the change in hardware architectures HPC applications are also widening their scope to `Big data' processing and analytics using machine learning algorithms and neural networks. In this work, in cooperation with the INTERTWinE FET-HPC project, we demonstrate how the GASPI (Global Address Space Programming Interface) programming model helps to address these Exascale challenges on examples of tensor contraction, K-means and Terasort algorithms

Balancing the Communication Load of Asynchronously Parallelized Machine Learning Algorithms

Stochastic Gradient Descent (SGD) is the standard numerical method used to solve the core optimization problem for the vast majority of machine learning (ML) algorithms. In the context of large scale learning, as utilized by many Big Data applications, efficient parallelization of SGD is in the focus of active research. Recently, we were able to show that the asynchronous communication paradigm can be applied to achieve a fast and scalable parallelization of SGD. Asynchronous Stochastic Gradient Descent (ASGD) outperforms other, mostly MapReduce based, parallel algorithms solving large scale machine learning problems. In this paper, we investigate the impact of asynchronous communication frequency and message size on the performance of ASGD applied to large scale ML on HTC cluster and cloud environments. We introduce a novel algorithm for the automatic balancing of the asynchronous communication load, which allows to adapt ASGD to changing network bandwidths and latencies.Comment: arXiv admin note: substantial text overlap with arXiv:1505.0495

A Theory of Partitioned Global Address Spaces

Partitioned global address space (PGAS) is a parallel programming model for the development of applications on clusters. It provides a global address space partitioned among the cluster nodes, and is supported in programming languages like C, C++, and Fortran by means of APIs. In this paper we provide a formal model for the semantics of single instruction, multiple data programs using PGAS APIs. Our model reflects the main features of popular real-world APIs such as SHMEM, ARMCI, GASNet, GPI, and GASPI. A key feature of PGAS is the support for one-sided communication: a node may directly read and write the memory located at a remote node, without explicit synchronization with the processes running on the remote side. One-sided communication increases performance by decoupling process synchronization from data transfer, but requires the programmer to reason about appropriate synchronizations between reads and writes. As a second contribution, we propose and investigate robustness, a criterion for correct synchronization of PGAS programs. Robustness corresponds to acyclicity of a suitable happens-before relation defined on PGAS computations. The requirement is finer than the classical data race freedom and rules out most false error reports. Our main result is an algorithm for checking robustness of PGAS programs. The algorithm makes use of two insights. Using combinatorial arguments we first show that, if a PGAS program is not robust, then there are computations in a certain normal form that violate happens-before acyclicity. Intuitively, normal-form computations delay remote accesses in an ordered way. We then devise an algorithm that checks for cyclic normal-form computations. Essentially, the algorithm is an emptiness check for a novel automaton model that accepts normal-form computations in streaming fashion. Altogether, we prove the robustness problem is PSpace-complete

Enhancing the interoperability between distributed-memory and task-based programming models

Hybrid applications allow to exploit both inter- and intra-node parallelism, however the programming models currently used are not designed to be combined. For this reason, we propose a generic mechanism to enhance the interoperability between distributed-memory and task-based programming models

Task-aware LPF: integrating a model-compliant communication layer with task-based programming models

The rapid advancement of high-performance computing (HPC) systems has led to the emergence of exascale computing, characterized by distributed memory nodes and high parallel computing capabilities. To effectively utilize these systems, the HPC community has embraced programming models that harness both inter-node and intra-node parallelism. Inter-node parallelism is typically addressed using distributed-memory programming models like MPI and GASPI, while intra-node parallelism is exploited through shared-memory programming models such as OpenMP and OmpSs-2. However, the two-sided communication model used in MPI, which requires both the sender and receiver processes to post an operation, can impose performance limitations due to the inherent synchronization. In contrast, one-sided communication models like GASPI and Lightweight Parallel Foundations (LPF) leverage modern network fabric features and remote direct memory access (RDMA) to efficiently exchange data in distributed memory systems without the need for explicit receive operations. In this project, we combine the Bulk Synchronous Parallel (BSP) model of LPF with the data-flow model of OmpSs-2 to exploit parallelism at both intra-node and inter-node levels. This approach maintains the simplicity of the BSP model and the performance of the data-flow model. By enabling optimal overlap between computation, communication, and synchronization phases, we effectively utilize available resources. The flexibility of the data-flow model allows for adjusting computation tasks that are not tightly bound to BSP model phases, facilitating early or delayed execution based on resource availability. To optimize the BSP model, new zero-cost synchronization methods are designed, improving performance and flexibility. These methods offer localized synchronization but require a fixed communication pattern or user-defined criteria, limiting programmability. Additionally, bi-directional communication is often required, necessitating the inclusion of empty messages in applications without bi-directional communication. Our implementation is evaluated against Task-Aware MPI (TAMPI), demonstrating that with a single coarse-grained synchronization primitive, we can still hide synchronization overheads and reach competitive performance. The results show that the zero-cost synchronization methods perform similarly to TAMPI, indicating that coarse synchronization is sufficient for iterative applications. The evaluation highlights the effectiveness of the proposed approach in improving performance and programmability in HPC applications

Parallel Asynchronous Matrix Multiplication for a Distributed Pipelined Neural Network

Machine learning is an approach to devise algorithms that compute an output without a given rule set but based on a self-learning concept. This approach is of great importance for several fields of applications in science and industry where traditional programming methods are not sufficient. In neural networks, a popular subclass of machine learning algorithms, commonly previous experience is used to train the network and produce good outputs for newly introduced inputs. By increasing the size of the network more complex problems can be solved which again rely on a huge amount of training data. Increasing the complexity also leads to higher computational demand and storage requirements and to the need for parallelization. Several parallelization approaches of neural networks have already been considered. Most approaches use special purpose hardware whilst other work focuses on using standard hardware. Often these approaches target the problem by parallelizing the training data. In this work a new parallelization method named poadSGD is proposed for the parallelization of fully-connected, largescale feedforward networks on a compute cluster with standard hardware. poadSGD is based on the stochastic gradient descent algorithm. A block-wise distribution of the network's layers to groups of processes and a pipelining scheme for batches of the training samples are used. The network is updated asynchronously without interrupting ongoing computations of subsequent batches. For this task a one-sided communication scheme is used. A main algorithmic part of the batch-wise pipelined version consists of matrix multiplications which occur for a special distributed setup, where each matrix is held by a different process group. GASPI, a parallel programming model from the field of "Partitioned Global Address Spaces" (PGAS) models is introduced and compared to other models from this class. As it mainly relies on one-sided and asynchronous communication it is a perfect candidate for the asynchronous update task in the poadSGD algorithm. Therefore, the matrix multiplication is also implemented based GASPI. In order to efficiently handle upcoming synchronizations within the process groups and achieve a good workload distribution, a two-dimensional block-cyclic data distribution is applied for the matrices. Based on this distribution, the multiplication algorithm is computed by diagonally iterating over the sub blocks of the resulting matrix and computing the sub blocks in subgroups of the processes. The sub blocks are computed by sharing the workload between the process groups and communicating mostly in pairs or in subgroups. The communication in pairs is set up to be overlapped by other ongoing computations. The implementations provide a special challenge, since the asynchronous communication routines must be handled with care as to which processor is working at what point in time with which data in order to prevent an unintentional dual use of data. The theoretical analysis shows the matrix multiplication to be superior to a naive implementation when the dimension of the sub blocks of the matrices exceeds 382. The performance achieved in the test runs did not withstand the expectations the theoretical analysis predicted. The algorithm is executed on up to 512 cores and for matrices up to a size of 131,072 x 131,072. The implementation using the GASPI API was found not be straightforward but to provide a good potential for overlapping communication with computations whenever the data dependencies of an application allow for it. The matrix multiplication was successfully implemented and can be used within an implementation of the poadSGD method that is yet to come. The poadSGD method seems to be very promising, especially as nowadays, with the larger amount of data and the increased complexity of the applications, the approaches to parallelization of neural networks are increasingly of interest

A hierarchic task-based programming model for distributed heterogeneous computing

Distributed computing platforms are evolving to heterogeneous ecosystems with Clusters, Grids and Clouds introducing in its computing nodes, processors with different core architectures, accelerators (i.e. GPUs, FPGAs), as well as different memories and storage devices in order to achieve better performance with lower energy consumption. As a consequence of this heterogeneity, programming applications for these distributed heterogeneous platforms becomes a complex task. Additionally to the complexity of developing an application for distributed platforms, developers must also deal now with the complexity of the different computing devices inside the node. In this article, we present a programming model that aims to facilitate the development and execution of applications in current and future distributed heterogeneous parallel architectures. This programming model is based on the hierarchical composition of the COMP Superscalar and Omp Superscalar programming models that allow developers to implement infrastructure-agnostic applications. The underlying runtime enables applications to adapt to the infrastructure without the need of maintaining different versions of the code. Our programming model proposal has been evaluated on real platforms, in terms of heterogeneous resource usage, performance and adaptation.This work has been supported by the European Commission through the Horizon 2020 Research and Innovation program under contract 687584 (TANGO project) by the Spanish Government under contract TIN2015-65316 and grant SEV-2015-0493 (Severo Ochoa Program) and by Generalitat de Catalunya under contracts 2014-SGR-1051 and 2014-SGR-1272.Peer ReviewedPostprint (author's final draft