arXiv subjects

Flavio Vella

Publications and source records attributed to Flavio Vella.

35 records · Page 2Linked to original sources

arXiv2024

High Performance Unstructured SpMM Computation Using Tensor Cores

High-performance sparse matrix-matrix (SpMM) multiplication is paramount for science and industry, as the ever-increasing sizes of data prohibit using dense data structures. Yet, existing hardware, such as Tensor Cores (TC), is ill-suited for SpMM, as it imposes strict constraints on data structures that cannot be met by unstructured sparsity found in many applications. To address this, we introduce (S)parse (Ma)trix Matrix (T)ensor Core-accelerated (SMaT): a novel SpMM library that utilizes TCs for unstructured sparse matrices. Our block-sparse library leverages the low-level CUDA MMA (matrix-matrix-accumulate) API, maximizing the performance offered by modern GPUs. Algorithmic optimizations such as sparse matrix permutation further improve performance by minimizing the number of non-zero blocks. The evaluation on NVIDIA A100 shows that SMaT outperforms SotA libraries (DASP, cuSPARSE, and Magicube) by up to 125x (on average 2.6x). SMaT can be used to accelerate many workloads in scientific computing, large-model training, inference, and others.

cs.DC↗

arXiv2024

Dependable Classical-Quantum Computer Systems Engineering

Quantum Computing (QC) offers the potential to enhance traditional High-Performance Computing (HPC) workloads by leveraging the unique properties of quantum computers, leading to the emergence of a new paradigm: HPC-QC. While this integration presents new opportunities, it also brings novel challenges, particularly in ensuring the dependability of such hybrid systems. This paper aims to identify integration challenges, anticipate failures, and foster a diverse co-design for HPC-QC systems by bringing together QC, cloud computing, HPC, and network security. The focus of this emerging inter-disciplinary effort is to develop engineering principles that ensure the dependability of hybrid systems, aiming for a more prescriptive co-design cycle. Our framework will help to prevent design pitfalls and accelerate the maturation of the QC technology ecosystem. Key aspects include building resilient HPC-QC systems, analyzing the applicability of conventional techniques to the quantum domain, and exploring the complexity of scaling in such hybrid systems. This underscores the need for performance-reliability metrics specific to this new computational paradigm.

quant-ph↗

arXiv2024

cuVegas: Accelerate Multidimensional Monte Carlo Integration through a Parallelized CUDA-based Implementation of the VEGAS Enhanced Algorithm

This paper introduces cuVegas, a CUDA-based implementation of the Vegas Enhanced Algorithm (VEGAS+), optimized for multi-dimensional integration in GPU environments. The VEGAS+ algorithm is an advanced form of Monte Carlo integration, recognized for its adaptability and effectiveness in handling complex, high-dimensional integrands. It employs a combination of variance reduction techniques, namely adaptive importance sampling and a variant of adaptive stratified sampling, that make it particularly adept at managing integrands with multiple peaks or those aligned with the diagonals of the integration volume. Being a Monte Carlo integration method, the task is well suited for parallelization and for GPU execution. Our implementation, cuVegas, aims to harness the inherent parallelism of GPUs, addressing the challenge of workload distribution that often hampers efficiency in standard implementations. We present a comprehensive analysis comparing cuVegas with existing CPU and GPU implementations, demonstrating significant performance improvements, from two to three orders of magnitude on CPUs, and from a factor of two on GPUs over the best existing implementation. We also demonstrate the speedup for integrands for which VEGAS+ was designed, with multiple peaks or other significant structures aligned with diagonals of the integration volume.

cs.DC↗

arXiv2024

On the Efficacy of Surface Codes in Compensating for Radiation Events in Superconducting Devices

Reliability is fundamental for developing large-scale quantum computers. Since the benefit of technological advancements to the qubit's stability is saturating, algorithmic solutions, such as quantum error correction (QEC) codes, are needed to bridge the gap to reliable computation. Unfortunately, the deployment of the first quantum computers has identified faults induced by natural radiation as an additional threat to qubits reliability. The high sensitivity of qubits to radiation hinders the large-scale adoption of quantum computers, since the persistence and area-of-effect of the fault can potentially undermine the efficacy of the most advanced QEC. In this paper, we investigate the resilience of various implementations of state-of-the-art QEC codes to radiation-induced faults. We report data from over 400 million fault injections and correlate hardware faults with the logical error observed after decoding the code output, extrapolating physical-to-logical error rates. We compare the code's radiation-induced logical error rate over the code distance, the number and role in the QEC of physical qubits, the underlying quantum computer topology, and particle energy spread in the chip. We show that, by simply selecting and tuning properly the surface code, thus without introducing any overhead, the probability of correcting a radiation-induced fault is increased by up to 10\%. Finally, we provide indications and guidelines for the design of future QEC codes to further increase their effectiveness against radiation-induced events.

quant-ph↗

arXiv2024

Gauss-Newton Natural Gradient Descent for Physics-Informed Computational Fluid Dynamics

We propose Gauss-Newton's method in function space for the solution of the Navier-Stokes equations in the physics-informed neural network (PINN) framework. Upon discretization, this yields a natural gradient method that provably mimics the function space dynamics. Our computational results demonstrate close to single-precision accuracy measured in relative $L^2$ norm on a number of benchmark problems. To the best of our knowledge, this constitutes the first contribution in the PINN literature that solves the Navier-Stokes equations to this degree of accuracy. Finally, we show that given a suitable integral discretization, the proposed optimization algorithm agrees with Gauss-Newton's method in parameter space. This allows a matrix-free formulation enabling efficient scalability to large network sizes.

math.OC↗

arXiv2023

Scaling Expected Force: Efficient Identification of Key Nodes in Network-based Epidemic Models

Centrality measures are fundamental tools of network analysis as they highlight the key actors within the network. This study focuses on a newly proposed centrality measure, Expected Force (EF), and its use in identifying spreaders in network-based epidemic models. We found that EF effectively predicts the spreading power of nodes and identifies key nodes and immunization targets. However, its high computational cost presents a challenge for its use in large networks. To overcome this limitation, we propose two parallel scalable algorithms for computing EF scores: the first algorithm is based on the original formulation, while the second one focuses on a cluster-centric approach to improve efficiency and scalability. Our implementations significantly reduce computation time, allowing for the detection of key nodes at large scales. Performance analysis on synthetic and real-world networks demonstrates that the GPU implementation of our algorithm can efficiently scale to networks with up to 44 million edges by exploiting modern parallel architectures, achieving speed-ups of up to 300x, and 50x on average, compared to the simple parallel solution.

cs.SI↗

arXiv2023

Multi-GPU aggregation-based AMG preconditioner for iterative linear solvers

We present and release in open source format a sparse linear solver which efficiently exploits heterogeneous parallel computers. The solver can be easily integrated into scientific applications that need to solve large and sparse linear systems on modern parallel computers made of hybrid nodes hosting NVIDIA Graphics Processing Unit (GPU) accelerators. The work extends our previous efforts in the exploitation of a single GPU accelerator and proposes an implementation, based on the hybrid MPI-CUDA software environment, of a Krylov-type linear solver relying on an efficient Algebraic MultiGrid (AMG) preconditioner already available in the BootCMatchG library. Our design for the hybrid implementation has been driven by the best practices for minimizing data communication overhead when multiple GPUs are employed, yet preserving the efficiency of the single GPU kernels. Strong and weak scalability results on well-known benchmark test cases of the new version of the library are discussed. Comparisons with the Nvidia AmgX solution show an improvement of up to 2.0x in the solve phase.

cs.DC↗

arXiv2022

Towards a learning-based performance modeling for accelerating Deep Neural Networks

Emerging applications such as Deep Learning are often data-driven, thus traditional approaches based on auto-tuners are not performance effective across the wide range of inputs used in practice. In the present paper, we start an investigation of predictive models based on machine learning techniques in order to optimize Convolution Neural Networks (CNNs). As a use-case, we focus on the ARM Compute Library which provides three different implementations of the convolution operator at different numeric precision. Starting from a collation of benchmarks, we build and validate models learned by Decision Tree and naive Bayesian classifier. Preliminary experiments on Midgard-based ARM Mali GPU show that our predictive model outperforms all the convolution operators manually selected by the library.

cs.LG↗

arXiv2022

ProbGraph: High-Performance and High-Accuracy Graph Mining with Probabilistic Set Representations

Important graph mining problems such as Clustering are computationally demanding. To significantly accelerate these problems, we propose ProbGraph: a graph representation that enables simple and fast approximate parallel graph mining with strong theoretical guarantees on work, depth, and result accuracy. The key idea is to represent sets of vertices using probabilistic set representations such as Bloom filters. These representations are much faster to process than the original vertex sets thanks to vectorizability and small size. We use these representations as building blocks in important parallel graph mining algorithms such as Clique Counting or Clustering. When enhanced with ProbGraph, these algorithms significantly outperform tuned parallel exact baselines (up to nearly 50x on 32 cores) while ensuring accuracy of more than 90% for many input graph datasets. Our novel bounds and algorithms based on probabilistic set representations with desirable statistical properties are of separate interest for the data analytics community.

cs.DC↗

arXiv2022

Asynchronous Distributed-Memory Triangle Counting and LCC with RMA Caching

Triangle count and local clustering coefficient are two core metrics for graph analysis. They find broad application in analyses such as community detection and link recommendation. Current state-of-the-art solutions suffer from synchronization overheads or expensive pre-computations needed to distribute the graph, achieving limited scaling capabilities. We propose a fully asynchronous implementation for triangle counting and local clustering coefficient based on 1D partitioning, using remote memory accesses for transferring data and avoid synchronization. Additionally, we show how these algorithms present data reuse on remote memory accesses and how the overall communication time can be improved by caching these accesses. Finally, we extend CLaMPI, a software-layer caching system for MPI RMA, to include application-specific scores for cached entries and influence the eviction procedure to improve caching efficiency. Our results show improvements on shared memory, and we achieve 14x speedup from 4 to 64 nodes for the LiveJournal1 graph on distributed memory. Moreover, we demonstrate how caching remote accesses reduces total running time by up to 73% with respect to a non-cached version. Finally, we compare our implementation to TriC, the 2020 graph champion paper, and achieve up to 100x faster results for scale-free graphs.

cs.DC↗

arXiv2022

Blocking Techniques for Sparse Matrix Multiplication on Tensor Accelerators

Tensor accelerators have gained popularity because they provide a cheap and efficient solution for speeding up computational-expensive tasks in Deep Learning and, more recently, in other Scientific Computing applications. However, since their features are specifically designed for tensor algebra (typically dense matrix-product), it is commonly assumed that they are not suitable for applications with sparse data. To challenge this viewpoint, we discuss methods and present solutions for accelerating sparse matrix multiplication on such architectures. In particular, we present a 1-dimensional blocking algorithm with theoretical guarantees on the density, which builds dense blocks from arbitrary sparse matrices. Experimental results show that, even for unstructured and highly-sparse matrices, our block-based solution which exploits Nvidia Tensor Cores is faster than its sparse counterpart. We observed significant speed-ups of up to two orders of magnitude on real-world sparse matrices.

cs.DC↗

arXiv2020

A Computational Model for Tensor Core Units

To respond to the need of efficient training and inference of deep neural networks, a plethora of domain-specific hardware architectures have been introduced, such as Google Tensor Processing Units and NVIDIA Tensor Cores. A common feature of these architectures is a hardware circuit for efficiently computing a dense matrix multiplication of a given small size. In order to broaden the class of algorithms that exploit these systems, we propose a computational model, named the TCU model, that captures the ability to natively multiply small matrices. We then use the TCU model for designing fast algorithms for several problems, including matrix operations (dense and sparse multiplication, Gaussian Elimination), graph algorithms (transitive closure, all pairs shortest distances), Discrete Fourier Transform, stencil computations, integer multiplication, and polynomial evaluation. We finally highlight a relation between the TCU model and the external memory model.

cs.DS↗

arXiv2019

GPU-based parallelism for ASP-solving

Answer Set Programming (ASP) has become, the paradigm of choice in the field of logic programming and non-monotonic reasoning. Thanks to the availability of efficient solvers, ASP has been successfully employed in a large number of application domains. The term GPU-computing indicates a recent programming paradigm aimed at enabling the use of modern parallel Graphical Processing Units (GPUs) for general purpose computing. In this paper we describe an approach to ASP-solving that exploits GPU parallelism. The design of a GPU-based solver poses various challenges due to the peculiarities of GPUs' software and hardware architectures and to the intrinsic nature of the satisfiability problem.

cs.AI↗

arXiv2018

A model-driven approach for a new generation of adaptive libraries

Efficient high-performance libraries often expose multiple tunable parameters to provide highly optimized routines. These can range from simple loop unroll factors or vector sizes all the way to algorithmic changes, given that some implementations can be more suitable for certain devices by exploiting hardware characteristics such as local memories and vector units. Traditionally, such parameters and algorithmic choices are tuned and then hard-coded for a specific architecture and for certain characteristics of the inputs. However, emerging applications are often data-driven, thus traditional approaches are not effective across the wide range of inputs and architectures used in practice. In this paper, we present a new adaptive framework for data-driven applications which uses a predictive model to select the optimal algorithmic parameters by training with synthetic and real datasets. We demonstrate the effectiveness of a BLAS library and specifically on its matrix multiplication routine. We present experimental results for two GPU architectures and show significant performance gains of up to 3x (on a high-end NVIDIA Pascal GPU) and 2.5x (on an embedded ARM Mali GPU) when compared to a traditionally optimized library.

cs.PF↗

arXiv2017

Accelerating Energy Games Solvers on Modern Architectures

Quantitative games, where quantitative objectives are defined on weighted game arenas, provide natural tools for designing faithful models of embedded controllers. Instances of these games that recently gained interest are the so called Energy Games. The fast-known algorithm solves Energy Games in O(EVW) where W is the maximum weight. Starting from a sequential baseline implementation, we investigate the use of massively data computation capabilities supported by modern Graphics Processing Units to solve the `initial credit problem' for Energy Games. We present four different parallel implementations on multi-core CPU and GPU systems. Our solution outperforms the baseline implementation by up to 36x speedup and obtains a faster convergence time on real-world graphs.

cs.DC↗

arXiv2017

Scaling betweenness centrality using communication-efficient sparse matrix multiplication

Betweenness centrality (BC) is a crucial graph problem that measures the significance of a vertex by the number of shortest paths leading through it. We propose Maximal Frontier Betweenness Centrality (MFBC): a succinct BC algorithm based on novel sparse matrix multiplication routines that performs a factor of $p^{1/3}$ less communication on $p$ processors than the best known alternatives, for graphs with $n$ vertices and average degree $k=n/p^{2/3}$. We formulate, implement, and prove the correctness of MFBC for weighted graphs by leveraging monoids instead of semirings, which enables a surprisingly succinct formulation. MFBC scales well for both extremely sparse and relatively dense graphs. It automatically searches a space of distributed data decompositions and sparse matrix multiplication algorithms for the most advantageous configuration. The MFBC implementation outperforms the well-known CombBLAS library by up to 8x and shows more robust performance. Our design methodology is readily extensible to other graph problems.

cs.DC↗

arXiv2016

Algorithms and Heuristics for Scalable Betweenness Centrality Computation on Multi-GPU Systems

Betweenness Centrality (BC) is steadily growing in popularity as a metrics of the influence of a vertex in a graph. The BC score of a vertex is proportional to the number of all-pairs-shortest-paths passing through it. However, complete and exact BC computation for a large-scale graph is an extraordinary challenge that requires high performance computing techniques to provide results in a reasonable amount of time. Our approach combines bi-dimensional (2-D) decomposition of the graph and multi-level parallelism together with a suitable data-thread mapping that overcomes most of the difficulties caused by the irregularity of the computation on GPUs. Furthermore, we propose novel heuristics which exploit the topology information of the graph in order to reduce time and space requirements of BC computation. Experimental results on synthetic and real-world graphs show that the proposed techniques allow the BC computation of graphs which are too large to fit in the memory of a single computational node along with a significant reduction of the computing time.

cs.DC↗