Optimized Sparse Matrix Operations for Reverse Mode Automatic Differentiation

Sparse matrix representations are ubiquitous in computational science and machine learning, leading to significant reductions in compute time, in comparison to dense representation, for problems that have local connectivity. The adoption of sparse representation in leading ML frameworks such as PyTorch is incomplete, however, with support for both automatic differentiation and GPU acceleration missing. In this work, we present an implementation of a CSR-based sparse matrix wrapper for PyTorch with CUDA acceleration for basic matrix operations, as well as automatic differentiability. We also present several applications of the resulting sparse kernels to optimization problems, demonstrating ease of implementation and performance measurements versus their dense counterparts

Large Scale Kernel Methods for Fun and Profit

Kernel methods are among the most flexible classes of machine learning models with strong theoretical guarantees. Wide classes of functions can be approximated arbitrarily well with kernels, while fast convergence and learning rates have been formally shown to hold. Exact kernel methods are known to scale poorly with increasing dataset size, and we believe that one of the factors limiting their usage in modern machine learning is the lack of scalable and easy to use algorithms and software. The main goal of this thesis is to study kernel methods from the point of view of efficient learning, with particular emphasis on large-scale data, but also on low-latency training, and user efficiency. We improve the state-of-the-art for scaling kernel solvers to datasets with billions of points using the Falkon algorithm, which combines random projections with fast optimization. Running it on GPUs, we show how to fully utilize available computing power for training kernel machines. To boost the ease-of-use of approximate kernel solvers, we propose an algorithm for automated hyperparameter tuning. By minimizing a penalized loss function, a model can be learned together with its hyperparameters, reducing the time needed for user-driven experimentation. In the setting of multi-class learning, we show that – under stringent but realistic assumptions on the separation between classes – a wide set of algorithms needs much fewer data points than in the more general setting (without assumptions on class separation) to reach the same accuracy. The first part of the thesis develops a framework for efficient and scalable kernel machines. This raises the question of whether our approaches can be used successfully in real-world applications, especially compared to alternatives based on deep learning which are often deemed hard to beat. The second part aims to investigate this question on two main applications, chosen because of the paramount importance of having an efficient algorithm. First, we consider the problem of instance segmentation of images taken from the iCub robot. Here Falkon is used as part of a larger pipeline, but the efficiency afforded by our solver is essential to ensure smooth human-robot interactions. In the second instance, we consider time-series forecasting of wind speed, analysing the relevance of different physical variables on the predictions themselves. We investigate different schemes to adapt i.i.d. learning to the time-series setting. Overall, this work aims to demonstrate, through novel algorithms and examples, that kernel methods are up to computationally demanding tasks, and that there are concrete applications in which their use is warranted and more efficient than that of other, more complex, and less theoretically grounded models

Using Ginkgo’s memory accessor for improving the accuracy of memory-bound low precision BLAS

The roofline model not only provides a powerful tool to relate an application\u27s performance with the specific constraints imposed by the target hardware but also offers a graphic representation of the balance between memory access cost and compute throughput. In this work, we present a strategy to break up the tight coupling between the precision format used for arithmetic operations and the storage format employed for memory operations. (At a high level, this idea is equivalent to compressing/decompressing the data in registers before/after invoking store/load memory operations.) In practice, we demonstrate that a “memory accessor” that hides the data compression behind the memory access, can virtually push the bandwidth-induced roofline, yielding higher performance for memory-bound applications using high precision arithmetic that can handle the numerical effects associated with lossy compression. We also demonstrate that memory-bound applications operating on low precision data can increase the accuracy by relying on the memory accessor to perform all arithmetic operations in high precision. In particular, we demonstrate that memory-bound BLAS operations (including the sparse matrix-vector product) can be re-engineered with the memory accessor and that the resulting accessor-enabled BLAS routines achieve lower rounding errors while delivering the same performance as the fast low precision BLAS

Survey of scientific programming techniques for the management of data-intensive engineering environments

The present paper introduces and reviews existing technology and research works in the field of scientific programming methods and techniques in data-intensive engineering environments. More specifically, this survey aims to collect those relevant approaches that have faced the challenge of delivering more advanced and intelligent methods taking advantage of the existing large datasets. Although existing tools and techniques have demonstrated their ability to manage complex engineering processes for the development and operation of safety-critical systems, there is an emerging need to know how existing computational science methods will behave to manage large amounts of data. That is why, authors review both existing open issues in the context of engineering with special focus on scientific programming techniques and hybrid approaches. 1193 journal papers have been found as the representative in these areas screening 935 to finally make a full review of 122. Afterwards, a comprehensive mapping between techniques and engineering and nonengineering domains has been conducted to classify and perform a meta-analysis of the current state of the art. As the main result of this work, a set of 10 challenges for future data-intensive engineering environments have been outlined.The current work has been partially supported by the Research Agreement between the RTVE (the Spanish Radio and Television Corporation) and the UC3M to boost research in the field of Big Data, Linked Data, Complex Network Analysis, and Natural Language. It has also received the support of the Tecnologico Nacional de Mexico (TECNM), National Council of Science and Technology (CONACYT), and the Public Education Secretary (SEP) through PRODEP

Adaptive Precision Block-Jacobi for High Performance Preconditioning in the Ginkgo Linear Algebra Software

© ACM, 2021. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in ACM Transactions on Mathematical Software, Volume 47, Issue , June 2021, http://doi.acm.org/10.1145/3441850[EN] The use of mixed precision in numerical algorithms is a promising strategy for accelerating scientific applications. In particular, the adoption of specialized hardware and data formats for low-precision arithmetic in high-end GPUs (graphics processing units) has motivated numerous efforts aiming at carefully reducing the working precision in order to speed up the computations. For algorithms whose performance is bound by the memory bandwidth, the idea of compressing its data before (and after) memory accesses has received considerable attention. One idea is to store an approximate operator-like a preconditioner-in lower than working precision hopefully without impacting the algorithm output. We realize the first high-performance implementation of an adaptive precision block-Jacobi preconditioner which selects the precision format used to store the preconditioner data on-the-fly, taking into account the numerical properties of the individual preconditioner blocks. We implement the adaptive block-Jacobi preconditioner as production-ready functionality in the Ginkgo linear algebra library, considering not only the precision formats that are part of the IEEE standard, but also customized formats which optimize the length of the exponent and significand to the characteristics of the preconditioner blocks. Experiments run on a state-of-the-art GPU accelerator show that our implementation offers attractive runtime savings.H. Anzt and T. Cojean were supported by the "Impuls und Vernetzungsfond of the Helmholtz Association" under grant VH-NG-1241. G. Flegar and E. S. Quintana-Orti were supported by project TIN2017-82972-R of the MINECO and FEDER and the H2020 EU FETHPC Project 732631 "OPRECOMP". This research was supported by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration. The authors want to acknowledge the access to the Piz Daint supercomputer at the Swiss National Supercomputing Centre (CSCS) granted under the project #d100 and the Summit supercomputer at the Oak Ridge National Lab (ORNL).Flegar, G.; Anzt, H.; Cojean, T.; Quintana-Ortí, ES. (2021). Adaptive Precision Block-Jacobi for High Performance Preconditioning in the Ginkgo Linear Algebra Software. ACM Transactions on Mathematical Software. 47(2):1-28. https://doi.org/10.1145/3441850S12847

Compiler Support for Sparse Tensor Computations in MLIR

Sparse tensors arise in problems in science, engineering, machine learning, and data analytics. Programs that operate on such tensors can exploit sparsity to reduce storage requirements and computational time. Developing and maintaining sparse software by hand, however, is a complex and error-prone task. Therefore, we propose treating sparsity as a property of tensors, not a tedious implementation task, and letting a sparse compiler generate sparse code automatically from a sparsity-agnostic definition of the computation. This paper discusses integrating this idea into MLIR

Heterogeneous multicore systems for signal processing

This thesis explores the capabilities of heterogeneous multi-core systems, based on multiple Graphics Processing Units (GPUs) in a standard desktop framework. Multi-GPU accelerated desk side computers are an appealing alternative to other high performance computing (HPC) systems: being composed of commodity hardware components fabricated in large quantities, their price-performance ratio is unparalleled in the world of high performance computing. Essentially bringing “supercomputing to the masses”, this opens up new possibilities for application fields where investing in HPC resources had been considered unfeasible before. One of these is the field of bioelectrical imaging, a class of medical imaging technologies that occupy a low-cost niche next to million-dollar systems like functional Magnetic Resonance Imaging (fMRI). In the scope of this work, several computational challenges encountered in bioelectrical imaging are tackled with this new kind of computing resource, striving to help these methods approach their true potential. Specifically, the following main contributions were made: Firstly, a novel dual-GPU implementation of parallel triangular matrix inversion (TMI) is presented, addressing an crucial kernel in computation of multi-mesh head models of encephalographic (EEG) source localization. This includes not only a highly efficient implementation of the routine itself achieving excellent speedups versus an optimized CPU implementation, but also a novel GPU-friendly compressed storage scheme for triangular matrices. Secondly, a scalable multi-GPU solver for non-hermitian linear systems was implemented. It is integrated into a simulation environment for electrical impedance tomography (EIT) that requires frequent solution of complex systems with millions of unknowns, a task that this solution can perform within seconds. In terms of computational throughput, it outperforms not only an highly optimized multi-CPU reference, but related GPU-based work as well. Finally, a GPU-accelerated graphical EEG real-time source localization software was implemented. Thanks to acceleration, it can meet real-time requirements in unpreceeded anatomical detail running more complex localization algorithms. Additionally, a novel implementation to extract anatomical priors from static Magnetic Resonance (MR) scansions has been included

NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems

We introduce version 3 of NetKet, the machine learning toolbox for many-body quantum physics. NetKet is built around neural-network quantum states and provides efficient algorithms for their evaluation and optimization. This new version is built on top of JAX, a differentiable programming and accelerated linear algebra framework for the Python programming language. The most significant new feature is the possibility to define arbitrary neural network ansätze in pure Python code using the concise notation of machine-learning frameworks, which allows for just-in-time compilation as well as the implicit generation of gradients thanks to automatic differentiation. NetKet 3 also comes with support for GPU and TPU accelerators, advanced support for discrete symmetry groups, chunking to scale up to thousands of degrees of freedom, drivers for quantum dynamics applications, and improved modularity, allowing users to use only parts of the toolbox as a foundation for their own code