arXiv subjects

Paolo Bientinesi

Publications and source records attributed to Paolo Bientinesi.

At least 37 records · Page 2Linked to original sources

arXiv2022

Benchmarking the Linear Algebra Awareness of TensorFlow and PyTorch

Linear algebra operations, which are ubiquitous in machine learning, form major performance bottlenecks. The High-Performance Computing community invests significant effort in the development of architecture-specific optimized kernels, such as those provided by the BLAS and LAPACK libraries, to speed up linear algebra operations. However, end users are progressively less likely to go through the error prone and time-consuming process of directly using said kernels; instead, frameworks such as TensorFlow (TF) and PyTorch (PyT), which facilitate the development of machine learning applications, are becoming more and more popular. Although such frameworks link to BLAS and LAPACK, it is not clear whether or not they make use of linear algebra knowledge to speed up computations. For this reason, in this paper we develop benchmarks to investigate the linear algebra optimization capabilities of TF and PyT. Our analyses reveal that a number of linear algebra optimizations are still missing; for instance, reducing the number of scalar operations by applying the distributive law, and automatically identifying the optimal parenthesization of a matrix chain. In this work, we focus on linear algebra computations in TF and PyT; we both expose opportunities for performance enhancement to the benefit of the developers of the frameworks and provide end users with guidelines on how to achieve performance gains.

cs.MS↗

arXiv2021

Accelerating jackknife resampling for the Canonical Polyadic Decomposition

The Canonical Polyadic (CP) tensor decomposition is frequently used as a model in applications in a variety of different fields. Using jackknife resampling to estimate parameter uncertainties is often desirable but results in an increase of the already high computational cost. Upon observation that the resampled tensors, though different, are nearly identical, we show that it is possible to extend the recently proposed Concurrent ALS (CALS) technique to a jackknife resampling scenario. This extension gives access to the computational efficiency advantage of CALS for the price of a modest increase (typically a few percent) in the number of floating point operations. Numerical experiments on both synthetic and real-world datasets demonstrate that the new workflow based on a CALS extension can be several times faster than a straightforward workflow where the jackknife submodels are processed individually.

cs.MS↗

arXiv2021

ADTOF: A large dataset of non-synthetic music for automatic drum transcription

The state-of-the-art methods for drum transcription in the presence of melodic instruments (DTM) are machine learning models trained in a supervised manner, which means that they rely on labeled datasets. The problem is that the available public datasets are limited either in size or in realism, and are thus suboptimal for training purposes. Indeed, the best results are currently obtained via a rather convoluted multi-step training process that involves both real and synthetic datasets. To address this issue, starting from the observation that the communities of rhythm games players provide a large amount of annotated data, we curated a new dataset of crowdsourced drum transcriptions. This dataset contains real-world music, is manually annotated, and is about two orders of magnitude larger than any other non-synthetic dataset, making it a prime candidate for training purposes. However, due to crowdsourcing, the initial annotations contain mistakes. We discuss how the quality of the dataset can be improved by automatically correcting different types of mistakes. When used to train a popular DTM model, the dataset yields a performance that matches that of the state-of-the-art for DTM, thus demonstrating the quality of the annotations.

cs.SD↗

arXiv2021

Discriminating Equivalent Algorithms via Relative Performance

In scientific computing, it is common that a mathematical expression can be computed by many different algorithms (sometimes over hundreds), each identifying a specific sequence of library calls. Although mathematically equivalent, those algorithms might exhibit significant differences in terms of performance. However in practice, due to fluctuations, there is not one algorithm that consistently performs noticeably better than the rest. For this reason, with this work we aim to identify not the one best algorithm, but the subset of algorithms that are reliably faster than the rest. To this end, instead of using the usual approach of quantifying the performance of an algorithm in absolute terms, we present a measurement-based clustering approach to sort the algorithms into equivalence (or performance) classes using pair-wise comparisons. We show that this approach, based on relative performance, leads to robust identification of the fastest algorithms even under noisy system conditions. Furthermore, it enables the development of practical machine learning models for automatic algorithm selection.

cs.PF↗

arXiv2021

Concurrent Alternating Least Squares for multiple simultaneous Canonical Polyadic Decompositions

Tensor decompositions, such as CANDECOMP/PARAFAC (CP), are widely used in a variety of applications, such as chemometrics, signal processing, and machine learning. A broadly used method for computing such decompositions relies on the Alternating Least Squares (ALS) algorithm. When the number of components is small, regardless of its implementation, ALS exhibits low arithmetic intensity, which severely hinders its performance and makes GPU offloading ineffective. We observe that, in practice, experts often have to compute multiple decompositions of the same tensor, each with a small number of components (typically fewer than 20), to ultimately find the best ones to use for the application at hand. In this paper, we illustrate how multiple decompositions of the same tensor can be fused together at the algorithmic level to increase the arithmetic intensity. Therefore, it becomes possible to make efficient use of GPUs for further speedups; at the same time the technique is compatible with many enhancements typically used in ALS, such as line search, extrapolation, and non-negativity constraints. We introduce the Concurrent ALS algorithm and library, which offers an interface to Matlab, and a mechanism to effectively deal with the issue that decompositions complete at different times. Experimental results on artificial and real datasets demonstrate a shorter time to completion due to increased arithmetic intensity.

cs.MS↗

arXiv2021

The Linear Algebra Mapping Problem. Current state of linear algebra languages and libraries

We observe a disconnect between the developers and the end users of linear algebra libraries. On the one hand, the numerical linear algebra and the high-performance communities invest significant effort in the development and optimization of highly sophisticated numerical kernels and libraries, aiming at the maximum exploitation of both the properties of the input matrices, and the architectural features of the target computing platform. On the other hand, end users are progressively less likely to go through the error-prone and time consuming process of directly using said libraries by writing their code in C or Fortran; instead, languages and libraries such as Matlab, Julia, Eigen and Armadillo, which offer a higher level of abstraction, are becoming more and more popular. Users are given the opportunity to code matrix computations with a syntax that closely resembles the mathematical description; it is then a compiler or an interpreter that internally maps the input program to lower level kernels, as provided by libraries such as BLAS and LAPACK. Unfortunately, our experience suggests that in terms of performance, this translation is typically vastly suboptimal. In this paper, we first introduce the Linear Algebra Mapping Problem, and then investigate how effectively a benchmark of test problems is solved by popular high-level programming languages. Specifically, we consider Matlab, Octave, Julia, R, Armadillo (C++), Eigen (C++), and NumPy (Python); the benchmark is meant to test both standard compiler optimizations such as common subexpression elimination and loop-invariant code motion, as well as linear algebra specific optimizations such as optimal parenthesization of a matrix product and kernel selection for matrices with properties. The aim of this study is to give concrete guidelines for the development of languages and libraries that support linear algebra computations.

cs.MS↗

arXiv2021

Performance Comparison for Scientific Computations on the Edge via Relative Performance

In a typical Internet-of-Things setting that involves scientific applications, a target computation can be evaluated in many different ways depending on the split of computations among various devices. On the one hand, different implementations (or algorithms)--equivalent from a mathematical perspective--might exhibit significant difference in terms of performance. On the other hand, some of the implementations are likely to show similar performance characteristics. In this paper, we focus on analyzing the performance of a given set of algorithms by clustering them into performance classes. To this end, we use a measurement-based approach to evaluate and score algorithms based on pair-wise comparisons; we refer to this approach as"Relative performance analysis". Each comparison yields one of three outcomes: one algorithm can be "better", "worse", or "equivalent" to another; those algorithms evaluating to have equivalent performance are merged into the same performance class. We show that our clustering methodology facilitates algorithm selection with respect to more than one metric; for instance, from the subset of equivalently fast algorithms, one could then select an algorithm that consumes the least energy on a certain device.

cs.PF↗

arXiv2020

Work-stealing prefix scan: Addressing load imbalance in large-scale image registration

Parallelism patterns (e.g., map or reduce) have proven to be effective tools for parallelizing high-performance applications. In this paper, we study the recursive registration of a series of electron microscopy images - a time consuming and imbalanced computation necessary for nano-scale microscopy analysis. We show that by translating the image registration into a specific instance of the prefix scan, we can convert this seemingly sequential problem into a parallel computation that scales to over thousand of cores. We analyze a variety of scan algorithms that behave similarly for common low-compute operators and propose a novel work-stealing procedure for a hierarchical prefix scan. Our evaluation shows that by identifying a suitable and well-optimized prefix scan algorithm, we reduce time-to-solution on a series of 4,096 images spanning ten seconds of microscopy acquisition from over 10 hours to less than 3 minutes (using 1024 Intel Haswell cores), enabling derivation of material properties at nanoscale for long microscopy image series.

cs.DC↗

arXiv2020

Automatic Generation of Efficient Linear Algebra Programs

The level of abstraction at which application experts reason about linear algebra computations and the level of abstraction used by developers of high-performance numerical linear algebra libraries do not match. The former is conveniently captured by high-level languages and libraries such as Matlab and Eigen, while the latter expresses the kernels included in the BLAS and LAPACK libraries. Unfortunately, the translation from a high-level computation to an efficient sequence of kernels is a task, far from trivial, that requires extensive knowledge of both linear algebra and high-performance computing. Internally, almost all high-level languages and libraries use efficient kernels; however, the translation algorithms are too simplistic and thus lead to a suboptimal use of said kernels, with significant performance losses. In order to both achieve the productivity that comes with high-level languages, and make use of the efficiency of low level kernels, we are developing Linnea, a code generator for linear algebra problems. As input, Linnea takes a high-level description of a linear algebra problem and produces as output an efficient sequence of calls to high-performance kernels. In 25 application problems, the code generated by Linnea always outperforms Matlab, Julia, Eigen and Armadillo, with speedups up to and exceeding 10x.

cs.MS↗

arXiv2020

Automatic Detection of Cue Points for DJ Mixing

The automatic identification of cue points is a central task in applications as diverse as music thumbnailing, mash-ups generation, and DJ mixing. Our focus lies in electronic dance music and in specific cue points, the "switch points", that make it possible to automatically construct transitions among tracks, mimicking what professional DJs do. We present an approach for the detection of switch points that embody a few general rules we established from interviews with professional DJs; the implementation of these rules is based on features extraction and novelty analysis. The quality of the generated switch points is assessed both by comparing them with a manually annotated dataset that we curated, and by evaluating them individually. We found that about 96\% of the points generated by our methodology are of good quality for use in a DJ mix.

cs.SD↗

arXiv2020

Rational spectral filters with optimal convergence rate

In recent years, contour-based eigensolvers have emerged as a standard approach for the solution of large and sparse eigenvalue problems. Building upon recent performance improvements through non-linear least square optimization of so-called rational filters, we introduce a systematic method to design these filters by minimizing the worst-case convergence ratio and eliminate the parametric dependence on weight functions. Further, we provide an efficient way to deal with the box-constraints which play a central role for the use of iterative linear solvers in contour-based eigensolvers. Indeed, these parameter-free filters consistently minimize the number of iterations and the number of FLOPs to reach convergence in the eigensolver. As a byproduct, our rational filters allow for a simple solution to load balancing when the solution of an interior eigenproblem is approached by the slicing of the sought after spectral interval.

math.NA↗

arXiv2019

Linnea: Automatic Generation of Efficient Linear Algebra Programs

The translation of linear algebra computations into efficient sequences of library calls is a non-trivial task that requires expertise in both linear algebra and high-performance computing. Almost all high-level languages and libraries for matrix computations (e.g., Matlab, Eigen) internally use optimized kernels such as those provided by BLAS and LAPACK; however, their translation algorithms are often too simplistic and thus lead to a suboptimal use of said kernels, resulting in significant performance losses. In order to combine the productivity offered by high-level languages, and the performance of low-level kernels, we are developing Linnea, a code generator for linear algebra problems. As input, Linnea takes a high-level description of a linear algebra problem; as output, it returns an efficient sequence of calls to high-performance kernels. Linnea uses a custom best-first search algorithm to find a first solution in less than a second, and increasingly better solutions when given more time. In 125 test problems, the code generated by Linnea almost always outperforms Matlab, Julia, Eigen and Armadillo, with speedups up to and exceeding 10x.

cs.MS↗

arXiv2019

Program Generation for Linear Algebra Using Multiple Layers of DSLs

Numerical software in computational science and engineering often relies on highly-optimized building blocks from libraries such as BLAS and LAPACK, and while such libraries provide portable performance for a wide range of computing architectures, they still present limitations in terms of flexibility. We advocate a domain-specific program generator capable of producing library routines tailored to the specific needs of the application in terms of sizes, interface, and target architecture.

cs.MS↗

arXiv2019

A Timer-Augmented Cost Function for Load Balanced DSMC

Due to a hard dependency between time steps, large-scale simulations of gas using the Direct Simulation Monte Carlo (DSMC) method proceed at the pace of the slowest processor. Scalability is therefore achievable only by ensuring that the work done each time step is as evenly apportioned among the processors as possible. Furthermore, as the simulated system evolves, the load shifts, and thus this load-balancing typically needs to be performed multiple times over the course of a simulation. Common methods generally use either crude performance models or processor-level timers. We combine both to create a timer-augmented cost function which both converges quickly and yields well-balanced processor decompositions. When compared to a particle-based performance model alone, our method achieves 2x speedup at steady-state on up to 1024 processors for a test case consisting of a Mach 9 argon jet impacting a solid wall.

cs.DC↗

arXiv2018

Optimizing AIREBO: Navigating the Journey from Complex Legacy Code to High Performance

Despite initiatives to improve the quality of scientific codes, there still is a large presence of legacy code. Such code often needs to implement a lot of functionality under time constrains, sacrificing quality. Additionally, quality is rarely improved by optimizations for new architectures. This development model leads to code that is increasingly difficult to work with. Our suggested solution includes complexity-reducing refactoring and hardware abstraction. We focus on the AIREBO potential from LAMMPS, where the challenge is that any potential kernel is rather large and complex, hindering systematic optimization. This issue is common to codes that model multiple physical phenomena. We present our journey from the C++ port of a previous Fortran code to performance-portable, KNC-hybrid, vectorized, scalable, optimized code supporting full and reduced precision. The journey includes extensive testing that fixed bugs in the original code. Large-scale, full-precision runs sustain speedups of more than 4x (KNL) and 3x (Skylake).

cs.CE↗

arXiv2018

Program Generation for Small-Scale Linear Algebra Applications

We present SLinGen, a program generation system for linear algebra. The input to SLinGen is an application expressed mathematically in a linear-algebra-inspired language (LA) that we define. LA provides basic scalar/vector/matrix additions/multiplications and higher level operations including linear systems solvers, Cholesky and LU factorizations. The output of SLinGen is performance-optimized single-source C code, optionally vectorized with intrinsics. The target of SLinGen are small-scale computations on fixed-size operands, for which a straightforward implementation using optimized libraries (e.g., BLAS or LAPACK) is known to yield suboptimal performance (besides increasing code size and introducing dependencies), but which are crucial in control, signal processing, computer vision, and other domains. Internally, SLinGen uses synthesis and DSL-based techniques to optimize at a high level of abstraction. We benchmark our program generator on three prototypical applications: the Kalman filter, Gaussian process regression, and an L1-analysis convex solver, as well as basic routines including Cholesky factorization and solvers for the continuous-time Lyapunov and Sylvester equations. The results show significant speed-ups compared to straightforward C with Intel icc and clang with a polyhedral optimizer, as well as library-based and template-based implementations.

cs.PL↗

arXiv2018

Extended pipeline for content-based feature engineering in music genre recognition

We present a feature engineering pipeline for the construction of musical signal characteristics, to be used for the design of a supervised model for musical genre identification. The key idea is to extend the traditional two-step process of extraction and classification with additive stand-alone phases which are no longer organized in a waterfall scheme. The whole system is realized by traversing backtrack arrows and cycles between various stages. In order to give a compact and effective representation of the features, the standard early temporal integration is combined with other selection and extraction phases: on the one hand, the selection of the most meaningful characteristics based on information gain, and on the other hand, the inclusion of the nonlinear correlation between this subset of features, determined by an autoencoder. The results of the experiments conducted on GTZAN dataset reveal a noticeable contribution of this methodology towards the model's performance in classification task.

cs.SD↗

arXiv2018

The Generalized Matrix Chain Algorithm

In this paper, we present a generalized version of the matrix chain algorithm to generate efficient code for linear algebra problems, a task for which human experts often invest days or even weeks of works. The standard matrix chain problem consists in finding the parenthesization of a matrix product $M := A_1 A_2 \cdots A_n$ that minimizes the number of scalar operations. In practical applications, however, one frequently encounters more complicated expressions, involving transposition, inversion, and matrix properties. Indeed, the computation of such expressions relies on a set of computational kernels that offer functionality well beyond the simple matrix product. The challenge then shifts from finding an optimal parenthesization to finding an optimal mapping of the input expression to the available kernels. Furthermore, it is often the case that a solution based on the minimization of scalar operations does not result in the optimal solution in terms of execution time. In our experiments, the generated code outperforms other libraries and languages on average by a factor of about 9. The motivation for this work comes from the fact that---despite great advances in the development of compilers---the task of mapping linear algebra problems to optimized kernels is still to be done manually. In order to relieve the user from this complex task, new techniques for the compilation of linear algebra expressions have to be developed.

cs.MS↗