Paolo Bientinesi

Lukas Krämer, Edoardo Di Napoli, Martin Galgon et al.

We analyze the FEAST method for computing selected eigenvalues and eigenvectors of large sparse matrix pencils. After establishing the close connection between FEAST and the well-known Rayleigh-Ritz method, we identify several critical issues that influence convergence and accuracy of the solver: the choice of the starting vector space, the stopping criterion, how the inner linear systems impact the quality of the solution, and the use of FEAST for computing eigenpairs from multiple intervals. We complement the study with numerical examples, and hint at possible improvements to overcome the existing problems.

Elmar Peise, Paolo Bientinesi

It is well known that the behavior of dense linear algebra algorithms is greatly influenced by factors like target architecture, underlying libraries and even problem size; because of this, the accurate prediction of their performance is a real challenge. In this article, we are not interested in creating accurate models for a given algorithm, but in correctly ranking a set of equivalent algorithms according to their performance. Aware of the hierarchical structure of dense linear algebra routines, we approach the problem by developing a framework for the automatic generation of statistical performance models for BLAS and LAPACK libraries. This allows us to obtain predictions through evaluating and combining such models. We demonstrate that our approach is successful in both single- and multi-core environments, not only in the ranking of algorithms but also in tuning their parameters.

Matthias Petschow, Elmar Peise, Paolo Bientinesi

We introduce a new collection of solvers - subsequently called EleMRRR - for large-scale dense Hermitian eigenproblems. EleMRRR solves various types of problems: generalized, standard, and tridiagonal eigenproblems. Among these, the last is of particular importance as it is a solver on its own right, as well as the computational kernel for the first two; we present a fast and scalable tridiagonal solver based on the Algorithm of Multiple Relatively Robust Representations - referred to as PMRRR. Like the other EleMRRR solvers, PMRRR is part of the freely available Elemental library, and is designed to fully support both message-passing (MPI) and multithreading parallelism (SMP). As a result, the solvers can equally be used in pure MPI or in hybrid MPI-SMP fashion. We conducted a thorough performance study of EleMRRR and ScaLAPACK's solvers on two supercomputers. Such a study, performed with up to 8,192 cores, provides precise guidelines to assemble the fastest solver within the ScaLAPACK framework; it also indicates that EleMRRR outperforms even the fastest solvers built from ScaLAPACK's components.

Diego Fabregat-Traver, Paolo Bientinesi

In this paper, we tackle the problem of automatically generating algorithms for linear algebra operations by taking advantage of problem-specific knowledge. In most situations, users possess much more information about the problem at hand than what current libraries and computing environments accept; evidence shows that if properly exploited, such information leads to uncommon/unexpected speedups. We introduce a knowledge-aware linear algebra compiler that allows users to input matrix equations together with properties about the operands and the problem itself; for instance, they can specify that the equation is part of a sequence, and how successive instances are related to one another. The compiler exploits all this information to guide the generation of algorithms, to limit the size of the search space, and to avoid redundant computations. We applied the compiler to equations arising as part of sensitivity and genome studies; the algorithms produced exhibit, respectively, 100- and 1000-fold speedups.

Per Sehlstedt, Jan Brandejs, Paolo Bientinesi et al.

The density matrix renormalization group (DMRG) algorithm is a cornerstone computational method for studying quantum many-body systems, renowned for its accuracy and adaptability. Despite DMRG's broad applicability across fields such as materials science, quantum chemistry, and quantum computing, numerous independent implementations have been developed. This survey maps the rapidly expanding DMRG software landscape, providing a comprehensive comparison of features among 35 existing packages. We found significant overlap in features among the packages when comparing key aspects, such as parallelism strategies for high-performance computing and symmetry-adapted formulations that enhance efficiency. This overlap suggests opportunities for modularization of common operations, including tensor operations, symmetry representations, and eigensolvers, as the packages are mostly independent and share few third-party library dependencies where functionality is factored out. More widespread modularization and standardization would result in reduced duplication of efforts and improved interoperability. We believe that the proliferation of packages and the current lack of standard interfaces and modularity are more social than technical. We aim to raise awareness of existing packages, guide researchers in finding a suitable package for their needs, and help developers identify opportunities for collaboration, modularity standardization, and optimization. Ultimately, this work emphasizes the value of greater cohesion and modularity, which would benefit DMRG software, allowing these powerful algorithms to tackle more complex and ambitious problems.

Marco Alunno, Paolo Bientinesi

The project described in this paper explores the informative sonification of data received in real time from a supercomputer. These data capture the current activities in all the nodes of the computer, therefore, their sonification functions as a form of continuous monitoring of the nodes' behavior and, by extension, of the system as a whole. Because such monitoring is theoretically unending, the resulting sonification must be musically capable of conveying information through sound in a way that remains both intelligible and engaging over long durations. Rather than imposing a predefined musical style onto the data, we sought to identify one which the data themselves could plausibly support. From a small set of candidates, we selected EDM because it is a family of genres whose structural and temporal characteristics align well with continuous, data-driven processes and long-term listening. Through this style-based approach, this research builds on the long tradition of computer data sonification while uniquely combining three elements rarely addressed together: monitoring (rather than debugging) as the primary goal, real-time (rather than post-mortem) data interpretation, and generation of virtually infinite and stylistically coherent (rather than incongruous) music.

Mickaël Zehren, Marco Alunno, Paolo Bientinesi

Automatic drum transcription is a critical tool in Music Information Retrieval for extracting and analyzing the rhythm of a music track, but it is limited by the size of the datasets available for training. A popular method used to increase the amount of data is by generating them synthetically from music scores rendered with virtual instruments. This method can produce a virtually infinite quantity of tracks, but empirical evidence shows that models trained on previously created synthetic datasets do not transfer well to real tracks. In this work, besides increasing the amount of data, we identify and evaluate three more strategies that practitioners can use to improve the realism of the generated data and, thus, narrow the synthetic-to-real transfer gap. To explore their efficacy, we used them to build a new synthetic dataset and then we measured how the performance of a model scales and, specifically, at what value it will stagnate when increasing the number of training tracks for different datasets. By doing this, we were able to prove that the aforementioned strategies contribute to make our dataset the one with the most realistic data distribution and the lowest synthetic-to-real transfer gap among the synthetic datasets we evaluated. We conclude by highlighting the limits of training with infinite data in drum transcription and we show how they can be overcome.

Elmar Peise, Paolo Bientinesi

Optimal use of computing resources requires extensive coding, tuning and benchmarking. To boost developer productivity in these time consuming tasks, we introduce the Experimental Linear Algebra Performance Studies framework (ELAPS), a multi-platform open source environment for fast yet powerful performance experimentation with dense linear algebra kernels, algorithms, and libraries. ELAPS allows users to construct experiments to investigate how performance and efficiency vary depending on factors such as caching, algorithmic parameters, problem size, and parallelism. Experiments are designed either through Python scripts or a specialized GUI, and run on the whole spectrum of architectures, ranging from laptops to clusters, accelerators, and supercomputers. The resulting experiment reports provide various metrics and statistics that can be analyzed both numerically and visually. We demonstrate the use of ELAPS in four concrete application scenarios and in as many computing environments, illustrating its practical value in supporting critical performance decisions.

Aravind Sankaran, Navid Akbari Alashti, Christos Psarras et al.

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.

Mickael Zehren, Marco Alunno, Paolo Bientinesi

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.

Christos Psarras, Lars Karlsson, Rasmus Bro et al.

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.

Mickaël Zehren, Marco Alunno, Paolo Bientinesi

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.

Tina Raissi, Alessandro Tibo, Paolo Bientinesi

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.

Ali Tarzan, Marco Alunno, Paolo Bientinesi

Given an input sound signal and a target virtual sound source, sound spatialisation algorithms manipulate the signal so that a listener perceives it as though it were emitted from the target source. There exist several established spatialisation approaches that deliver satisfactory results when loudspeakers are used to playback the manipulated signal. As headphones have a number of desirable characteristics over loudspeakers, such as portability, isolation from the surrounding environment, cost and ease of use, it is interesting to explore how a sense of acoustic space can be conveyed through them. This article first surveys traditional spatialisation approaches intended for loudspeakers, and then reviews them with regard to their adaptability to headphones.

Matthias Petschow, Enrique Quintana-Orti, Paolo Bientinesi

The real symmetric tridiagonal eigenproblem is of outstanding importance in numerical computations; it arises frequently as part of eigensolvers for standard and generalized dense Hermitian eigenproblems that are based on a reduction to tridiagonal form. For its solution, the algorithm of Multiple Relatively Robust Representations (MRRR) is among the fastest methods. Although fast, the solvers based on MRRR do not deliver the same accuracy as competing methods like Divide & Conquer or the QR algorithm. In this paper, we demonstrate that the use of mixed precisions leads to improved accuracy of MRRR-based eigensolvers with limited or no performance penalty. As a result, we obtain eigensolvers that are not only equally or more accurate than the best available methods, but also -in most circumstances- faster and more scalable than the competition.

Matthias Petschow, Edoardo Di Napoli, Paolo Bientinesi

One of the most used approaches in simulating materials is the tight-binding approximation. When using this method in a material simulation, it is necessary to compute the eigenvalues and eigenvectors of the Hamiltonian describing the system. In general, the system possesses few explicit symmetries. Due to them, the problem has many degenerate eigenvalues. The ambiguity in choosing a orthonormal basis of the invariant subspaces, associated with degenerate eigenvalues, will result in eigenvectors which are not invariant under the action of the symmetry operators in matrix form. A meaningful computation of the eigenvectors needs to take those symmetries into account. A natural choice is a set of eigenvectors, which simultaneously diagonalizes the Hamiltonian and the symmetry matrices. This is possible because all the matrices commute with each other. The simultaneous eigenvectors and the corresponding eigenvalues will be in a parametrized form in terms of the lattice momentum components. This functional dependence of the eigenvalues is the dispersion relation and describes the band structure of a material. Therefore it is important to find this functional dependence in any numerical computation related to material properties.