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Demmel, James

Publications and source records attributed to Demmel, James.

10 records
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DOE OSTI2025

Surrogate-Based Autotuning for Randomized Sketching Algorithms in Regression Problems

Algorithms from Randomized Numerical Linear Algebra (RandNLA) are known to be effective in handling high-dimensional computational problems, providing high-quality empirical performance as well as strong probabilistic guarantees. However, their practical application is complicated by the fact that the user needs to set various algorithm-specific tuning parameters which are different from those used in traditional NLA. This paper demonstrates how a surrogate-based autotuning approach can be used to address fundamental problems of parameter selection in RandNLA algorithms. In particular, we provide a detailed investigation of surrogate-based autotuning for sketch-and-precondition (SAP)-based randomized least squares methods, which have been one of the great success stories in modern RandNLA. Empirical results show that our surrogate-based autotuning approach can achieve near-optimal performance with much less tuning cost than a random search (up to about 7.6x fewer trials of different parameter configurations). Moreover, while our experiments focus on least squares, our results demonstrate a general-purpose autotuning pipeline applicable to any kind of RandNLA algorithm.

Cho, Younghyun↗
DOE OSTI2020

Algorithms for Efficient Reproducible Floating Point Summation

We define “reproducibility” as getting bitwise identical results from multiple runs of the same program, perhaps with different hardware resources or other changes that should not affect the answer. Many users depend on reproducibility for debugging or correctness. However, dynamic scheduling of parallel computing resources, combined with nonassociative floating point addition, makes reproducibility challenging even for summation, or operations like the BLAS. We describe a “reproducible accumulator” data structure (the “binned number”) and associated algorithms to reproducibly sum binary floating point numbers, independent of summation order. We use a subset of the IEEE Floating Point Standard 754-2008 and bitwise operations on the standard representations in memory. Our approach requires only one read-only pass over the data, and one reduction in parallel, using a 6-word reproducible accumulator (more words can be used for higher accuracy), enabling standard tiling optimization techniques. Summing n words with a 6-word reproducible accumulator requires approximately 9 n floating point operations (arithmetic, comparison, and absolute value) and approximately 3 n bitwise operations. The final error bound with a 6-word reproducible accumulator and our default settings can be up to 2 29 times smaller than the error bound for conventional (recursive) summation on ill-conditioned double-precision inputs.

Computer Science↗
DOE OSTI2019

On Holder-Brascamp-Lieb inequalities for torsion-free discrete Abelian groups

H\"older-Brascamp-Lieb inequalities provide upper bounds for a class of multilinear expressions, in terms of $L^p$ norms of the functions involved. They have been extensively studied for functions defined on Euclidean spaces. Bennett-Carbery-Christ-Tao have initiated the study of these inequalities for discrete Abelian groups and, in terms of suitable data, have characterized the set of all tuples of exponents for which such an inequality holds for specified data, as the convex polyhedron defined by a particular finite set of affine inequalities. In this paper we advance the theory of such inequalities for torsion-free discrete Abelian groups in three respects. The optimal constant in any such inequality is shown to equal $1$ whenever it is finite. An algorithm that computes the admissible polyhedron of exponents is developed. It is shown that nonetheless, existence of an algorithm that computes the full list of inequalities in the Bennett-Carbery-Christ-Tao description of the admissible polyhedron for all data, is equivalent to an affirmative solution of Hilbert's Tenth Problem over the rationals. That problem remains open. Applications to computer science will be explored in a forthcoming companion paper.

Christ, Michael↗
DOE OSTI2019

Avoiding Communication in Primal and Dual Block Coordinate Descent Methods

Primal and dual block coordinate descent methods are iterative methods for solving regularized and unregularized optimization problems. Distributed-memory parallel implementations of these methods have become popular in analyzing large machine learning datasets. However, existing implementations communicate at every iteration, which, on modern data center and supercomputing architectures, often dominates the cost of floating-point computation. Recent results on communication-avoiding Krylov subspace methods suggest that large speedups are possible by re-organizing iterative algorithms to avoid communication. We show how applying similar algorithmic transformations can lead to primal and dual block coordinate descent methods that only communicate every $s$ iterations---where $s$ is a tuning parameter---instead of every iteration for the regularized least-squares problem. We show that the communication-avoiding variants reduce the number of synchronizations by a factor of $s$ on distributed-memory parallel machines without altering the convergence rate and attain strong scaling speedups of up to $6.1\times$ over the “standard algorithm" on a Cray XC30 supercomputer.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A 3D Parallel Algorithm for QR Decomposition

Interprocessor communication often dominates the runtime of large matrix computations. Here, we present a parallel algorithm for computing QR decompositions whose bandwidth cost (communication volume) can be decreased at the cost of increasing its latency cost (number of messages). By varying a parameter to navigate the bandwidth/latency tradeoff, we can tune this algorithm for machines with different communication costs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Accurate, Fast and Scalable Kernel Ridge Regression on Parallel and Distributed Systems

Kernel Ridge Regression (KRR) is a fundamental method in machine learning. Given an n-by-d data matrix as input, a traditional implementation requires Θ(n2) memory to form an n-by-n kernel matrix and Θ(n3) flops to compute the final model. These time and storage costs prohibit KRR from scaling up to large datasets. For example, even on a relatively small dataset (a 520k-by-90 input requiring 357 MB), KRR requires 2 TB memory just to store the kernel matrix. Additionally, the reason is that n usually is much larger than d for real-world applications. On the other hand, weak scaling becomes a problem: if we keep d and n/p fixed as p grows (p is # machines), the memory needed grows as Θ(p) per processor and the flops as Θ(p2) per processor. In the perfect weak scaling situation, both the memory needed and the flops grow as Θ(1) per processor (i.e. memory and flops are constant). The traditional Distributed KRR implementation (DKRR) only achieved 0.32% weak scaling efficiency from 96 to 1536 processors. In this work, we propose two new methods to address these problems: the Balanced KRR (BKRR) and K-means KRR (KKRR). These methods consider alternative ways to partition the input dataset into p different parts, generating p different models, and then selecting the best model among them. Compared to a conventional implementation, KKRR2 (optimized version of KKRR) improves the weak scaling efficiency from 0.32% to 38% and achieves a 591x speedup for getting the same accuracy by using the same data and the same hardware (1536 processors). BKRR2 (optimized version of BKRR) achieves a higher accuracy than the current fastest method using less training time for a variety of datasets. For the applications requiring only approximate solutions, BKRR2 improves the weak scaling efficiency to 92% and achieves 3505x speedup (theoretical speedup: 4096x).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

DEGAS: Dynamic Exascale Global Address Space Programming Environments

The Dynamic, Exascale Global Address Space programming environment (DEGAS) project will develop the next generation of programming models and runtime systems to meet the challenges of Exascale computing. The Berkeley part of the project concentrated on communication-optimal code generation to optimize speed and energy efficiency by reducing data movement. Our work developed communication lower bounds, and/or communication avoiding algorithms (that either meet the lower bound, or do much less communication than their conventional counterparts) for a variety of algorithms, including linear algebra, machine learning and genomics. The Berkeley part of the project concentrated on communication-optimal code generation to optimize speed and energy efficiency by reducing data movement. Our work developed communication lower bounds, and/or communication avoiding algorithms (that either meet the lower bound, or do much less communication than their conventional counterparts) for a variety of algorithms, including linear algebra, machine learning and genomics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Final Report from The University of Texas at Austin for DEGAS: Dynamic Global Address Space programming environments

The Dynamic, Exascale Global Address Space programming environment (DEGAS) project will develop the next generation of programming models and runtime systems to meet the challenges of Exascale computing. Our approach is to provide an efficient and scalable programming model that can be adapted to application needs through the use of dynamic runtime features and domain-specific languages for computational kernels. We address the following technical challenges: Programmability: Rich set of programming constructs based on a Hierarchical Partitioned Global Address Space (HPGAS) model, demonstrated in UPC++. Scalability: Hierarchical locality control, lightweight communication (extended GASNet), and ef- ficient synchronization mechanisms (Phasers). Performance Portability: Just-in-time specialization (SEJITS) for generating hardware-specific code and scheduling libraries for domain-specific adaptive runtimes (Habanero). Energy Efficiency: Communication-optimal code generation to optimize energy efficiency by re- ducing data movement. Resilience: Containment Domains for flexible, domain-specific resilience, using state capture mechanisms and lightweight, asynchronous recovery mechanisms. Interoperability: Runtime and language interoperability with MPI and OpenMP to encourage broad adoption.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Scaling Deep Learning on GPU and Knights Landing clusters

The speed of deep neural networks training has become a big bottleneck of deep learning research and development. For example, training GoogleNet by ImageNet dataset on one Nvidia K20 GPU needs 21 days. To speed up the training process, the current deep learning systems heavily rely on the hardware accelerators. However, these accelerators have limited on-chip memory compared with CPUs. To handle large datasets, they need to fetch data from either CPU memory or remote processors. We use both self-hosted Intel Knights Landing (KNL) clusters and multi-GPU clusters as our target platforms. From an algorithm aspect, current distributed machine learning systems are mainly designed for cloud systems. These methods are asynchronous because of the slow network and high fault-tolerance requirement on cloud systems. We focus on Elastic Averaging SGD (EASGD) to design algorithms for HPC clusters. Original EASGD used round-robin method for communication and updating. The communication is ordered by the machine rank ID, which is inefficient on HPC clusters. First, we redesign four efficient algorithms for HPC systems to improve EASGD's poor scaling on clusters. Async EASGD, Async MEASGD, and Hogwild EASGD are faster \textcolor{black}{than} their existing counterparts (Async SGD, Async MSGD, and Hogwild SGD, resp.) in all the comparisons. Finally, we design Sync EASGD, which ties for the best performance among all the methods while being deterministic. In addition to the algorithmic improvements, we use some system-algorithm codesign techniques to scale up the algorithms. By reducing the percentage of communication from 87% to 14%, our Sync EASGD achieves 5.3x speedup over original EASGD on the same platform. We get 91.5% weak scaling efficiency on 4253 KNL cores, which is higher than the state-of-the-art implementation.

60 APPLIED LIFE SCIENCES↗