Reducing the Power Consumption of Matrix Multiplications by Vectorization

Jakobs, Thomas; Hofmann, Michaël; Rünger, Gudula

doi:10.1109/cse-euc-dcabes.2016.187

Cited by 10 publications

(5 citation statements)

References 7 publications

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“…Jakobs et al [15] examined vectorization techniques' impact on dense matrix multiplication algorithms' power and energy. They used loop unrolling, frequency control, and compiler optimization levels.…”

Section: A Literature Reviewmentioning

confidence: 99%

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Investigation of Energy and Power Characteristics of Various Matrix Multiplication Algorithms

Alsari,

Al-Hashimi

2024

Energies

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This work studied the energy behavior of six matrix multiplication algorithms with various physical asset usage patterns. Two were variants of the straight inner product of rows and columns. The rest were variants of Strassen’s divide-and-conquer. Cases varied in ways that were expected to affect energy behavior. The study collected data for square matrix dimensions up to 4000. The research used reliable on-chip integrated voltage regulators embedded in a recent HPC-class AMD CPU for power measurements. Inner product methods used much less energy than the others for small to moderately large matrices. The advantage diminished for sufficiently large dimensions. The power draw of the inner product methods was less for small dimensions. After a point, the power advantage shifted significantly in favor of the divide-and-conquer group (average of 24% better), with the more block-optimized versions showing increased power efficiency (at least 8.3% better than the base method). The study explored the interplay between algorithm design, power efficiency, and computational resources. It aims to help advance the cause of power efficiency in HPC and other scenarios that rely on this vital computation.

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Section: A Literature Reviewmentioning

confidence: 99%

“…Jakobs et al [15] 2016 Explored reduction in power and energy consumption for matrix multiplications through vectorization on modern computer systems.…”

Section: Kouya Et Al [14] 2016mentioning

confidence: 99%

Investigation of Energy and Power Characteristics of Various Matrix Multiplication Algorithms

Alsari,

Al-Hashimi

2024

Energies

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“…The power management architecture utilizing extra hardware measurement equipment for Intel's Sandy bridge has been proposed in [14]. Jakobs et al suggested that using vectorization can reduce the system's power consumption [15].…”

Section: Related Workmentioning

confidence: 99%

Power Efficient Strassen’s Algorithm using AVX512 and OpenMP in a Multi-core Architecture

Oo¹,

Chaikan²

2023

ECTI-CIT Transactions

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This paper presents an effective implementation of Strassen's algorithm for matrix-matrix multiplication on shared memory multi-core architecture. The proposed algorithm aims to augment the computation speed in terms of GFLOPS performance on average 4.5 and 4.1 times faster than Eigen and OpenBLAS, respectively while reducing the power consumption to as low as possible. Our algorithm relies on using AVX512 intrinsics, loop unrolling factor, and OpenMP directives. A new 2D blocking data allocation pattern is proposed for Strassen's algorithm to provide optimized cache temporal and spatial locality. The proposed implementation reduced not only the amount of main memory but also the burden of unnecessary memory allocation/deallocation and data transferring for each level of recursion in Strassen's algorithm. Moreover, the proposed algorithm consumed, on average, 4.25 and 3.67 times lower energy than the multiplication functions of the Eigen and OpenBLAS libraries, respectively. To measure the computational performance with the awareness of power consumption, GFLOPS per Watt (GFPW) is calculated, which out- performed on average 3.78 and 3.47 times higher than those of Eigen and OpenBLAS libraries, respectively.

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“…For the training task (in CL), being an intensive processing task, we assume an average power =384 Watts, based on Google's TPU benchmarking [22]. For the (less-intensive) aggregation task (in EL, FL), we assume =15 Watts, based on measurements for matrix multiplication tasks [23], which are similar in complexity to weighted averaging (aggregation). The cloud energy consumption then becomes:…”

Section: E Energy Consumptionmentioning

confidence: 99%

On the Resource Consumption of Distributed ML

Drainakis

Pantazopoulos

Κατσαρός

et al. 2021

2021 IEEE International Symposium on Local and Metropolitan Area Networks (LANMAN)

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The convergence of Machine Learning (ML) with the edge computing paradigm has paved the way for distributing processing-heavy ML tasks to the network's extremes. As the edge deployment details still remain an open issue, distributed ML schemes tend to be network-agnostic; thus, their effect on the underlying network's resource consumption is largely ignored.In our work, assuming a network tree structure of varying size and edge computing characteristics, we introduce an analytical system model based on credible real-world measurements to capture the end-to-end consumption of ML schemes. In this context, we employ an edge-based (EL) and a federated (FL) ML scheme and in-depth compare their bandwidth needs and energy footprint against a cloud-based (CL) baseline approach.Our numerical evaluation suggests that EL exhibits a minimum of 25% bandwidth-efficiency compared to CL and FL, if employed by a few nodes higher in the edge network, while halving the network's energy costs.

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Reducing the Power Consumption of Matrix Multiplications by Vectorization

Cited by 10 publications

References 7 publications

Investigation of Energy and Power Characteristics of Various Matrix Multiplication Algorithms

Investigation of Energy and Power Characteristics of Various Matrix Multiplication Algorithms

Power Efficient Strassen’s Algorithm using AVX512 and OpenMP in a Multi-core Architecture

On the Resource Consumption of Distributed ML

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