Browsing by Subject "Approximate matrix multiplication"

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Open Access
Straggler mitigation through unequal error protection for distributed approximate matrix multiplication
(Institute of Electrical and Electronics Engineers Inc., 2022-02-01) Tegin, Büşra; Hernandez, Eduin E.; Rini, Stefano; Duman, Tolga Mete
Large-scale machine learning and data mining methods routinely distribute computations across multiple agents to parallelize processing. The time required for the computations at the agents is affected by the availability of local resources and/or poor channel conditions, thus giving rise to the “straggler problem.” In this paper, we address this problem for distributed approximate matrix multiplication. In particular, we employ Unequal Error Protection (UEP) codes to obtain an approximation of the matrix product to provide higher protection for the blocks with a higher effect on the multiplication outcome. We characterize the performance of the proposed approach from a theoretical perspective by bounding the expected reconstruction error for matrices with uncorrelated entries. We also apply the proposed coding strategy to the computation of the back-propagation step in the training of a Deep Neural Network (DNN) for an image classification task in the evaluation of the gradients. Our numerical experiments show that it is indeed possible to obtain significant improvements in the overall time required to achieve DNN training convergence by producing approximation of matrix products using UEP codes in the presence of stragglers.
Open Access
Straggler mitigation through unequal error protection for distributed matrix multiplication
(IEEE, 2021-08-06) Tegin, Büşra; Hernandez, Eduin E.; Rini, Stefano; Duman, Tolga M.
Large-scale machine learning and data mining methods routinely distribute computations across multiple agents to parallelize processing. The time required for computation at the agents is affected by the availability of local resources giving rise to the "straggler problem" in which the computation results are held back by unresponsive agents. For this problem, linear coding of the matrix sub-blocks can be used to introduce resilience toward straggling. The Parameter Server (PS) utilizes a channel code and distributes the matrices to the workers for multiplication. It then produces an approximation to the desired matrix multiplication using the results of the computations received at a given deadline. In this paper, we propose to employ Unequal Error Protection (UEP) codes to alleviate the straggler problem. The resiliency level of each sub-block is chosen according to its norm as blocks with larger norms have higher effects on the result of the matrix multiplication. We validate the effectiveness of our scheme both theoretically and through numerical evaluations. We derive a theoretical characterization of the performance of UEP using random linear codes, and compare it the case of equal error protection. We also apply the proposed coding strategy to the computation of the back-propagation step in the training of a Deep Neural Network (DNN), for which we investigate the fundamental trade-off between precision and the time required for the computations.