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A Simplified Reduction for Error Correcting Matrix Multiplication Algorithms

Authors Igor Shinkar , Harsimran Singh

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ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
Keywords
  • Matrix Multiplication
  • Reductions
  • Worst case to average case reductions

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Abstract

We study the problem of transforming an algorithm for matrix multiplication, whose output has a small fraction of the entries correct into a matrix multiplication algorithm, whose output is fully correct for all inputs. In this work, we provide a new and simple way to transform an average-case algorithm that takes two matrices A,B ∈ 𝔽_p^{n×n} for a prime p, and outputs a matrix that agrees with the matrix product AB on a 1/p + ε fraction of entries on average for a small ε > 0, into a worst-case algorithm that correctly computes the matrix product for all possible inputs. 
Our reduction employs list-decodable codes to transform an average-case algorithm into an algorithm with one-sided error, which are known to admit efficient reductions from the work of Gola, Shinkar, and Singh [Gola et al., 2024]. Our reduction is more concise and straightforward compared to the recent work of Hirahara and Shimizu [Hirahara and Shimizu, 2025], and improves the overhead in the running time incurred during the reduction.

Cite As Get BibTex

Igor Shinkar and Harsimran Singh. A Simplified Reduction for Error Correcting Matrix Multiplication Algorithms. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 29:1-29:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2025.29

Author Details

Igor Shinkar
  • Simon Fraser University, Burnaby, Canada
Harsimran Singh
  • Simon Fraser University, Burnaby, Canada

Acknowledgements

We thank Valentine Kabanets for suggesting to extend the result of [Gola et al., 2024] to zero error model over arbitrary finite fields. We are also thankful to the anonymous reviewers for their valuable comments.

References

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