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Dual-Entangled Polynomial Code: Three-Dimensional Coding for Distributed Matrix Multiplication Pedro Soto, Jun Li, Xiaodi Fan Florida International University Matrix Multiplication Matrix multiplication is a fundamental building block in

  1. Dual-Entangled Polynomial Code: Three-Dimensional Coding for Distributed Matrix Multiplication Pedro Soto, Jun Li, Xiaodi Fan Florida International University

  2. Matrix Multiplication ‣ Matrix multiplication is a fundamental building block in various machine learning algorithms. ‣ When the matrix comes from a large dataset, the multiplication will be split into smaller multiplications of submatrices on different nodes. � 2

  3. <latexit sha1_base64="sTfApjh8/Ig5dxgjSg4JiRvuvTc=">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</latexit> � � � Matrix Multiplication ‣ Matrix multiplication is a fundamental building block in various machine learning algorithms. ‣ When the matrix comes from a large dataset, the multiplication will be split into smaller multiplications of submatrices on different nodes. � 2

  4. <latexit sha1_base64="sTfApjh8/Ig5dxgjSg4JiRvuvTc=">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</latexit> � � � � �� � � � � � � <latexit sha1_base64="jvZ1pEC6o51a+h06RGOKnBfQifU=">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</latexit> Matrix Multiplication ‣ Matrix multiplication is a fundamental building block in various machine learning algorithms. ‣ When the matrix comes from a large dataset, the multiplication will be split into smaller multiplications of submatrices on different nodes. � 2

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