Chapter 8: Coded Convolution and Tensor Operations

Learning Objectives

• Extend the coded-computing framework from matrix multiplication to tensor operations and convolutions
• Construct entangled polynomial codes that achieve better recovery thresholds by joint encoding
• State and apply the Lagrange coded computing (LCC) framework for arbitrary multivariate-polynomial functions
• Quantify the storage / recovery-threshold tradeoff for convolutions in CNN training
• Recognize when LCC provides the right tool vs. polynomial codes vs. approximate methods
• Identify which tensor-shaped computations in modern ML can be coded, and which remain open