Cache-Aided Matrix Multiplication Retrieval

TL;DR

This paper introduces cache-aided matrix multiplication retrieval, proposing structure-aware caching schemes that improve efficiency over traditional methods, especially for 'fat' matrices, with proven order optimality under certain conditions.

Contribution

It formulates a new cache-aided matrix multiplication retrieval problem and develops structure-aware caching schemes that outperform structure-agnostic approaches.

Findings

Structure-aware schemes improve caching efficiency.

Row-partition scheme is order optimal for 'fat' matrices.

Proposed methods outperform traditional cache schemes.

Abstract

Coded caching is a promising technique to smooth out network traffic by storing part of the library content at the users' local caches. The seminal work on coded caching for single file retrieval by Maddah-Ali and Niesen (MAN) showed the existence of a global caching gain that scales with the total memory in the system, in addition to the known local caching gain in uncoded systems. This paper formulates a novel cache-aided matrix multiplication retrieval problem, relevant for data analytics and machine learning applications. In the considered problem, each cache-aided user requests the product of two matrices from the library. A structure-agnostic solution is to treat each possible matrix product as an independent file and use the MAN coded caching scheme for single file retrieval. This paper proposes two structure-aware schemes, which partition each matrix in the library by either rows or columns and let a subset of users cache some sub-matrices, that improve on the structure-agnostic scheme. For the case where the library matrices are "fat" matrices, the structure-aware row-partition scheme is shown to be order optimal under some constraint.