# Tensor Relational Algebra for Machine Learning System Design

Machine learning (ML) systems have to support various tensor operations. However, such ML systems were largely developed without asking: what are the foundational abstractions necessary for building machine learning systems? We believe that proper computational and implementation abstractions will allow for the construction of self-configuring, declarative ML systems, especially when the goal is to execute tensor operations in a distributed environment, or partitioned across multiple AI accelerators (ASICs). To this end, we first introduce a tensor relational algebra (TRA), which is expressive to encode any tensor operation that can be written in the Einstein notation. We consider how TRA expressions can be re-written into an implementation algebra (IA) that enables effective implementation in a distributed environment, as well as how expressions in the IA can be optimized. Our empirical study shows that the optimized implementation provided by IA can reach or even out-perform carefully engineered HPC or ML systems for large scale tensor manipulations and ML workflows in distributed clusters.

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