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 represented by the Einstein notation; we then transform it to an implementation algebra (IA) that enables effective logical and physical optimizations for paralleled and distributed environment.
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