Tensor Relational Algebra for Distributed Machine Learning System Design

We consider the question: what is the abstraction that should be implemented by the computational engine of a machine learning system? Current machine learning systems typically push whole tensors through a series of compute kernels such as matrix multiplications or activation functions, where each kernel runs on an AI accelerator (ASIC) such as a GPU. This implementation abstraction provides little built-in support for ML systems to scale past a single machine, or for handling large models with matrices or tensors that do not easily fit into the RAM of an ASIC. In this paper, we present an alternative implementation abstraction called the tensor relational algebra (TRA). The TRA is a set-based algebra based on the relational algebra. Expressions in the TRA operate over binary tensor relations, where keys are multi-dimensional arrays and values are tensors. The TRA is easily executed with high efficiency in a parallel or distributed environment, and amenable to automatic optimization. Our empirical study shows that the optimized TRA-based back-end can significantly outperform alternatives for running ML workflows in distributed clusters. 1 Throughout the paper, we use the term front-end to refer to the programmer-facing API and compiler; in PyTorch, for example, this would be the part of the system that accepts Einstein notation and transforms it into a set of executable operations. We use the term back-end to refer to the sub-system that actually executes the computation.