We consider the problem of automatic parallelism in high-performance, tensor-based systems. Our focus is on intra-operator parallelism for inference tasks on a single GPU server or CPU cluster, where each operator is automatically broken op so that it runs on multiple devices. We assert that tensor-based systems should offer a programming abstraction based on an extended Einstein summation notation , which is a fully declarative, mathematical specification for tensor computations. We show that any computation specified in the Einstein summation notation can be re-written into an equivalent tensor-relational computation that facilitates intra-operator parallelism, and this re-write generalizes existing notations of tensor parallelism such as "data parallel" and "model parallel." We consider the algorithmic problem of optimally computing a tensor-relational decomposition of a graph of operations specified in our extended Einstein summation notation.

The relational data model was designed to facilitate large-scale data management and analytics. We consider the problem of how to differentiate computations expressed relationally. We show experimentally that a relational engine running an auto-differentiated relational algorithm can easily scale to very large datasets, and is competitive with state-of-the-art, special-purpose systems for large-scale distributed machine learning.

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.