A Linear Algebraic Approach to Model Parallelism in Deep Learning

TL;DR

This paper introduces a linear algebra-based framework for model parallelism in deep learning, enabling flexible distribution of tensors across compute nodes and facilitating distributed training without relying on automatic differentiation tools.

Contribution

It presents a novel linear algebraic approach to model parallelism, defining parallel operations as linear operators and constructing the necessary adjoint operators for gradient computation.

Findings

Developed distributed DNN layers using linear algebraic primitives

Built and trained a distributed DNN with the DistDL toolkit

Demonstrated effective parallelism in large-scale neural network training

Abstract

Training deep neural networks (DNNs) in large-cluster computing environments is increasingly necessary, as networks grow in size and complexity. Local memory and processing limitations require robust data and model parallelism for crossing compute node boundaries. We propose a linear-algebraic approach to model parallelism in deep learning, which allows parallel distribution of any tensor in the DNN. Rather than rely on automatic differentiation tools, which do not universally support distributed memory parallelism models, we show that parallel data movement operations, e.g., broadcast, sum-reduce, and halo exchange, are linear operators, and by defining the relevant spaces and inner products, we manually develop the adjoint, or backward, operators required for gradient-based training of DNNs. We build distributed DNN layers using these parallel primitives, composed with sequential layer implementations, and demonstrate their application by building and training a distributed DNN using DistDL, a PyTorch and MPI-based distributed deep learning toolkit.