  Linear algebra operations, which are ubiquitous in machine learning, form
major performance bottlenecks. The High-Performance Computing community invests
significant effort in the development of architecture-specific optimized
kernels, such as those provided by the BLAS and LAPACK libraries, to speed up
linear algebra operations. However, end users are progressively less likely to
go through the error prone and time-consuming process of directly using said
kernels; instead, frameworks such as TensorFlow (TF) and PyTorch (PyT), which
facilitate the development of machine learning applications, are becoming more
and more popular. Although such frameworks link to BLAS and LAPACK, it is not
clear whether or not they make use of linear algebra knowledge to speed up
computations. For this reason, in this paper we develop benchmarks to
investigate the linear algebra optimization capabilities of TF and PyT. Our
analyses reveal that a number of linear algebra optimizations are still
missing; for instance, reducing the number of scalar operations by applying the
distributive law, and automatically identifying the optimal parenthesization of
a matrix chain. In this work, we focus on linear algebra computations in TF and
PyT; we both expose opportunities for performance enhancement to the benefit of
the developers of the frameworks and provide end users with guidelines on how
to achieve performance gains.
