Evaluating matrix representations for error-tolerant computing

We propose a methodology to determine the suitability of different data representations in terms of their error-tolerance for a given application with accelerator-based computing. This methodology helps match the characteristics of a representation to the data access patterns in an application. For this, we first identify a benchmark of key kernels from linear algebra that can be used to construct applications of interest using any of several widely used data representations. This is then used in an experimental framework for studying the error tolerance of a specific data format for an application. As case studies, we evaluate the error-tolerance of seven dataformats on sparse matrix to vector multiplication, diagonal add, and two machine learning applications i) principal component analysis (PCA), which is a statistical technique widely used in data analysis and ii) movie recommendation system with Restricted Boltzmann Machine (RBM) as the core. We observe that the Dense format behaves well for complicated data accesses such as diagonal accessing but is poor in utilizing local memory. Sparse formats with simpler addressing methods and a careful selection of stored information, e.g., CRS and ELLPACK, demonstrate a better error-tolerance for most of our target applications.