HEAP: A Holistic Error Assessment Framework for Multiple Approximations Using Probabilistic Graphical Models

Abstract

Approximate computing has been a good paradigm of energy-efficient accelerator design. Accurate and fast error estimation is critical for appropriate approximate techniques selection so that power saving (or performance improvement) can be maximized with acceptable output quality in approximate accelerators. In the paper, we propose HEAP, a Holistic Error assessment framework to characterize multiple Approximate techniques with Probabilistic graphical models (PGM) in a joint way. HEAP maps the problem of evaluating errors induced by different approximate techniques into a PGM issue, including: (1) A heterogeneous Bayesian network is represented by converting an application’s data flow graph, where various approximate options are {precise, approximate} two-state X*-type nodes, while input or operating variables are {precise, approximate, unacceptable} three-state X-type nodes. These two different kinds of nodes are separately used to configure the available approximate techniques and track the corresponding error propagation for guaranteed configurability; (2) node learning is accomplished via an approximate library, which consists of probability mass functions of multiple approximate techniques to fast calculate each node’s Conditional Probability Table by mechanistic modeling or empirical modeling; (3) exact inference provides the probability distribution of output quality at three levels of precise, approximate, and unacceptable. We do a complete case study of 3 × 3 Gaussian kernels with different approximate configurations to verify HEAP. The comprehensive results demonstrate that HEAP is helpful to explore design space for power-efficient approximate accelerators, with just 4.18% accuracy loss and 3.34 × 105 speedup on average over Mentor Carlo simulation.