Design Space Exploration for Approximate Circuits via Checkpointing and DNN-Based Estimators

Approximate computing (AC) is a design paradigm that trades in reductions in hardware area, power, and delay of digital circuits for an increased error. Workflows for synthesizing approximate accelerators are often implemented as search-approximate–evaluate cycles that build a search tree by iteratively approximating components of the original circuit. Design space exploration (DSE) for approximate accelerators is challenging due to the sheer size of the design space and the computational costs for validating the error bound during the search. While early work employed rather slow simulation-based methods, more recent approaches use machine learning (ML) to create fast estimators for validating error bounds. For larger accelerators and design spaces, however, the mispredictions of ML-based methods can steer the search process to explore invalid regions of the design space. In this article, we introduce the framework <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DeepApprox</i> for approximate accelerator synthesis. The novelty of this framework is its combination of fast ML-based quality estimators with occasional simulations to correct possible mispredictions. The simulations are performed at the so-called checkpoints during the search, and we propose two methods: static and dynamic checkpointing (DC). We present the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DeepApprox</i> flow and elaborate on the ML quality estimators and the checkpointing mechanisms. Using a set of smaller and larger benchmarks, we compare <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DeepApprox</i> with two state-of-the-art flows: a simulation-based method leveraging Monte Carlo tree search (MCTS) and an ML-based method with fast estimators. Our experiments demonstrate that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DeepApprox</i> can achieve similar reductions in hardware area and power consumption compared to simulation-based methods, albeit at much lower runtimes, and higher reductions in these metrics compared to methods relying exclusively on ML-based estimators. Thus, by combining ML-based techniques with simulations, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DeepApprox</i> provides a scalable DSE for approximate accelerators.