Computing Quality Driven Agile Design Space Exploration for Approximation based Matrix-Vector-Multiplication

Matrix-vector multiplication (MVM) presents critical efficiency challenges in post-Moore computing architectures within data-intensive applications. To improve hardware efficiency in the post-Moore era, approximate computing (AxC) has been integrated in MVM hardware, making more profits from the data redundancy. This paper proposes a systematic design space exploration (DSE) framework to optimize AxC MVM modules (AxMVM) through multi-objective optimization (MOO). This framework rigorously integrates domain-specific constraints, such as error tolerance thresholds and hardware resource limitations, to derive Pareto-optimal solutions that balance performance, efficiency, and scalability under heterogeneous design requirements. The DSE problem incorporates an approximation degree metric for computational quality and an analytical model for hardware-accuracy trade-off evaluation. Pareto-optimal solutions are efficiently derived using NSGA-II, achieving 102× faster than simulation-based methods. Evaluations in MVM dimensions (4/16/32/64) demonstrate the scalability and adaptability of the framework, with a prediction accuracy of 95. 99% compared to Monte Carlo simulations. Experimental results demonstrate that optimized AxC implementations achieve a 10-20% area reduction in synthesized hardware with controlled degradation of computational quality.