AxOMaP: Designing FPGA-based Approximate Arithmetic Operators using Mathematical Programming

TL;DR

This paper introduces AxOMaP, a novel mathematical programming approach for designing FPGA-based approximate arithmetic operators that optimize power, performance, and accuracy for resource-constrained machine learning systems.

Contribution

It presents a new data analysis-driven mixed integer quadratic programming method for synthesizing approximate operators, improving optimization efficiency over traditional evolutionary algorithms.

Findings

Up to 21% improvement in hypervolume for joint PPA and BEHAV optimization.

Effective synthesis of FPGA-based approximate signed 8-bit multipliers.

Enhanced directed search approach compared to traditional methods.

Abstract

With the increasing application of machine learning (ML) algorithms in embedded systems, there is a rising necessity to design low-cost computer arithmetic for these resource-constrained systems. As a result, emerging models of computation, such as approximate and stochastic computing, that leverage the inherent error-resilience of such algorithms are being actively explored for implementing ML inference on resource-constrained systems. Approximate computing (AxC) aims to provide disproportionate gains in the power, performance, and area (PPA) of an application by allowing some level of reduction in its behavioral accuracy (BEHAV). Using approximate operators (AxOs) for computer arithmetic forms one of the more prevalent methods of implementing AxC. AxOs provide the additional scope for finer granularity of optimization, compared to only precision scaling of computer arithmetic. To this end, designing platform-specific and cost-efficient approximate operators forms an important research goal. Recently, multiple works have reported using AI/ML-based approaches for synthesizing novel FPGA-based AxOs. However, most of such works limit usage of AI/ML to designing ML-based surrogate functions used during iterative optimization processes. To this end, we propose a novel data analysis-driven mathematical programming-based approach to synthesizing approximate operators for FPGAs. Specifically, we formulate mixed integer quadratically constrained programs based on the results of correlation analysis of the characterization data and use the solutions to enable a more directed search approach for evolutionary optimization algorithms. Compared to traditional evolutionary algorithms-based optimization, we report up to 21% improvement in the hypervolume, for joint optimization of PPA and BEHAV, in the design of signed 8-bit multipliers.