With the growing complexity of applications, design-ers need to fit more and more computing kernels into a limited energy or area budget. Therefore, improving the quality of results of applications in electronic devices with a constraint on its cost is becoming a critical problem. Word Length Optimization (WLO) is the process of determining bit-width for variables or operations represented using fixed-point arithmetic to trade-off between quality and cost. State-of-the-art approaches mainly solve WLO given a quality (accuracy) constraint. In this paper, we first show that existing WLO procedures are not adapted to solve the problem of optimizing accuracy given a cost constraint. It is then interesting and challenging to propose new methods to solve this problem. Then, we propose a Bayesian optimization based algorithm to maximize the quality of computations under a cost constraint (i.e., energy in this paper). Experimental results indicate that our approach outperforms conventional WLO approaches by improving the quality of the solutions by more than 170%.

Using just the right amount of numerical precision is an important aspect for guaranteeing performance and energy efficiency requirements. Word-Length Optimization (WLO) is the automatic process for tuning the precision, i.e., bit-width, of variables and operations represented using fixed-point arithmetic. However, state-of-the-art precision tuning approaches do not scale well in large applications where many variables are involved. In this paper, we propose a hybrid algorithm combining Bayesian optimization (BO) and a fast local search to speed up the WLO procedure. Through experiments, we first show some evidence on how this combination can improve exploration time. Then, we propose an algorithm to automatically determine a reasonable transition point between the two algorithms. By statistically analyzing the convergence of the probabilistic models constructed during BO, we derive a stopping condition that determines when to switch to the local search phase. Experimental results indicate that our algorithm can reduce exploration time by up to 50%-80% for large benchmarks.

In this paper, we propose a method to improve the scalability of Word-Length Optimization (WLO) for large applications that use complex quality metrics such as Structural Similarity (SSIM). The input application is decomposed into smaller kernels to avoid uncontrolled explosion of the exploration time, which is known as noise budgeting. The main challenge addressed in this paper is how to allocate noise budgets to each kernel. This requires capturing the interactions across kernels. The main idea is to characterize the impact of approximating each kernel on accuracy/cost through simulation and regression. Our approach improves the scalability while finding better solutions for Image Signal Processor pipeline.