We propose an application-tailored data-driven fully automated method for functional approximation of combinational circuits. We demonstrate how an application-level error metric such as the classification accuracy can be translated to a component-level error metric needed for an efficient and fast search in the space of approximate low-level components that are used in the application. This is possible by employing a weighted mean error distance (WMED) metric for steering the circuit approximation process which is conducted by means of genetic programming. WMED introduces a set of weights (calculated from the data distribution measured on a selected signal in a given application) determining the importance of each input vector for the approximation process. The method is evaluated using synthetic benchmarks and application-specific approximate MAC (multiply-and-accumulate) units that are designed to provide the best trade-offs between the classification accuracy and power consumption of two image classifiers based on neural networks.
Approximate circuits and approximate circuit design methodologies attracted a significant attention of researchers as well as industry in recent years. In order to accelerate the approximate circuit and system design process and to support a fair benchmarking of circuit approximation methods, we propose a library of approximate adders and multipliers called EvoApprox8b. This library contains 430 non-dominated 8-bit approximate adders created from 13 conventional adders and 471 non-dominated 8-bit approximate multipliers created from 6 conventional multipliers. These implementations were evolved by a multi-objective Cartesian genetic programming. The EvoApprox8b library provides Verilog, Matlab and C models of all approximate circuits. In addition to standard circuit parameters, the error is given for seven different error metrics. The EvoApprox8b library is available at: www.fit.vutbr.cz research groups ehw approxlib Artificial neural networks (NN) have shown a significant promise in difficult tasks like image classification or speech recognition. Even well-optimized hardware implementations of digital NNs show significant power consumption. It is mainly due to non-uniform pipeline structures and inherent redundancy of numerous arithmetic operations that have to be performed to produce each single output vector. This paper provides a methodology for the design of well-optimized power-efficient NNs with a uniform structure suitable for hardware implementation. An error resilience analysis was performed in order to determine key constraints for the design of approximate multipliers that are employed in the resulting structure of NN. By means of a search based approximation method, approximate multipliers showing desired tradeoffs between the accuracy and implementation cost were created. Resulting approximate NNs, containing the approximate multipliers, were evaluated using standard benchmarks (MNIST dataset) and a real-world classification problem of Street-View House Numbers. Significant improvement in power efficiency was obtained in both cases with respect to regular NNs. In some cases, 91 power reduction of multiplication led to classification accuracy degradation of less than 2.80 . Moreover, the paper showed the capability of the back propagation learning algorithm to adapt with NNs containing the approximate multipliers. 