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.
One of the key challenges in this area is to provide fast and energy efficient (i.e. the application of an already trained network). The reason is that trained CNNs are employed in embedded systems and have to process enormous volumes of data in a real-time scenario. As CNNs are highly error resilient, a good strategy is to reduce the bit width for all involved operations and storage elements. This approach has been taken by the Tensor Processing Unit (TPU), where only 8-bit operations are implemented in MAC units. The highly parallel processing enabled by TPU exploits a systolic array composed of 65,536 8-bit MAC units @cite_9 .
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Many architects believe that major improvements in cost-energy-performance must now come from domain-specific hardware. This paper evaluates a custom ASIC---called a Tensor Processing Unit (TPU) --- deployed in datacenters since 2015 that accelerates the inference phase of neural networks (NN). The heart of the TPU is a 65,536 8-bit MAC matrix multiply unit that offers a peak throughput of 92 TeraOps second (TOPS) and a large (28 MiB) software-managed on-chip memory. The TPU's deterministic execution model is a better match to the 99th-percentile response-time requirement of our NN applications than are the time-varying optimizations of CPUs and GPUs that help average throughput more than guaranteed latency. The lack of such features helps explain why, despite having myriad MACs and a big memory, the TPU is relatively small and low power. We compare the TPU to a server-class Intel Haswell CPU and an Nvidia K80 GPU, which are contemporaries deployed in the same datacenters. Our workload, written in the high-level TensorFlow framework, uses production NN applications (MLPs, CNNs, and LSTMs) that represent 95 of our datacenters' NN inference demand. Despite low utilization for some applications, the TPU is on average about 15X -- 30X faster than its contemporary GPU or CPU, with TOPS Watt about 30X -- 80X higher. Moreover, using the CPU's GDDR5 memory in the TPU would triple achieved TOPS and raise TOPS Watt to nearly 70X the GPU and 200X the CPU.