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Implementing an accurate and fast activation function with low cost is acrucial aspect to the implementation of Deep Neural Networks (DNNs) on FPGAs.We propose a high-accuracy approximation approach for the hyperbolic tangentactivation function of artificial neurons in DNNs. It is based on the DiscreteCosine Transform Interpolation Filter (DCTIF). The proposed architecturecombines simple arithmetic operations on stored samples of the hyperbolictangent function and on input data. The proposed DCTIF implementation achievestwo orders of magnitude greater precision than previous work while using thesame or fewer computational resources. Various combinations of DCTIF parameterscan be chosen to tradeoff the accuracy and complexity of the hyperbolic tangentfunction. In one case, the proposed architecture approximates the hyperbolictangent activation function with 10E-5 maximum error while requiring only 1.52Kbits memory and 57 LUTs of a Virtex-7 FPGA. We also discuss how the activationfunction accuracy affects the performance of DNNs in terms of their trainingand testing accuracies. We show that a high accuracy approximation can benecessary in order to maintain the same DNN training and testing performancesrealized by the exact function.

Accurate and Efficient Hyperbolic Tangent Activation Function on FPGA using the DCT Interpolation Filter