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Multiplication is the most resource-hungry operation in neural networks (NNs). Logarithmic multipliers (LMs) simplify multiplication to shift and addition operations and thus reduce the energy consumption. Since implementing the logarithm in a compact circuit often introduces approximation, some accuracy loss is inevitable in LMs. However, this inaccuracy accords with the inherent error tolerance of NNs and their associated applications. This article proposes an improved logarithmic multiplier (ILM) that, unlike existing designs, rounds both inputs to their nearest powers of two by using a proposed nearest-one detector (NOD) circuit. Considering that the output of the NOD uses a one-hot representation, some entries in the truth table of a conventional adder cannot occur. Hence, a compact adder is designed for the reduced truth table. The 8×8 ILM achieves up to 17.48 percent saving in power consumption compared to a recent LM in the literature while being almost 8 percent more accurate. Moreover, the evaluation of the ILM for two benchmark NN workloads shows up to 21.85 percent reduction in energy consumption compared to the NNs implemented with other LMs. Interestingly, using the ILM increases the classification accuracy of the considered NNs by up to 1.4 percent compared to a NN implementation that uses exact multipliers. [ABSTRACT FROM AUTHOR]

Improving the accuracy of a neural network (NN) usually requires using larger hardware that consumes more energy. However, the error tolerance of NNs and their applications allow approximate computing techniques to be applied to reduce implementation costs. Given that multiplication is the most resource-intensive and power-hungry operation in NNs, more economical approximate multipliers (AMs) can significantly reduce hardware costs. In this article, we show that using AMs can also improve the NN accuracy by introducing noise. We consider two categories of AMs: 1) deliberately designed and 2) Cartesian genetic programing (CGP)-based AMs. The exact multipliers in two representative NNs, a multilayer perceptron (MLP) and a convolutional NN (CNN), are replaced with approximate designs to evaluate their effect on the classification accuracy of the Mixed National Institute of Standards and Technology (MNIST) and Street View House Numbers (SVHN) data sets, respectively. Interestingly, up to 0.63% improvement in the classification accuracy is achieved with reductions of 71.45% and 61.55% in the energy consumption and area, respectively. Finally, the features in an AM are identified that tend to make one design outperform others with respect to NN accuracy. Those features are then used to train a predictor that indicates how well an AM is likely to work in an NN. [ABSTRACT FROM AUTHOR]