Modified Logarithmic Multiplication Approximation for Machine Learning

In this paper, a novel approximation that allows exploitation of the full potential of logarithmic multiplication is proposed. More specifically, the proposed approximation is quantified in terms of mean square error (MSE) and compared to a competitive recent publication. Subsequently, an LSTM network is used as an illustrative test case and the proposed approximation is validated in terms of the accuracy of the netowrk. It has been shown that for short data wordlengths, the proposed approximation can achieve small loss values, for the particular LSTM network. Finally, the circuit implementation of the logarithmic multiplier is synthesized in a 28 nm standard-cell library. Results show reduced hardware complexity for similar loss values on the specific LSTM network.