Neural networks for neurocomputing circuits: a computational study of tolerance to noise and activation function non-uniformity when machine learning materials properties

Dedicated analog neurocomputing circuits are promising for high-throughput, low power consumption applications of machine learning (ML) and for applications where implementing a digital computer is unwieldy (remote locations; small, mobile, and autonomous devices, extreme conditions, etc.). Neural networks (NN) implemented in such circuits, however, must contend with circuit noise and the non-uniform shapes of the neuron activation function (NAF) due to the dispersion of performance characteristics of circuit elements (such as transistors or diodes implementing the neurons). We present a computational study of the impact of circuit noise and NAF inhomogeneity in function of NN architecture and training regimes. We focus on one application that requires high-throughput ML: materials informatics, using as representative problem ML of formation energies vs. lowest-energy isomer of peri-condensed hydrocarbons, formation energies and band gaps of double perovskites, and zero point vibrational energies of molecules from QM9 dataset. We show that NNs generally possess low noise tolerance with the model accuracy rapidly degrading with noise level. Single-hidden layer NNs, and NNs with larger-than-optimal sizes are somewhat more noise-tolerant. Models that show less overfitting (not necessarily the lowest test set error) are more noise-tolerant. Importantly, we demonstrate that the effect of activation function inhomogeneity can be palliated by retraining the NN using practically realized shapes of NAFs.