### A Hardware-efficient Weight Sampling Circuit for Bayesian Neural Networks

#### Abstract

The main problems of deep learning are requiring a large amount of data for learning, and prediction with excessive confidence. A Bayesian neural network (BNN), in which a Bayesian approach is incorporated into a neural network (NN), has drawn attention as a method for solving these problems. In a BNN, the probability distribution is assumed for the weight, in contrast to a conventional NN, in which the weight is point estimated. This makes it possible to obtain the prediction as a distribution and to evaluate how uncertain the prediction is. However, a BNN has more computational complexity and a greater number of parameters than an NN. To obtain an inference result as a distribution, a BNN uses weight sampling to generate the respective weight values, and thus, a BNN accelerator requires weight sampling hardware based on a random number generator in addition to the standard components of a deep learning neural network accelerator. Therefore, the throughput of weight sampling must be sufficiently high at a low hardware resource cost. We propose a resource-efficient weight sampling method using inversion transform sampling and a lookup-table (LUT)-based function approximation for hardware implementation of a BNN. Inversion transform sampling simplifies the mechanism of generating a Gaussian random number from a uniform random number provided by a common random number generator, such as a linear feedback shift register. Employing an LUT-based low-bit precision function approximation enables inversion transform sampling to be implemented at a low hardware cost. The evaluation results indicate that this approach effectively reduces the occupied hardware resources while maintaining accuracy and prediction variance equivalent to that with a non-approximated sampling method.

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