An Implementation Method Using Cut-Off Bits for Restricted Boltzmann Machines Without Random Number Generators

Abstract

This study proposes an implementation method of a hardware-oriented restricted Boltzmann machine (RBM) without random number generators (RNGs) that employ cut-off bits, which are obtained from fixed-point binary arithmetic operations on digital hardware, such as field-programmable gate arrays (FPGAs), instead of random numbers. Most FPGA circuits employ fixed-point binary arithmetic operations to improve hardware resource efficiency. Therefore, the proposed method applies the unique feature of the operation, which is bit width extension and cut-off bits. Stochastic neural networks, including RBMs, employ sampling processes based on a probability distribution associated with the network, and the processes require many random numbers. However, implementing RNGs in hardware is costly because it requires considerable hardware resources. The proposed method can mitigate this requirement. To validate the proposed method, we implement an RBM with the proposed method on the software, emulate fixed-point binary arithmetic operations, and train the RBM using the MNIST and Fashion MNIST datasets. Furthermore, we apply the chi-square goodness-of-fit test to evaluate the uniformity of the cut-off bits. Additionally, we compare hardware resource requirements and power consumption for the proposed method and some major RNGs, a linear feedback shift register (LFSR), and a xorshift. Experimental results showed that it was possible to use the cut-off bits for training the RBM using the datasets and clarified the properties of the cut-off bits using statistical analyses. Moreover, hardware implementation of the proposed method involved the lowest hardware resource requirements and power consumption among the RNGs compared in this study.