@article{oai:kyutech.repo.nii.ac.jp:02000825,
 author = {Yoshioka, Kanta and Katori, Yuichi and Tanaka, Yuichiro and 田中, 悠一朗 and 野村, 修 and Nomura, Osamu and Morie, Takashi and 森江, 隆 and Tamukoh, Hakaru and 田向, 権},
 journal = {2023 International Joint Conference on Neural Networks (IJCNN)},
 month = {Aug},
 note = {Ising machines are attracting attention for their ability to solve large-scale combinatorial optimization problems because these problems are difficult to solve. To accelerate the computing of Ising machines, implementation of Ising machines with digital circuits such as simulated annealing (SA) machines is in progress. However, these Ising machines on digital circuits require random number generators, which are implemented with large circuit resources. This work focuses on chaotic Boltzmann machines (CBMs), which imitate the stochastic behavior of Boltzmann machines (BMs) with deterministic chaotic dynamics. CBMs are one of the models that work as chaotic simulated annealing (CSA) machines within Ising machines. Therefore, we can implement the Ising machines without random number generators by using CBMs. In conventional work, CSA machines using CBMs (CBM-CSAs) are implemented with some hardware-oriented algorithms, but the CBM-CSA circuit is not optimized for these hardware-oriented algorithms. In the conventional CBM-CSA circuit, memory circuits are implemented separately, which prevents making the CBM-CSA from larger, and neuron circuits require the reset of accumulated values, which causes the increase in the calculation time. To solve these problems, we implement only one large memory circuit to make the CBM-CSA larger and improve the neuron circuits to allow dynamic changes of inputs to arithmetic circuits to inhibit the increase in the calculation time. As a result, we implement a CBM-CSA with 4096 nodes on an FPGA (Alveo U250), and the CBM-CSA can control 16-bit width weights and run at 100MHz. We evaluate the implemented CBM-CSA by solving K4000, max-cut problem, which is one of the combinatorial optimization problems. The best solution of CBM-CSA is comparable to that of the SA on the central processing unit (CPU). Moreover, the CBM-CSA is approximately 600 times as fast as the SA on the CPU and approximately twice as fast as the conventional Ising machine on an FPGA based on the improvements in this work. Furthermore, this work implements one of the highest-performance Ising machines on a single FPGA., 2023 International Joint Conference on Neural Networks (IJCNN), 18-23 June, 2023, Gold Coast, Australia},
 pages = {1--8},
 title = {FPGA Implementation of a Chaotic Boltzmann Machine Annealer},
 year = {2023}
}