arXiv subjects

Hirotaka Tamura

Publications and source records attributed to Hirotaka Tamura.

10 recordsLinked to original sources

arXiv2026

Adaptive Importance Tempering: A flexible approach to improve computational efficiency of Metropolis Coupled Markov Chain Monte Carlo algorithms on binary spaces

Based on the algorithm Informed Importance Tempering (IIT) proposed by Li et al. (2023) we propose an algorithm that uses an adaptive bounded balancing function. We argue why implementing parallel tempering where each replica uses a rejection free MCMC algorithm can be inefficient in high dimensional spaces and show how the proposed adaptive algorithm can overcome these computational inefficiencies. We present two equivalent versions of the adaptive algorithm (A-IIT and SS-IIT) and establish that both have the same limiting distribution, making either suitable for use within a parallel tempering framework. To evaluate performance, we benchmark the adaptive algorithm against several MCMC methods: IIT, Rejection free Metropolis-Hastings (RF-MH) and RF-MH using a multiplicity list. Simulation results demonstrate that Adaptive IIT identifies high-probability states more efficiently than these competing algorithms in high-dimensional binary spaces with multiple modes.

stat.CO↗

arXiv2025

Performance of the Extended Ising Machine for the Quadratic Knapsack Problem

The extended Ising machine (EIM) enhances conventional Ising models, which handle only binary quadratic forms by allowing constraints through real-valued dependent variables. We address the quadratic knapsack problem (QKP), hard to solve using Ising machines when formulated as a quadratic unconstrained binary optimization (QUBO). We demonstrated the EIM's superiority by comparing it with the conventional Ising model-based approach, a commercial exact solver, and a state-of-the-art heuristic solver for QKP.

cond-mat.stat-mech↗

arXiv2024

Characterization of Locality in Spin States and Forced Moves for Optimizations

Ising formulations are widely utilized to solve combinatorial optimization problems, and a variety of quantum or semiconductor-based hardware has recently been made available. In combinatorial optimization problems, the existence of local minima in energy landscapes is problematic to use to seek the global minimum. We note that the aim of the optimization is not to obtain exact samplings from the Boltzmann distribution, and there is thus no need to satisfy detailed balance conditions. In light of this fact, we develop an algorithm to get out of the local minima efficiently while it does not yield the exact samplings. For this purpose, we utilize a feature that characterizes locality in the current state, which is easy to obtain with a type of specialized hardware. Furthermore, as the proposed algorithm is based on a rejection-free algorithm, the computational cost is low. In this work, after presenting the details of the proposed algorithm, we report the results of numerical experiments that demonstrate the effectiveness of the proposed feature and algorithm.

physics.app-ph↗

arXiv2023

Generating gradients in the energy landscape using rectified linear type cost functions for efficiently solving 0/1 matrix factorization in Simulated Annealing

The 0/1 matrix factorization defines matrix products using logical AND and OR as product-sum operators, revealing the factors influencing various decision processes. Instances and their characteristics are arranged in rows and columns. Formulating matrix factorization as an energy minimization problem and exploring it with Simulated Annealing (SA) theoretically enables finding a minimum solution in sufficient time. However, searching for the optimal solution in practical time becomes problematic when the energy landscape has many plateaus with flat slopes. In this work, we propose a method to facilitate the solution process by applying a gradient to the energy landscape, using a rectified linear type cost function readily available in modern annealing machines. We also propose a method to quickly obtain a solution by updating the cost function's gradient during the search process. Numerical experiments were conducted, confirming the method's effectiveness with both noise-free artificial and real data.

cs.LG↗

arXiv2023

Efficient correlation-based discretization of continuous variables for annealing machines

Annealing machines specialized for combinatorial optimization problems have been developed, and some companies offer services to use those machines. Such specialized machines can only handle binary variables, and their input format is the quadratic unconstrained binary optimization (QUBO) formulation. Therefore, discretization is necessary to solve problems with continuous variables. However, there is a severe constraint on the number of binary variables with such machines. Although the simple binary expansion in the previous research requires many binary variables, we need to reduce the number of such variables in the QUBO formulation due to the constraint. We propose a discretization method that involves using correlations of continuous variables. We numerically show that the proposed method reduces the number of necessary binary variables in the QUBO formulation without a significant loss in prediction accuracy.

quant-ph↗

arXiv2022

Sampling via Rejection-Free Partial Neighbor Search

The Metropolis algorithm involves producing a Markov chain to converge to a specified target density $π$. In order to improve its efficiency, we can use the Rejection-Free version of the Metropolis algorithm, which avoids the inefficiency of rejections by evaluating all neighbors. Rejection-Free can be made more efficient through the use of parallelism hardware. However, for some specialized hardware, such as Digital Annealing Unit, the number of units will limit the number of neighbors being considered at each step. Hence, we propose an enhanced version of Rejection-Free known as Partial Neighbor Search, which only considers a portion of the neighbors while using the Rejection-Free technique. This method will be tested on several examples to demonstrate its effectiveness and advantages under different circumstances.

stat.CO↗

arXiv2022

Optimization via Rejection-Free Partial Neighbor Search

Simulated Annealing using Metropolis steps at decreasing temperatures is widely used to solve complex combinatorial optimization problems. In order to improve its efficiency, we can use the Rejection-Free version of the Metropolis algorithm, which avoids the inefficiency of rejections by considering all the neighbors at every step. As a solution to avoid the algorithm from becoming stuck in local extreme areas, we propose an enhanced version of Rejection-Free called Partial Neighbor Search (PNS), which only considers random parts of the neighbors while applying Rejection-Free. We demonstrate the superior performance of the Rejection-Free PNS algorithm by applying these methods to several examples, such as the QUBO question, the Knapsack problem, the 3R3XOR problem, and the quadratic programming.

math.OC↗

arXiv2020

Derivation of QUBO formulations for sparse estimation

We propose a quadratic unconstrained binary optimization (QUBO) formulation of the l1-norm, which enables us to perform sparse estimation of Ising-type annealing methods such as quantum annealing. The QUBO formulation is derived using the Legendre transformation and the Wolfe theorem, which have recently been employed to derive the QUBO formulations of ReLU-type functions. It is shown that a simple application of the derivation method to the l1-norm case results in a redundant variable. Finally a simplified QUBO formulation is obtained by removing the redundant variable.

quant-ph↗

arXiv2019

Physics-Inspired Optimization for Quadratic Unconstrained Problems Using a Digital Annealer

The Fujitsu Digital Annealer (DA) is designed to solve fully connected quadratic unconstrained binary optimization (QUBO) problems. It is implemented on application-specific CMOS hardware and currently solves problems of up to 1024 variables. The DA's algorithm is currently based on simulated annealing; however, it differs from it in its utilization of an efficient parallel-trial scheme and a dynamic escape mechanism. In addition, the DA exploits the massive parallelization that custom application-specific CMOS hardware allows. We compare the performance of the DA to simulated annealing and parallel tempering with isoenergetic cluster moves on two-dimensional and fully connected spin-glass problems with bimodal and Gaussian couplings. These represent the respective limits of sparse versus dense problems, as well as high-degeneracy versus low-degeneracy problems. Our results show that the DA currently exhibits a time-to-solution speedup of roughly two orders of magnitude for fully connected spin-glass problems with bimodal or Gaussian couplings, over the single-core implementations of simulated annealing and parallel tempering Monte Carlo used in this study. The DA does not appear to exhibit a speedup for sparse two-dimensional spin-glass problems, which we explain on theoretical grounds. We also benchmarked an early implementation of the Parallel Tempering DA. Our results suggest an improved scaling over the other algorithms for fully connected problems of average difficulty with bimodal disorder. The next generation of the DA is expected to be able to solve fully connected problems up to 8192 variables in size. This would enable the study of fundamental physics problems and industrial applications that were previously inaccessible using standard computing hardware or special-purpose quantum annealing machines.

physics.comp-ph↗

arXiv2019

Quadratic unconstrained binary optimization formulation for rectified-linear-unit-type functions

We propose a quadratic unconstrained binary optimization (QUBO) formulation of rectified linear unit (ReLU) type functions. Different from the q-loss function proposed by Denchev et al. (2012), a simple discussion based on the Legendre duality is not sufficient to obtain the QUBO formulation of the ReLU-type functions. In addition to the Legendre duality, we employ the Wolfe duality, and the QUBO formulation of the ReLU-type is derived. The QUBO formulation is available in Ising-type annealing methods, including quantum annealing machines.

quant-ph↗