Hyakka Nakada

Hyakka Nakada, Shu Tanaka

Random matrix theory has played an important role in various areas of pure mathematics, mathematical physics, and machine learning. From a practical perspective of data science, input data are usually normalized prior to processing. Thus, this study investigates the statistical properties of min-max normalized eigenvalues in random matrices. Previously, the effective distribution for such normalized eigenvalues has been proposed. In this study, we apply it to evaluate a scaling law of the cumulative distribution. Furthermore, we derive the residual error that arises during matrix factorization of random matrices. We conducted numerical experiments to verify these theoretical predictions.

Hyakka Nakada, Marika Kubota

The advent of generative models has dramatically improved the accuracy of image inpainting. In particular, by removing specific text from document images, reconstructing original images is extremely important for industrial applications. However, most existing methods of text removal focus on deleting simple scene text which appears in images captured by a camera in an outdoor environment. There is little research dedicated to complex and practical images with dense text. Therefore, we created benchmark data for text removal from images including a large amount of text. From the data, we found that text-removal performance becomes vulnerable against mask profile perturbation. Thus, for practical text-removal tasks, precise tuning of the mask shape is essential. This study developed a method to model highly flexible mask profiles and learn their parameters using Bayesian optimization. The resulting profiles were found to be character-wise masks. It was also found that the minimum cover of a text region is not optimal. Our research is expected to pave the way for a user-friendly guideline for manual masking.

Hyakka Nakada, Shu Tanaka

Quantum Annealing (QA) can efficiently solve combinatorial optimization problems whose objective functions are represented by Quadratic Unconstrained Binary Optimization (QUBO) formulations. For broader applicability of QA, quadratization methods are used to transform higher-order problems into QUBOs. However, quadratization methods for complex problems involving Machine Learning (ML) remain largely unknown. In these problems, strong nonlinearity and dense interactions prevent conventional methods from being applied. Therefore, we model target functions by the sum of rectified linear unit bases, which not only have the ability of universal approximation, but also have an equivalent quadratic-polynomial representation. In this study, the proof of concept is verified both numerically and analytically. In addition, by combining QA with the proposed quadratization, we design a new black-box optimization scheme, in which ML surrogate regressors are inputted to QA after the quadratization process.

Yuya Seki, Hyakka Nakada, Shu Tanaka

This paper presents an initialization method that can approximate a given approximate Ising model with a high degree of accuracy using a factorization machine (FM), a machine learning model. The construction of an Ising models using an FM is applied to black-box combinatorial optimization problems using factorization machine with quantum annealing (FMQA). It is anticipated that the optimization performance of FMQA will be enhanced through an implementation of the warm-start method. Nevertheless, the optimal initialization method for leveraging the warm-start approach in FMQA remains undetermined. Consequently, the present study compares initialization methods based on random initialization and low-rank approximation, and then identifies a suitable one for use with warm-start in FMQA through numerical experiments. Furthermore, the properties of the initialization method by the low-rank approximation for the FM are analyzed using random matrix theory, demonstrating that the approximation accuracy of the proposed method is not significantly influenced by the specific Ising model under consideration. The findings of this study will facilitate advancements of research in the field of black-box combinatorial optimization through the use of Ising machines.