arXiv subjects

Hyakka Nakada

Publications and source records attributed to Hyakka Nakada.

7 recordsLinked to original sources

arXiv2025

Statistics of Min-max Normalized Eigenvalues in Random Matrices

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.

cs.LG↗

arXiv2025

What Shape Is Optimal for Masks in Text Removal?

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.

cs.CV↗

arXiv2025

Robustness of Structured Data Extraction from Perspectively Distorted Documents

Optical Character Recognition (OCR) for data extraction from documents is essential to intelligent informatics, such as digitizing medical records and recognizing road signs. Multi-modal Large Language Models (LLMs) can solve this task and have shown remarkable performance. Recently, it has been noticed that the accuracy of data extraction by multi-modal LLMs can be affected when in-plane rotations are present in the documents. However, real-world document images are usually not only in-plane rotated but also perspectively distorted. This study investigates the impacts of such perturbations on the data extraction accuracy for the state-of-the-art model, Gemini-1.5-pro. Because perspective distortions have a high degree of freedom, designing experiments in the same manner as single-parametric rotations is difficult. We observed typical distortions of document images and showed that most of them approximately follow an isosceles-trapezoidal transformation, which allows us to evaluate distortions with a small number of parameters. We were able to reduce the number of independent parameters from eight to two, i.e. rotation angle and distortion ratio. Then, specific entities were extracted from synthetically generated sample documents with varying these parameters. As the performance of LLMs, we evaluated not only a character-recognition accuracy but also a structure-recognition accuracy. Whereas the former represents the classical indicators for optical character recognition, the latter is related to the correctness of reading order. In particular, the structure-recognition accuracy was found to be significantly degraded by document distortion. In addition, we found that this accuracy can be improved by a simple rotational correction. This insight will contribute to the practical use of multi-modal LLMs for OCR tasks.

cs.CV↗

arXiv2025

Quick design of feasible tensor networks for constrained combinatorial optimization

Quantum computers are expected to enable fast solving of large-scale combinatorial optimization problems. However, their limitations in fidelity and the number of qubits prevent them from handling real-world problems. Recently, a quantum-inspired solver using tensor networks has been proposed, which works on classical computers. Particularly, tensor networks have been applied to constrained combinatorial optimization problems for practical applications. By preparing a specific tensor network to sample states that satisfy constraints, feasible solutions can be searched for without the method of penalty functions. Previous studies have been based on profound physics, such as U(1) gauge schemes and high-dimensional lattice models. In this study, we devise to design feasible tensor networks using elementary mathematics without such a specific knowledge. One approach is to construct tensor networks with nilpotent-matrix manipulation. The second is to algebraically determine tensor parameters. We showed mathematically that such feasible tensor networks can be constructed to accommodate various types of constraints. For the principle verification, we numerically constructed a feasible tensor network for facility location problem, to find much faster construction than conventional methods. Then, by performing imaginary time evolution, feasible solutions were always obtained, ultimately leading to the optimal solution.

cond-mat.stat-mech↗

arXiv2025

Initialization Method for Factorization Machine Based on Low-Rank Approximation for Constructing a Corrected Approximate Ising Model

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.

cs.LG↗

arXiv2025

Systematic and Efficient Construction of Quadratic Unconstrained Binary Optimization Forms for High-order and Dense Interactions

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.

quant-ph↗

arXiv2025

Inductive Construction of Variational Quantum Circuit for Constrained Combinatorial Optimization

In this study, we propose a new method for constrained combinatorial optimization using variational quantum circuits. Quantum computers are considered to have the potential to solve large combinatorial optimization problems faster than classical computers. Variational quantum algorithms, such as Variational Quantum Eigensolver (VQE), have been studied extensively because they are expected to work on noisy intermediate scale devices. Unfortunately, many optimization problems have constraints, which induces infeasible solutions during VQE process. Recently, several methods for efficiently solving constrained combinatorial optimization problems have been proposed by designing a quantum circuit so as to output only the states that satisfy the constraints. However, the types of available constraints are still limited. Therefore, we have started to develop variational quantum circuits that can handle a wider range of constraints. The proposed method utilizes a forwarding operation that maps from feasible states for subproblems to those for larger subproblems. As long as appropriate forwarding operations can be defined, iteration of this process can inductively construct variational circuits outputting feasible states even in the case of multiple and complex constraints. In this paper, the proposed method was applied to facility location problem and was found to increase the probability for measuring feasible solutions or optimal solutions. In addition, the cost of the obtained circuit was comparable to that of conventional variational circuits.

quant-ph↗