arXiv subjects

Yasushi Hasegawa

Publications and source records attributed to Yasushi Hasegawa.

3 recordsLinked to original sources

arXiv2026

Performance Evaluation of Ising and QUBO Variable Encodings in Boltzmann Machine Learning

We compare Ising ({-1, +1}) and QUBO ({0, 1}) encodings for Boltzmann machine learning under controlled protocols that fix the sampler, optimizer, and learning-rate design within each comparison. Exploiting the identity that the Fisher information matrix (FIM) equals the covariance of sufficient statistics, we visualize empirical moments from model samples and reveal systematic, representation-dependent differences. QUBO induces larger cross terms between first- and second-order statistics, creating more small-eigenvalue directions in the FIM and lowering spectral entropy. This ill-conditioning explains slower convergence under stochastic gradient descent (SGD). In contrast, full-FIM natural gradient descent (NGD), which rescales updates by the FIM metric, achieves similar convergence across encodings, whereas diagonal-FIM approximation can reintroduce representation-dependent differences. Practically, for SGD-based training, the Ising encoding provides more isotropic curvature and faster convergence; for QUBO, centering/scaling or NGD-style preconditioning mitigates curvature pathologies. These results clarify how representation shapes information geometry and finite-time learning dynamics in Boltzmann machines and yield actionable guidelines for variable encoding and preprocessing.

cs.LG↗

arXiv2026

Kernel Learning by quantum annealer

The Boltzmann machine is one of the various applications using quantum annealer. We propose an application of the Boltzmann machine to the kernel matrix used in various machine-learning techniques. We focus on the fact that shift-invariant kernel functions can be expressed in terms of the expected value of a spectral distribution by the Fourier transformation. Using this transformation, random Fourier feature (RFF) samples the frequencies and approximates the kernel function. In this paper, furthermore, we propose a method to obtain a spectral distribution suitable for the data using a Boltzmann machine. As a result, we show that the prediction accuracy is comparable to that of the method using the Gaussian distribution. We also show that it is possible to create a spectral distribution that could not be feasible with the Gaussian distribution.

quant-ph↗

arXiv2026

Kernel Learning for Regression via Quantum Annealing Based Spectral Sampling

While quantum annealing (QA) has been developed for combinatorial optimization, practical QA devices operate at finite temperature and under noise, and their outputs can be regarded as stochastic samples close to a Gibbs--Boltzmann distribution. In this study, we propose a QA-in-the-loop kernel learning framework that integrates QA not merely as a substitute for Markov-chain Monte Carlo sampling but as a component that directly determines the learned kernel for regression. Based on Bochner's theorem, a shift-invariant kernel is represented as an expectation over a spectral distribution, and random Fourier features (RFF) approximate the kernel by sampling frequencies. We model the spectral distribution with a (multi-layer) restricted Boltzmann machine (RBM), generate discrete RBM samples using QA, and map them to continuous frequencies via a Gaussian--Bernoulli transformation. Using the resulting RFF, we construct a data-adaptive kernel and perform Nadaraya--Watson (NW) regression. Because the RFF approximation based on $\cos(\bmω^{\top}Δ\bm{x})$ can yield small negative values and cancellation across neighbors, the Nadaraya--Watson denominator $\sum_j k_{ij}$ may become close to zero. We therefore employ nonnegative squared-kernel weights $w_{ij}=k(\bm{x}_i,\bm{x}_j)^2$, which also enhances the contrast of kernel weights. The kernel parameters are trained by minimizing the leave-one-out NW mean squared error, and we additionally evaluate local linear regression with the same squared-kernel weights at inference. Experiments on multiple benchmark regression datasets demonstrate a decrease in training loss, accompanied by structural changes in the kernel matrix, and show that the learned kernel tends to improve $R^2$ and RMSE over the baseline Gaussian-kernel NW. Increasing the number of random features at inference further enhances accuracy.

quant-ph↗