arXiv subjects

Hirotaka Takahashi

Publications and source records attributed to Hirotaka Takahashi.

At least 19 recordsLinked to original sources

arXiv2026

Grad-CAM for Visualizing Attention Regions of PCA and SVM Layers in Convolutional Neural Networks

Convolutional Neural Networks (CNNs) are an effective approach for classification tasks, particularly when the training dataset is large. Although CNNs have long been considered a black-box classification method, they can be used as a white-box method through visualization techniques such as Grad-CAM. When the training samples are limited, incorporating a Principal Component Analysis (PCA) layer and/or a Support Vector Machine (SVM) classifier into a CNN can effectively improve the classification performance. However, a conventional Grad-CAM cannot be directly applied to PCA and/or SVM layers. Generating attention regions for PCA and/or SVM layers in CNNs is important to facilitate the development of white-box methods. Therefore, we propose ``PCA-Grad-CAM'', a method for visualizing attention regions in PCA feature vectors, and ``SVM-Grad-CAM'', a method for visualizing attention regions in an SVM classifier layer. Solving a closed-form Jacobian problem comprising partial derivatives from the last convolutional layer to the PCA and/or SVM layers is necessary to complete the proposed methods analytically. In this paper, we present the exact closed-form Jacobian and visualization results of the proposed methods applied to several major datasets. In addition, the insertion and deletion metrics, which are major evaluation metrics in explainable AI, were applied to PCA- and SVM-Grad-CAM. The results suggest that the proposed method can successfully visualize the attention regions of PCA and SVM.

cs.LG↗

arXiv2026

Parameter Estimation of Ringdown Quasinormal Modes with Autoencoder

Ringdown gravitational waves from binary black hole mergers can be modeled as superpositions of quasinormal modes (QNMs), whose frequencies and excitation factors encode properties of the remnant Kerr black hole. Reliable extraction of multiple QNM components is challenging because of mode overlap and noise. We develop an autoencoder-based framework for multi-component QNM analysis, in which the latent space is trained to represent the physical parameters of individual modes, enabling waveform denoising and parameter estimation within a common framework. Using controlled model waveforms constructed as finite sums of Kerr QNMs with recently established high-precision frequencies and excitation factors, including their nontrivial spin dependence near resonant excitation, we assess the method across partitioned spin intervals. The model achieves good in-domain waveform reconstruction and parameter recovery for the two longest-lived components of eight-component input waveforms, while its performance degrades when the validation spins lie far outside the training range. In a selected spin interval, the framework also recovers the 32 parameters of an eight-component waveform with good overall agreement. These results demonstrate the feasibility of physics-informed autoencoder-based inference for a prescribed multi-component ringdown waveform family and motivate further tests with progressively more realistic signals.

gr-qc↗

arXiv2026

Autoencoder-Based Parameter Estimation for Superposed Multi-Component Damped Sinusoidal Signals

Damped sinusoidal oscillations are widely observed in many physical systems, and their analysis provides access to underlying physical properties. However, parameter estimation becomes difficult when the signal decays rapidly, multiple components are superposed, and observational noise is present. In this study, we develop an autoencoder-based method that uses the latent space to estimate the frequency, phase, decay time, and amplitude of each component in noisy multi-component damped sinusoidal signals. We investigate multi-component cases under Gaussian-distribution training and further examine the effect of the training-data distribution through comparisons between Gaussian and uniform training. The performance is evaluated through waveform reconstruction and parameter-estimation accuracy. We find that the proposed method can estimate the parameters with high accuracy even in challenging setups, such as those involving a subdominant component or nearly opposite-phase components, while remaining reasonably robust when the training distribution is less informative. This demonstrates its potential as a tool for analyzing short-duration, noisy signals.

cs.LG↗

arXiv2026

Closed-Form Steepest Descent Direction toward Flat Minima: Reducing Upper Bounds on the Loss Hessian Eigenspectrum in Neural Networks

The flatness hypothesis suggests that flatness of the loss landscape, as measured by the eigenvalues of the loss Hessian, correlates with better neural network generalization. While various algorithms reduce these eigenvalues, most focus on procedural design, leaving it unclear how data distributions and NN parameters structurally determine directions toward flat minima. Characterizing these directions analytically is generally intractable. To overcome this mathematical difficulty, recent studies derived the Wolkowicz-Styan (WS) upper bound on the maximum eigenvalue of the cross-entropy loss Hessian in three-layer NNs. Although this upper bound is differentiable, its gradient was not derived. Therefore, we analytically derive the gradient of the WS upper bound to characterize directions leading to flat minima. Based on this, we propose Hessian Spectral Range (HSR) Regularization, which updates parameters along the steepest descent direction of the WS bound. Experiments demonstrate that HSR Regularization narrows the Hessian eigenvalue spectrum, avoids sharp minima and saddle points, and promotes convergence to flat minima. Although the applicability of this method is currently limited to cross-entropy loss and three-layer architectures, to the best of the authors' knowledge, this is the first study to report a closed-form gradient that promotes convergence to flat minima without numerical approximations. Therefore, the theoretical analysis of this gradient is expected to contribute to the further development of NNs.

cs.LG↗

arXiv2026

Wavelet-Based Extraction of Transient Noise in Gravitational-Wave Interferometers using a Saliency-Guided Learning Architecture

Gravitational-wave interferometers exhibit a wide variety of short-duration non-Gaussian transients, commonly referred to as glitches, that complicate the detection of astrophysical signals, bias parameter estimation, and detector characterisation. Existing machine-learning approaches classify glitch morphologies but do not provide a complete mechanism to segment and extract these disturbances from the strain data. We introduce a wavelet-based, saliency-guided framework for the supervised extraction of transient noise. Candidates are first pre-tagged using Uniform Manifold Approximation and Projection, which is also used as a diagnostic of the learned representations. A traditional learning model operating on Continuous Wavelet Transform spectrograms then identifies relevant time-frequency regions through saliency maps. These saliency patterns are transferred to an invertible multiresolution representation via the Discrete Wavelet Transform, where adaptive coefficient masking enables exact reconstruction of both glitch-only and glitch-suppressed waveforms. We demonstrate effective extraction across several representative glitch families, including 'Whistle' and 'Scattered-Light' transients, and show robustness in challenging regimes such as low signal-to-noise events and partially overlapping structures, where classical thresholding or band-limited filtering methods typically fail or introduce leakage. The proposed framework offers an interpretable and computationally efficient approach to transient-noise extraction, establishing a foundation for scalable applications to larger glitch catalogs and future observing runs.

astro-ph.IM↗

arXiv2026

Analytical Evaluation of DCA Convergence Properties for Minimizing Prediction Functions of Gaussian RBF Support Vector Regression

For nonconvex optimization problems whose objective is the prediction function of a trained Support Vector Regression (SVR) model with the Gaussian radial basis function (RBF) kernel (RBF-SVR), we present a framework that applies the difference of convex functions (DC) algorithm (DCA) by exploiting the analytical structure of the RBF kernel to construct an explicit DC decomposition. Specifically, we derive in closed form both the lower bound $μ$ of the strong convexity parameter of the DC components and the upper bound $L$ of the gradient Lipschitz constant of the subproblem. Both $μ$ and $L$ are determined solely by the post-training dual-coefficient sum $C_α$ and the RBF kernel parameter $γ$, together with the DC decomposition parameter $ρ$, and they share a common leading term $C_αρ$. Through numerical experiments on six benchmark functions, we show that $C_αρ$ is the primary single quantity characterizing both the convergence properties and the initial-point dependence of DCA, and further demonstrate that it decomposes into two independent pathways, $C \to C_α$ and $γ\to ρ$, with its primary variation governed by the SVR hyperparameters $(C, γ)$. Together, these results allow the convergence properties of DCA on RBF-SVR to be assessed in advance through the single scalar quantity $C_αρ$: approximately from $(C, γ)$ before training, and exactly in closed form after training.

cs.LG↗

arXiv2026

Wolkowicz-Styan Upper Bound on the Hessian Eigenspectrum for Cross-Entropy Loss in Nonlinear Smooth Neural Networks

Neural networks (NNs) are central to modern machine learning and achieve state-of-the-art results in many applications. However, the relationship between loss geometry and generalization is still not well understood. The local geometry of the loss function near a critical point is well-approximated by its quadratic form, obtained through a second-order Taylor expansion. The coefficients of the quadratic term correspond to the Hessian matrix, whose eigenspectrum allows us to evaluate the sharpness of the loss at the critical point. Extensive research suggests flat critical points generalize better, while sharp ones lead to higher generalization error. However, sharpness requires the Hessian eigenspectrum, but general matrix characteristic equations have no closed-form solution. Therefore, most existing studies on evaluating loss sharpness rely on numerical approximation methods. Existing closed-form analyses of the eigenspectrum are primarily limited to simplified architectures, such as linear or ReLU-activated networks; consequently, theoretical analysis of smooth nonlinear multilayer neural networks remains limited. Against this background, this study focuses on nonlinear, smooth multilayer neural networks and derives a closed-form upper bound for the maximum eigenvalue of the Hessian with respect to the cross-entropy loss by leveraging the Wolkowicz-Styan bound. Specifically, the derived upper bound is expressed as a function of the affine transformation parameters, hidden layer dimensions, and the degree of orthogonality among the training samples. The primary contribution of this paper is an analytical characterization of loss sharpness in smooth nonlinear multilayer neural networks via a closed-form expression, avoiding explicit numerical eigenspectrum computation. We hope that this work provides a small yet meaningful step toward unraveling the mysteries of deep learning.

cs.LG↗

arXiv2025

Glitch noise classification in KAGRA O3GK observing data using unsupervised machine learning

Gravitational wave interferometers are disrupted by various types of nonstationary noise, referred to as glitch noise, that affect data analysis and interferometer sensitivity. The accurate identification and classification of glitch noise are essential for improving the reliability of gravitational wave observations. In this study, we demonstrated the effectiveness of unsupervised machine learning for classifying images with nonstationary noise in the KAGRA O3GK data. Using a variational autoencoder (VAE) combined with spectral clustering, we identified eight distinct glitch noise categories. The latent variables obtained from VAE were dimensionally compressed, visualized in three-dimensional space, and classified using spectral clustering to better understand the glitch noise characteristics of KAGRA during the O3GK period. Our results highlight the potential of unsupervised learning for efficient glitch noise classification, which may in turn potentially facilitate interferometer upgrades and the development of future third-generation gravitational wave observatories.

gr-qc↗

arXiv2025

Regression of Suspension Violin Modes in KAGRA O3GK Data with Kalman Filters

Suspension thermal modes in interferometric gravitational-wave detectors produce narrow, high-Q spectral lines that can contaminate gravitational searches and bias parameter estimation. In KAGRA, cryogenic mirrors are held by thick suspension fibers, designed to sustain such a low-temperature environment, which may further affect inharmonicity modes, fiber dimensions, and mechanical behavior compared to typical interferometers. As these modes remain a prominent source of narrowband contamination, we implement a Kalman filter to model and track violin lines, building on the methodology introduced in [1], and apply subtraction to KAGRA O3GK data. Using gravitational-wave template injections, we validate that the subtraction preserves matched-filter SNR while effectively suppressing line power. Comparisons of power spectral densities and residual analyses confirm that the method removes deterministic line contributions without introducing waveform distortions. This approach provides a cleaner strain channel for searches and parameter estimation and will become increasingly important for future low-temperature detectors with higher-Q suspensions, such as the Einstein Telescope.

gr-qc↗

arXiv2025

Gravitational Wave Memory from Accelerating Relativistic Jets in Multiple Thick Shell Scenarios

Gravitational wave (GW) memory, a permanent distortion of the space-time metric, is anticipated during the acceleration of relativistic jets in gamma-ray bursts (GRBs). While the precise mechanism behind GRBs is not yet fully understood, detecting GW memory may contribute to clarifying their nature. In this paper, we consider various scenarios of GW memory emission, including both single and multiple shells with thin- and thick-shells. In particular, the memory spectrum for each scenario is compared with the sensitivity of next-generation detectors, namely DECIGO and ET-D. Physical properties spread over a broad-band region, emphasizing the importance of combined and wide-band observations. We also simulate GW memory based on nearby, realistic scenarios and demonstrate its detectability.

astro-ph.HE↗

arXiv2025

Computing the Wave: Where the Gravitational Wave Community benefits from High-Energy Physics, and where it differs ?

High-Energy Physics (HEP) and Gravitational Wave (GW) communities serve different scientific purposes. However, their methodologies might potentially offer mutual enrichment through common software developments. A suite of libraries is currently being prototyped and made available at https://git.ligo.org/kagra/libraries-addons/root, extending at no cost the CERN ROOT data analysis framework toward advanced signal processing. We will also present a performance benchmark comparing the FFTW and KFR library performances.

astro-ph.IM↗

arXiv2024

Parameter estimation of protoneutron stars from gravitational wave signals using the Hilbert-Huang transform

Core-collapse supernovae (CCSNe) are potential multimessenger events detectable by current and future gravitational wave (GW) detectors. The GW signals emitted during these events are expected to provide insights into the explosion mechanism and the internal structures of neutron stars. In recent years, several studies have empirically derived the relationship between the frequencies of the GW signals originating from the oscillations of protoneutron stars (PNSs) and the physical parameters of these stars. This study applies the Hilbert-Huang transform (HHT) [Proc. R. Soc. A 454, 903 (1998)] to extract the frequencies of these modes to infer the physical properties of the PNSs. The results exhibit comparable accuracy to a short-time Fourier transform-based estimation, highlighting the potential of this approach as a complementary method for extracting physical information from GW signals of CCSNe.

gr-qc↗

arXiv2024

Comparative study of 1D and 2D convolutional neural network models with attribution analysis for gravitational wave detection from compact binary coalescences

Recent advancements in gravitational wave astronomy have seen the application of convolutional neural networks (CNNs) in signal detection from compact binary coalescences. This study presents a comparative analysis of two CNN architectures: one-dimensional (1D) and two-dimensional (2D) along with an ensemble model combining both. We trained these models to detect gravitational wave signals from binary black hole (BBH) mergers, neutron star-black hole (NSBH) mergers, and binary neutron star (BNS) mergers within real detector noise. Our investigation entailed a comprehensive evaluation of the detection performance of each model type across different signal classes. To understand the models' decision-making processes, we employed feature map visualization and attribution analysis. The findings revealed that while the 1D model showed superior performance in detecting BBH signals, the 2D model excelled in identifying NSBH and BNS signals. Notably, the ensemble model outperformed both individual models across all signal types, demonstrating enhanced detection capabilities. Additionally, input feature visualization indicated distinct areas of focus in the data for the 1D and 2D models, emphasizing the effectiveness of their combination.

gr-qc↗

arXiv2023

Visualizing convolutional neural network for classifying gravitational waves from core-collapse supernovae

In this study, we employ a convolutional neural network to classify gravitational waves originating from core-collapse supernovae. Training is conducted using spectrograms derived from three-dimensional numerical simulations of waveforms, which are injected onto real noise data from the third observing run of both Advanced LIGO and Advanced Virgo. To gain insights into the decision-making process of the model, we apply class activation mapping techniques to visualize the regions in the input image that are significant for the model's prediction. The class activation maps reveal that the model's predictions predominantly rely on specific features within the input spectrograms, namely, the $g$-mode and low-frequency modes. The visualization of convolutional neural network models provides interpretability to enhance their reliability and offers guidance for improving detection efficiency.

astro-ph.IM↗

arXiv2023

FG-SSA: Features Gradient-based Signals Selection Algorithm of Linear Complexity for Convolutional Neural Networks

Recently, many convolutional neural networks (CNNs) for classification by time domain data of multisignals have been developed. Although some signals are important for correct classification, others are not. When data that do not include important signals for classification are taken as the CNN input layer, the calculation, memory, and data collection costs increase. Therefore, identifying and eliminating nonimportant signals from the input layer are important. In this study, we proposed features gradient-based signals selection algorithm (FG-SSA), which can be used for finding and removing nonimportant signals for classification by utilizing features gradient obtained by the calculation process of grad-CAM. When we define N as the number of signals, the computational complexity of the proposed algorithm is linear time O(N), that is, it has a low calculation cost. We verified the effectiveness of the algorithm using the OPPORTUNITY Activity Recognition dataset, which is an open dataset comprising acceleration signals of human activities. In addition, we checked the average 6.55 signals from a total of 15 acceleration signals (five triaxial sensors) that were removed by FG-SSA while maintaining high generalization scores of classification. Therefore, the proposed algorithm FG-SSA has an effect on finding and removing signals that are not important for CNN-based classification.

eess.SP↗

arXiv2022

Training Process of Unsupervised Learning Architecture for Gravity Spy Dataset

Transient noise appearing in the data from gravitational-wave detectors frequently causes problems, such as instability of the detectors and overlapping or mimicking gravitational-wave signals. Because transient noise is considered to be associated with the environment and instrument, its classification would help to understand its origin and improve the detector's performance. In a previous study, an architecture for classifying transient noise using a time-frequency 2D image (spectrogram) is proposed, which uses unsupervised deep learning combined with variational autoencoder and invariant information clustering. The proposed unsupervised-learning architecture is applied to the Gravity Spy dataset, which consists of Advanced Laser Interferometer Gravitational-Wave Observatory (Advanced LIGO) transient noises with their associated metadata to discuss the potential for online or offline data analysis. In this study, focused on the Gravity Spy dataset, the training process of unsupervised-learning architecture of the previous study is examined and reported.

gr-qc↗

arXiv2022

Unsupervised Learning Architecture for Classifying the Transient Noise of Interferometric Gravitational-wave Detectors

In the data obtained by laser interferometric gravitational wave detectors, transient noise with non-stationary and non-Gaussian features occurs at a high rate. This often results in problems such as detector instability and the hiding and/or imitation of gravitational-wave signals. This transient noise has various characteristics in the time--frequency representation, which is considered to be associated with environmental and instrumental origins. Classification of transient noise can offer clues for exploring its origin and improving the performance of the detector. One approach for accomplishing this is supervised learning. However, in general, supervised learning requires annotation of the training data, and there are issues with ensuring objectivity in the classification and its corresponding new classes. By contrast, unsupervised learning can reduce the annotation work for the training data and ensure objectivity in the classification and its corresponding new classes. In this study, we propose an unsupervised learning architecture for the classification of transient noise that combines a variational autoencoder and invariant information clustering. To evaluate the effectiveness of the proposed architecture, we used the dataset (time--frequency two-dimensional spectrogram images and labels) of the Laser Interferometer Gravitational-wave Observatory (LIGO) first observation run prepared by the Gravity Spy project. The classes provided by our proposed unsupervised learning architecture were consistent with the labels annotated by the Gravity Spy project, which manifests the potential for the existence of unrevealed classes.

gr-qc↗

arXiv2022

Localization of gravitational waves using machine learning

An observation of gravitational waves is a trigger of the multi-messenger search of an astronomical event. A combination of the data from two or three gravitational wave telescopes indicates the location of a source and low-latency data analysis is key to transferring the information to other telescopes sensitive at different wavelengths. In contrast to the current method, which relies on the matched-filtering technique, we proposed the use of machine learning that is much faster and possibly more accurate than matched filtering. Our machine-learning method is a combination of the method proposed by Chatterjee {\it et al.} and a method using the temporal convolutional network. We demonstrate the sky localization of a gravitational-wave source using four telescopes: LIGO H1, LIGO L1, Virgo, and KAGRA, and compare the result in the case without KAGRA to examine the positive influence of having the fourth telescope in the global gravitational-wave network.

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