arXiv subjects

Toshiyuki Tanaka

Publications and source records attributed to Toshiyuki Tanaka.

At least 19 recordsLinked to original sources

arXiv2025

Neural Collapse in Cumulative Link Models for Ordinal Regression: An Analysis with Unconstrained Feature Model

A phenomenon known as ''Neural Collapse (NC)'' in deep classification tasks, in which the penultimate-layer features and the final classifiers exhibit an extremely simple geometric structure, has recently attracted considerable attention, with the expectation that it can deepen our understanding of how deep neural networks behave. The Unconstrained Feature Model (UFM) has been proposed to explain NC theoretically, and there emerges a growing body of work that extends NC to tasks other than classification and leverages it for practical applications. In this study, we investigate whether a similar phenomenon arises in deep Ordinal Regression (OR) tasks, via combining the cumulative link model for OR and UFM. We show that a phenomenon we call Ordinal Neural Collapse (ONC) indeed emerges and is characterized by the following three properties: (ONC1) all optimal features in the same class collapse to their within-class mean when regularization is applied; (ONC2) these class means align with the classifier, meaning that they collapse onto a one-dimensional subspace; (ONC3) the optimal latent variables (corresponding to logits or preactivations in classification tasks) are aligned according to the class order, and in particular, in the zero-regularization limit, a highly local and simple geometric relationship emerges between the latent variables and the threshold values. We prove these properties analytically within the UFM framework with fixed threshold values and corroborate them empirically across a variety of datasets. We also discuss how these insights can be leveraged in OR, highlighting the use of fixed thresholds.

cs.LG↗

arXiv2025

Approximate Modeling for Supercritical Galton-Watson Branching Processes with Compound Poisson-Gamma Distribution

We study asymptotic properties of supercritical Galton-Watson (GW) branching processes in the asymptotic where the mean of the offspring distribution approaches 1 from above. We show that the population-size distribution of the GW branching processes at a sufficiently large generation in this asymptotic can be approximated by a compound Poisson-gamma distribution. Numerical experiments revealed that the compound Poisson-gamma models were in good agreement with the corresponding GW models for sufficiently large generations under a reasonable parameter regime. Our results can be regarded as supporting the use of the compound Poisson-gamma model as a model for cascaded multiplication processes, such as detection signals of electron multipliers and population sizes of individuals with specific biological characteristics.

math.PR↗

arXiv2025

When resampling/reweighting improves feature learning in imbalanced classification?: A toy-model study

A toy model of binary classification is studied with the aim of clarifying the class-wise resampling/reweighting effect on the feature learning performance under the presence of class imbalance. In the analysis, a high-dimensional limit of the input space is taken while keeping the ratio of the dataset size against the input dimension finite and the non-rigorous replica method from statistical mechanics is employed. The result shows that there exists a case in which the no resampling/reweighting situation gives the best feature learning performance irrespectively of the choice of losses or classifiers, supporting recent findings in Cao et al. (2019); Kang et al. (2019). It is also revealed that the key of the result is the symmetry of the loss and the problem setting. Inspired by this, we propose a further simplified model exhibiting the same property in the multiclass setting. These clarify when the class-wise resampling/reweighting becomes effective in imbalanced classification.

stat.ML↗

arXiv2025

Universality of reservoir systems with recurrent neural networks

Approximation capability of reservoir systems whose reservoir is a recurrent neural network (RNN) is discussed. We show what we call uniform strong universality of RNN reservoir systems for a certain class of dynamical systems. This means that, given an approximation error to be achieved, one can construct an RNN reservoir system that approximates each target dynamical system in the class just via adjusting its linear readout. To show the universality, we construct an RNN reservoir system via parallel concatenation that has an upper bound of approximation error independent of each target in the class.

cs.NE↗

arXiv2024

Negative-prompt Inversion: Fast Image Inversion for Editing with Text-guided Diffusion Models

In image editing employing diffusion models, it is crucial to preserve the reconstruction fidelity to the original image while changing its style. Although existing methods ensure reconstruction fidelity through optimization, a drawback of these is the significant amount of time required for optimization. In this paper, we propose negative-prompt inversion, a method capable of achieving equivalent reconstruction solely through forward propagation without optimization, thereby enabling ultrafast editing processes. We experimentally demonstrate that the reconstruction fidelity of our method is comparable to that of existing methods, allowing for inversion at a resolution of 512 pixels and with 50 sampling steps within approximately 5 seconds, which is more than 30 times faster than null-text inversion. Reduction of the computation time by the proposed method further allows us to use a larger number of sampling steps in diffusion models to improve the reconstruction fidelity with a moderate increase in computation time.

cs.CV↗

arXiv2024

Harmonizing Attention: Training-free Texture-aware Geometry Transfer

Extracting geometry features from photographic images independently of surface texture and transferring them onto different materials remains a complex challenge. In this study, we introduce Harmonizing Attention, a novel training-free approach that leverages diffusion models for texture-aware geometry transfer. Our method employs a simple yet effective modification of self-attention layers, allowing the model to query information from multiple reference images within these layers. This mechanism is seamlessly integrated into the inversion process as Texture-aligning Attention and into the generation process as Geometry-aligning Attention. This dual-attention approach ensures the effective capture and transfer of material-independent geometry features while maintaining material-specific textural continuity, all without the need for model fine-tuning.

cs.CV↗

arXiv2024

Remarks on Loss Function of Threshold Method for Ordinal Regression Problem

Threshold methods are popular for ordinal regression problems, which are classification problems for data with a natural ordinal relation. They learn a one-dimensional transformation (1DT) of observations of the explanatory variable, and then assign label predictions to the observations by thresholding their 1DT values. In this paper, we study the influence of the underlying data distribution and of the learning procedure of the 1DT on the classification performance of the threshold method via theoretical considerations and numerical experiments. Consequently, for example, we found that threshold methods based on typical learning procedures may perform poorly when the probability distribution of the target variable conditioned on an observation of the explanatory variable tends to be non-unimodal. Another instance of our findings is that learned 1DT values are concentrated at a few points under the learning procedure based on a piecewise-linear loss function, which can make difficult to classify data well.

cs.LG↗

arXiv2024

Parallel Algorithm for Optimal Threshold Labeling of Ordinal Regression Methods

Ordinal regression (OR) is classification of ordinal data in which the underlying categorical target variable has a natural ordinal relation for the underlying explanatory variable. For $K$-class OR tasks, threshold methods learn a one-dimensional transformation (1DT) of the explanatory variable so that 1DT values for observations of the explanatory variable preserve the order of label values $1,\ldots,K$ for corresponding observations of the target variable well, and then assign a label prediction to the learned 1DT through threshold labeling, namely, according to the rank of an interval to which the 1DT belongs among intervals on the real line separated by $(K-1)$ threshold parameters. In this study, we propose a parallelizable algorithm to find the optimal threshold labeling, which was developed in previous research, and derive sufficient conditions for that algorithm to successfully output the optimal threshold labeling. In a numerical experiment we performed, the computation time taken for the whole learning process of a threshold method with the optimal threshold labeling could be reduced to approximately 60\,\% by using the proposed algorithm with parallel processing compared to using an existing algorithm based on dynamic programming.

cs.LG↗

arXiv2024

Spatio-temporal reconstruction of substance dynamics using compressed sensing in multi-spectral magnetic resonance spectroscopic imaging

The objective of our study is to observe dynamics of multiple substances in vivo with high temporal resolution from multi-spectral magnetic resonance spectroscopic imaging (MRSI) data. The multi-spectral MRSI can effectively separate spectral peaks of multiple substances and is useful to measure spatial distributions of substances. However it is difficult to measure time-varying substance distributions directly by ordinary full sampling because the measurement requires a significantly long time. In this study, we propose a novel method to reconstruct the spatio-temporal distributions of substances from randomly undersampled multi-spectral MRSI data on the basis of compressed sensing (CS) and the partially separable function model with base spectra of substances. In our method, we have employed spatio-temporal sparsity and temporal smoothness of the substance distributions as prior knowledge to perform CS. The effectiveness of our method has been evaluated using phantom data sets of glass tubes filled with glucose or lactate solution in increasing amounts over time and animal data sets of a tumor-bearing mouse to observe the metabolic dynamics involved in the Warburg effect in vivo. The reconstructed results are consistent with the expected behaviors, showing that our method can reconstruct the spatio-temporal distribution of substances with a temporal resolution of four seconds which is extremely short time scale compared with that of full sampling. Since this method utilizes only prior knowledge naturally assumed for the spatio-temporal distributions of substances and is independent of the number of the spectral and spatial dimensions or the acquisition sequence of MRSI, it is expected to contribute to revealing the underlying substance dynamics in MRSI data already acquired or to be acquired in the future.

eess.SP↗

arXiv2024

Convergence Analysis of Blurring Mean Shift

Blurring mean shift (BMS) algorithm, a variant of the mean shift algorithm, is a kernel-based iterative method for data clustering, where data points are clustered according to their convergent points via iterative blurring. In this paper, we analyze convergence properties of the BMS algorithm by leveraging its interpretation as an optimization procedure, which is known but has been underutilized in existing convergence studies. Whereas existing results on convergence properties applicable to multi-dimensional data only cover the case where all the blurred data point sequences converge to a single point, this study provides a convergence guarantee even when those sequences can converge to multiple points, yielding multiple clusters. This study also shows that the convergence of the BMS algorithm is fast by further leveraging geometrical characterization of the convergent points.

cs.LG↗

arXiv2023

Convergence Analysis of Mean Shift

The mean shift (MS) algorithm seeks a mode of the kernel density estimate (KDE). This study presents a convergence guarantee of the mode estimate sequence generated by the MS algorithm and an evaluation of the convergence rate, under fairly mild conditions, with the help of the argument concerning the Łojasiewicz inequality. Our findings extend existing ones covering analytic kernels and the Epanechnikov kernel. Those are significant in that they cover the biweight kernel, which is optimal among non-negative kernels in terms of the asymptotic statistical efficiency for the KDE-based mode estimation.

stat.ML↗

arXiv2023

Label Smoothing is Robustification against Model Misspecification

Label smoothing (LS) adopts smoothed targets in classification tasks. For example, in binary classification, instead of the one-hot target $(1,0)^\top$ used in conventional logistic regression (LR), LR with LS (LSLR) uses the smoothed target $(1-\fracα{2},\fracα{2})^\top$ with a smoothing level $α\in(0,1)$, which causes squeezing of values of the logit. Apart from the common regularization-based interpretation of LS that leads to an inconsistent probability estimator, we regard LSLR as modifying the loss function and consistent estimator for probability estimation. In order to study the significance of each of these two modifications by LSLR, we introduce a modified LSLR (MLSLR) that uses the same loss function as LSLR and the same consistent estimator as LR, while not squeezing the logits. For the loss function modification, we theoretically show that MLSLR with a larger smoothing level has lower efficiency with correctly-specified models, while it exhibits higher robustness against model misspecification than LR. Also, for the modification of the probability estimator, an experimental comparison between LSLR and MLSLR showed that this modification and squeezing of the logits in LSLR have negative effects on the probability estimation and classification performance. The understanding of the properties of LS provided by these comparisons allows us to propose MLSLR as an improvement over LSLR.

stat.ML↗

arXiv2023

Optimal Kernel for Kernel-Based Modal Statistical Methods

Kernel-based modal statistical methods include mode estimation, regression, and clustering. Estimation accuracy of these methods depends on the kernel used as well as the bandwidth. We study effect of the selection of the kernel function to the estimation accuracy of these methods. In particular, we theoretically show a (multivariate) optimal kernel that minimizes its analytically-obtained asymptotic error criterion when using an optimal bandwidth, among a certain kernel class defined via the number of its sign changes.

stat.ML↗

arXiv2022

Aggregated Multi-output Gaussian Processes with Knowledge Transfer Across Domains

Aggregate data often appear in various fields such as socio-economics and public security. The aggregate data are associated not with points but with supports (e.g., spatial regions in a city). Since the supports may have various granularities depending on attributes (e.g., poverty rate and crime rate), modeling such data is not straightforward. This article offers a multi-output Gaussian process (MoGP) model that infers functions for attributes using multiple aggregate datasets of respective granularities. In the proposed model, the function for each attribute is assumed to be a dependent GP modeled as a linear mixing of independent latent GPs. We design an observation model with an aggregation process for each attribute; the process is an integral of the GP over the corresponding support. We also introduce a prior distribution of the mixing weights, which allows a knowledge transfer across domains (e.g., cities) by sharing the prior. This is advantageous in such a situation where the spatially aggregated dataset in a city is too coarse to interpolate; the proposed model can still make accurate predictions of attributes by utilizing aggregate datasets in other cities. The inference of the proposed model is based on variational Bayes, which enables one to learn the model parameters using the aggregate datasets from multiple domains. The experiments demonstrate that the proposed model outperforms in the task of refining coarse-grained aggregate data on real-world datasets: Time series of air pollutants in Beijing and various kinds of spatial datasets from New York City and Chicago.

stat.ML↗

arXiv2020

Modelling Population III stars for semi-numerical simulations

Theoretically modelling the 21-cm signals caused by Population III stars (Pop III stars) is the key to extracting fruitful information on Pop III stars from current and forthcoming 21-cm observations. In this work we develop a new module of Pop III stars in which the escape fractions of ionizing photons and Lyman-Werner (LW) photons, photo-heating by UV radiation, and LW feedback are consistently incorporated. By implementing the module into a public 21-cm semi-numerical simulation code, 21CMFAST, we demonstrate 21-cm signal calculations and investigate the importance of Pop III star modelling. What we find is that the contribution from Pop III stars to cosmic reionization significantly depends on the treatment of the escape fraction. With our escape fraction model, Pop III stars hardly contribute to reionization because less massive halos, whose escape fraction are high, cannot host Pop III stars due to LW feedback. On the other hand, Pop III stars well contribute to reionization with the conventional constant escape fraction. We also find that UV photo-heating has non-negligible impact on the 21-cm global signal and the 21-cm power spectrum if the ionization fraction of the Universe is higher than roughly 1 percent. In this case, the strength of the 21-cm global signal depends on the photo-heating efficiency and thus on the Pop III star mass. We conclude that detailed modelling of Pop III stars is imperative to predict 21-cm observables accurately for future observations.

astro-ph.GA↗

arXiv2020

The 21-cm signals from ultracompact minihalos as a probe of primordial small-scale fluctuations

Ultracompact minihalos~(UCMHs) can form after the epoch of matter-radiation equality, if the density fluctuations of dark matter have significantly large amplitude on small scales. The constraint on the UCMH abundance allows us to access such small-scale fluctuations. In this paper, we present that, through the measurement of 21-cm fluctuations before the epoch of reionization~ we can obtain a constraint on the UCMH abundance. We calculate the 21-cm signal from UCMHs and show that UCMHs provide the enhancement of the 21-cm fluctuations. We also investigate the constraint on the UCMH abundance and small-scale curvature perturbations. Our results indicate that the upcoming 21-cm observation, the Square Kilometre Array (SKA), provides the constraint on amplitude of primordial curvature power spectrum, ${\cal A}_ζ \lesssim 10^{-6}$ on $100~{\rm Mpc}^{-1} \lesssim k \lesssim 1000~{\rm Mpc}^{-1}$. Although it is not stronger than the one from the non-detection of gamma rays induced by dark matter annihilation in UCMHs, the constraint by the SKA will be important because this constraint is independent of the dark matter particle model.

astro-ph.CO↗

arXiv2020

Linear algebraic structure of zero-determinant strategies in repeated games

Zero-determinant (ZD) strategies, a recently found novel class of strategies in repeated games, has attracted much attention in evolutionary game theory. A ZD strategy unilaterally enforces a linear relation between average payoffs of players. Although existence and evolutional stability of ZD strategies have been studied in simple games, their mathematical properties have not been well-known yet. For example, what happens when more than one players employ ZD strategies have not been clarified. In this paper, we provide a general framework for investigating situations where more than one players employ ZD strategies in terms of linear algebra. First, we theoretically prove that a set of linear relations of average payoffs enforced by ZD strategies always has solutions, which implies that incompatible linear relations are impossible. Second, we prove that linear payoff relations are independent of each other under some conditions. These results hold for general games with public monitoring including perfect-monitoring games. Furthermore, we provide a simple example of a two-player game in which one player can simultaneously enforce two linear relations, that is, simultaneously control her and her opponent's average payoffs. All of these results elucidate general mathematical properties of ZD strategies.

cs.GT↗

arXiv2020

Kernel Selection for Modal Linear Regression: Optimal Kernel and IRLS Algorithm

Modal linear regression (MLR) is a method for obtaining a conditional mode predictor as a linear model. We study kernel selection for MLR from two perspectives: "which kernel achieves smaller error?" and "which kernel is computationally efficient?". First, we show that a Biweight kernel is optimal in the sense of minimizing an asymptotic mean squared error of a resulting MLR parameter. This result is derived from our refined analysis of an asymptotic statistical behavior of MLR. Secondly, we provide a kernel class for which iteratively reweighted least-squares algorithm (IRLS) is guaranteed to converge, and especially prove that IRLS with an Epanechnikov kernel terminates in a finite number of iterations. Simulation studies empirically verified that using a Biweight kernel provides good estimation accuracy and that using an Epanechnikov kernel is computationally efficient. Our results improve MLR of which existing studies often stick to a Gaussian kernel and modal EM algorithm specialized for it, by providing guidelines of kernel selection.

stat.ML↗