Takashi Matsubara

Nigel T. Andersen, Takashi Matsubara

Physics-Informed Neural Networks (PINNs) are a common class of machine learning-based partial differential equation (PDE) solvers which train a network to represent a solution by minimizing a residual loss that encodes the PDE. Despite their successes, they are known to fail on certain simple equations, converging to an incorrect solution despite low loss. These failure modes have garnered significant attention in the literature over the past several years, motivating both architectural and optimization based solutions. By directly visualizing the residual, we show that failure modes are the result of overfitting: the loss is minimized on the collocation points, but not elsewhere. Applying regularization causes the failure modes to vanish. Finally, we extend double backpropagation over the full set of residuals, and use it to achieve state-of-the-art performance on four standard failure mode equations with up to $23\times$ fewer collocation points and a vanilla architecture.

Zheng Chen, Ziwei Yang, Lingwei Zhu et al.

Defining and separating cancer subtypes is essential for facilitating personalized therapy modality and prognosis of patients. The definition of subtypes has been constantly recalibrated as a result of our deepened understanding. During this recalibration, researchers often rely on clustering of cancer data to provide an intuitive visual reference that could reveal the intrinsic characteristics of subtypes. The data being clustered are often omics data such as transcriptomics that have strong correlations to the underlying biological mechanism. However, while existing studies have shown promising results, they suffer from issues associated with omics data: sample scarcity and high dimensionality. As such, existing methods often impose unrealistic assumptions to extract useful features from the data while avoiding overfitting to spurious correlations. In this paper, we propose to leverage a recent strong generative model, Vector Quantized Variational AutoEncoder (VQ-VAE), to tackle the data issues and extract informative latent features that are crucial to the quality of subsequent clustering by retaining only information relevant to reconstructing the input. VQ-VAE does not impose strict assumptions and hence its latent features are better representations of the input, capable of yielding superior clustering performance with any mainstream clustering method. Extensive experiments and medical analysis on multiple datasets comprising 10 distinct cancers demonstrate the VQ-VAE clustering results can significantly and robustly improve prognosis over prevalent subtyping systems.

Takashi Matsubara, Takaharu Yaguchi

Many real-world dynamical systems are associated with first integrals (a.k.a. invariant quantities), which are quantities that remain unchanged over time. The discovery and understanding of first integrals are fundamental and important topics both in the natural sciences and in industrial applications. First integrals arise from the conservation laws of system energy, momentum, and mass, and from constraints on states; these are typically related to specific geometric structures of the governing equations. Existing neural networks designed to ensure such first integrals have shown excellent accuracy in modeling from data. However, these models incorporate the underlying structures, and in most situations where neural networks learn unknown systems, these structures are also unknown. This limitation needs to be overcome for scientific discovery and modeling of unknown systems. To this end, we propose first integral-preserving neural differential equation (FINDE). By leveraging the projection method and the discrete gradient method, FINDE finds and preserves first integrals from data, even in the absence of prior knowledge about underlying structures. Experimental results demonstrate that FINDE can predict future states of target systems much longer and find various quantities consistent with well-known first integrals in a unified manner.

Zheng Chen, Lingwei Zhu, Ziwei Yang et al.

Cancer subtyping is crucial for understanding the nature of tumors and providing suitable therapy. However, existing labelling methods are medically controversial, and have driven the process of subtyping away from teaching signals. Moreover, cancer genetic expression profiles are high-dimensional, scarce, and have complicated dependence, thereby posing a serious challenge to existing subtyping models for outputting sensible clustering. In this study, we propose a novel clustering method for exploiting genetic expression profiles and distinguishing subtypes in an unsupervised manner. The proposed method adaptively learns categorical correspondence from latent representations of expression profiles to the subtypes output by the model. By maximizing the problem -- agnostic mutual information between input expression profiles and output subtypes, our method can automatically decide a suitable number of subtypes. Through experiments, we demonstrate that our proposed method can refine existing controversial labels, and, by further medical analysis, this refinement is proven to have a high correlation with cancer survival rates.

Takehiro Aoshima, Takashi Matsubara

Semantic editing of images is the fundamental goal of computer vision. Although deep learning methods, such as generative adversarial networks (GANs), are capable of producing high-quality images, they often do not have an inherent way of editing generated images semantically. Recent studies have investigated a way of manipulating the latent variable to determine the images to be generated. However, methods that assume linear semantic arithmetic have certain limitations in terms of the quality of image editing, whereas methods that discover nonlinear semantic pathways provide non-commutative editing, which is inconsistent when applied in different orders. This study proposes a novel method called deep curvilinear editing (DeCurvEd) to determine semantic commuting vector fields on the latent space. We theoretically demonstrate that owing to commutativity, the editing of multiple attributes depends only on the quantities and not on the order. Furthermore, we experimentally demonstrate that compared to previous methods, the nonlinear and commutative nature of DeCurvEd facilitates the disentanglement of image attributes and provides higher-quality editing.

Haohui Jia, Zheng Chen, Lingwei Zhu et al.

Modeling neural population dynamics is crucial for foundational neuroscientific research and various clinical applications. Conventional latent variable methods typically model continuous brain dynamics through discretizing time with recurrent architecture, which necessarily results in compounded cumulative prediction errors and failure of capturing instantaneous, nonlinear characteristics of EEGs. We propose ODEBRAIN, a Neural ODE latent dynamic forecasting framework to overcome these challenges by integrating spatio-temporal-frequency features into spectral graph nodes, followed by a Neural ODE modeling the continuous latent dynamics. Our design ensures that latent representations can capture stochastic variations of complex brain states at any given time point. Extensive experiments verify that ODEBRAIN can improve significantly over existing methods in forecasting EEG dynamics with enhanced robustness and generalization capabilities.

Takashi Matsubara, Takaharu Yaguchi

Physics-informed neural networks solve partial differential equations by training neural networks. Since this method approximates infinite-dimensional PDE solutions with finite collocation points, minimizing discretization errors by selecting suitable points is essential for accelerating the learning process. Inspired by number theoretic methods for numerical analysis, we introduce good lattice training and periodization tricks, which ensure the conditions required by the theory. Our experiments demonstrate that GLT requires 2-7 times fewer collocation points, resulting in lower computational cost, while achieving competitive performance compared to typical sampling methods.

Haohui Jia, Zheng Chen, Lingwei Zhu et al.

Decoding brain activity from electroencephalography (EEG) is crucial for neuroscience and clinical applications. Among recent advances in deep learning for EEG, geometric learning stands out as its theoretical underpinnings on symmetric positive definite (SPD) allows revealing structural connectivity analysis in a physics-grounded manner. However, current SPD-based methods focus predominantly on statistical aggregation of EEGs, with frequency-specific synchronization and local topological structures of brain regions neglected. Given this, we propose RepSPD, a novel geometric deep learning (GDL)-based model. RepSPD implements a cross-attention mechanism on the Riemannian manifold to modulate the geometric attributes of SPD with graph-derived functional connectivity features. On top of this, we introduce a global bidirectional alignment strategy to reshape tangent-space embeddings, mitigating geometric distortions caused by curvature and thereby enhancing geometric consistency. Extensive experiments demonstrate that our proposed framework significantly outperforms existing EEG representation methods, exhibiting superior robustness and generalization capabilities.

Yeang Makara, Yusuke Tanaka, Takashi Matsubara et al.

The modeling and simulation of infinite-dimensional Hamiltonian systems are central problems in mathematical physics and engineering, however they pose significant computational and structural challenges for standard data-driven architectures. In this work, we introduce the Symplectic Neural Operator, a neural operator architecture designed to preserve the symplectic structure intrinsic to Hamiltonian PDEs. We provide a theoretical characterization of their symplecticity and establish a rigorous long-term stability result based on the combination of symplectic structure preservation and learning accuracy. Numerical experiments on canonical Hamiltonian PDEs corroborate this theoretical result and show that SNOs exhibit improved energy behavior compared with non-structure-preserving neural operators.

Kota Sueyoshi, Takashi Matsubara

Diffusion models have achieved remarkable results in generating high-quality, diverse, and creative images. However, when it comes to text-based image generation, they often fail to capture the intended meaning presented in the text. For instance, a specified object may not be generated, an unnecessary object may be generated, and an adjective may alter objects it was not intended to modify. Moreover, we found that relationships indicating possession between objects are often overlooked. While users' intentions in text are diverse, existing methods tend to specialize in only some aspects of these. In this paper, we propose Predicated Diffusion, a unified framework to express users' intentions. We consider that the root of the above issues lies in the text encoder, which often focuses only on individual words and neglects the logical relationships between them. The proposed method does not solely rely on the text encoder, but instead, represents the intended meaning in the text as propositions using predicate logic and treats the pixels in the attention maps as the fuzzy predicates. This enables us to obtain a differentiable loss function that makes the image fulfill the proposition by minimizing it. When compared to several existing methods, we demonstrated that Predicated Diffusion can generate images that are more faithful to various text prompts, as verified by human evaluators and pretrained image-text models.

Shinnosuke Saito, Takashi Matsubara

Diffusion models excel in content generation by implicitly learning the data manifold, yet they lack a practical method to leverage this manifold - unlike other deep generative models equipped with latent spaces. This paper introduces a novel framework that treats the data space of pre-trained diffusion models as a Riemannian manifold, with a metric derived from the score function. Experiments with MNIST and Stable Diffusion show that this geometry-aware approach yields image interpolations that are more realistic, less noisy, and more faithful to prompts than existing methods, demonstrating its potential for improved content generation and editing.

Yosuke Nishimoto, Takashi Matsubara

World models have been developed to support sample-efficient deep reinforcement learning agents. However, it remains challenging for world models to accurately replicate environments that are high-dimensional, non-stationary, and composed of multiple objects with rich interactions since most world models learn holistic representations of all environmental components. By contrast, humans perceive the environment by decomposing it into discrete objects, facilitating efficient decision-making. Motivated by this insight, we propose \emph{Slot Transformer Imagination with CAusality-aware reinforcement learning} (STICA), a unified framework in which object-centric Transformers serve as the world model and causality-aware policy and value networks. STICA represents each observation as a set of object-centric tokens, together with tokens for the agent action and the resulting reward, enabling the world model to predict token-level dynamics and interactions. The policy and value networks then estimate token-level cause--effect relations and use them in the attention layers, yielding causality-guided decision-making. Experiments on object-rich benchmarks demonstrate that STICA consistently outperforms state-of-the-art agents in both sample efficiency and final performance.

Daiki Yoshikawa, Takashi Matsubara

Vision-language models have achieved remarkable success in multi-modal representation learning from large-scale pairs of visual scenes and linguistic descriptions. However, they still struggle to simultaneously express two distinct types of semantic structures: the hierarchy within a concept family (e.g., dog $\preceq$ mammal $\preceq$ animal) and the compositionality across different concept families (e.g., "a dog in a car" $\preceq$ dog, car). Recent works have addressed this challenge by employing hyperbolic space, which efficiently captures tree-like hierarchy, yet its suitability for representing compositionality remains unclear. To resolve this dilemma, we propose PHyCLIP, which employs an $\ell_1$-Product metric on a Cartesian product of Hyperbolic factors. With our design, intra-family hierarchies emerge within individual hyperbolic factors, and cross-family composition is captured by the $\ell_1$-product metric, analogous to a Boolean algebra. Experiments on zero-shot classification, retrieval, hierarchical classification, and compositional understanding tasks demonstrate that PHyCLIP outperforms existing single-space approaches and offers more interpretable structures in the embedding space.

Shinnosuke Saito, Takashi Matsubara

Diffusion models are powerful deep generative models (DGMs) that generate high-fidelity, diverse content. However, unlike classical DGMs, they lack an explicit, tractable low-dimensional latent space that parameterizes the data manifold. This absence limits manifold-aware analysis and operations, such as interpolation and editing. Existing interpolation methods for diffusion models typically follow paths through high-density regions, which are not necessarily aligned with the data manifold and can yield perceptually unnatural transitions. To exploit the data manifold learned by diffusion models, we propose a novel Riemannian metric on the noise space, inspired by recent findings that the Jacobian of the score function captures the tangent spaces to the local data manifold. This metric encourages geodesics in the noise space to stay within or run parallel to the learned data manifold. Experiments on image interpolation show that our metric produces perceptually more natural and faithful transitions than existing density-based and naive baselines.

Baige Xu, Yusuke Tanaka, Takashi Matsubara et al.

In recent years, deep learning for modeling physical phenomena which can be described by partial differential equations (PDEs) have received significant attention. For example, for learning Hamiltonian mechanics, methods based on deep neural networks such as Hamiltonian Neural Networks (HNNs) and their variants have achieved progress. However, existing methods typically depend on the discretization of data, and the determination of required differential operators is often necessary. Instead, in this work, we propose an operator learning approach for modeling wave equations. In particular, we present a method to compute the variational derivatives that are needed to formulate the equations using the automatic differentiation algorithm. The experiments demonstrated that the proposed method is able to learn the operator that defines the Hamiltonian density of waves from data with unspecific discretization without determination of the differential operators.

Razmik Arman Khosrovian, Takaharu Yaguchi, Hiroaki Yoshimura et al.

Deep learning has achieved great success in modeling dynamical systems, providing data-driven simulators to predict complex phenomena, even without known governing equations. However, existing models have two major limitations: their narrow focus on mechanical systems and their tendency to treat systems as monolithic. These limitations reduce their applicability to dynamical systems in other domains, such as electrical and hydraulic systems, and to coupled systems. To address these limitations, we propose Poisson-Dirac Neural Networks (PoDiNNs), a novel framework based on the Dirac structure that unifies the port-Hamiltonian and Poisson formulations from geometric mechanics. This framework enables a unified representation of various dynamical systems across multiple domains as well as their interactions and degeneracies arising from couplings. Our experiments demonstrate that PoDiNNs offer improved accuracy and interpretability in modeling unknown coupled dynamical systems from data.

Yuhan Chen, Takashi Matsubara, Takaharu Yaguchi

Many physical phenomena are described by Hamiltonian mechanics using an energy function (the Hamiltonian). Recently, the Hamiltonian neural network, which approximates the Hamiltonian as a neural network, and its extensions have attracted much attention. This is a very powerful method, but its use in theoretical studies remains limited. In this study, by combining the statistical learning theory and Kolmogorov-Arnold-Moser (KAM) theory, we provide a theoretical analysis of the behavior of Hamiltonian neural networks when the learning error is not completely zero. A Hamiltonian neural network with non-zero errors can be considered as a perturbation from the true dynamics, and the perturbation theory of the Hamilton equation is widely known as the KAM theory. To apply the KAM theory, we provide a generalization error bound for Hamiltonian neural networks by deriving an estimate of the covering number of the gradient of the multi-layer perceptron, which is the key ingredient of the model. This error bound gives an $L^\infty$ bound on the Hamiltonian that is required in the application of the KAM theory.

Takashi Matsubara, Yuto Miyatake, Takaharu Yaguchi

A neural network model of a differential equation, namely neural ODE, has enabled the learning of continuous-time dynamical systems and probabilistic distributions with high accuracy. The neural ODE uses the same network repeatedly during a numerical integration. The memory consumption of the backpropagation algorithm is proportional to the number of uses times the network size. This is true even if a checkpointing scheme divides the computation graph into sub-graphs. Otherwise, the adjoint method obtains a gradient by a numerical integration backward in time. Although this method consumes memory only for a single network use, it requires high computational cost to suppress numerical errors. This study proposes the symplectic adjoint method, which is an adjoint method solved by a symplectic integrator. The symplectic adjoint method obtains the exact gradient (up to rounding error) with memory proportional to the number of uses plus the network size. The experimental results demonstrate that the symplectic adjoint method consumes much less memory than the naive backpropagation algorithm and checkpointing schemes, performs faster than the adjoint method, and is more robust to rounding errors.

Takumi Kimura, Takashi Matsubara, Kuniaki Uehara

A point cloud serves as a representation of the surface of a three-dimensional (3D) shape. Deep generative models have been adapted to model their variations typically using a map from a ball-like set of latent variables. However, previous approaches did not pay much attention to the topological structure of a point cloud, despite that a continuous map cannot express the varying numbers of holes and intersections. Moreover, a point cloud is often composed of multiple subparts, and it is also difficult to express. In this study, we propose ChartPointFlow, a flow-based generative model with multiple latent labels for 3D point clouds. Each label is assigned to points in an unsupervised manner. Then, a map conditioned on a label is assigned to a continuous subset of a point cloud, similar to a chart of a manifold. This enables our proposed model to preserve the topological structure with clear boundaries, whereas previous approaches tend to generate blurry point clouds and fail to generate holes. The experimental results demonstrate that ChartPointFlow achieves state-of-the-art performance in terms of generation and reconstruction compared with other point cloud generators. Moreover, ChartPointFlow divides an object into semantic subparts using charts, and it demonstrates superior performance in case of unsupervised segmentation.

Takashi Matsubara

Multimodal embedding is a crucial research topic for cross-modal understanding, data mining, and translation. Many studies have attempted to extract representations from given entities and align them in a shared embedding space. However, because entities in different modalities exhibit different abstraction levels and modality-specific information, it is insufficient to embed related entities close to each other. In this study, we propose the Target-Oriented Deformation Network (TOD-Net), a novel module that continuously deforms the embedding space into a new space under a given condition, thereby adjusting similarities between entities. Unlike methods based on cross-modal attention, TOD-Net is a post-process applied to the embedding space learned by existing embedding systems and improves their performances of retrieval. In particular, when combined with cutting-edge models, TOD-Net gains the state-of-the-art cross-modal retrieval model associated with the MSCOCO dataset. Qualitative analysis reveals that TOD-Net successfully emphasizes entity-specific concepts and retrieves diverse targets via handling higher levels of diversity than existing models.

Makoto Naruse, Takashi Matsubara, Nicolas Chauvet et al.

Generative adversarial network (GAN) is gaining increased importance in artificially constructing natural images and related functionalities wherein two networks called generator and discriminator are evolving through adversarial mechanisms. Using deep convolutional neural networks and related techniques, high-resolution, highly realistic scenes, human faces, among others have been generated. While GAN in general needs a large amount of genuine training data sets, it is noteworthy that vast amounts of pseudorandom numbers are required. Here we utilize chaotic time series generated experimentally by semiconductor lasers for the latent variables of GAN whereby the inherent nature of chaos can be reflected or transformed into the generated output data. We show that the similarity in proximity, which is a degree of robustness of the generated images with respects to a minute change in the input latent variables, is enhanced while the versatility as a whole is not severely degraded. Furthermore, we demonstrate that the surrogate chaos time series eliminates the signature of generated images that is originally observed corresponding to the negative autocorrelation inherent in the chaos sequence. We also discuss the impact of utilizing chaotic time series in retrieving images from the trained generator.

Takashi Matsubara, Ai Ishikawa, Takaharu Yaguchi

Physical phenomena in the real world are often described by energy-based modeling theories, such as Hamiltonian mechanics or the Landau theory, which yield various physical laws. Recent developments in neural networks have enabled the mimicking of the energy conservation law by learning the underlying continuous-time differential equations. However, this may not be possible in discrete time, which is often the case in practical learning and computation. Moreover, other physical laws have been overlooked in the previous neural network models. In this study, we propose a deep energy-based physical model that admits a specific differential geometric structure. From this structure, the conservation or dissipation law of energy and the mass conservation law follow naturally. To ensure the energetic behavior in discrete time, we also propose an automatic discrete differential algorithm that enables neural networks to employ the discrete gradient method.

Kenta Hama, Takashi Matsubara, Kuniaki Uehara et al.

With the wide development of black-box machine learning algorithms, particularly deep neural network (DNN), the practical demand for the reliability assessment is rapidly rising. On the basis of the concept that `Bayesian deep learning knows what it does not know,' the uncertainty of DNN outputs has been investigated as a reliability measure for the classification and regression tasks. However, in the image-caption retrieval task, well-known samples are not always easy-to-retrieve samples. This study investigates two aspects of image-caption embedding-and-retrieval systems. On one hand, we quantify feature uncertainty by considering image-caption embedding as a regression task, and use it for model averaging, which can improve the retrieval performance. On the other hand, we further quantify posterior uncertainty by considering the retrieval as a classification task, and use it as a reliability measure, which can greatly improve the retrieval performance by rejecting uncertain queries. The consistent performance of two uncertainty measures is observed with different datasets (MS COCO and Flickr30k), different deep learning architectures (dropout and batch normalization), and different similarity functions.

Ryo Takahashi, Takashi Matsubara, Kuniaki Uehara

Deep convolutional neural networks (CNNs) have achieved remarkable results in image processing tasks. However, their high expression ability risks overfitting. Consequently, data augmentation techniques have been proposed to prevent overfitting while enriching datasets. Recent CNN architectures with more parameters are rendering traditional data augmentation techniques insufficient. In this study, we propose a new data augmentation technique called random image cropping and patching (RICAP) which randomly crops four images and patches them to create a new training image. Moreover, RICAP mixes the class labels of the four images, resulting in an advantage similar to label smoothing. We evaluated RICAP with current state-of-the-art CNNs (e.g., the shake-shake regularization model) by comparison with competitive data augmentation techniques such as cutout and mixup. RICAP achieves a new state-of-the-art test error of $2.19\%$ on CIFAR-10. We also confirmed that deep CNNs with RICAP achieve better results on classification tasks using CIFAR-100 and ImageNet and an image-caption retrieval task using Microsoft COCO.

Takashi Matsubara, Kenta Hama, Ryosuke Tachibana et al.

Accurate and automated detection of anomalous samples in a natural image dataset can be accomplished with a probabilistic model for end-to-end modeling of images. Such images have heterogeneous complexity, however, and a probabilistic model overlooks simply shaped objects with small anomalies. This is because the probabilistic model assigns undesirably lower likelihoods to complexly shaped objects that are nevertheless consistent with set standards. To overcome this difficulty, we propose an unregularized score for deep generative models (DGMs), which are generative models leveraging deep neural networks. We found that the regularization terms of the DGMs considerably influence the anomaly score depending on the complexity of the samples. By removing these terms, we obtain an unregularized score, which we evaluated on a toy dataset and real-world manufacturing datasets. Empirical results demonstrate that the unregularized score is robust to the inherent complexity of samples and can be used to better detect anomalies.

Takashi Matsubara, Tetsuo Tashiro, Kuniaki Uehara

Accurate diagnosis of psychiatric disorders plays a critical role in improving the quality of life for patients and potentially supports the development of new treatments. Many studies have been conducted on machine learning techniques that seek brain imaging data for specific biomarkers of disorders. These studies have encountered the following dilemma: A direct classification overfits to a small number of high-dimensional samples but unsupervised feature-extraction has the risk of extracting a signal of no interest. In addition, such studies often provided only diagnoses for patients without presenting the reasons for these diagnoses. This study proposed a deep neural generative model of resting-state functional magnetic resonance imaging (fMRI) data. The proposed model is conditioned by the assumption of the subject's state and estimates the posterior probability of the subject's state given the imaging data, using Bayes' rule. This study applied the proposed model to diagnose schizophrenia and bipolar disorders. Diagnostic accuracy was improved by a large margin over competitive approaches, namely classifications of functional connectivity, discriminative/generative models of region-wise signals, and those with unsupervised feature-extractors. The proposed model visualizes brain regions largely related to the disorders, thus motivating further biological investigation.

Ryo Takahashi, Takashi Matsubara, Kuniaki Uehara

Convolutional neural networks (CNNs) have demonstrated remarkable results in image classification for benchmark tasks and practical applications. The CNNs with deeper architectures have achieved even higher performance recently thanks to their robustness to the parallel shift of objects in images as well as their numerous parameters and the resulting high expression ability. However, CNNs have a limited robustness to other geometric transformations such as scaling and rotation. This limits the performance improvement of the deep CNNs, but there is no established solution. This study focuses on scale transformation and proposes a network architecture called the weight-shared multi-stage network (WSMS-Net), which consists of multiple stages of CNNs. The proposed WSMS-Net is easily combined with existing deep CNNs such as ResNet and DenseNet and enables them to acquire robustness to object scaling. Experimental results on the CIFAR-10, CIFAR-100, and ImageNet datasets demonstrate that existing deep CNNs combined with the proposed WSMS-Net achieve higher accuracies for image classification tasks with only a minor increase in the number of parameters and computation time.