arXiv subjects

Takashi Matsubara

Publications and source records attributed to Takashi Matsubara.

30 records · Page 2Linked to original sources

arXiv2022

KAM Theory Meets Statistical Learning Theory: Hamiltonian Neural Networks with Non-Zero Training Loss

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.

math.DS↗

arXiv2021

An Error Analysis Framework for Neural Network Modeling of Dynamical Systems

We propose a theoretical framework for investigating a modeling error caused by numerical integration in the learning process of dynamics. Recently, learning equations of motion to describe dynamics from data using neural networks has been attracting attention. During such training, numerical integration is used to compare the data with the solution of the neural network model; however, discretization errors due to numerical integration prevent the model from being trained correctly. In this study, we formulate the modeling error using the Dahlquist test equation that is commonly used in the analysis of numerical methods and apply it to some of the Runge--Kutta methods.

math.NA↗

arXiv2021

Symplectic Adjoint Method for Exact Gradient of Neural ODE with Minimal Memory

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.

cs.LG↗

arXiv2021

ChartPointFlow for Topology-Aware 3D Point Cloud Generation

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.

cs.CV↗

arXiv2020

Deep Energy-Based Modeling of Discrete-Time Physics

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.

math.NA↗

arXiv2019

Target-Oriented Deformation of Visual-Semantic Embedding Space

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.

cs.CV↗

arXiv2019

Data Augmentation using Random Image Cropping and Patching for Deep CNNs

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.

cs.CV↗

arXiv2019

Generative adversarial network based on chaotic time series

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.

cs.LG↗

arXiv2019

Deep Neural Generative Model of Functional MRI Images for Psychiatric Disorder Diagnosis

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.

stat.ML↗

arXiv2019

A Novel Weight-Shared Multi-Stage CNN for Scale Robustness

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.

cs.CV↗

arXiv2019

Exploring Uncertainty Measures for Image-Caption Embedding-and-Retrieval Task

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.

cs.CV↗

arXiv2018

Deep Generative Model using Unregularized Score for Anomaly Detection with Heterogeneous Complexity

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.

cs.LG↗