Unsupervised Legendre-Galerkin Neural Network for Stiff Partial Differential Equations

Machine learning methods have been lately used to solve differential equations and dynamical systems. These approaches have been developed into a novel research field known as scientific machine learning in which techniques such as deep neural networks and statistical learning are applied to classical problems of applied mathematics. Because neural networks provide an approximation capability, computational parameterization through machine learning and optimization methods achieve noticeable performance when solving various partial differential equations (PDEs). In this paper, we develop a novel numerical algorithm that incorporates machine learning and artificial intelligence to solve PDEs. In particular, we propose an unsupervised machine learning algorithm based on the Legendre-Galerkin neural network to find an accurate approximation to the solution of different types of PDEs. The proposed neural network is applied to the general 1D and 2D PDEs as well as singularly perturbed PDEs that possess boundary layer behavior.Comment: 29 pages, 8 figure

Font Representation Learning via Paired-glyph Matching

Fonts can convey profound meanings of words in various forms of glyphs. Without typography knowledge, manually selecting an appropriate font or designing a new font is a tedious and painful task. To allow users to explore vast font styles and create new font styles, font retrieval and font style transfer methods have been proposed. These tasks increase the need for learning high-quality font representations. Therefore, we propose a novel font representation learning scheme to embed font styles into the latent space. For the discriminative representation of a font from others, we propose a paired-glyph matching-based font representation learning model that attracts the representations of glyphs in the same font to one another, but pushes away those of other fonts. Through evaluations on font retrieval with query glyphs on new fonts, we show our font representation learning scheme achieves better generalization performance than the existing font representation learning techniques. Finally on the downstream font style transfer and generation tasks, we confirm the benefits of transfer learning with the proposed method. The source code is available at https://github.com/junhocho/paired-glyph-matching.Comment: Accepted to BMVC202

Unified Contrastive Fusion Transformer for Multimodal Human Action Recognition

Various types of sensors have been considered to develop human action recognition (HAR) models. Robust HAR performance can be achieved by fusing multimodal data acquired by different sensors. In this paper, we introduce a new multimodal fusion architecture, referred to as Unified Contrastive Fusion Transformer (UCFFormer) designed to integrate data with diverse distributions to enhance HAR performance. Based on the embedding features extracted from each modality, UCFFormer employs the Unified Transformer to capture the inter-dependency among embeddings in both time and modality domains. We present the Factorized Time-Modality Attention to perform self-attention efficiently for the Unified Transformer. UCFFormer also incorporates contrastive learning to reduce the discrepancy in feature distributions across various modalities, thus generating semantically aligned features for information fusion. Performance evaluation conducted on two popular datasets, UTD-MHAD and NTU RGB+D, demonstrates that UCFFormer achieves state-of-the-art performance, outperforming competing methods by considerable margins

Large NN Superconformal Indices for 3d Holographic SCFTs

We study a limit of the superconformal index of the ABJM theory on $S^1\times S^2$ in which the size of the circle is much smaller than the radius of the two-sphere. We derive closed form expressions for the two leading terms in this Cardy-like limit which are valid to all orders in the $1/N$ expansion. These results are facilitated by a judicious rewriting of the superconformal index which establishes a connection with the Bethe Ansatz Equations that control the topologically twisted index. Using the same technique we extend these results to the superconformal index of another holographic theory: 3d $\mathcal{N}=4$ SYM coupled to one adjoint and $N_f$ fundamental hypermultiplets. We discuss the implications of our results for holography and the physics of charged rotating black holes in AdS$_4$.Comment: v1: 40 page

Bank partnership and liquidity crisis

This study empirically investigates the relationship between banking integration and liquidity management. To measure banks’ connectivity, we use the number of partnerships proxied via the syndicated loan arrangements in which they serve as lead arrangers. If banks establish more business partnerships through syndicated loan arrangements, those under market stress are more likely to face increased funding costs, create reduced liquidity, and originate declined small business loans and mortgages. Those banks with more partners are shown to have a lower liquidity coverage ratio, suggesting that business partnerships create a disincentive toward liquidity risk management

Identification of Cascading Failure Scenarios of Infrastructure Systems using Multi-Group Non-Dominant Sorting Algorithm

Power transmission networks are critical infrastructure systems of urban communities, but are prone to cascading failures due to their high level of interconnectivity. Therefore, it is of great interest to identify critical components of the network that may trigger cascading failures. However, existing approaches to identify critical cascading failures focus on topological effect for a limited number of initial component failures. Meanwhile, identification based on load flow analysis without a limit on the number of triggering component failures has not been extensively studied. In this study, we simulate the overload-induced cascading failures to find the most critical scenarios of initial failure events in a power grid. The proposed approach uses the multi-group non-dominant sorting algorithm (Choi and Song, 2017) with two objective functions, i.e. network impact measure, and the number of initial component failures. Numerical experiments on a 30-bus network demonstrate that the identified critical cascading scenarios, triggered by single and multiple component failures, may not share common components necessarily. The proposed approach is expected to identify a group of critical components, which may be neglected by existing approaches.The research was supported by the National Research Foundation of Korea (NRF) Grant (No. 2018M2A8A4052), funded by the Korean Government (MSIP)

CPO: Change Robust Panorama to Point Cloud Localization

We present CPO, a fast and robust algorithm that localizes a 2D panorama with respect to a 3D point cloud of a scene possibly containing changes. To robustly handle scene changes, our approach deviates from conventional feature point matching, and focuses on the spatial context provided from panorama images. Specifically, we propose efficient color histogram generation and subsequent robust localization using score maps. By utilizing the unique equivariance of spherical projections, we propose very fast color histogram generation for a large number of camera poses without explicitly rendering images for all candidate poses. We accumulate the regional consistency of the panorama and point cloud as 2D/3D score maps, and use them to weigh the input color values to further increase robustness. The weighted color distribution quickly finds good initial poses and achieves stable convergence for gradient-based optimization. CPO is lightweight and achieves effective localization in all tested scenarios, showing stable performance despite scene changes, repetitive structures, or featureless regions, which are typical challenges for visual localization with perspective cameras.Comment: Accepted to ECCV 202

Unsupervised Hyperbolic Representation Learning via Message Passing Auto-Encoders

Most of the existing literature regarding hyperbolic embedding concentrate upon supervised learning, whereas the use of unsupervised hyperbolic embedding is less well explored. In this paper, we analyze how unsupervised tasks can benefit from learned representations in hyperbolic space. To explore how well the hierarchical structure of unlabeled data can be represented in hyperbolic spaces, we design a novel hyperbolic message passing auto-encoder whose overall auto-encoding is performed in hyperbolic space. The proposed model conducts auto-encoding the networks via fully utilizing hyperbolic geometry in message passing. Through extensive quantitative and qualitative analyses, we validate the properties and benefits of the unsupervised hyperbolic representations. Codes are available at https://github.com/junhocho/HGCAE