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Medical images and reports offer invaluable insights into patient health. The heterogeneity and complexity of these data hinder effective analysis. To bridge this gap, we investigate contrastive learning models for cross-domain retrieval, which associates medical images with their corresponding clinical reports. This study benchmarks the robustness of four state-of-the-art contrastive learning models: CLIP, CXR-RePaiR, MedCLIP, and CXR-CLIP. We introduce an occlusion retrieval task to evaluate model performance under varying levels of image corruption. Our findings reveal that all evaluated models are highly sensitive to out-of-distribution data, as evidenced by the proportional decrease in performance with increasing occlusion levels. While MedCLIP exhibits slightly more robustness, its overall performance remains significantly behind CXR-CLIP and CXR-RePaiR. CLIP, trained on a general-purpose dataset, struggles with medical image-report retrieval, highlighting the importance of domain-specific training data. The evaluation of this work suggests that more effort needs to be spent on improving the robustness of these models. By addressing these limitations, we can develop more reliable cross-domain retrieval models for medical applications., Comment: This work is accepted to AAAI 2025 Workshop -- the 9th International Workshop on Health Intelligence

Greedy algorithms, particularly the orthogonal greedy algorithm (OGA), have proven effective in training shallow neural networks for fitting functions and solving partial differential equations (PDEs). In this paper, we extend the application of OGA to the tasks of linear operator learning, which is equivalent to learning the kernel function through integral transforms. Firstly, a novel greedy algorithm is developed for kernel estimation rate in a new semi-inner product, which can be utilized to approximate the Green's function of linear PDEs from data. Secondly, we introduce the OGA for point-wise kernel estimation to further improve the approximation rate, achieving orders of accuracy improvement across various tasks and baseline models. In addition, we provide a theoretical analysis on the kernel estimation problem and the optimal approximation rates for both algorithms, establishing their efficacy and potential for future applications in PDEs and operator learning tasks.

Retrieval-augmented generation (RAG) has recently become a very popular task for Large Language Models (LLMs). Evaluating them on multi-turn RAG conversations, where the system is asked to generate a response to a question in the context of a preceding conversation is an important and often overlooked task with several additional challenges. We present MTRAG: an end-to-end human-generated multi-turn RAG benchmark that reflects several real-world properties across diverse dimensions for evaluating the full RAG pipeline. MTRAG contains 110 conversations averaging 7.7 turns each across four domains for a total of 842 tasks. We also explore automation paths via synthetic data and LLM-as-a-Judge evaluation. Our human and automatic evaluations show that even state-of-the-art LLM RAG systems struggle on MTRAG. We demonstrate the need for strong retrieval and generation systems that can handle later turns, unanswerable questions, non-standalone questions, and multiple domains. MTRAG is available at https://github.com/ibm/mt-rag-benchmark.

We present new convergence analyses for subspace correction methods for semicoercive and nearly semicoercive convex optimization problems, generalizing the theory of singular and nearly singular linear problems to the nonlinear domain. Our results demonstrate that the elegant theoretical framework developed for singular and nearly singular linear problems can be extended to semicoercive and nearly semicoercive convex optimization problems. For semicoercive problems, we show that the convergence rate can be estimated in terms of a seminorm stable decomposition over the subspaces and the kernel of the problem, aligning with the theory for singular linear problems. For nearly semicoercive problems, we establish a parameter-independent convergence rate, assuming the kernel of the semicoercive part can be decomposed into a sum of local kernels, which aligns with the theory for nearly singular problems. To demonstrate the applicability of our results, we provide convergence analyses of two-level additive Schwarz methods for solving a nonlinear Neumann boundary value problem and its perturbation within the proposed abstract framework., Comment: 30 pages, 0 figures

Research on manipulating materials using light has garnered significant interest, yet examples of controlling electronic polarization in magnetic materials remain scarce. Here, we demonstrate the hysteresis of electronic polarization in the antiferromagnetic semiconductor FePS3 via light. Below the N\'eel temperature, we observe linear dichroism (i.e., optical anisotropy) without structural symmetry breaking. Light-induced net polarization aligns along the a-axis (zigzag direction) at 1.6 eV due to the dipolar polarization and along the b-axis (armchair direction) at 2.0 eV due to the combined effects of dipolar and octupolar polarizations, resulting from charge transfer from the armchair to the zigzag direction by light. Unexpected hysteresis of the electronic polarization occurs at 2.0 eV due to the octupolar polarization, in contrast to the absence of such hysteresis at 1.6 eV. We attribute this to a symmetry breaking of the light-induced phase of FePS3 involving electronic polarization within the spin lattice. This study suggests a new mechanism for generating and controlling electronic polarization in magnetic materials using light, with implications for future device applications., Comment: 34 pages, 5 figures, 13 supplementary figures

Modern vehicles equip dashcams that primarily collect visual evidence for traffic accidents. However, most of the video data collected by dashcams that is not related to traffic accidents is discarded without any use. In this paper, we present a use case for dashcam videos that aims to improve driving safety. By analyzing the real-time videos captured by dashcams, we can detect driving hazards and driver distractedness to alert the driver immediately. To that end, we design and implement a Distributed Edge-based dashcam Video Analytics system (DEVA), that analyzes dashcam videos using personal edge (mobile) devices in a vehicle. DEVA consolidates available in-vehicle edge devices to maintain the resource pool, distributes video frames for analysis to devices considering resource availability in each device, and dynamically adjusts frame rates of dashcams to control the overall workloads. The entire video analytics task is divided into multiple independent phases and executed in a pipelined manner to improve the overall frame processing throughput. We implement DEVA in an Android app and also develop a dashcam emulation app to be used in vehicles that are not equipped with dashcams. Experimental results using the apps and commercial smartphones show that DEVA can process real-time videos from two dashcams with frame rates of around 22~30 FPS per camera within 200 ms of latency, using three high-end devices., Comment: Submitted to Elsevier Internet of Things

Extraction of hot carriers (HCs) over the band-edge is a key to harvest solar energy beyond Shockley-Queisser limit1. Graphene is known as a HC-layered material due to phonon bottleneck effect near Dirac point, but limited by low photocarrier density2. Graphene/transition metal dichalcogenide (TMD) heterostructures circumvent this issue by ultrafast carrier transfer from TMD to graphene2,3. Nevertheless, efficient extraction of photocurrent by means of HCs together with carrier multiplication (CM) is still missing. Here, we introduce an ultrathin broadband resonant tunneling (BRT) barrier, TiOX to efficiently extract photocurrent with simultaneous CM and HC measurements in MoS2/graphene/TiOX heterostructure. The BRT layer gives rise to boosting open circuit voltage which is linearly proportional to incident photon energy. Meanwhile, short circuit current rises rapidly over 2Eg with obvious CM feature. This was explained by defining the joint density of states between graphene and TiOX layer over positive and negative voltage. The broadband resonant tunneling states inherently constructed from oxidation states varying from Ti3+ to Ti4+ allow the ultrafast HCs to efficiently transfer from graphene to TiOX layer. We find that the number of available tunneling states is directly proportional to short circuit current, which is well corroborated with TiOX and MoS2 thickness variance. We obtained an optimum thickness of BRT layer of ~2.8 nm, yielding cascade open circuit voltage as high as ~0.7 V, two orders of magnitude higher than that without BRT layer to reach a record efficiency of 5.3% with improved fill factor owing to synergistic HC and CM conversion under 1-SUN with long-term stability.

Type Ia supernovae (SNe Ia) serve as the most crucial standardizable candles in cosmology, providing direct measurements of the universe's expansion history. However, it is well-known that the post-standardization brightness of SNe Ia is influenced by the properties of their host galaxies, such as mass and star formation rate, both of which are closely related to progenitor age. In this study, we reaffirm the ubiquitous and robust correlation between SN Ia luminosity and host age, showing that this host property dependence arises primarily from stellar population age of the host galaxy. This analysis was conducted using an expanded sample of over 300 hosts across a broad redshift range up to $z \sim 0.4$, ensuring sufficient statistical significance of the result. To quantify the relationship between host age and Hubble residual (HR), we employed two linear regression techniques: LINMIX, which assumes a Gaussian error, and Bayesian hierarchical linear regression, which utilizes a full posterior for the age error. Both models demonstrate a robust correlation between host age and HR, with high statistical significance approaching $5.5 \sigma$. While our new regression analyses yield the slopes that are similar or slightly shallower compared to our previous results, the significance of these slopes has notably increased. These findings robustly validate our previous suggestions that post-standardization SN Ia luminosity varies with progenitor age, which is currently not properly accounted for in SN cosmology., Comment: 13 pages, 10 figures, 2 tables. Submitted to ApJ

To increase social bonding with interlocutors, humans naturally acquire the ability to respond appropriately in a given situation by considering which conversational skill is most suitable for the response - a process we call skill-of-mind. For large language model (LLM)-based conversational agents, planning appropriate conversational skills, as humans do, is challenging due to the complexity of social dialogue, especially in interactive scenarios. To address this, we propose a skill-of-mind-annotated conversation dataset, named Multifaceted Skill-of-Mind, which includes multi-turn and multifaceted conversational skills across various interactive scenarios (e.g., long-term, counseling, task-oriented), grounded in diverse social contexts (e.g., demographics, persona, rules of thumb). This dataset consists of roughly 100K conversations. Using this dataset, we introduce a new family of skill-of-mind-infused LLMs, named Thanos, with model sizes of 1B, 3B, and 8B parameters. With extensive experiments, these models successfully demonstrate the skill-of-mind process and exhibit strong generalizability in inferring multifaceted skills across a variety of domains. Moreover, we show that Thanos significantly enhances the quality of responses generated by LLM-based conversational agents and promotes prosocial behavior in human evaluations., Comment: Code: https://github.com/passing2961/Thanos

We examined the double red clump (RC) observed in the Galactic bulge, interpreted as a difference in distance ("X-shaped bulge scenario") or in chemical composition ("multiple population scenario"). To verify chemical differences between the RC groups, we performed low-resolution spectroscopy for RC and red giant branch (RGB) stars using Gemini-South/GMOS in three fields of the bulge, and collected diverse data from literature. We divided our sample stars not only into bright and faint RC groups, but also into bluer ([Fe/H] < -0.1) and redder ([Fe/H] > -0.1) groups following the recent u-band photometric studies. For the metal-poor stars, no statistically significant difference in CN index was detected between the bright and faint RC groups for all observed fields. However, we found, from cross-matching with high-resolution spectroscopic data, a sign of Na enhancement in the "metal-poor and bright" RC group compared to the "metal-poor and faint" group at (l,b)=(-1 deg,-8.5 deg). When the contributions of the RGB stars on the RC regimes are taken into account, the Na abundance difference between genuine RCs would correspond to approximately 0.23 dex, similar to globular cluster (GCs) with multiple populations. In contrast, the metal-rich stars do not show chemical differences between the bright and faint RCs. It implies that the double RC observed in the metal-poor component of the bulge might be linked to the multiple populations originated from GC-like subsystem, whereas that of the metal-rich component would have produced by the X-shaped structure. Our results support the previous studies suggesting composite nature of the Milky Way bulge., Comment: Accepted for publication in ApJ

Context. With the increasing number of discoveries of globular clusters in the inner Milky Way, the need for spectroscopic confirmation and further investigation of their stellar populations and chemodynamical properties has become crucial. Aims. Gran 5 is a newly reported low-mass globular cluster located close to the Galactic center, and it is thought to be an accreted object associated with the Gaia-Enceladus structure. This study aims to investigate the stellar populations of Gran 5 and their detailed chemical properties. Methods. We performed high-resolution near-infrared spectroscopy on seven stars in the field of Gran 5 using IGRINS on the Gemini-South telescope. Results. We identified six stars as cluster members and reveal that they are divided into two stellar populations with different metallicities, with mean [Fe/H] values of -0.76 dex and -0.55 dex, respectively. In addition, the chemodynamical properties of Gran 5 agree with those of in situ globular clusters. Conclusions. Our findings represent the first detection of two stellar populations with different metallicities in a low-mass globular cluster. This suggests that the metallicity variation in Gran 5 may have arisen from processes different from those in other globular clusters with metallicity variation, or that it may have lost a substantial amount of its initial mass during its evolution., Comment: 12 pages, 9 figures, accepted for publication in A&A

Keyphrase ranking plays a crucial role in information retrieval and summarization by indexing and retrieving relevant information efficiently. Advances in natural language processing, especially large language models (LLMs), have improved keyphrase extraction and ranking. However, traditional methods often overlook diversity, resulting in redundant keyphrases. We propose a novel approach using Submodular Function Optimization (SFO) to balance relevance and diversity in keyphrase ranking. By framing the task as submodular maximization, our method selects diverse and representative keyphrases. Experiments on benchmark datasets show that our approach outperforms existing methods in both relevance and diversity metrics, achieving SOTA performance in execution time. Our code is available online.

The paper presents a priori error analysis of the shallow neural network approximation to the solution to the indefinite elliptic equation and and cutting-edge implementation of the Orthogonal Greedy Algorithm (OGA) tailored to overcome the challenges of indefinite elliptic problems, which is a domain where conventional approaches often struggle due to nontraditional difficulties due to the lack of coerciveness. A rigorous a priori error analysis that shows the neural networks ability to approximate indefinite problems is confirmed numerically by OGA methods. We also present a discretization error analysis of the relevant numerical quadrature. In particular, massive numerical implementations are conducted to justify the theory, some of which showcase the OGAs superior performance in comparison to the traditional finite element method. This advancement illustrates the potential of neural networks enhanced by OGA to solve intricate computational problems more efficiently, thereby marking a significant leap forward in the application of machine learning techniques to mathematical problem-solving., Comment: 17 pages

We study the formation of stars with varying amounts of heavy elements synthesized by the rapid neutron-capture process ($r$-process) based on our detailed cosmological zoom-in simulation of a Milky Way-like galaxy with an $N$-body/smoothed particle hydrodynamics code, ASURA. Most stars with no overabundance in $r$-process elements, as well as the strongly $r$-process enhanced $r$-II stars ([Eu/Fe] $>+0.7$), are formed in dwarf galaxies accreted by the Milky Way within the 6 Gyr after the Big Bang. In contrast, over half of the moderately enhanced $r$-I stars ($+0.3 <$ [Eu/Fe] $\leq +0.7$) are formed in the main in-situ disk after 6 Gyr. Our results suggest that the fraction of $r$-I and $r$-II stars formed in disrupted dwarf galaxies is larger the higher their [Eu/Fe] is. Accordingly, the most strongly enhanced $r$-III stars ([Eu/Fe] $> +2.0$) are formed in accreted components. These results suggest that non-$r$-process-enhanced stars and $r$-II stars are mainly formed in low-mass dwarf galaxies that hosted either none or a single neutron star merger, while the $r$-I stars tend to form in the well-mixed in-situ disk. We compare our findings with high-resolution spectroscopic observations of $r$-process-enhanced metal-poor stars in the halo and dwarf galaxies, including those collected by the R-Process Alliance. We conclude that observed [Eu/Fe] and [Eu/Mg] ratios can be employed in chemical tagging of the Milky Way's accretion history., Comment: 16 pages, 11 figures, submitted to ApJ

We mimic the conventional explicit Total Variation Diminishing Runge-Kutta (TVDRK) schemes and propose a class of numerical integrators to solve differential equations on a unit sphere. Our approach utilizes the exponential map inherent to the sphere and employs spherical linear interpolation (SLERP). These modified schemes, named SLERP-TVDRK methods or STVDRK, offer improved accuracy compared to typical projective RK methods. Furthermore, they eliminate the need for any projection and provide a straightforward implementation. While we have successfully constructed STVDRK schemes only up to third-order accuracy, we explain the challenges in deriving STVDRK-r for r \ge 4. To showcase the effectiveness of our approach, we will demonstrate its application in solving the eikonal equation on the unit sphere and simulating p-harmonic flows using our proposed method.

Recently, large language and vision models (LLVMs) have received significant attention and development efforts due to their remarkable generalization performance across a wide range of tasks requiring perception and cognitive abilities. A key factor behind their success is their simple architecture, which consists of a vision encoder, a projector, and a large language model (LLM). Despite their achievements in advanced reasoning tasks, their performance on fundamental perception-related tasks (e.g., MMVP) remains surprisingly low. This discrepancy raises the question of how LLVMs truly perceive images and exploit the advantages of the vision encoder. To address this, we systematically investigate this question regarding several aspects: permutation invariance, robustness, math reasoning, alignment preserving and importance, by evaluating the most common LLVM's families (i.e., LLaVA) across 10 evaluation benchmarks. Our extensive experiments reveal several intriguing properties of current LLVMs: (1) they internally process the image in a global manner, even when the order of visual patch sequences is randomly permuted; (2) they are sometimes able to solve math problems without fully perceiving detailed numerical information; (3) the cross-modal alignment is overfitted to complex reasoning tasks, thereby, causing them to lose some of the original perceptual capabilities of their vision encoder; (4) the representation space in the lower layers (<25%) plays a crucial role in determining performance and enhancing visual understanding. Lastly, based on the above observations, we suggest potential future directions for building better LLVMs and constructing more challenging evaluation benchmarks., Comment: Code is available in https://github.com/passing2961/IP-LLVM

In this paper, we explore the finite difference approximation of the fractional Laplace operator in conjunction with a neural network method for solving it. We discretized the fractional Laplace operator using the Riemann-Liouville formula relevant to fractional equations. A shallow neural network was constructed to address the discrete fractional operator, coupled with the OGA algorithm. To validate the feasibility of our approach, we conducted numerical experiments, testing both the Laplace operator and the fractional Laplace operator, yielding favorable convergence results., Comment: 15 pages

We consider the variational problem with a mass constraint arising from the two-dimensional dispersion managed nonlinear Schr\"odinger equation with power-law type nonlinearity. We prove a threshold phenomenon with respect to mass for the existence of minimizers for all possible powers of nonlinearities, including at the threshold itself. This threshold is closely related to the best constant for the Gagliardo-Nirenberg-Strichartz type inequality whose extremizers are found as a byproduct., Comment: 21 pages

We introduce a technique for multi-document grounded multi-turn synthetic dialog generation that incorporates three main ideas. First, we control the overall dialog flow using taxonomy-driven user queries that are generated with Chain-of-Thought (CoT) prompting. Second, we support the generation of multi-document grounded dialogs by mimicking real-world use of retrievers to update the grounding documents after every user-turn in the dialog. Third, we apply LLM-as-a-Judge to filter out queries with incorrect answers. Human evaluation of the synthetic dialog data suggests that the data is diverse, coherent, and includes mostly correct answers. Both human and automatic evaluations of answerable queries indicate that models fine-tuned on synthetic dialogs consistently out-perform those fine-tuned on existing human generated training data across four publicly available multi-turn document grounded benchmark test sets.

Atomically thin two-dimensional (2D) hexagonal boron nitride (hBN) has emerged as an essential material for the encapsulation layer in van der Waals heterostructures and efficient deep ultra-violet optoelectronics. This is primarily due to its remarkable physical properties and ultrawide bandgap (close to 6 eV, and even larger in some cases) properties. Color centers in hBN refer to intrinsic vacancies and extrinsic impurities within the 2D crystal lattice, which result in distinct optical properties in the ultraviolet (UV) to near-infrared (IR) range. Furthermore, each color center in hBN exhibits a unique emission spectrum and possesses various spin properties. These characteristics open up possibilities for the development of next-generation optoelectronics and quantum information applications, including room-temperature single-photon sources and quantum sensors. Here, we provide a comprehensive overview of the atomic configuration, optical and quantum properties, and different techniques employed for the formation of color centers in hBN. A deep understanding of color centers in hBN allows for advances in the development of next-generation UV optoelectronic applications, solid-state quantum technologies, and nanophotonics by harnessing the exceptional capabilities offered by hBN color centers.

Keyphrase Prediction (KP) is essential for identifying keyphrases in a document that can summarize its content. However, recent Natural Language Processing (NLP) advances have developed more efficient KP models using deep learning techniques. The limitation of a comprehensive exploration jointly both keyphrase extraction and generation using pre-trained language models spotlights a critical gap in the literature, compelling our survey paper to bridge this deficiency and offer a unified and in-depth analysis to address limitations in previous surveys. This paper extensively examines the topic of pre-trained language models for keyphrase prediction (PLM-KP), which are trained on large text corpora via different learning (supervisor, unsupervised, semi-supervised, and self-supervised) techniques, to provide respective insights into these two types of tasks in NLP, precisely, Keyphrase Extraction (KPE) and Keyphrase Generation (KPG). We introduce appropriate taxonomies for PLM-KPE and KPG to highlight these two main tasks of NLP. Moreover, we point out some promising future directions for predicting keyphrases.

We present a catalog of stellar parameters (effective temperature $T_{\rm eff}$, surface gravity $\log g$, age, and metallicity [Fe/H]) and elemental-abundance ratios ([C/Fe], [Mg/Fe], and [$\alpha$/Fe]) for some five million stars (4.5 million dwarfs and 0.5 million giants stars) in the Milky Way, based on stellar colors from the Javalambre Photometric Local Universe Survey (J-PLUS) DR3 and \textit{Gaia} EDR3. These estimates are obtained through the construction of a large spectroscopic training set with parameters and abundances adjusted to uniform scales, and trained with a Kernel Principal Component Analysis. Owing to the seven narrow/medium-band filters employed by J-PLUS, we obtain precisions in the abundance estimates that are as good or better than derived from medium-resolution spectroscopy for stars covering a wide range of the parameter space: 0.10-0.20 dex for [Fe/H] and [C/Fe], and 0.05 dex for [Mg/Fe] and [$\alpha$/Fe]. Moreover, systematic errors due to the influence of molecular carbon bands on previous photometric-metallicity estimates (which only included two narrow/medium-band blue filters) have now been removed, resulting in photometric-metallicity estimates down to [Fe/H] $\sim -4.0$, with typical uncertainties of 0.25 dex and 0.40 dex for dwarfs and giants, respectively. This large photometric sample should prove useful for the exploration of the assembly and chemical-evolution history of our Galaxy., Comment: 31 pages, 20 figures, 3 tables, accepeted by ApJ

Spin- and charge-lattice interactions are potential key factors in the microscopic mechanism of high-temperature superconductivity in cuprates. Although both interactions can dramatically shape the low-energy electronic structure, their phenomenological roles in superconductivity are usually investigated independently. Employing angle-resolved photoemission spectroscopy, we reveal the spectroscopic fingerprint of short-range antiferromagnetic order in conjunction with enhanced electron-phonon interaction in the electron-doped cuprate superconductor $\mathrm{Nd_{1.85}Ce_{0.15}CuO_4}$. The observed mode coupling exhibits a strong momentum dependence that is in striking contrast to the node-antinode dichotomy previously observed in the hole-doped cuprates. Our results reveal an intimate relationship between electron-phonon coupling and antiferromagnetic fluctuations, which collectively sets the stage for unconventional superconductivity in the electron-doped cuprates.

Syntactic elements, such as word order and case markers, are fundamental in natural language processing. Recent studies show that syntactic information boosts language model performance and offers clues for people to understand their learning mechanisms. Unlike languages with a fixed word order such as English, Korean allows for varied word sequences, despite its canonical structure, due to case markers that indicate the functions of sentence components. This study explores whether Korean language models can accurately capture this flexibility. We note that incomplete word orders and omitted case markers frequently appear in ordinary Korean communication. To investigate this further, we introduce the Syntactically Incomplete Korean (SIKO) dataset. Through SIKO, we assessed Korean language models' flexibility with incomplete syntax and confirmed the dataset's training value. Results indicate these models reflect Korean's inherent flexibility, accurately handling incomplete inputs. Moreover, fine-tuning with SIKO enhances the ability to handle common incomplete Korean syntactic forms. The dataset's simple construction process, coupled with significant performance enhancements, solidifies its standing as an effective data augmentation technique., Comment: COLM 2024; Code and dataset is available in https://github.com/grayapple-git/SIKO

Humans share a wide variety of images related to their personal experiences within conversations via instant messaging tools. However, existing works focus on (1) image-sharing behavior in singular sessions, leading to limited long-term social interaction, and (2) a lack of personalized image-sharing behavior. In this work, we introduce Stark, a large-scale long-term multi-modal conversation dataset that covers a wide range of social personas in a multi-modality format, time intervals, and images. To construct Stark automatically, we propose a novel multi-modal contextualization framework, Mcu, that generates long-term multi-modal dialogue distilled from ChatGPT and our proposed Plan-and-Execute image aligner. Using our Stark, we train a multi-modal conversation model, Ultron 7B, which demonstrates impressive visual imagination ability. Furthermore, we demonstrate the effectiveness of our dataset in human evaluation. We make our source code and dataset publicly available., Comment: Project website: https://stark-dataset.github.io

GreenLearning networks (GL) directly learn Green's function in physical space, making them an interpretable model for capturing unknown solution operators of partial differential equations (PDEs). For many PDEs, the corresponding Green's function exhibits asymptotic smoothness. In this paper, we propose a framework named Green Multigrid networks (GreenMGNet), an operator learning algorithm designed for a class of asymptotically smooth Green's functions. Compared with the pioneering GL, the new framework presents itself with better accuracy and efficiency, thereby achieving a significant improvement. GreenMGNet is composed of two technical novelties. First, Green's function is modeled as a piecewise function to take into account its singular behavior in some parts of the hyperplane. Such piecewise function is then approximated by a neural network with augmented output(AugNN) so that it can capture singularity accurately. Second, the asymptotic smoothness property of Green's function is used to leverage the Multi-Level Multi-Integration (MLMI) algorithm for both the training and inference stages. Several test cases of operator learning are presented to demonstrate the accuracy and effectiveness of the proposed method. On average, GreenMGNet achieves $3.8\%$ to $39.15\%$ accuracy improvement. To match the accuracy level of GL, GreenMGNet requires only about $10\%$ of the full grid data, resulting in a $55.9\%$ and $92.5\%$ reduction in training time and GPU memory cost for one-dimensional test problems, and a $37.7\%$ and $62.5\%$ reduction for two-dimensional test problems.

In this paper, we present Period Singer, a novel end-to-end singing voice synthesis (SVS) model that utilizes variational inference for periodic and aperiodic components, aimed at producing natural-sounding waveforms. Recent end-to-end SVS models have demonstrated the capability of synthesizing high-fidelity singing voices. However, owing to deterministic pitch conditioning, they do not fully address the one-to-many problem. To address this problem, we present the Period Singer architecture, which integrates variational autoencoders for the periodic and aperiodic components. Additionally, our methodology eliminates the dependency on an external aligner by estimating the phoneme alignment through a monotonic alignment search within note boundaries. Our empirical evaluations show that Period Singer outperforms existing end-to-end SVS models on Mandarin and Korean datasets. The efficacy of the proposed method was further corroborated by ablation studies., Comment: Accepted by Interspeech 2024