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Yu Deng

Publications and source records attributed to Yu Deng.

At least 91 records · Page 5Linked to original sources
arXiv2023

Full derivation of the wave kinetic equation

We provide the rigorous derivation of the wave kinetic equation from the cubic nonlinear Schrödinger (NLS) equation at the kinetic timescale, under a particular scaling law that describes the limiting process. This solves a main conjecture in the theory of wave turbulence, i.e. the kinetic theory of nonlinear wave systems. Our result is the wave analog of Lanford's theorem on the derivation of the Boltzmann kinetic equation from particle systems, where in both cases one takes the thermodynamic limit as the size of the system diverges to infinity, and as the interaction strength of waves or radius of particles vanishes to $0$, according to a particular scaling law (Boltzmann-Grad in the particle case). More precisely, in dimensions $d\geq 3$, we consider the (NLS) equation in a large box of size $L$ with a weak nonlinearity of strength $α$. In the limit $L\to\infty$ and $α\to 0$, under the scaling law $α\sim L^{-1}$, we show that the long-time behavior of (NLS) is statistically described by the wave kinetic equation, with well justified approximation, up to times that are $O(1)$ (i.e independent of $L$ and $α$) multiples of the kinetic timescale $T_{\text{kin}}\sim α^{-2}$. This is the first result of its kind for any nonlinear dispersive system.

math.AP↗
arXiv2022

On uniqueness and ill-posedness for the deautoconvolution problem in the multi-dimensional case

This paper analyzes the inverse problem of deautoconvolution in the multi-dimensional case with respect to solution uniqueness and ill-posedness. Deautoconvolution means here the reconstruction of a real-valued $L^2$-function with support in the $n$-dimensional unit cube $[0,1]^n$ from observations of its autoconvolution either in the full data case (i.e. on $[0,2]^n$) or in the limited data case (i.e. on $[0,1]^n$). Based on multi-dimensional variants of the Titchmarsh convolution theorem due to Lions and Mikusiński, we prove in the full data case a twofoldness assertion, and in the limited data case uniqueness of non-negative solutions for which the origin belongs to the support. The latter assumption is also shown to be necessary for any uniqueness statement in the limited data case. A glimpse of rate results for regularized solutions completes the paper.

math.NA↗
arXiv2022

Entity Set Co-Expansion in StackOverflow

Given a few seed entities of a certain type (e.g., Software or Programming Language), entity set expansion aims to discover an extensive set of entities that share the same type as the seeds. Entity set expansion in software-related domains such as StackOverflow can benefit many downstream tasks (e.g., software knowledge graph construction) and facilitate better IT operations and service management. Meanwhile, existing approaches are less concerned with two problems: (1) How to deal with multiple types of seed entities simultaneously? (2) How to leverage the power of pre-trained language models (PLMs)? Being aware of these two problems, in this paper, we study the entity set co-expansion task in StackOverflow, which extracts Library, OS, Application, and Language entities from StackOverflow question-answer threads. During the co-expansion process, we use PLMs to derive embeddings of candidate entities for calculating similarities between entities. Experimental results show that our proposed SECoExpan framework outperforms previous approaches significantly.

cs.CL↗
arXiv2022

Progressive Disentangled Representation Learning for Fine-Grained Controllable Talking Head Synthesis

We present a novel one-shot talking head synthesis method that achieves disentangled and fine-grained control over lip motion, eye gaze&blink, head pose, and emotional expression. We represent different motions via disentangled latent representations and leverage an image generator to synthesize talking heads from them. To effectively disentangle each motion factor, we propose a progressive disentangled representation learning strategy by separating the factors in a coarse-to-fine manner, where we first extract unified motion feature from the driving signal, and then isolate each fine-grained motion from the unified feature. We introduce motion-specific contrastive learning and regressing for non-emotional motions, and feature-level decorrelation and self-reconstruction for emotional expression, to fully utilize the inherent properties of each motion factor in unstructured video data to achieve disentanglement. Experiments show that our method provides high quality speech&lip-motion synchronization along with precise and disentangled control over multiple extra facial motions, which can hardly be achieved by previous methods.

cs.CV↗
arXiv2022

Deautoconvolution in the two-dimensional case

There is extensive mathematical literature on the inverse problem of deautoconvolution for a function with support in the unit interval $[0,1] \subset \mathbb R$, but little is known about the multidimensional situation. This article tries to fill this gap with analytical and numerical studies on the reconstruction of a real function of two real variables over the unit square from observations of its autoconvolution on $[0,2]^2 \subset \mathbb R^2$ (full data case) or on $[0,1]^2$ (limited data case). In an $L^2$-setting, twofoldness and uniqueness assertions are proven for the deautoconvolution problem in 2D. Moreover, its ill-posedness is characterized and illustrated. Extensive numerical case studies give an overview of the behaviour of stable approximate solutions to the two-dimensional deautoconvolution problem obtained by Tikhonov-type regularization with different penalties and the iteratively regularized Gauss-Newton method.

math.NA↗
arXiv2022

AniFaceGAN: Animatable 3D-Aware Face Image Generation for Video Avatars

Although 2D generative models have made great progress in face image generation and animation, they often suffer from undesirable artifacts such as 3D inconsistency when rendering images from different camera viewpoints. This prevents them from synthesizing video animations indistinguishable from real ones. Recently, 3D-aware GANs extend 2D GANs for explicit disentanglement of camera pose by leveraging 3D scene representations. These methods can well preserve the 3D consistency of the generated images across different views, yet they cannot achieve fine-grained control over other attributes, among which facial expression control is arguably the most useful and desirable for face animation. In this paper, we propose an animatable 3D-aware GAN for multiview consistent face animation generation. The key idea is to decompose the 3D representation of the 3D-aware GAN into a template field and a deformation field, where the former represents different identities with a canonical expression, and the latter characterizes expression variations of each identity. To achieve meaningful control over facial expressions via deformation, we propose a 3D-level imitative learning scheme between the generator and a parametric 3D face model during adversarial training of the 3D-aware GAN. This helps our method achieve high-quality animatable face image generation with strong visual 3D consistency, even though trained with only unstructured 2D images. Extensive experiments demonstrate our superior performance over prior works. Project page: https://yuewuhkust.github.io/AniFaceGAN

cs.CV↗
arXiv2022

Generative Deformable Radiance Fields for Disentangled Image Synthesis of Topology-Varying Objects

3D-aware generative models have demonstrated their superb performance to generate 3D neural radiance fields (NeRF) from a collection of monocular 2D images even for topology-varying object categories. However, these methods still lack the capability to separately control the shape and appearance of the objects in the generated radiance fields. In this paper, we propose a generative model for synthesizing radiance fields of topology-varying objects with disentangled shape and appearance variations. Our method generates deformable radiance fields, which builds the dense correspondence between the density fields of the objects and encodes their appearances in a shared template field. Our disentanglement is achieved in an unsupervised manner without introducing extra labels to previous 3D-aware GAN training. We also develop an effective image inversion scheme for reconstructing the radiance field of an object in a real monocular image and manipulating its shape and appearance. Experiments show that our method can successfully learn the generative model from unstructured monocular images and well disentangle the shape and appearance for objects (e.g., chairs) with large topological variance. The model trained on synthetic data can faithfully reconstruct the real object in a given single image and achieve high-quality texture and shape editing results.

cs.CV↗
arXiv2022

GRAM: Generative Radiance Manifolds for 3D-Aware Image Generation

3D-aware image generative modeling aims to generate 3D-consistent images with explicitly controllable camera poses. Recent works have shown promising results by training neural radiance field (NeRF) generators on unstructured 2D images, but still can not generate highly-realistic images with fine details. A critical reason is that the high memory and computation cost of volumetric representation learning greatly restricts the number of point samples for radiance integration during training. Deficient sampling not only limits the expressive power of the generator to handle fine details but also impedes effective GAN training due to the noise caused by unstable Monte Carlo sampling. We propose a novel approach that regulates point sampling and radiance field learning on 2D manifolds, embodied as a set of learned implicit surfaces in the 3D volume. For each viewing ray, we calculate ray-surface intersections and accumulate their radiance generated by the network. By training and rendering such radiance manifolds, our generator can produce high quality images with realistic fine details and strong visual 3D consistency.

cs.CV↗
arXiv2022

Rigorous justification of the wave kinetic theory

The main purpose of this expository note is to give a short account of the recent developments in mathematical wave kinetic theory. After reviewing the physical theory, we explain the importance of the notion of a scaling law, which dictates the relation between the asymptotic parameters as the kinetic limit is taken. This sets some natural limitations on the kinetic approximation that were not precisely understood in the literature as far as we know. We then describe our recent and upcoming works that give the first full, mathematically rigorous, derivation of the wave kinetic theory at the natural kinetic timescale. The key new ingredient is a delicate analysis of the diagrammatic expansion that allows to a) uncover highly elaborate cancellations at arbitrary large order of diagrams, and b) overcome difficulties coming from factorial divergences in the expansion and the criticality of the problem. The results mentioned in this note appear in our recent works [16, 17] as well as an upcoming one in [18].

math.AP↗
arXiv2022

All-optical spatio-temporal metrology for isolated attosecond pulses

Characterizing an isolated attosecond pulse (IAP) is essential for its potential applications. A complete characterization of an IAP ultimately requires the determination of its electric field in both time and space domains. However, previous methods, like the widely-used RABBITT and attosecond streaking, only measure the temporal profile of the attosecond pulse. Here we demonstrate an all-optical method for the measurement of the space-time properties of an IAP. By introducing a non-collinear perturbing pulse to the driving field, the process of IAP generation is modified both spatially and temporally, manifesting as a spatial and a frequency modulation in the harmonic spectrum. By using a FROG-like retrieval method, the spatio-spectral phases of the harmonic spectrum are faithfully extracted from the induced spatio-spectral modulations, which allows a thoroughgoing characterization of the IAP in both time and space. With this method, the spatio-temporal structures of the IAP generated in a two-color driving field in both the near- and far-field are fully reconstructed, from which a weak spatio-temporal coupling in the IAP generation is revealed. Our approach overcomes the limitation in the temporal measurement in conventional in situ scheme, providing a reliable and holistic metrology for IAP characterization.

physics.optics↗
arXiv2022

Invariant Gibbs measures for the three dimensional cubic nonlinear wave equation

We prove the invariance of the Gibbs measure under the dynamics of the three-dimensional cubic wave equation, which is also known as the hyperbolic $Φ^4_3$-model. This result is the hyperbolic counterpart to seminal works on the parabolic $Φ^4_3$-model by Hairer '14 and Hairer-Matetski '18. The heart of the matter lies in establishing local in time existence and uniqueness of solutions on the statistical ensemble, which is achieved by using a para-controlled Ansatz for the solution, the analytical framework of the random tensor theory, and the combinatorial molecule estimates. The singularity of the Gibbs measure with respect to the Gaussian free field brings out a new caloric representation of the Gibbs measure and a synergy between the parabolic and hyperbolic theories embodied in the analysis of heat-wave stochastic objects. Furthermore from a purely hyperbolic standpoint our argument relies on key new ingredients that include a hidden cancellation between sextic stochastic objects and a new bilinear random tensor estimate.

math.AP↗
arXiv2022

Evidence for quasi-two-dimensional superconductivity in infinite-layer nickelates

After being expected as a promising analogue to cuprates for decades, superconductivity was recently discovered in infinite-layer nickelates, providing new opportunities to explore mechanisms of high-temperature superconductivity. However, in sharp contrast to the single-band quasi-two-dimensional superconductivity in cuprates, nickelates exhibit a multi-band electronic structure and an unexpected isotropic superconductivity as reported recently, which challenges the cuprate-like picture in nickelates. Here, we show the superconductivity in nickelates is actually anisotropic and quasi-two-dimensional in nature, as that in cuprates. By synthesizing high-quality lanthanide nickelate films with enhanced crystallinity and superconductivity ($T_{c}^{onset}$ = 18.8 K, $T_{c}^{zero}$ = 16.5 K), strong anisotropic magnetotransport behaviors have been observed. The quasi-two-dimensional nature is further confirmed by the existence of a cusp-like peak of the angle-dependent $T_{c}$, and a Berezinskii-Kosterlitz-Thouless transition near $T_{c}$. Our work thus suggests a quasi-two-dimensional superconductivity in infinite-layer nickelates, implying a single-3$d_{x^2-y^2}$-band cuprate-like picture may remain valid in these compounds.

cond-mat.supr-con↗
arXiv2022

Propagation of chaos and the higher order statistics in the wave kinetic theory

This manuscript continues and extends in various directions the result in arXiv:2104.11204, which gave a full derivation of the wave kinetic equation (WKE) from the nonlinear Schrödinger (NLS) equation in dimensions $d\geq 3$. The wave kinetic equation describes the effective dynamics of the second moments of the Fourier modes of the NLS solution at the kinetic timescale, and in the kinetic limit in which the size of the system diverges to infinity and the strength of the nonlinearity vanishes asymptotically according to a specified scaling law. Here, we investigate the behavior of the joint distribution of these Fourier modes and derive their effective limit dynamics at the kinetic timescale. In particular, we prove propagation of chaos in the wave setting: initially independent Fourier modes retain this independence in the kinetic limit. Such statements are central to the formal derivations of all kinetic theories, dating back to the work of Boltzmann (Stosszahlansatz). We obtain this by deriving the asymptotics of the higher Fourier moments, which are given by solutions of the wave kinetic heirarchy (WKH) with factorized initial data. As a byproduct, we also provide a rigorous justification of this hierarchy for general (not necessarily factorized) initial data. We treat both Gaussian and non-Gaussian initial distributions. In the Gaussian setting, we prove propagation of Gaussianity as we show that the asymptotic distribution retains the Gaussianity of the initial data in the limit. In the non-Gaussian setting, we derive the limiting equations for the higher order moments, as well as for the density function (PDF) of the solution. Some of the results we prove were conjectured in the physics literature, others appear to be new. This gives a complete description of the statistics of the solutions in the kinetic limit.

math.AP↗
arXiv2022

Deep Learning in Human Activity Recognition with Wearable Sensors: A Review on Advances

Mobile and wearable devices have enabled numerous applications, including activity tracking, wellness monitoring, and human--computer interaction, that measure and improve our daily lives. Many of these applications are made possible by leveraging the rich collection of low-power sensors found in many mobile and wearable devices to perform human activity recognition (HAR). Recently, deep learning has greatly pushed the boundaries of HAR on mobile and wearable devices. This paper systematically categorizes and summarizes existing work that introduces deep learning methods for wearables-based HAR and provides a comprehensive analysis of the current advancements, developing trends, and major challenges. We also present cutting-edge frontiers and future directions for deep learning-based HAR.

cs.HC↗
arXiv2021

Natural language processing to identify lupus nephritis phenotype in electronic health records

Systemic lupus erythematosus (SLE) is a rare autoimmune disorder characterized by an unpredictable course of flares and remission with diverse manifestations. Lupus nephritis, one of the major disease manifestations of SLE for organ damage and mortality, is a key component of lupus classification criteria. Accurately identifying lupus nephritis in electronic health records (EHRs) would therefore benefit large cohort observational studies and clinical trials where characterization of the patient population is critical for recruitment, study design, and analysis. Lupus nephritis can be recognized through procedure codes and structured data, such as laboratory tests. However, other critical information documenting lupus nephritis, such as histologic reports from kidney biopsies and prior medical history narratives, require sophisticated text processing to mine information from pathology reports and clinical notes. In this study, we developed algorithms to identify lupus nephritis with and without natural language processing (NLP) using EHR data. We developed four algorithms: a rule-based algorithm using only structured data (baseline algorithm) and three algorithms using different NLP models. The three NLP models are based on regularized logistic regression and use different sets of features including positive mention of concept unique identifiers (CUIs), number of appearances of CUIs, and a mixture of three components respectively. The baseline algorithm and the best performed NLP algorithm were external validated on a dataset from Vanderbilt University Medical Center (VUMC). Our best performing NLP model incorporating features from both structured data, regular expression concepts, and mapped CUIs improved F measure in both the NMEDW (0.41 vs 0.79) and VUMC (0.62 vs 0.96) datasets compared to the baseline lupus nephritis algorithm.

cs.LG↗
arXiv2021

Technical Question Answering across Tasks and Domains

Building automatic technical support system is an important yet challenge task. Conceptually, to answer a user question on a technical forum, a human expert has to first retrieve relevant documents, and then read them carefully to identify the answer snippet. Despite huge success the researchers have achieved in coping with general domain question answering (QA), much less attentions have been paid for investigating technical QA. Specifically, existing methods suffer from several unique challenges (i) the question and answer rarely overlaps substantially and (ii) very limited data size. In this paper, we propose a novel framework of deep transfer learning to effectively address technical QA across tasks and domains. To this end, we present an adjustable joint learning approach for document retrieval and reading comprehension tasks. Our experiments on the TechQA demonstrates superior performance compared with state-of-the-art methods.

cs.CL↗
arXiv2021

Deformed Implicit Field: Modeling 3D Shapes with Learned Dense Correspondence

We propose a novel Deformed Implicit Field (DIF) representation for modeling 3D shapes of a category and generating dense correspondences among shapes. With DIF, a 3D shape is represented by a template implicit field shared across the category, together with a 3D deformation field and a correction field dedicated for each shape instance. Shape correspondences can be easily established using their deformation fields. Our neural network, dubbed DIF-Net, jointly learns a shape latent space and these fields for 3D objects belonging to a category without using any correspondence or part label. The learned DIF-Net can also provides reliable correspondence uncertainty measurement reflecting shape structure discrepancy. Experiments show that DIF-Net not only produces high-fidelity 3D shapes but also builds high-quality dense correspondences across different shapes. We also demonstrate several applications such as texture transfer and shape editing, where our method achieves compelling results that cannot be achieved by previous methods.

cs.CV↗