Searcharxiv⌕ Search

arXiv subjects

Yukun Li

Publications and source records attributed to Yukun Li.

At least 37 records · Page 2Linked to original sources

CoLeCLIP: Open-Domain Continual Learning via Joint Task Prompt and Vocabulary Learning

This paper explores the problem of continual learning (CL) of vision-language models (VLMs) in open domains, where the models need to perform continual updating and inference on a streaming of datasets from diverse seen and unseen domains with novel classes. Such a capability is crucial for various applications in open environments, e.g., AI assistants, autonomous driving systems, and robotics. Current CL studies mostly focus on closed-set scenarios in a single domain with known classes. Large pre-trained VLMs like CLIP have demonstrated superior zero-shot recognition ability, and a number of recent studies leverage this ability to mitigate catastrophic forgetting in CL, but they focus on closed-set CL in a single domain dataset. Open-domain CL of large VLMs is significantly more challenging due to 1) large class correlations and domain gaps across the datasets and 2) the forgetting of zero-shot knowledge in the pre-trained VLMs in addition to the knowledge learned from the newly adapted datasets. In this work we introduce a novel approach, termed CoLeCLIP, that learns an open-domain CL model based on CLIP. It addresses these challenges by a joint learning of a set of task prompts and a cross-domain class vocabulary. Extensive experiments on 11 domain datasets show that CoLeCLIP outperforms state-of-the-art methods for open-domain CL under both task- and class-incremental learning settings.

cs.CV↗

Higher order time discretization method for a class of semilinear stochastic partial differential equations with multiplicative noise

In this paper, we consider a new approach for semi-discretization in time and spatial discretization of a class of semi-linear stochastic partial differential equations (SPDEs) with multiplicative noise. The drift term of the SPDEs is only assumed to satisfy a one-sided Lipschitz condition and the diffusion term is assumed to be globally Lipschitz continuous. Our new strategy for time discretization is based on the Milstein method from stochastic differential equations. We use the energy method for its error analysis and show a strong convergence order of nearly $1$ for the approximate solution. The proof is based on new Hölder continuity estimates of the SPDE solution and the nonlinear term. For the general polynomial-type drift term, there are difficulties in deriving even the stability of the numerical solutions. We propose an interpolation-based finite element method for spatial discretization to overcome the difficulties. Then we obtain $H^1$ stability, higher moment $H^1$ stability, $L^2$ stability, and higher moment $L^2$ stability results using numerical and stochastic techniques. The nearly optimal convergence orders in time and space are hence obtained by coupling all previous results. Numerical experiments are presented to implement the proposed numerical scheme and to validate the theoretical results.

math.NA↗

Analysis of a mixed finite element method for stochastic Cahn-Hilliard equation with multiplicative noise

This paper proposes and analyzes a novel fully discrete finite element scheme with the interpolation operator for stochastic Cahn-Hilliard equations with functional-type noise. The nonlinear term satisfies a one-side Lipschitz condition and the diffusion term is globally Lipschitz continuous. The novelties of this paper are threefold. First, the $L^2$-stability ($L^\infty$ in time) and the discrete $H^2$-stability ($L^2$ in time) are proved for the proposed scheme. The idea is to utilize the special structure of the matrix assembled by the nonlinear term. None of these stability results has been proved for the fully implicit scheme in existing literature due to the difficulty arising from the interaction of the nonlinearity and the multiplicative noise. Second, the higher moment stability in $L^2$-norm of the discrete solution is established based on the previous stability results. Third, the Hölder continuity in time for the strong solution is established under the minimum assumption of the strong solution. Based on these, the discrete $H^{-1}$-norm of the strong convergence is discussed. Several numerical experiments including stability and convergence are also presented to validate our theoretical results.

math.NA↗

NVDiff: Graph Generation through the Diffusion of Node Vectors

Learning to generate graphs is challenging as a graph is a set of pairwise connected, unordered nodes encoding complex combinatorial structures. Recently, several works have proposed graph generative models based on normalizing flows or score-based diffusion models. However, these models need to generate nodes and edges in parallel from the same process, whose dimensionality is unnecessarily high. We propose NVDiff, which takes the VGAE structure and uses a score-based generative model (SGM) as a flexible prior to sample node vectors. By modeling only node vectors in the latent space, NVDiff significantly reduces the dimension of the diffusion process and thus improves sampling speed. Built on the NVDiff framework, we introduce an attention-based score network capable of capturing both local and global contexts of graphs. Experiments indicate that NVDiff significantly reduces computations and can model much larger graphs than competing methods. At the same time, it achieves superior or competitive performances over various datasets compared to previous methods.

cs.LG↗

Fully discrete finite element methods for nonlinear stochastic elastic wave equations with multiplicative noise

This paper is concerned with fully discrete finite element methods for approximating variational solutions of nonlinear stochastic elastic wave equations with multiplicative noise. A detailed analysis of the properties of the weak solution is carried out and a fully discrete finite element method is proposed. Strong convergence in the energy norm with rate $\cal{O}(k+h^r)$ is proved, where $k$ and $h$ denote respectively the temporal and spatial mesh sizes, and $r(\geq 1)$ is the order of the finite element. Numerical experiments are provided to test the efficiency of proposed numerical methods and to validate the theoretical error estimate results.

math.NA↗

Pre-trained Language Model for Web-scale Retrieval in Baidu Search

Retrieval is a crucial stage in web search that identifies a small set of query-relevant candidates from a billion-scale corpus. Discovering more semantically-related candidates in the retrieval stage is very promising to expose more high-quality results to the end users. However, it still remains non-trivial challenges of building and deploying effective retrieval models for semantic matching in real search engine. In this paper, we describe the retrieval system that we developed and deployed in Baidu Search. The system exploits the recent state-of-the-art Chinese pretrained language model, namely Enhanced Representation through kNowledge IntEgration (ERNIE), which facilitates the system with expressive semantic matching. In particular, we developed an ERNIE-based retrieval model, which is equipped with 1) expressive Transformer-based semantic encoders, and 2) a comprehensive multi-stage training paradigm. More importantly, we present a practical system workflow for deploying the model in web-scale retrieval. Eventually, the system is fully deployed into production, where rigorous offline and online experiments were conducted. The results show that the system can perform high-quality candidate retrieval, especially for those tail queries with uncommon demands. Overall, the new retrieval system facilitated by pretrained language model (i.e., ERNIE) can largely improve the usability and applicability of our search engine.

cs.IR↗

Transferable Knowledge-Based Multi-Granularity Aggregation Network for Temporal Action Localization: Submission to ActivityNet Challenge 2021

This technical report presents an overview of our solution used in the submission to 2021 HACS Temporal Action Localization Challenge on both Supervised Learning Track and Weakly-Supervised Learning Track. Temporal Action Localization (TAL) requires to not only precisely locate the temporal boundaries of action instances, but also accurately classify the untrimmed videos into specific categories. However, Weakly-Supervised TAL indicates locating the action instances using only video-level class labels. In this paper, to train a supervised temporal action localizer, we adopt Temporal Context Aggregation Network (TCANet) to generate high-quality action proposals through ``local and global" temporal context aggregation and complementary as well as progressive boundary refinement. As for the WSTAL, a novel framework is proposed to handle the poor quality of CAS generated by simple classification network, which can only focus on local discriminative parts, rather than locate the entire interval of target actions. Further inspired by the transfer learning method, we also adopt an additional module to transfer the knowledge from trimmed videos (HACS Clips dataset) to untrimmed videos (HACS Segments dataset), aiming at promoting the classification performance on untrimmed videos. Finally, we employ a boundary regression module embedded with Outer-Inner-Contrastive (OIC) loss to automatically predict the boundaries based on the enhanced CAS. Our proposed scheme achieves 39.91 and 29.78 average mAP on the challenge testing set of supervised and weakly-supervised temporal action localization track respectively.

cs.CV↗

Finite Element Approximations of a Class of Nonlinear Stochastic Wave Equation with Multiplicative Noise

Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite element method for a class of nonlinear stochastic wave equations, where the diffusion term is globally Lipschitz continuous while the drift term is only assumed to satisfy weaker conditions as in [11]. The novelties of this paper are threefold. First, the error estimates cannot not be directly obtained if the numerical scheme in primal form is used. The numerical scheme in mixed form is introduced and several Hölder continuity results of the strong solution are proved, which are used to establish the error estimates in both $L^2$ norm and energy norms. Second, two types of discretization of the nonlinear term are proposed to establish the $L^2$ stability and energy stability results of the discrete solutions. These two types of discretization and proper test functions are designed to overcome the challenges arising from the stochastic scaling in time issues and the nonlinear interaction. These stability results play key roles in proving the probability of the set on which the error estimates hold approaches one. Third, higher order moment stability results of the discrete solutions are proved based on an energy argument and the underlying energy decaying property of the method. Numerical experiments are also presented to show the stability results of the discrete solutions and the convergence rates in various norms.

math.NA↗

Some algorithms for the mean curvature flow under topological changes

This paper considers and proposes some algorithms to compute the mean curvature flow under topological changes. Instead of solving the fully nonlinear partial differential equations based on the level set approach, we propose some minimization algorithms based on the phase field approach. It is well known that zero-level set of the Allen-Cahn equation approaches the mean curvature flow before the onset of the topological changes; however, there are few papers systematically studying the evolution of the mean curvature flow under the topological changes. There are three main contributions of this paper. First, in order to consider various random initial conditions, we design several benchmark problems with topological changes, and we find different patterns of the evolutions of the solutions can be obtained if the interaction length (width of the interface) is slightly changed, which is different from the problems without topological changes. Second, we propose an energy penalized minimization algorithm which works very well for these benchmark problems, and thus furthermore, for the problems with random initial conditions. Third, we propose a multilevel minimization algorithm. This algorithm is shown to be more tolerant of the unsatisfying initial guess when there are and there are no topological changes in the evolutions of the solutions.

math.NA↗

Analysis of adaptive two-grid finite element algorithms for linear and nonlinear problems

This paper proposes some efficient and accurate adaptive two-grid (ATG) finite element algorithms for linear and nonlinear partial differential equations (PDEs). The main idea of these algorithms is to utilize the solutions on the $k$-th level adaptive meshes to find the solutions on the $(k+1)$-th level adaptive meshes which are constructed by performing adaptive element bisections on the $k$-th level adaptive meshes. These algorithms transform non-symmetric positive definite (non-SPD) PDEs (resp., nonlinear PDEs) into symmetric positive definite (SPD) PDEs (resp., linear PDEs). The proposed algorithms are both accurate and efficient due to the following advantages: they do not need to solve the non-symmetric or nonlinear systems; the degrees of freedom (d.o.f.) are very small; they are easily implemented; the interpolation errors are very small. Next, this paper constructs residue-type {\em a posteriori} error estimators, which are shown to be reliable and efficient. The key ingredient in proving the efficiency is to establish an upper bound of the oscillation terms, which may not be higher-order terms (h.o.t.) due to the low regularity of the numerical solution. Furthermore, the convergence of the algorithms is proved when bisection is used for the mesh refinements. Finally, numerical experiments are provided to verify the accuracy and efficiency of the ATG finite element algorithms, compared to regular adaptive finite element algorithms and two-grid finite element algorithms [27].

math.NA↗

ERNIE-GEN: An Enhanced Multi-Flow Pre-training and Fine-tuning Framework for Natural Language Generation

Current pre-training works in natural language generation pay little attention to the problem of exposure bias on downstream tasks. To address this issue, we propose an enhanced multi-flow sequence to sequence pre-training and fine-tuning framework named ERNIE-GEN, which bridges the discrepancy between training and inference with an infilling generation mechanism and a noise-aware generation method. To make generation closer to human writing patterns, this framework introduces a span-by-span generation flow that trains the model to predict semantically-complete spans consecutively rather than predicting word by word. Unlike existing pre-training methods, ERNIE-GEN incorporates multi-granularity target sampling to construct pre-training data, which enhances the correlation between encoder and decoder. Experimental results demonstrate that ERNIE-GEN achieves state-of-the-art results with a much smaller amount of pre-training data and parameters on a range of language generation tasks, including abstractive summarization (Gigaword and CNN/DailyMail), question generation (SQuAD), dialogue generation (Persona-Chat) and generative question answering (CoQA).

cs.CL↗

ERNIE 2.0: A Continual Pre-training Framework for Language Understanding

Recently, pre-trained models have achieved state-of-the-art results in various language understanding tasks, which indicates that pre-training on large-scale corpora may play a crucial role in natural language processing. Current pre-training procedures usually focus on training the model with several simple tasks to grasp the co-occurrence of words or sentences. However, besides co-occurring, there exists other valuable lexical, syntactic and semantic information in training corpora, such as named entity, semantic closeness and discourse relations. In order to extract to the fullest extent, the lexical, syntactic and semantic information from training corpora, we propose a continual pre-training framework named ERNIE 2.0 which builds and learns incrementally pre-training tasks through constant multi-task learning. Experimental results demonstrate that ERNIE 2.0 outperforms BERT and XLNet on 16 tasks including English tasks on GLUE benchmarks and several common tasks in Chinese. The source codes and pre-trained models have been released at https://github.com/PaddlePaddle/ERNIE.

cs.CL↗

ERNIE: Enhanced Representation through Knowledge Integration

We present a novel language representation model enhanced by knowledge called ERNIE (Enhanced Representation through kNowledge IntEgration). Inspired by the masking strategy of BERT, ERNIE is designed to learn language representation enhanced by knowledge masking strategies, which includes entity-level masking and phrase-level masking. Entity-level strategy masks entities which are usually composed of multiple words.Phrase-level strategy masks the whole phrase which is composed of several words standing together as a conceptual unit.Experimental results show that ERNIE outperforms other baseline methods, achieving new state-of-the-art results on five Chinese natural language processing tasks including natural language inference, semantic similarity, named entity recognition, sentiment analysis and question answering. We also demonstrate that ERNIE has more powerful knowledge inference capacity on a cloze test.

cs.CL↗

Fully Discrete Mixed Finite Element Methods for the Stochastic Cahn-Hilliard Equation with Gradient-type Multiplicative Noise

This paper develops and analyzes some fully discrete mixed finite element methods for the stochastic Cahn-Hilliard equation with gradient-type multiplicative noise that is white in time and correlated in space. The stochastic Cahn-Hilliard equation is formally derived as a phase field formulation of the stochastically perturbed Hele-Shaw flow. The main result of this paper is to prove strong convergence with optimal rates for the proposed mixed finite element methods. To overcome the difficulty caused by the low regularity in time of the solution to the stochastic Cahn-Hilliard equation, the Hölder continuity in time with respect to various norms for the stochastic PDE solution is established, and it plays a crucial role in the error analysis. Numerical experiments are also provided to validate the theoretical results and to study the impact of noise on the Hele-Shaw flow as well as the interplay of the geometric evolution and gradient-type noise.

math.NA↗

Strong convergence of a fully discrete finite element method for a class of semilinear stochastic partial differential equations with multiplicative noise

This paper develops and analyzes a fully discrete finite element method for a class of semilinear stochastic partial differential equations (SPDEs) with multiplicative noise. The nonlinearity in the diffusion term of the SPDEs is assumed to be globally Lipschitz and the nonlinearity in the drift term is only assumed to satisfy a one-side Lipschitz condition. The semilinear SPDEs considered in this paper is a direct generalization of the SODEs considered in [13]. There are several difficulties which need to be overcome for this generalization. First, obviously the spatial discretization, which does not appear in the SODE case, adds an extra layer of difficulty. It turns out a special discretization must be designed to guarantee certain properties for the numerical scheme and its stiffness matrix. In this paper we use a finite element interpolation technique to discretize the nonlinear drift term. Second, in order to prove the strong convergence of the proposed fully discrete finite element method, stability estimates for higher order moments of the $H^1$-seminorm of the numerical solution must be established, which are difficult and delicate. A judicious combination of the properties of the drift and diffusion terms and a nontrivial technique borrowed from [16] is used in this paper to achieve the goal. Finally, stability estimates for the second and higher order moments of the $L^2$-norm of the numerical solution is also difficult to obtain due to the fact that the mass matrix may not be diagonally dominant. This is done by utilizing the interpolation theory and the higher moment estimates for the $H^1$-seminorm of the numerical solution. After overcoming these difficulties, it is proved that the proposed fully discrete finite element method is convergent in strong norms with nearly optimal rates of convergence.

math.NA↗

Energy Conserving Galerkin Approximation of Two Dimensional Wave Equations with Random Coefficients

Wave propagation problems for heterogeneous media are known to have many applications in physics and engineering. Recently, there has been an increasing interest in stochastic effects due to the uncertainty, which may arise from impurities of the media. This work considers a two-dimensional wave equation with random coefficients which may be discontinuous in space. Generalized polynomial chaos method is used in conjunction with stochastic Galerkin approximation, and local discontinuous Galerkin method is used for spatial discretization. Our method is shown to be energy preserving in semi-discrete form as well as in fully discrete form, when leap-frog time discretization is used. Its convergence rate is proved to be optimal and the error grows linearly in time. The theoretical properties of the proposed scheme are validated by numerical tests.

math.NA↗

Error analysis of a fully discrete Morley finite element approximation for the Cahn-Hilliard equation

This paper proposes and analyzes the Morley element method for the Cahn-Hilliard equation. It is a fourth order nonlinear singular perturbation equation arises from the binary alloy problem in materials science, and its limit is proved to approach the Hele-Shaw flow. If the $L^2(Ω)$ error estimate is considered directly as in paper \cite{elliott1989nonconforming}, we can only prove that the error bound depends on the exponential function of $\frac{1}ε$. Instead, this paper derives the error bound which depends on the polynomial function of $\frac{1}ε$ by considering the discrete $H^{-1}$ error estimate first. There are two main difficulties in proving this polynomial dependence of the discrete $H^{-1}$ error estimate. Firstly, it is difficult to prove discrete energy law and discrete stability results due to the complex structure of the bilinear form of the Morley element discretization. This paper overcomes this difficulty by defining four types of discrete inverse Laplace operators and exploring the relations between these discrete inverse Laplace operators and continuous inverse Laplace operator. Each of these operators plays important roles, and their relations are crucial in proving the discrete energy law, discrete stability results and error estimates. Secondly, it is difficult to prove the discrete spectrum estimate in the Morley element space because the Morley element space intersects with the $C^1$ conforming finite element space but they are not contained in each other. Instead of proving this discrete spectrum estimate in the Morley element space, this paper proves a generalized coercivity result by exploring properties of the enriching operators and using the discrete spectrum estimate in its $C^1$ conforming relative finite element space, which can be obtained by using the spectrum estimate of the Cahn-Hilliard operator.

math.NA↗

Analysis of the Morley element for the Cahn-Hilliard equation and the Hele-Shaw flow

The paper analyzes the Morley element method for the Cahn-Hilliard equation. The objective is to derive the optimal error estimates and to prove the zero-level sets of the Cahn-Hilliard equation approximate the Hele-Shaw flow. If the piecewise $L^{\infty}(H^2)$ error bound is derived by choosing test function directly, we cannot obtain the optimal error order, and we cannot establish the error bound which depends on $\frac{1}ε$ polynomially either. To overcome this difficulty, this paper proves them by the following steps, and the result in each next step cannot be established without using the result in its previous one. First, it proves some a priori estimates of the exact solution $u$, and these regularity results are minimal to get the main results; Second, it establishes ${L^{\infty}(L^2)}$ and piecewise ${L^2(H^2)}$ error bounds which depend on $\frac{1}ε$ polynomially based on the piecewise ${L^{\infty}(H^{-1})}$ and ${L^2(H^1)}$ error bounds; Third, it establishes piecewise ${L^{\infty}(H^2)}$ optimal error bound which depends on $\frac{1}ε$ polynomially based on the piecewise ${L^{\infty}(L^2)}$ and ${L^2(H^2)}$ error bounds; Finally, it proves the ${L^\infty(L^\infty)}$ error bound and the approximation to the Hele-Shaw flow based on the piecewise ${L^{\infty}(H^2)}$ error bound. The nonstandard techniques are used in these steps such as the generalized coercivity result, integration by part in space, summation by part in time, and special properties of the Morley elements. If one of these techniques is lacked, either we can only obtain the sub-optimal piecewise ${L^{\infty}(H^2)}$ error order, or we can merely obtain the error bounds which are exponentially dependent on $\frac{1}ε$. Numerical results are presented to validate the optimal $L^\infty(H^2)$ error order and the asymptotic behavior of the solutions of the Cahn-Hilliard equation.

math.NA↗