arXiv subjects

Tian Wu

Publications and source records attributed to Tian Wu.

26 records · Page 2Linked to original sources

arXiv2025

Liouville theorem of the subcritical biharmonic equation on complete manifolds

In this paper, we study the subcritical biharmonic equation \[Δ^2 u=u^α\] on a complete, connected, and non-compact Riemannian manifold $(M^n,g)$ with nonnegative Ricci curvature. Using the method of invariant tensors, we derive a differential identity to obtain a Liouville theorem, i.e., there is no positive $C^4$ solution if $n\geqslant5$ and $1<α<\frac{n+4}{n-4}$. We establish a crucial second-order derivative estimate, which is established via Bernstein's technique and the continuity method.

math.AP↗

arXiv2025

Liouville theorems for anisotropic $p$-Laplace equations with a semilinear term

In this paper, we investigate Liouville theorems for solutions to the anisotropic $p$-Laplace equation $$-Δ_p^H u=-\operatorname{div}(a(\nabla u))=f(u),\quad\text{in }\mathbb{R}^n,$$ where the semilinear term $f$ may be positive, negative, or sign-changing. When $f$ is positive (negative) and satisfies certain conditions, Serrin's technique is applied to show that every positive supersolution (subsolution) must be constant. For the subcritical case, we use the invariant tensor method to prove nonexistence results for positive solutions. In particular, by applying the differential identity established in the subcritical case to the critical case, we provide a simplified new proof of the classification of positive solutions to the critical case $f(u)=u^{p^*-1}$. For sign-changing solutions, every stable solution or solution that is stable outside a compact set is trivial under certain conditions on $f$.

math.AP↗

arXiv2024

Jerison-Lee identity and Semi-linear subelliptic equation on CR manifold

In the study of the extremal for Sobolev inequality on the Heisenberg group and the Cauchy-Riemann(CR) Yamabe problem, Jerison-Lee found a three-dimensional family of differential identities for critical exponent subelliptic equation on Heisenberg group $\mathbb H^n$ by using the computer in [11]. They wanted to know whether there is a theoretical framework that would predict the existence and the structure of such formulae. With the help of dimensional conservation and invariant tensors, we can answer the above question. For a class of subcritical exponent subelliptic equations on the CR manifold, several new types of differential identities are found. Then we use those identities to get the rigidity result, where rigidity means that subelliptic equations have no other solution than some constant at least when parameters are in a certain range. The rigidity result also deduces the sharp Folland-Stein inequality on closed CR manifolds.

math.AP↗

arXiv2022

Documentation based Semantic-Aware Log Parsing

With the recent advances of deep learning techniques, there are rapidly growing interests in applying machine learning to log data. As a fundamental part of log analytics, accurate log parsing that transforms raw logs to structured events is critical for subsequent machine learning and data mining tasks. Previous approaches either analyze the source code for parsing or are data-driven such as text clustering. They largely neglect to exploit another widely available and valuable resource, software documentation that provides detailed explanations for the messages, to improve accuracy. In this paper, we propose an approach and system framework to use documentation knowledge for log parsing. With parameter value identification, it not only can improve the parsing accuracy for documented messages but also for undocumented messages. In addition, it can discover the linkages between event templates that are established by sharing parameters and indicate the correlation of the event context.

cs.SE↗

arXiv2021

ERNIE 3.0 Titan: Exploring Larger-scale Knowledge Enhanced Pre-training for Language Understanding and Generation

Pre-trained language models have achieved state-of-the-art results in various Natural Language Processing (NLP) tasks. GPT-3 has shown that scaling up pre-trained language models can further exploit their enormous potential. A unified framework named ERNIE 3.0 was recently proposed for pre-training large-scale knowledge enhanced models and trained a model with 10 billion parameters. ERNIE 3.0 outperformed the state-of-the-art models on various NLP tasks. In order to explore the performance of scaling up ERNIE 3.0, we train a hundred-billion-parameter model called ERNIE 3.0 Titan with up to 260 billion parameters on the PaddlePaddle platform. Furthermore, we design a self-supervised adversarial loss and a controllable language modeling loss to make ERNIE 3.0 Titan generate credible and controllable texts. To reduce the computation overhead and carbon emission, we propose an online distillation framework for ERNIE 3.0 Titan, where the teacher model will teach students and train itself simultaneously. ERNIE 3.0 Titan is the largest Chinese dense pre-trained model so far. Empirical results show that the ERNIE 3.0 Titan outperforms the state-of-the-art models on 68 NLP datasets.

cs.CL↗

arXiv2021

End-to-end Adaptive Distributed Training on PaddlePaddle

Distributed training has become a pervasive and effective approach for training a large neural network (NN) model with processing massive data. However, it is very challenging to satisfy requirements from various NN models, diverse computing resources, and their dynamic changes during a training job. In this study, we design our distributed training framework in a systematic end-to-end view to provide the built-in adaptive ability for different scenarios, especially for industrial applications and production environments, by fully considering resource allocation, model partition, task placement, and distributed execution. Based on the unified distributed graph and the unified cluster object, our adaptive framework is equipped with a global cost model and a global planner, which can enable arbitrary parallelism, resource-aware placement, multi-mode execution, fault-tolerant, and elastic distributed training. The experiments demonstrate that our framework can satisfy various requirements from the diversity of applications and the heterogeneity of resources with highly competitive performance. The ERNIE language model with 260 billion parameters is efficiently trained on thousands of AI processors with 91.7% weak scalability. The throughput of the model from the recommender system by employing the heterogeneous pipeline asynchronous execution can be increased up to 2.1 times and 3.3 times that of the GPU-only and CPU-only training respectively. Moreover, the fault-tolerant and elastic distributed training have been successfully applied to the online industrial applications, which give a reduction of 34.49% in the number of failed long-term training jobs and an increase of 33.91% for the global scheduling efficiency in the production environment.

cs.DC↗

arXiv2018

DuReader: a Chinese Machine Reading Comprehension Dataset from Real-world Applications

This paper introduces DuReader, a new large-scale, open-domain Chinese ma- chine reading comprehension (MRC) dataset, designed to address real-world MRC. DuReader has three advantages over previous MRC datasets: (1) data sources: questions and documents are based on Baidu Search and Baidu Zhidao; answers are manually generated. (2) question types: it provides rich annotations for more question types, especially yes-no and opinion questions, that leaves more opportunity for the research community. (3) scale: it contains 200K questions, 420K answers and 1M documents; it is the largest Chinese MRC dataset so far. Experiments show that human performance is well above current state-of-the-art baseline systems, leaving plenty of room for the community to make improvements. To help the community make these improvements, both DuReader and baseline systems have been posted online. We also organize a shared competition to encourage the exploration of more models. Since the release of the task, there are significant improvements over the baselines.

cs.CL↗

arXiv2018

Joint Training of Candidate Extraction and Answer Selection for Reading Comprehension

While sophisticated neural-based techniques have been developed in reading comprehension, most approaches model the answer in an independent manner, ignoring its relations with other answer candidates. This problem can be even worse in open-domain scenarios, where candidates from multiple passages should be combined to answer a single question. In this paper, we formulate reading comprehension as an extract-then-select two-stage procedure. We first extract answer candidates from passages, then select the final answer by combining information from all the candidates. Furthermore, we regard candidate extraction as a latent variable and train the two-stage process jointly with reinforcement learning. As a result, our approach has improved the state-of-the-art performance significantly on two challenging open-domain reading comprehension datasets. Further analysis demonstrates the effectiveness of our model components, especially the information fusion of all the candidates and the joint training of the extract-then-select procedure.

cs.CL↗