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Weiqiang Wang

Publications and source records attributed to Weiqiang Wang.

At least 217 records · Page 12Linked to original sources

Serre-Lusztig relations for $\imath$quantum groups III

let $\widetilde{\bf U}^\imath$ be a quasi-split universal $\imath$quantum group associated to a quantum symmetric pair $(\widetilde{\bf U}, \widetilde{\bf U}^\imath)$ of Kac-Moody type with a diagram involution $τ$. We establish the Serre-Lusztig relations for $\widetilde{\bf U}^\imath$ associated to a simple root $i$ such that $i \neq τi$, complementary to the Serre-Lusztig relations associated to $i=τi$ which we obtained earlier. A conjecture on braid group symmetries on $\widetilde{\bf U}^\imath$ associated to $i$ disjoint from $τi$ is formulated.

math.QA↗

Formulae of $\imath$-divided powers in ${\bf U}_q(\mathfrak{sl}_2)$, II

The coideal subalgebra of the quantum $\mathfrak{sl}_2$ is a polynomial algebra in a generator $t$ which depends on a parameter $κ$. The existence of the $\imath$-canonical basis (also known as the $\imath$-divided powers) for the coideal subalgebra of the quantum $\mathfrak{sl}_2$ were established by Bao and Wang. We establish closed formulae for the $\imath$-divided powers as polynomials in $t$ and also in terms of Chevalley generators of the quantum $\mathfrak{sl}_2$ when the parameter $κ$ is an arbitrary $q$-integer. The formulae were known earlier when $κ=0,1$.

math.RT↗

Explore Faster Localization Learning For Scene Text Detection

Generally pre-training and long-time training computation are necessary for obtaining a good-performance text detector based on deep networks. In this paper, we present a new scene text detection network (called FANet) with a Fast convergence speed and Accurate text localization. The proposed FANet is an end-to-end text detector based on transformer feature learning and normalized Fourier descriptor modeling, where the Fourier Descriptor Proposal Network and Iterative Text Decoding Network are designed to efficiently and accurately identify text proposals. Additionally, a Dense Matching Strategy and a well-designed loss function are also proposed for optimizing the network performance. Extensive experiments are carried out to demonstrate that the proposed FANet can achieve the SOTA performance with fewer training epochs and no pre-training. When we introduce additional data for pre-training, the proposed FANet can achieve SOTA performance on MSRATD500, CTW1500 and TotalText. The ablation experiments also verify the effectiveness of our contributions.

cs.CV↗

XYLayoutLM: Towards Layout-Aware Multimodal Networks For Visually-Rich Document Understanding

Recently, various multimodal networks for Visually-Rich Document Understanding(VRDU) have been proposed, showing the promotion of transformers by integrating visual and layout information with the text embeddings. However, most existing approaches utilize the position embeddings to incorporate the sequence information, neglecting the noisy improper reading order obtained by OCR tools. In this paper, we propose a robust layout-aware multimodal network named XYLayoutLM to capture and leverage rich layout information from proper reading orders produced by our Augmented XY Cut. Moreover, a Dilated Conditional Position Encoding module is proposed to deal with the input sequence of variable lengths, and it additionally extracts local layout information from both textual and visual modalities while generating position embeddings. Experiment results show that our XYLayoutLM achieves competitive results on document understanding tasks.

cs.CV↗

How to Inject Backdoors with Better Consistency: Logit Anchoring on Clean Data

Since training a large-scale backdoored model from scratch requires a large training dataset, several recent attacks have considered to inject backdoors into a trained clean model without altering model behaviors on the clean data. Previous work finds that backdoors can be injected into a trained clean model with Adversarial Weight Perturbation (AWP). Here AWPs refers to the variations of parameters that are small in backdoor learning. In this work, we observe an interesting phenomenon that the variations of parameters are always AWPs when tuning the trained clean model to inject backdoors. We further provide theoretical analysis to explain this phenomenon. We formulate the behavior of maintaining accuracy on clean data as the consistency of backdoored models, which includes both global consistency and instance-wise consistency. We extensively analyze the effects of AWPs on the consistency of backdoored models. In order to achieve better consistency, we propose a novel anchoring loss to anchor or freeze the model behaviors on the clean data, with a theoretical guarantee. Both the analytical and the empirical results validate the effectiveness of the anchoring loss in improving the consistency, especially the instance-wise consistency.

cs.LG↗

Variational Policy Propagation for Multi-agent Reinforcement Learning

We propose a \emph{collaborative} multi-agent reinforcement learning algorithm named variational policy propagation (VPP) to learn a \emph{joint} policy through the interactions over agents. We prove that the joint policy is a Markov Random Field under some mild conditions, which in turn reduces the policy space effectively. We integrate the variational inference as special differentiable layers in policy such that the actions can be efficiently sampled from the Markov Random Field and the overall policy is differentiable. We evaluate our algorithm on several large scale challenging tasks and demonstrate that it outperforms previous state-of-the-arts.

cs.LG↗

MT-GBM: A Multi-Task Gradient Boosting Machine with Shared Decision Trees

Despite the success of deep learning in computer vision and natural language processing, Gradient Boosted Decision Tree (GBDT) is yet one of the most powerful tools for applications with tabular data such as e-commerce and FinTech. However, applying GBDT to multi-task learning is still a challenge. Unlike deep models that can jointly learn a shared latent representation across multiple tasks, GBDT can hardly learn a shared tree structure. In this paper, we propose Multi-task Gradient Boosting Machine (MT-GBM), a GBDT-based method for multi-task learning. The MT-GBM can find the shared tree structures and split branches according to multi-task losses. First, it assigns multiple outputs to each leaf node. Next, it computes the gradient corresponding to each output (task). Then, we also propose an algorithm to combine the gradients of all tasks and update the tree. Finally, we apply MT-GBM to LightGBM. Experiments show that our MT-GBM improves the performance of the main task significantly, which means the proposed MT-GBM is efficient and effective.

cs.LG↗

Lectures on dualities ABC in representation theory

In these lecture notes for a summer mini-course, we provide an exposition on quantum groups and Hecke algebras, including (quasi) R-matrix, canonical basis, and $q$-Schur duality. Then we formulate their counterparts in the setting of $\imath$quantum groups arising from quantum symmetric pairs, including (quasi) K-matrix, $\imath$-canonical basis, and $\imath$Schur duality. As an application, the ($\imath$-)canonical bases are used to formulate Kazhdan-Lusztig theories and character formulas in the BGG categories for Lie (super)algebras of type A-D. Finally, geometric constructions for $q$-Schur and $\imath$Schur dualities are provided.

math.RT↗

Vacuum and singularity formation for compressible Euler equations with time-dependent damping

In this paper, vacuum and singularity formation are considered for compressible Euler equations with time-dependent damping. For $1<γ\leq 3$, by constructing some new control functions ingeniously, we obtain the lower bounds estimates on density for arbitrary classical solutions. Basing on these lower estimates, we succeed in proving the singular formation theorem for all $λ$, which was open in [1] for some cases.Moreover, the singularity formation of the compressible Euler equations when $γ=3$ is investigated, too.

math.AP↗

PBW bases for modified quantum groups

We construct a basis for a modified quantum group of finite type, extending the PBW bases of positive and negative halves of a quantum group. Generalizing Lusztig's classic results on PBW bases, we show that this basis is orthogonal with respect to its natural bilinear form (and hence called a PBW basis), and moreover, the matrix for the PBW-expansion of the canonical basis is unital triangular. All these follow by a new construction of the modified quantum group of arbitrary type, which is built on limits of sequences of elements in tensor products of lowest and highest weight modules. Explicitly formulas are worked out in the rank one case.

math.RT↗

Hall algebras and quantum symmetric pairs III: Quiver varieties

The $\imath$quiver algebras were introduced recently by the authors to provide a Hall algebra realization of universal $\imath$quantum groups, which is a generalization of Bridgeland's Hall algebra construction for (Drinfeld doubles of) quantum groups; here an $\imath$quantum group and a corresponding Drinfeld-Jimbo quantum group form a quantum symmetric pair. In this paper, the Dynkin $\imath$quiver algebras are shown to arise as new examples of singular Nakajima-Keller-Scherotzke categories. Then we provide a geometric construction of the universal $\imath$quantum groups and their ``dual canonical bases" with positivity, via the quantum Grothendieck rings of Nakajima-Keller-Scherotzke quiver varieties, generalizing Qin's geometric realization of quantum groups of type ADE.

math.RT↗

A Drinfeld type presentation of affine $\imath$quantum groups I: split ADE type

We establish a Drinfeld type new presentation for the $\imath$quantum groups arising from quantum symmetric pairs of split affine ADE type, which includes the $q$-Onsager algebra as the rank 1 case. This presentation takes a form which can be viewed as a deformation of half an affine quantum group in the Drinfeld presentation.

math.RT↗

GraFormer: Graph Convolution Transformer for 3D Pose Estimation

Exploiting relations among 2D joints plays a crucial role yet remains semi-developed in 2D-to-3D pose estimation. To alleviate this issue, we propose GraFormer, a novel transformer architecture combined with graph convolution for 3D pose estimation. The proposed GraFormer comprises two repeatedly stacked core modules, GraAttention and ChebGConv block. GraAttention enables all 2D joints to interact in global receptive field without weakening the graph structure information of joints, which introduces vital features for later modules. Unlike vanilla graph convolutions that only model the apparent relationship of joints, ChebGConv block enables 2D joints to interact in the high-order sphere, which formulates their hidden implicit relations. We empirically show the superiority of GraFormer through conducting extensive experiments across popular benchmarks. Specifically, GraFormer outperforms state of the art on Human3.6M dataset while using 18$\%$ parameters. The code is available at https://github.com/Graformer/GraFormer .

cs.CV↗

SHORING: Design Provable Conditional High-Order Interaction Network via Symbolic Testing

Deep learning provides a promising way to extract effective representations from raw data in an end-to-end fashion and has proven its effectiveness in various domains such as computer vision, natural language processing, etc. However, in domains such as content/product recommendation and risk management, where sequence of event data is the most used raw data form and experts derived features are more commonly used, deep learning models struggle to dominate the game. In this paper, we propose a symbolic testing framework that helps to answer the question of what kinds of expert-derived features could be learned by a neural network. Inspired by this testing framework, we introduce an efficient architecture named SHORING, which contains two components: \textit{event network} and \textit{sequence network}. The \textit{event} network learns arbitrarily yet efficiently high-order \textit{event-level} embeddings via a provable reparameterization trick, the \textit{sequence} network aggregates from sequence of \textit{event-level} embeddings. We argue that SHORING is capable of learning certain standard symbolic expressions which the standard multi-head self-attention network fails to learn, and conduct comprehensive experiments and ablation studies on four synthetic datasets and three real-world datasets. The results show that SHORING empirically outperforms the state-of-the-art methods.

cs.LG↗

Hall algebras and quantum symmetric pairs I: foundations

A quantum symmetric pair consists of a quantum group $\mathbf U$ and its coideal subalgebra ${\mathbf U}^{\imath}_{\boldsymbolς}$ with parameters $\boldsymbolς$ (called an $\imath$quantum group). We initiate a Hall algebra approach for the categorification of $\imath$quantum groups. A universal $\imath$quantum group $\widetilde{\mathbf U}^{\imath}$ is introduced and ${\mathbf U}^{\imath}_{\boldsymbolς}$ is recovered by a central reduction of $\widetilde{\mathbf U}^{\imath}$. The semi-derived Ringel-Hall algebras of the first author and Peng, which are closely related to semi-derived Hall algebras of Gorsky and motivated by Bridgeland's work, are extended to the setting of 1-Gorenstein algebras, as shown in Appendix A by the first author. A new class of 1-Gorenstein algebras (called $\imath$quiver algebras) arising from acyclic quivers with involutions is introduced. The semi-derived Ringel-Hall algebras for the Dynkin $\imath$quiver algebras are shown to be isomorphic to the universal quasi-split $\imath$quantum groups of finite type. Monomial bases and PBW bases for these Hall algebras and $\imath$quantum groups are constructed.

math.RT↗

A Vertical Federated Learning Framework for Graph Convolutional Network

Recently, Graph Neural Network (GNN) has achieved remarkable success in various real-world problems on graph data. However in most industries, data exists in the form of isolated islands and the data privacy and security is also an important issue. In this paper, we propose FedVGCN, a federated GCN learning paradigm for privacy-preserving node classification task under data vertically partitioned setting, which can be generalized to existing GCN models. Specifically, we split the computation graph data into two parts. For each iteration of the training process, the two parties transfer intermediate results to each other under homomorphic encryption. We conduct experiments on benchmark data and the results demonstrate the effectiveness of FedVGCN in the case of GraphSage.

cs.LG↗

Canonical bases arising from quantum symmetric pairs of Kac-Moody type

For quantum symmetric pairs $(\mathbf{U}, \textbf{U}^\imath)$ of Kac-Moody type, we construct $\imath$canonical bases for the highest weight integrable $\mathbf{U}$-modules and their tensor products regarded as $\mathbf{U}^\imath$-modules, as well as an $\imath$canonical basis for the modified form of the $\imath$quantum group $\mathbf{U}^\imath$. A key new ingredient is a family of explicit elements called $\imath$divided powers, which are shown to generate the integral form of $\dot{\bf{U}}^\imath$. We prove a conjecture of Balagovic-Kolb, removing a major technical assumption in the theory of quantum symmetric pairs. Even for quantum symmetric pairs of finite type, our new approach simplifies and strengthens the integrality of quasi-K-matrix and the constructions of $\imath$canonical bases, by avoiding a case-by-case rank one analysis and removing the strong constraints on the parameters in a previous work.

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