BZPEERReading, trust and collaboration for research
Menu

Discover

GraphFollow connections around a paper, topic or saved view.

Workspaces

HomePick up where your research flow left off.InboxHandle requests, replies and notifications from one place.CollectionsCurate reading lists, evidence sets and shareable dossiers.ResearchSee your private provenance graph, trail and imports.CollaborationMove from discovery into focused discussion rooms.PublishDraft, preview and publish full-text research articles.

Network

ExpertsFind specialists worth following or asking for help.CommunitiesJoin research circles organized around shared work.PartnersSee external organizations active around the same topics.

Opportunities

ListingsBrowse roles, calls and collaborations with clearer fit signals.

Account

Log inReturn to your reading and collaboration workspace.Create accountStart saving work, following people and joining teams.
Log inCreate account

Researcher profile

Weiqiang Wang

Weiqiang Wang contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
math.RTmath.QAComputer VisionMachine LearningComputation and LanguageArtificial Intelligencemath.AGmath.COCryptography and SecurityInformation Retrievalmath.APMultiagent Systemsphysics.ins-detphysics.opticsquant-ph

Trust snapshot

Quick read

Trust 21 - EmergingVerification L1Unclaimed author
38works
0followers
15topics
4close collaborators

Actions

Decide how to stay connected

Follow researcher0

Identity and collaboration

How to connect with this researcher

Claiming links this public author record to a researcher profile and unlocks direct collaboration workflows.

Log in to claim

Direct collaboration

Open a focused conversation when the fit is right

Claim this author entity first to unlock direct invitations.

Research graph

See the researcher in context

Open full explorer

Inspect adjacent work, topics, institutions and collaborators without jumping out to a separate graph page.

Building this graph slice

BZPEER is loading the nearby papers, people, topics and institutions for this page.

Published work

38 published item(s)

preprint2026arXiv

Causal Probing for Internal Visual Representations in Multimodal Large Language Models

Despite the remarkable success of Multimodal Large Language Models (MLLMs) across diverse tasks, the internal mechanisms governing how they encode and ground distinct visual concepts remain poorly understood. To bridge this gap, we propose a causal framework based on activation steering to actively probe and manipulate internal visual representations. Through systematic intervention across four visual concept categories, our results reveal a divergence in concept encoding: entities exhibit distinct localized memorization, whereas abstract concepts are globally distributed across the network. Critically, this divergence uncovers a mechanistic driver of scaling laws: increasing model depth is indispensable for encoding distributed and complex abstract concepts, whereas entity localization remains remarkably invariant to scale. Furthermore, reverse steering uncovers that blocking explicit output triggers a surge in latent activations, exposing a compensatory mechanism between perception and generation. Finally, extending our analysis to visual reasoning, we expose a disconnect between perception and reasoning although MLLMs successfully recognize geometric relations, they treat them merely as static visual features, failing to trigger the procedural execution necessary for abstract problem-solving.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Generalizable and Adaptive Continual Learning Framework for AI-generated Image Detection

The malicious misuse and widespread dissemination of AI-generated images pose a significant threat to the authenticity of online information. Current detection methods often struggle to generalize to unseen generative models, and the rapid evolution of generative techniques continuously exacerbates this challenge. Without adaptability, detection models risk becoming ineffective in real-world applications. To address this critical issue, we propose a novel three-stage domain continual learning framework designed for continuous adaptation to evolving generative models. In the first stage, we employ a strategic parameter-efficient fine-tuning approach to develop a transferable offline detection model with strong generalization capabilities. Building upon this foundation, the second stage integrates unseen data streams into a continual learning process. To efficiently learn from limited samples of novel generated models and mitigate overfitting, we design a data augmentation chain with progressively increasing complexity. Furthermore, we leverage the Kronecker-Factored Approximate Curvature (K-FAC) method to approximate the Hessian and alleviate catastrophic forgetting. Finally, the third stage utilizes a linear interpolation strategy based on Linear Mode Connectivity, effectively capturing commonalities across diverse generative models and further enhancing overall performance. We establish a comprehensive benchmark of 27 generative models, including GANs, deepfakes, and diffusion models, chronologically structured up to August 2024 to simulate real-world scenarios. Extensive experiments demonstrate that our initial offline detectors surpass the leading baseline by +5.51% in terms of mean average precision. Our continual learning strategy achieves an average accuracy of 92.20%, outperforming state-of-the-art methods.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

iQuantum groups and iHopf algebras II: dual canonical bases

Building on the iHopf algebra realization of quasi-split universal iquantum groups developed in a prequel, we construct the dual canonical basis for a universal iquantum group of arbitrary finite type, which are further shown to be preserved by the ibraid group action; this recovers the results of Lu-Pan in ADE type obtained earlier in a geometric approach. Moreover, we identify the dual canonical basis for the Drinfeld double quantum group of arbitrary finite type, which is realized via iHopf algebra on the double Borel, with Berenstein-Greenstein's double canonical basis, settling several of their conjectures.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

KBQA-R1: Reinforcing Large Language Models for Knowledge Base Question Answering

Knowledge Base Question Answering (KBQA) challenges models to bridge the gap between natural language and strict knowledge graph schemas by generating executable logical forms. While Large Language Models (LLMs) have advanced this field, current approaches often struggle with a dichotomy of failure: they either generate hallucinated queries without verifying schema existence or exhibit rigid, template-based reasoning that mimics synthesized traces without true comprehension of the environment. To address these limitations, we present \textbf{KBQA-R1}, a framework that shifts the paradigm from text imitation to interaction optimization via Reinforcement Learning. Treating KBQA as a multi-turn decision process, our model learns to navigate the knowledge base using a list of actions, leveraging Group Relative Policy Optimization (GRPO) to refine its strategies based on concrete execution feedback rather than static supervision. Furthermore, we introduce \textbf{Referenced Rejection Sampling (RRS)}, a data synthesis method that resolves cold-start challenges by strictly aligning reasoning traces with ground-truth action sequences. Extensive experiments on WebQSP, GrailQA, and GraphQuestions demonstrate that KBQA-R1 achieves state-of-the-art performance, effectively grounding LLM reasoning in verifiable execution.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Predict the Retrieval! Test time adaptation for Retrieval Augmented Generation

Retrieval-Augmented Generation (RAG) has emerged as a powerful approach for enhancing large language models' question-answering capabilities through the integration of external knowledge. However, when adapting RAG systems to specialized domains, challenges arise from distribution shifts, resulting in suboptimal generalization performance. In this work, we propose TTARAG, a test-time adaptation method that dynamically updates the language model's parameters during inference to improve RAG system performance in specialized domains. Our method introduces a simple yet effective approach where the model learns to predict retrieved content, enabling automatic parameter adjustment to the target domain. Through extensive experiments across six specialized domains, we demonstrate that TTARAG achieves substantial performance improvements over baseline RAG systems. Code available at https://github.com/sunxin000/TTARAG.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

ROAD: Adaptive Data Mixing for Offline-to-Online Reinforcement Learning via Bi-Level Optimization

Offline-to-online reinforcement learning harnesses the stability of offline pretraining and the flexibility of online fine-tuning. A key challenge lies in the non-stationary distribution shift between offline datasets and the evolving online policy. Common approaches often rely on static mixing ratios or heuristic-based replay strategies, which lack adaptability to different environments and varying training dynamics, resulting in suboptimal tradeoff between stability and asymptotic performance. In this work, we propose Reinforcement Learning with Optimized Adaptive Data-mixing (ROAD), a dynamic plug-and-play framework that automates the data replay process. We identify a fundamental objective misalignment in existing approaches. To tackle this, we formulate the data selection problem as a bi-level optimization process, interpreting the data mixing strategy as a meta-decision governing the policy performance (outer-level) during online fine-tuning, while the conventional Q-learning updates operate at the inner level. To make it tractable, we propose a practical algorithm using a multi-armed bandit mechanism. This is guided by a surrogate objective approximating the bi-level gradient, which simultaneously maintains offline priors and prevents value overestimation. Our empirical results demonstrate that this approach consistently outperforms existing data replay methods across various datasets, eliminating the need for manual, context-specific adjustments while achieving superior stability and asymptotic performance.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

TabEmbed: Benchmarking and Learning Generalist Embeddings for Tabular Understanding

Foundation models have established unified representations for natural language processing, yet this paradigm remains largely unexplored for tabular data. Existing methods face fundamental limitations: LLM-based approaches lack retrieval-compatible vector outputs, whereas text embedding models often fail to capture tabular structure and numerical semantics. To bridge this gap, we first introduce the Tabular Embedding Benchmark (TabBench), a comprehensive suite designed to evaluate the tabular understanding capability of embedding models. We then propose TabEmbed, the first generalist embedding model that unifies tabular classification and retrieval within a shared embedding space. By reformulating diverse tabular tasks as semantic matching problems, TabEmbed leverages large-scale contrastive learning with positive-aware hard negative mining to discern fine-grained structural and numerical nuances. Experimental results on TabBench demonstrate that TabEmbed significantly outperforms state-of-the-art text embedding models, establishing a new baseline for universal tabular representation learning. Code and datasets are publicly available at https://github.com/qiangminjie27/TabEmbed and https://huggingface.co/datasets/qiangminjie27/TabBench.

0 citations0 reviewsNo code linkedOpen access
preprint2025arXiv

Affine and cyclotomic webs

Generalizing the polynomial web category, we introduce a diagrammatic $\Bbbk$-linear monoidal category, the affine web category, for any commutative ring $\Bbbk$. Integral bases consisting of elementary diagrams are obtained for the affine web category and its cyclotomic quotient categories. Connections between cyclotomic web categories and finite $W$-algebras are established, leading to a diagrammatic presentation of idempotent subalgebras of $W$-Schur algebras introduced by Brundan-Kleshchev. The affine web category will be used as a basic building block of another $\Bbbk$-linear monoidal category, the affine Schur category, formulated in a sequel.

0 citations0 reviewsNo code linkedOpen access
preprint2024arXiv

Super duality for Whittaker modules and finite $W$-algebras

We establish a super duality as an equivalence between Whittaker module categories over a pair of classical Lie algebra and Lie superalgebra in the infinite-rank limit. Building on this result and utilizing the Losev-Shu-Xiao decomposition, we obtain a super duality which is an equivalence between module categories over a pair of finite $W$-algebras and $W$-superalgebras at the infinite-rank limit.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

$\imath$Hall algebra of Jordan quiver and $\imath$Hall-Littlewood functions

We show that the $\imath$Hall algebra of the Jordan quiver is a polynomial ring in infinitely many generators and obtain transition relations among several generating sets. We establish a ring isomorphism from this $\imath$Hall algebra to the ring of symmetric functions in two parameters $t, θ$, which maps the $\imath$Hall basis to a class of (modified) inhomogeneous Hall-Littlewood ($\imath$HL) functions. The (modified) $\imath$HL functions admit a formulation via raising and lowering operators. We formulate and prove Pieri rules for (modified) $\imath$HL functions. The modified $\imath$HL functions specialize at $θ=0$ to the modified HL functions; they specialize at $θ=1$ to the deformed universal characters of type C, which further specialize at $(t=0, θ=1)$ to the universal characters of type C.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

$\imath$Hall algebras and $\imath$quantum groups

We survey some recent development on the theory of $\imath$Hall algebras. Starting from $\imath$quivers (aka quivers with involutions), we construct a class of 1-Gorenstein algebras called $\imath$quiver algebras, whose semi-derived Hall algebras give us $\imath$Hall algebras. We then use these $\imath$Hall algebras to realize quasi-split $\imath$quantum groups arising from quantum symmetric pairs. Relative braid group symmetries on $\imath$quantum groups are realized via reflection functors. In case of Jordan $\imath$quiver, the $\imath$Hall algebra is commutative and connections to $\imath$Hall-Littlewood symmetric functions are developed. In case of $\imath$quivers of diagonal type, our construction amounts to a reformulation of Bridgeland-Hall algebra realization of the Drinfeld double quantum groups (which in turn generalizes Ringel-Hall algebra realization of halves of quantum groups). Many rank 1 and rank 2 computations are supplied to illustrate the general constructions. We also briefly review $\imath$Hall algebras of weighted projective lines, and use them to realize Drinfeld type presentations of $\imath$quantum loop algebras.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Cells in affine q-Schur algebras

We develop algebraic and geometrical approaches toward canonical bases for affine q-Schur algebras of arbitrary type introduced in this paper. A duality between an affine q-Schur algebra and a corresponding affine Hecke algebra is established. We introduce an inner product on the affine q-Schur algebra, with respect to which the canonical basis is shown to be positive and almost orthonormal. We then formulate the cells and asymptotic forms for affine q-Schur algebras, and develop their basic properties analogous to the cells and asymptotic forms for affine Hecke algebras established by Lusztig. The results on cells and asymptotic algebras are also valid for q-Schur algebras of arbitrary finite type.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

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 $κ=0,1$.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

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

The $\imath$-divided powers (depending on a parity) form the $\imath$canonical basis for the split rank 1 $\imath$quantum group and they are a basic ingredient for $\imath$quantum groups of higher rank. We obtain closed formulae for the structure constants for multiplication of the $\imath$-divided powers. Closed formulae for the comultiplication of the $\imath$-divided powers are also obtained. These structure constants are integral and positive.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

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&#39;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.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

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&#39;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&#34; with positivity, via the quantum Grothendieck rings of Nakajima-Keller-Scherotzke quiver varieties, generalizing Qin&#39;s geometric realization of quantum groups of type ADE.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Canonical bases for tensor products and super Kazhdan-Lusztig theory

We generalize a construction in [BW18] (arXiv:1610.09271) by showing that the tensor product of a based $\textbf{U}^{\imath}$-module and a based $\textbf{U}$-module is a based $\textbf{U}^{\imath}$-module. This is then used to formulate a Kazhdan-Lusztig theory for an arbitrary parabolic BGG category $\mathcal{O}$ of the ortho-symplectic Lie superalgebras, extending a main result in [BW13] (arXiv:1310.0103).

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Characters as Graphs: Recognizing Online Handwritten Chinese Characters via Spatial Graph Convolutional Network

Chinese is one of the most widely used languages in the world, yet online handwritten Chinese character recognition (OLHCCR) remains challenging. To recognize Chinese characters, one popular choice is to adopt the 2D convolutional neural network (2D-CNN) on the extracted feature images, and another one is to employ the recurrent neural network (RNN) or 1D-CNN on the time-series features. Instead of viewing characters as either static images or temporal trajectories, here we propose to represent characters as geometric graphs, retaining both spatial structures and temporal orders. Accordingly, we propose a novel spatial graph convolution network (SGCN) to effectively classify those character graphs for the first time. Specifically, our SGCN incorporates the local neighbourhood information via spatial graph convolutions and further learns the global shape properties with a hierarchical residual structure. Experiments on IAHCC-UCAS2016, ICDAR-2013, and UNIPEN datasets demonstrate that the SGCN can achieve comparable recognition performance with the state-of-the-art methods for character recognition.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

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

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, with conjectural explicit formulae. In this paper we prove the conjectured formulae of these $\imath$-divided powers. This is achieved by first establishing closed formulae of the $\imath$-divided powers in basis for quantum $\mathfrak{sl}_2$ and then formulae for the $\imath$-canonical basis in terms of Lusztig&#39;s divided powers in each finite-dimensional simple module of quantum $\mathfrak{sl}_2$. These formulae exhibit integrality and positivity properties.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Long distance measurement using single soliton microcomb

Dispersive interferometry (DPI) takes a major interest in optical frequency comb (OFC) based long distance laser-based light detection and ranging (LIDAR) for the merits of strong anti-interference ability and long coherent length. However, the mismatch between the repetition rate of OFC and the resolution of optical spectrum acquisition system induces a large dead-zone which is a major obstacle for practical applications. Here, a new DPI LIDAR on the strength of high-repetition-rate soliton microcomb is demonstrated, which reaches a minimum Allan deviation of 27 nm for an outdoor 1179 m ranging experiment. The proposed scheme approaches a compact, high-accuracy, and none-dead-zone long distance ranging system, opening up new opportunities for emerging applications of frontier scientific researches and advanced manufacturing.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Quantum key distribution with dissipative Kerr soliton generated by on-chip microresonators

Quantum key distribution (QKD) can distribute symmetric key bits between remote legitimate users with the guarantee of quantum mechanics principles. For practical applications, the compact and robust photonic components for QKD are essential, and there are increasing attention to integrate the source, detector and modulators on a photonic chip. However, the massive and parallel QKD based on wavelength multiplexing are still challenge, due to the limited coherent light sources on the chip. Here, we introduce the Kerr dissipative soliton in a microresonator, which provides the locked coherent frequency comb with 49GHz frequency spacing, for QKD. We demonstrate the parallel QKD by demulplexing the coherent comb lines form the soliton, and showing the potential of Gbps secret key rate if the hundreds of channels covering C and L bands are fully exploited. The demonstrated soliton based QKD architecture are compatible with the efforts of quantum photonic integrated circuits, which are compact, robust and low-cost, and provides a competitive platform of practical QKD chip.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Reinterpreting CTC training as iterative fitting

The connectionist temporal classification (CTC) enables end-to-end sequence learning by maximizing the probability of correctly recognizing sequences during training. The outputs of a CTC-trained model tend to form a series of spikes separated by strongly predicted blanks, know as the spiky problem. To figure out the reason for it, we reinterpret the CTC training process as an iterative fitting task that is based on frame-wise cross-entropy loss. It offers us an intuitive way to compare target probabilities with model outputs for each iteration, and explain how the model outputs gradually turns spiky. Inspired by it, we put forward two ways to modify the CTC training. The experiments demonstrate that our method can well solve the spiky problem and moreover, lead to faster convergence over various training settings. Beside this, the reinterpretation of CTC, as a brand new perspective, may be potentially useful in other situations. The code is publicly available at https://github.com/hzli-ucas/caffe/tree/ctc.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

The $q$-Schur algebras and $q$-Schur dualities of finite type

We formulate a $q$-Schur algebra associated to an arbitrary $W$-invariant finite set $X_{\texttt f}$ of integral weights for a complex simple Lie algebra with Weyl group $W$. We establish a $q$-Schur duality between the $q$-Schur algebra and Hecke algebra associated to $W$. We then realize geometrically the $q$-Schur algebra and duality, and construct a canonical basis for the $q$-Schur algebra with positivity. With suitable choices of $X_{\texttt f}$ in classical types, we recover the $q$-Schur algebras in the literature. Our $q$-Schur algebras are closely related to the category $\mathcal O$, where the type $G_2$ is studied in detail.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Anti-commuting varieties

We study the anti-commuting variety which consists of pairs of anti-commuting $n\times n$ matrices. We provide an explicit description of its irreducible components and their dimensions. The GIT quotient of the anti-commuting variety with respect to the conjugation action of $GL_n$ is shown to be of pure dimension $n$. We also show the semi-nilpotent anti-commuting variety (in which one matrix is required to be nilpotent) is of pure dimension $n^2$ and describe its irreducible components.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Odd singular vector formula for general linear Lie superalgebras

We establish a closed formula for a singular vector of weight $λ-β$ in the Verma module of highest weight $λ$ for Lie superalgebra $\mathfrak{gl}(m|n)$ when $λ$ is atypical with respect to an odd positive root $β$. It is further shown that this vector is unique up to a scalar multiple, and it descends to a singular vector, again unique up to a scalar multiple, in the corresponding Kac module when both $λ$ and $λ-β$ are dominant integral.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Quantum supergroups VI. Roots of $1$

A quantum covering group is an algebra with parameters $q$ and $π$ subject to $π^2=1$ and it admits an integral form; it specializes to the usual quantum group at $π=1$ and to a quantum supergroup of anisotropic type at $π=-1$. In this paper we establish the Frobenius-Lusztig homomorphism and Lusztig-Steinberg tensor product theorem in the setting of quantum covering groups at roots of 1. The specialization of these constructions at $π=1$ recovers Lusztig&#39;s constructions for quantum groups at roots of 1.

0 citations0 reviewsNo code linkedOpen access
preprint2001arXiv

Twisted vertex representations and spin characters

We establish a new group-theoretic realization of the basic representations of the twisted affine and twisted toroidal algebras of ADE types in the same spirit of our new approach to the McKay correspondence. Our vertex operator construction provides a unified description to the character tables for the spin cover of the wreath product of the twisted hyperoctahedral groups and an arbitrary finite group.

0 citations0 reviewsNo code linkedOpen access