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Yiqiang Li

Publications and source records attributed to Yiqiang Li.

At least 19 recordsLinked to original sources

PEVLM: Parallel Encoding for Vision-Language Models

Vision-Language Models (VLMs) have demonstrated strong capabilities in multimodal understanding and generation tasks. However, their application to long video understanding remains hindered by the quadratic complexity of standard attention mechanisms. In this work, we introduce \textbf{PEVLM}, a fine-tuning-free parallel encoding method designed to enhance the prefilling efficiency of VLMs in long video scenarios. PEVLM partitions the input video into context blocks with a shared sink block, while preserving sequential position embeddings to align the attention weight distribution with that of Full-Attention. This design reduces attention complexity from $O((T \times N)^2)$ to $O(T \times N)$ where $T$ is the number of frames and $N$ the number of tokens per frame, without sacrificing accuracy. Extensive experiments across multiple state-of-the-art models and benchmarks demonstrate that PEVLM consistently outperforms existing parallel encoding approaches, achieving up to \textbf{7.47x} speedup in attention computation and reducing end-to-end latency by \textbf{40\%}. Remarkably, PEVLM not only maintains high accuracy, but in some settings even surpasses Full-Attention performance. Under strict latency constraints, it achieves substantial gains, improving accuracy from \textbf{23.26\%} to \textbf{61.03\%}. These results underscore the effectiveness of PEVLM for low-latency, long-context video understanding, making it a promising solution for real-world applications.

cs.CV

Moral Reasoning Across Languages: The Critical Role of Low-Resource Languages in LLMs

In this paper, we introduce the Multilingual Moral Reasoning Benchmark (MMRB) to evaluate the moral reasoning abilities of large language models (LLMs) across five typologically diverse languages and three levels of contextual complexity: sentence, paragraph, and document. Our results show moral reasoning performance degrades with increasing context complexity, particularly for low-resource languages such as Vietnamese. We further fine-tune the open-source LLaMA-3-8B model using curated monolingual data for alignment and poisoning. Surprisingly, low-resource languages have a stronger impact on multilingual reasoning than high-resource ones, highlighting their critical role in multilingual NLP.

cs.CL

Hecke algebras and edge contractions

We establish an embedding from the Hecke algebra associated with the edge contraction of a Coxeter system along an edge to the Hecke algebra associated with the original Coxeter system.

math.RT

GUI-World: A Video Benchmark and Dataset for Multimodal GUI-oriented Understanding

Recently, Multimodal Large Language Models (MLLMs) have been used as agents to control keyboard and mouse inputs by directly perceiving the Graphical User Interface (GUI) and generating corresponding commands. However, current agents primarily demonstrate strong understanding capabilities in static environments and are mainly applied to relatively simple domains, such as Web or mobile interfaces. We argue that a robust GUI agent should be capable of perceiving temporal information on the GUI, including dynamic Web content and multi-step tasks. Additionally, it should possess a comprehensive understanding of various GUI scenarios, including desktop software and multi-window interactions. To this end, this paper introduces a new dataset, termed GUI-World, which features meticulously crafted Human-MLLM annotations, extensively covering six GUI scenarios and eight types of GUI-oriented questions in three formats. We evaluate the capabilities of current state-of-the-art MLLMs, including Image LLMs and Video LLMs, in understanding various types of GUI content, especially dynamic and sequential content. Our findings reveal that current models struggle with dynamic GUI content without manually annotated keyframes or operation history. On the other hand, Video LLMs fall short in all GUI-oriented tasks given the sparse GUI video dataset. Therefore, we take the initial step of leveraging a fine-tuned Video LLM, GUI-Vid, as a GUI-oriented assistant, demonstrating an improved understanding of various GUI tasks. However, due to the limitations in the performance of base LLMs, we conclude that using video LLMs as GUI agents remains a significant challenge. We believe our work provides valuable insights for future research in dynamic GUI content understanding. All the dataset and code are publicly available at: https://gui-world.github.io.

cs.CV

The $q$-Schur algebras in type $D$, I: fundamental multiplication formulas

By embedding the Hecke algebra $\check H_q$ of type $D$ into the Hecke algebra $H_{q,1}$ of type $B$ with unequal parameters $(q,1)$, the $q$-Schur algebras $S^\kappa_q(n,r)$ of type $D$ is naturally defined as the endomorphism algebra of the tensor space with the $\check H_q$-action restricted from the $H_{q,1}$-action that defines the $(q,1)$-Schur algebra $S^\jmath_{q,1}(n,r)$ of type $B$. We investigate the algebras $S^\jmath_{q,1}(n,r)$ and $S^\kappa_q(n,r)$ both algebraically and geometrically and describe their standard bases, dimension formulas and weight idempotents. Most importantly, we use the geometrically derived two sets of the fundamental multiplication formulas in $S^\jmath_{q,1}(n,r)$ to derive multi-sets (9 sets in total!) of the fundamental multiplication formulas in $S^\kappa_q(n,r)$.

math.QA

Critical Cohomological Hall Algebra and Edge Contraction

We study the behaviors of cohomological Hall algebras and relevant subjects under an edge contraction. Given a quiver with potential and fix an arrow, the edge contraction is a way to construct a new quiver with potential. We show that there is an algebra homomorphism between the cohomological Hall algebras induced by the edge contraction, which preserves the Hopf algebra structure, Drinfeld double, mutation, and the dimensional reduction, and induces relations between scattering diagram and Donaldson-Thomas series.

math.AG

Quantum groups and edge contractions

We study the behaviors of quantum groups under an edge contraction. We show that there exists an explicit embedding induced by an edge contraction operation. We further conjecture that this explicit embedding is a section of an explicit subquotient. This conjecture is proved when restricts to negative/positive half of a quantum group. The compatibility of the Hopf algebra structure of, and many other intrinsic structures associated with, a quantum group with the embedding and subquotient is studied along the way. The embedding phenomena are further observed in various representation theoretic objects such as Weyl groups and Chevalley groups.

math.QA

Embeddings among quantum affine $\mathfrak{sl}_n$

We establish an explicit embedding of a quantum affine $\mathfrak{sl}_n$ into a quantum affine $\mathfrak{sl}_{n+1}$. This embedding serves as a common generalization of two natural, but seemingly unrelated, embeddings, one on the quantum affine Schur algebra level and the other on the non-quantum level. The embedding on the quantum affine Schur algebras is used extensively in the analysis of canonical bases of quantum affine $\mathfrak{sl}_n$ and $\mathfrak{gl}_n$. The embedding on the non-quantum level is used crucially in a work of Riche and Williamson on the study of modular representation theory of general linear groups over a finite field. The same embedding is also used in a work of Maksimau on the categorical representations of affine general linear algebras. We further provide a more natural compatibility statement of the embedding on the idempotent version with that on the quantum affine Schur algebra level. A $\mathfrak{gl}_n$-variant of the embedding is also established.

math.QA

Quasi-split symmetric pairs of $U(\mathfrak{sl}_n)$ and Steinberg varieties of classical type

We provide a Lagrangian construction for the fixed-point subalgebra, together with its idempotent form, in a quasi-split symmetric pair of type $A_{n-1}$. This is obtained inside the limit of a projective system of Borel-Moore homologies of the Steinberg varieties of $n$-step isotropic flag varieties. Arising from the construction are a basis of homological origin for the idempotent form and a geometric realization of rational modules.

math.RT

Quasi-split symmetric pairs of $U(\mathfrak{gl}_N)$ and their Schur algebras

We establish explicit isomorphisms of two seemingly-different algebras, and their Schur algebras, arising from the centralizers of two different type B Weyl group actions in Schur-like dualities. We provide a presentation of the geometric counterpart of the above Schur algebras in Bao-Kujawa-Li-Wang (2018) specialized at $q=1$.

math.RT

Spaltenstein varieties of pure dimension

We show that Spaltenstein varieties of classical groups are pure dimensional when the Jordan type of the nilpotent element involved is an even or odd partition. We further show that they are Lagrangian in the partial resolutions of the associated nilpotent Slodowy slices, from which their dimensions are known to be one half of the dimension of the partial resolution minus the dimension of the nilpotent orbit. The results are then extended to the $σ$-quiver-variety setting.

math.RT

Affine Hecke algebras and quantum symmetric pairs

We introduce an affine Schur algebra via the affine Hecke algebra associated to Weyl group of affine type C. We establish multiplication formulas on the affine Hecke algebra and affine Schur algebra. Then we construct monomial bases and canonical bases for the affine Schur algebra. The multiplication formula allows us to establish a stabilization property of the family of affine Schur algebras that leads to the modified version of an algebra ${\mathbf K}^{\mathfrak c}_n$. We show that ${\mathbf K}^{\mathfrak c}_n$ is a coideal subalgebra of quantum affine algebra ${\bf U}(\hat{\mathfrak{gl}}_n)$, and $\big({\mathbf U}(\hat{ \mathfrak{gl}}_n), {\mathbf K}^{\mathfrak c}_n)$ forms a quantum symmetric pair. The modified coideal subalgebra is shown to admit monomial and stably canonical bases. We also formulate several variants of the affine Schur algebra and the (modified) coideal subalgebra above, as well as their monomial and canonical bases. This work provides a new and algebraic approach which complements and sheds new light on our previous geometric approach on the subject. In the appendix by four of the authors, new length formulas for the Weyl groups of affine classical types are obtained in a symmetrized fashion.

math.QA

On canonical bases of Letzter algebra $\mathbf U^{\imath}(\mathfrak{sl}_2)$

Let $\mathbf U^{\imath}\equiv\mathbf U^{\imath} (\mathfrak{sl}_2)$ be Letzter's coideal subalgebra of quantum $\mathfrak{sl}_2$ corresponding to the symmetric pair $(\mathfrak{sl}_2(\mathbb C),\mathbb C)$. As a subalgebra of quantum $\mathfrak{sl}_2$, $\mathbf U^{\imath}$ is generated by the sum $\mathbf E + v\mathbf K\mathbf F+\mathbf K$ of standard generators, and hence can be identified with the polynomial ring $\mathbb Q(v)[t]$. In [BW13] and [LW18], two distinguished bases, called $\imath$canonical bases, are constructed inside the modified form of $\mathbf U^{\imath}$ via algebraic and geometric approaches respectively. The modified form of $\mathbf U^{\imath}$ can be identified with a direct sum of two copies of $\mathbf U^{\imath}\cong\mathbb Q(v)[t]$ itself. An explicit and elegant formula, as a polynomial in $t$, of algebraic basis elements is conjectured in [BW13] and proved in [BeW18]. The purpose of this short paper is to show that the geometric basis in [LW18] admits the same description and, consequently, that the two bases coincide.

math.RT

Affine flag varieties and quantum symmetric pairs, II. Multiplication formula

We establish a multiplication formula for a tridiagonal standard basis element in the idempotented coideal subalgebras of quantum affine $\mathfrak{gl}_n$ arising from the geometry of affine partial flag varieties of type $C$. We apply this formula to obtain the stabilization algebras $\dot{\mathbf K}^{\mathfrak{c}}_n$, $\dot{\mathbf K}^{\jmath \imath}_{\mathfrak{n}}$, $\dot{\mathbf K}^{\imath \jmath}_{\mathfrak{n}}$ and $\dot{\mathbf K}^{\imath \imath}_η$, which are idempotented coideal subalgebras of quantum affine $\mathfrak{gl}_n$. The symmetry in the formula leads to an isomorphism of the idempotented coideal subalgebras $\dot{\mathbf K}^{\jmath \imath}_{\mathfrak{n}}$ and $\dot{\mathbf K}^{\imath \jmath}_{\mathfrak{n}}$ with compatible monomial, standard and canonical bases.

math.QA

Quiver varieties and symmetric pairs

We study fixed-point loci of Nakajima varieties under symplectomorphisms and their anti-symplectic cousins, which are compositions of a diagram automorphism, a reflection functor and a transpose defined by certain bilinear forms. These subvarieties provide a natural home for geometric representation theory of symmetric pairs. In particular, the cohomology of a Steinberg-type variety of the symplectic fixed-point subvarieties is conjecturally related to the universal enveloping algebra of the subalgebra in a symmetric pair. The latter symplectic subvarieties are further used to construct geometrically an action of a twisted Yangian on torus equivariant cohomology of Nakajima varieties. In type $A$ case, these subvarieties provide a quiver model for partial Springer resolutions of nilpotent Slodowy slices of classical groups and associated symmetric spaces, which leads to a rectangular symmetry and a refinement of Kraft-Procesi row/column removal reductions.

math.RT

Geometric Schur duality of classical type

This is a generalization of the classic work of Beilinson, Lusztig and MacPherson. In this paper (and an Appendix) we show that the quantum algebras obtained via a BLM-type stabilization procedure in the setting of partial flag varieties of type $B/C$ are two (modified) coideal subalgebras of the quantum general linear Lie algebra, $\dot{\mathbf U}^{\jmath}$ and $\dot{\mathbf U}^{\imath}$. We provide a geometric realization of the Schur-type duality of Bao-Wang between such a coideal algebra and Iwahori-Hecke algebra of type $B$. The monomial bases and canonical bases of the Schur algebras and the modified coideal algebra $\dot{\mathbf U}^{\jmath}$ are constructed. In an Appendix by three authors, a more subtle $2$-step stabilization procedure leading to $\dot{\mathbf U}^{\imath}$ is developed, and then monomial and canonical bases of $\dot{\mathbf U}^{\imath}$ are constructed. It is shown that $\dot{\mathbf U}^{\imath}$ is a subquotient of $\dot{\mathbf U}^{\jmath}$ with compatible canonical bases. Moreover, a compatibility between canonical bases for modified coideal algebras and Schur algebras is established.

math.RT

Positivity vs negativity of canonical bases

We provide examples for negativity of structure constants of the stably canonical basis of modified quantum $\mathfrak{gl}_n$ and an analogous basis of modified quantum coideal algebra of $\mathfrak{gl}_n$. In contrast, we construct the canonical basis of the modified quantum coideal algebra of $\mathfrak{sl}_n$, establish the positivity of its structure constants, the positivity with respect to a geometric bilinear form as well as the positivity of its action on the tensor powers of the natural representation. The matrix coefficients of the transfer map on these Schur algebras with respect to the canonical bases are shown to be positive. Formulas for canonical basis of the iSchur algebra of rank one are obtained.

math.RT