arXiv subjects

Yufeng Yao

Publications and source records attributed to Yufeng Yao.

15 recordsLinked to original sources

arXiv2026

Exploiting Multicast for Accelerating Collective Communication

Reducing collective communication latency is a critical goal for large model training and inference in both academia and industry. Many-to-many communications, such as AllGather and AlltoAll (dispatch), are core components of modern parallelization strategies. State-of-the-art implementations of these communications rely on unicast-based writes and transmit duplicate copies of the same data across physical links for multiple receivers. This redundant transmission congests network bottlenecks and degrades end-to-end latency. We present MultiWrite, a novel many-to-many transmission semantic that eliminates redundant packets to directly reduce operator latency. MultiWrite adopts multicast principles while addressing critical limitations of traditional multicast for AI workloads. These limitations include heavy management plane overhead and ecosystem compatibility issues. We implement MultiWrite on Ascend NPUs. Long-term stress tests demonstrate that our MultiWrite-based operators achieve up to 33% latency reduction on commercially deployed devices.

cs.DC↗

arXiv2026

On enhanced reductive groups (II): Finiteness of nilpotent orbits under enhanced group action and their closures

This is a sequel to \cite{osy} and \cite{sxy}. Associated with $G:=\GL_n$ and its rational representation $(ρ, M)$ over an algebraically closed filed $\bk$, we define an enhanced algebraic group $\uG:=G\ltimes_ρM$ which is a product variety $\GL_n\times M$, endowed with an enhanced cross product. In this paper, we first show that the nilpotent cone $\ucaln:=\caln(\ugg)$ of the enhanced Lie algebra $\ugg:=\Lie(\uG)$ has finite nilpotent orbits under adjoint $\uG$-action if and only if up to tensors with one-dimensional modules, $M$ is isomorphic to one of the three kinds of modules: (i) a one-dimensional module, (ii) the natural module $\bk^n$, (iii) the linear dual of $\bk^n$ when $n>2$; and $M$ is an irreducible module of dimension not bigger than $3$ when $n=2$. We then investigate the geometry of enhanced nilpotent orbits when the finiteness occurs. Our focus is on the enhanced group $\uG=\GL(V)\ltimes_ηV$ with the natural representation $(η, V)$ of $\GL(V)$, for which we give a precise classification of finite nilpotent orbits via a finite set $\scrpe$ of so-called enhanced partitions of $n=\dim V$, then give a precise description of the closures of enhanced nilpotent orbits via constructing so-called enhanced flag varieties. Finally, the $\uG$-equivariant intersection cohomology decomposition on the nilpotent cone of $\ugg$ along the closures of nilpotent orbits is established.

math.RT↗

arXiv2025

Derivations and Biderivations of affine-Virasoro Lie algebras

In this paper we determine all derivations and biderivations of an affine-Virasoro Lie algebra associated with a finite-dimensional complex simple Lie algebra $\mathfrak{g}$. We prove that all the derivations and biderivations of affine-Virasoro Lie algebras are inner.

math.RA↗

arXiv2025

Lie-Cartan modules and cohomology

As a sequel to [Duan-Shu-Yao], we introduce here a category $\mathscr{LC}$ arising from the BGG category $\mathcal{O}$ defined in [Duan-Shu-Yao] for Lie algebras of polynomial vector fields. The objects of $\mathscr{LC}$ are so-called Lie-Cartan modules which admit both Lie-module structure and compatible $R$-module structure ($R$ denotes the corresponding polynomial ring). This terminology is natural, coming from affine connections in differential geometry through which the structure sheaves in topology and the vector fields in geometry are integrated for differential manifolds. In this paper, we study Lie-Cartan modules and their categorical and cohomology properties. The category $\mathscr{LC}$ is abelian, and a ``highest weight category" with depths. Notably, the set of co-standard objects in the category $\mathcal{O}$ turns out to represent the isomorphism classes of simple objects of $\mathscr{LC}$. We then establish the cohomology for this category (called the $\mathscr{uLC}$-cohomology), extending Chevalley-Eilenberg cohomology theory. Another notable result says that in the fundamental case $\mathfrak{g}= W(n)$, the extension ring $\text{Ext}^\bullet_{\mathscr{uLC}}(R,R)$ for the polynomial algebra $R$ in the $\mathscr{uLC}$-cohomology is isomorphic to the usual cohomology ring $H^\bullet(\mathfrak{gl}(n))$ of the general linear Lie algebra $\mathfrak{gl}(n)$.

math.RT↗

arXiv2025

Simple smooth modules over the Ramond algebra and applications to vertex operator superalgebras

Simple smooth modules over the Virasoro algebra and one of the super-Virasoro algebras, named the Neveu-Schwarz algebra, have been classified. This problem remained unsolved for the other super-Virasoro algebra called the Ramond algebra.In this paper, all simple smooth modules over the Ramond algebra are classified. More precisely, we show that a simple smooth module over the Ramond algebra is either a simple highest weight module or isomorphic to an induced module from a simple module over a finite dimensional solvable Lie superalgebra.As an application we obtain all simple weak $ψ$-twisted modules over some vertex operator superalgebras.

math.RT↗

arXiv2025

Towards high-fidelity wind farm layout optimization using polynomial chaos expansion and Kriging model

This paper presents a wind farm layout optimization framework that integrates polynomial chaos expansion, a Kriging model, and the expected improvement algorithm. The proposed framework addresses the computational challenges associated with high-fidelity wind farm simulations by significantly reducing the number of function evaluations required for accurate annual energy production predictions. The polynomial chaos expansion-based prediction method achieves exceptional accuracy with reduced computational cost for over 96%, significantly lowering the expense of training the ensuing surrogate model. The Kriging model, combined with a genetic algorithm, is used for surrogate-based optimization, achieving comparable performance to direct optimization at a much-reduced computational cost. The integration of the expected improvement algorithm enhances the global optimization capability of the framework, allowing it to escape local optima and achieve results that are either nearly identical to or even outperform those obtained through direct optimization. The feasibility of the polynomial chaos expansion-Kriging framework is demonstrated through four case studies, including the optimization of wind farms with 8, 16, and 32 turbines using low-fidelity wake models, and a high-fidelity case using computational fluid dynamics simulations. The results show that the proposed framework is highly effective in optimizing wind farm layouts, significantly reducing computational costs while maintaining or improving the accuracy of annual energy production predictions.

math.OC↗

arXiv2024

Biderivations of Lie algebras

In this paper, we first introduce the concept of symmetric biderivation radicals and characteristic subalgebras of Lie algebras, and study their properties. Based on these results, we precisely determine biderivations of some Lie algebras including finite-dimensional simple Lie algebras over arbitrary fields of characteristic not $2$ or $3$, and the Witt algebras $\mathcal{W}^+_n$ over fields of characteristic $0$. As an application, commutative post-Lie algebra structure on aforementioned Lie algebras is shown to be trivial.

math.RA↗

arXiv2024

Joint Coordinate Regression and Association For Multi-Person Pose Estimation, A Pure Neural Network Approach

We introduce a novel one-stage end-to-end multi-person 2D pose estimation algorithm, known as Joint Coordinate Regression and Association (JCRA), that produces human pose joints and associations without requiring any post-processing. The proposed algorithm is fast, accurate, effective, and simple. The one-stage end-to-end network architecture significantly improves the inference speed of JCRA. Meanwhile, we devised a symmetric network structure for both the encoder and decoder, which ensures high accuracy in identifying keypoints. It follows an architecture that directly outputs part positions via a transformer network, resulting in a significant improvement in performance. Extensive experiments on the MS COCO and CrowdPose benchmarks demonstrate that JCRA outperforms state-of-the-art approaches in both accuracy and efficiency. Moreover, JCRA demonstrates 69.2 mAP and is 78\% faster at inference acceleration than previous state-of-the-art bottom-up algorithms. The code for this algorithm will be publicly available.

cs.CV↗

arXiv2021

Simple restricted modules over the Heisenberg-Virasoro algebra as VOA modules

In this paper, we determine all simple restricted modules over the mirror Heisenberg-Virasoro algebra ${\mathfrak{D}}$, and the twisted Heisenberg-Virasoro algebra $\bar\mathfrak{D}$ with nonzero level. As applications, we characterize simple Whittaker modules and simple highest weight modules over ${\mathfrak{D}}$. A vertex-algebraic interpretation of our result is the classification of simple weak twisted and untwisted modules over the Heisenberg-Virasoro vertex operator algebras $\mathcal V^{c} \cong V_{Vir}^{c}\otimes M(1)$. We also present a few examples of simple restricted ${\mathfrak{D}}$-modules and $\bar\mathfrak{D}$-modules induced from simple modules over finite dimensional solvable Lie algebras, that are not tensor product modules of Virasoro modules and Heisenberg modules. This is very different from the case of simple highest weight modules over $\mathfrak{D}$ and $\bar\mathfrak{D}$ which are always tensor products of simple Virasoro modules and simple Heisenberg modules.

math.RT↗

arXiv2020

On enhanced reductive groups (I): Parabolic Schur algebras and the dualities related to degenerate double Hecke algebras

An enhanced algebraic group $\uG$ of $G=\GL(V)$ over $\bbc$ is a product variety $\GL(V)\times V$, endowed with an enhanced cross product. Associated with a natural tensor representation of $\uG$, there are naturally Levi and parabolic Schur algebras $\mathcal{L}$ and $\mathcal{P}$ respectively. We precisely investigate their structures, and study the dualities on the enhanced tensor representations for variant groups and algebras. In this course, an algebraic model of so-called degenerate double Hecke algebras (DDHA) is produced, and becomes a powerful implement. The connection between $\mathcal{L}$ and DDHA gives rise to two results for the classical representations of $\GL(V)$: (i) A duality between $\GL(V)\times\Gm$ and DDHA where $\Gm$ is the one-dimensional multiplicative group; (ii) A branching duality formula. With aid of the above discussion, we further obtain a parabolic Schur-Weyl duality for $\uG\rtimes \Gm$. What is more, the parabolic Schur subalgebra turns out to have only one block. The Cartan invariants for this algebra are precisely determined.

math.RT↗

arXiv2020

2-local derivations on the Jacobson-Witt algebras in prime characteristic

This paper initiates the study of 2-local derivations on Lie algebras over fields of prime characteristic. Let $\mathfrak{g}$ be a simple Jacobson-Witt algebra $W_n$ over a field of prime characteristic $p$ with cardinality no less than $p^n$. In this paper, we study properties of 2-local derivations on $\mathfrak{g}$, and show that every 2-local derivation on $\mathfrak{g}$ is a derivation.

math.RA↗

arXiv2020

Whittaker modules for the planar Galilean conformal algebra and its central extension

Let $\mathcal{G}$ be the planar Galilean conformal algebra and $\widetilde{\mathcal{G}}$ be its universal central extension. Then $\mathcal{G}$ (resp. $\widetilde{\mathcal{G}}$) admits a triangular decomposition: $\mathcal{G}=\mathcal{G}^{+}\oplus\mathcal{G}^{0}\oplus\mathcal{G}^{-}$ (resp. $\widetilde{\mathcal{G}}=\widetilde{\mathcal{G}}^{+}\oplus\widetilde{\mathcal{G}}^{0}\oplus\widetilde{\mathcal{G}}^{-}$). In this paper, we study universal and generic Whittaker $\mathcal{G}$-modules (resp. $\widetilde{\mathcal{G}}$-modules) of type $ϕ$, where $ϕ:\mathcal{G}^{+}=\widetilde{\mathcal{G}}^{+}\longrightarrow\mathbb{C}$ is a Lie algebra homomorphism. We classify the isomorphism classes of universal and generic Whittaker modules. Moreover, we show that a generic Whittaker modules of type $ϕ$ is irreducible if and only if $ϕ$ is nonsingular. For the nonsingular case, we completely determine the Whittaker vectors in universal and generic Whittaker modules. For the singular case, we concretely construct some proper submodules of generic Whittaker modules.

math.RT↗

arXiv2020

On non-weight representations of the $N=2$ superconformal algebras

In this paper, we construct a family of non-weight modules over the untwisted $N=2$ superconformal algebras. Those modules when regarded as modules over the Cartan subalgebra (modulo the center) are free of rank $2$. We give a classification of isomorphism classes of such modules. Moreover, all submodules of such modules are precisely determined. In particular, those modules are not simple. The corresponding simple quotient modules are classified. Furthermore, these simple modules when restricted as modules over $N=1$ superconformal algebras coincide with those modules constructed in [H. Yang, Y. Yao, L. Xia, A family of non-weight modules over the super-Virasoro algebras, J. Algebra 547 (2020), 538-555].

math.RT↗

arXiv2019

A family of non-weight modules over the super-Virasoro algebras

In this paper, we construct a family of non-weight modules over the super-Virasoro algebras. Those modules when regarded as modules of the Ramond algebra and further restricted as modules over the Cartan subalgebra $\mathfrak{h}$ are free of rank $1$, while when regarded as modules of the Neveu-Schwarz algebra and further restricted as modules over the Cartan subalgebra $\mathfrak{H}$ are free of rank $2$. We obtain a sufficient and necessary condition for such modules to be simple. Moreover, we determine the isomorphism classes of these modules. Finally, we show that these modules constitute a complete classification of free $U(\mathfrak{h})$-modules of rank $1$ over the super-Virasoro algebra of Ramond type, and also constitute a complete classification of free $U(\mathfrak{H})$-modules of rank $2$ over the super-Virasoro algebra of Neveu-Schwarz type.

math.RT↗

arXiv2017

Simple modules over the Lie algebras of divergence zero vector fields on a torus

Let $n\ge2$ be an integer, $\mathcal{K}_n$ the Weyl algebra over the Laurent polynomial algebra $A_n=\mathbb{C} [x_1^{\pm1}, x_2^{\pm1}, ..., x_n^{\pm1}]$, and $\mathbb{S}_n$ the Lie algebra of divergence zero vector fields on an $n$-dimensional torus. For any $\mathfrak{sl}_n$-module $V$ and any module $P$ over $\mathcal{K}_n$, we define an $\mathbb{S}_n$-module structure on the tensor product $P\otimes V$. In this paper, necessary and sufficient conditions for the $\mathbb{S}_n$-modules $P\otimes V$ to be simple are given, and an isomorphism criterion for nonminuscule $\mathbb{S}_n$-modules is provided. More precisely, all nonminuscule $\mathbb{S}_n$-modules are simple, and pairwise nonisomorphic. For minuscule $\mathbb{S}_n$-modules, minimal and maximal submodules are concretely constructed.

math.RT↗