arXiv subjects

Jianqi Liu

Publications and source records attributed to Jianqi Liu.

25 records · Page 2Linked to original sources

arXiv2023

Twisted restricted conformal blocks of vertex operator algebras I: $g$-twisted correlation functions and fusion rules

In this paper, we introduce a notion of $g$-twisted restricted conformal block on the three-pointed twisted projective line $\mathfrak{x}\colon\overline{C}\to\mathbb{P^1}$ associated with an untwisted module $M^1$ and the bottom levels of two $g$-twisted modules $M^2$ and $M^3$ over a vertex operator algebra $V$. We show that the space of twisted restricted conformal blocks is isomorphic to the space of $g$-twisted (restricted) correlation functions defined by the same datum and to the space of intertwining operators among these twisted modules. As an application, we derive a twisted version of the Fusion Rules Theorem.

math.QA↗

arXiv2023

RTrack: Accelerating Convergence for Visual Object Tracking via Pseudo-Boxes Exploration

Single object tracking (SOT) heavily relies on the representation of the target object as a bounding box. However, due to the potential deformation and rotation experienced by the tracked targets, the genuine bounding box fails to capture the appearance information explicitly and introduces cluttered background. This paper proposes RTrack, a novel object representation baseline tracker that utilizes a set of sample points to get a pseudo bounding box. RTrack automatically arranges these points to define the spatial extents and highlight local areas. Building upon the baseline, we conducted an in-depth exploration of the training potential and introduced a one-to-many leading assignment strategy. It is worth noting that our approach achieves competitive performance to the state-of-the-art trackers on the GOT-10k dataset while reducing training time to just 10% of the previous state-of-the-art (SOTA) trackers' training costs. The substantial reduction in training costs brings single-object tracking (SOT) closer to the object detection (OD) task. Extensive experiments demonstrate that our proposed RTrack achieves SOTA results with faster convergence.

cs.CV↗

arXiv2023

LiteTrack: Layer Pruning with Asynchronous Feature Extraction for Lightweight and Efficient Visual Tracking

The recent advancements in transformer-based visual trackers have led to significant progress, attributed to their strong modeling capabilities. However, as performance improves, running latency correspondingly increases, presenting a challenge for real-time robotics applications, especially on edge devices with computational constraints. In response to this, we introduce LiteTrack, an efficient transformer-based tracking model optimized for high-speed operations across various devices. It achieves a more favorable trade-off between accuracy and efficiency than the other lightweight trackers. The main innovations of LiteTrack encompass: 1) asynchronous feature extraction and interaction between the template and search region for better feature fushion and cutting redundant computation, and 2) pruning encoder layers from a heavy tracker to refine the balnace between performance and speed. As an example, our fastest variant, LiteTrack-B4, achieves 65.2% AO on the GOT-10k benchmark, surpassing all preceding efficient trackers, while running over 100 fps with ONNX on the Jetson Orin NX edge device. Moreover, our LiteTrack-B9 reaches competitive 72.2% AO on GOT-10k and 82.4% AUC on TrackingNet, and operates at 171 fps on an NVIDIA 2080Ti GPU. The code and demo materials will be available at https://github.com/TsingWei/LiteTrack.

cs.CV↗

arXiv2023

On Rota-Baxter vertex operator algebras

Derivations play a fundamental role in the definition of vertex (operator) algebras, sometimes regarded as a generalization of differential commutative algebras. This paper studies the role played by the integral counterpart of the derivations, namely Rota-Baxter operators, in vertex (operator) algebras. The closely related notion of dendriform algebras is also defined for vertex operator algebras. It is shown that the classical relations among dendriform algebras, associative algebras, and Rota-Baxter algebras are preserved for their vertex algebra analogs.

math.QA↗

arXiv2023

Classical Yang-Baxter equation for vertex operator algebras and its operator forms

In this paper we introduce an analog of the (classical) Yang-Baxter equation (CYBE) for vertex operator algebras (VOAs) in its tensor form, called the vertex operator Yang-Baxter equation (VOYBE). When specialized to level one of a vertex operator algebra, the VOYBE reduces to the CYBE for Lie algebras. To give an operator form of the VOYBE, we also introduce the notion of relative Rota-Baxter operators (RBOs) as the VOA analog of relative RBOs (classically called $\mathcal{O}$-operators) for Lie algebras. It is shown that skewsymmetric solutions $r$ to the VOYBE in a VOA $U$ are characterized by the condition that their corresponding linear maps $T_r:U'\to U$ from the graded dual $U'$ of $U$ are relative RBOs. On the other hand, strong relative RBOs on a VOA $V$ associated to an ordinary $V$-module $W$ are characterized by the condition that their antisymmetrizers are solutions to the $0$-VOYBE in the semidirect product VOA $V\rtimes W'$. Specializing to the first level of a VOA, these relations between the solutions of the VOYBE and the relative RBOs for VOAs recover the classical relations between the solutions of the CYBE and the relative RBOs for Lie algebras.

math.QA↗

arXiv2023

Endomorphism property of vertex operator algebras over arbitrary fields

In this paper, we study the endomorphism properties of vertex operator algebras over an arbitrary field $\mathbb{F}$, with $\text{Char}(\mathbb{F}) \neq 2$. Let $V$ be a strongly finitely generated vertex operator algebra over $\mathbb{F}$, and $M$ be an irreducible admissible $V$-module. We prove that every element in $\text{End}_V(M)$ is algebraic over $\mathbb{F}$ and that $\text{End}_V(M)$ is also finite-dimensional. As an application, we prove Schur's lemma for strongly finitely generated vertex operator algebras over arbitrary algebraically closed fields, and we give a test for absolute irreducibility of $V$-modules.

math.QA↗

arXiv2022

A proof of the fusion rules theorem

We prove that the space of intertwining operators associated with certain admissible modules over vertex operator algebras is isomorphic to a quotient of the vector space of conformal blocks on a three-pointed rational curve defined by the same data. This provides a new proof and alternative version of Frenkel and Zhu's fusion rules theorem in terms of the dimension of certain bimodules over Zhu's algebra, without the assumption of rationality.

math.QA↗