arXiv subjects

Xiaoqiu Zhong

Publications and source records attributed to Xiaoqiu Zhong.

2 recordsLinked to original sources

arXiv2026

DreamWorld: Unified World Modeling in Video Generation

Despite impressive progress in video generation, existing models remain limited to surface-level plausibility, lacking a coherent and unified understanding of the world. Prior approaches typically incorporate only a single form of world-related knowledge or rely on rigid alignment strategies to introduce additional knowledge. However, aligning the single world knowledge is insufficient to constitute a world model that requires jointly modeling multiple heterogeneous dimensions (e.g., physical commonsense, 3D and temporal consistency). To address this limitation, we introduce \textbf{DreamWorld}, a unified framework that integrates complementary world knowledge into video generators via a \textbf{Joint World Modeling Paradigm}, jointly predicting video pixels and features from foundation models to capture temporal dynamics, spatial geometry, and semantic consistency. However, naively optimizing these heterogeneous objectives can lead to visual instability and temporal flickering. To mitigate this issue, we propose \textit{Consistent Constraint Annealing (CCA)} to progressively regulate world-level constraints during training, and \textit{Multi-Source Inner-Guidance} to enforce learned world priors at inference. Extensive evaluations show that DreamWorld improves world consistency, outperforming Wan2.1 by 2.26 points on VBench. Code will be made publicly available at \href{https://github.com/ABU121111/DreamWorld}{\textcolor{mypink}{\textbf{Github}}}.

cs.CV↗

arXiv2026

Quasi-Hereditary Orderings of Nakayama Algebras

Let $A$ be an algebra, and let $\mathcal{S}$ be the set of isomorphism classes of simple $A$-modules, with $|\mathcal{S}|=n$. In this paper, a total ordering of $\mathcal{S}$ is called a quasi-hereditary ordering, or a $q$-ordering, for $A$ if every Weyl module is Schurian and every indecomposable projective $A$-module is filtered by Weyl modules. The number of such total orderings is denoted by $q(A)$. Determining whether a given total ordering of $\mathcal{S}$ is a $q$-ordering is a difficult problem. A result of Dlab and Ringel states that $A$ is hereditary if and only if every total ordering of $\mathcal{S}$ is a $q$-ordering; equivalently, $q(A)=n!$. The $q$-ordering conjecture, proposed in 2000, asserts that every non-hereditary algebra $A$ satisfies $q(A)\le\dfrac{2}{3}n!$. The main result of this paper is a necessary and sufficient criterion for a total ordering of the simple modules of a Nakayama algebra to be a $q$-ordering. More precisely, we show that a total ordering is a $q$-ordering if and only if, for every minimal relation $g$, the maximal element of $\operatorname{Hod}(g)$ does not belong to $\operatorname{Int}(g)$. As consequences, we characterize quasi-hereditary Nakayama algebras by the non-emptiness of the $X$-set, derive an iteration formula for $q(A)$, and prove the $q$-ordering conjecture for Nakayama algebras. Finally, we give a non-monomial example showing that the conjecture does not hold for general finite-dimensional algebras.

math.RT↗