arXiv subjects

Zijun Zhou

Publications and source records attributed to Zijun Zhou.

18 recordsLinked to original sources

arXiv2026

User Representation via Cross Multi-source Behavior Pre-training for Mobile Games

User representation pre-training has become a fundamental paradigm for alleviating data sparsity in downstream personalization tasks. However, existing studies predominantly focus on single-app or app-level behaviors, overlooking the inherently cross-source and multi-granular nature of user activities on mobile devices. At the device level, user intent emerges from complex interactions among heterogeneous behavior sources and hierarchical action structures, posing challenges that cannot be addressed by conventional app-centric modeling. To tackle this issue, we propose CM-PTM, a novel Cross Multi-source Behavior Pre-Training Model tailored for mobile game user representation learning on device-level behavioral logs. CM-PTM employs hierarchical cascaded mask-then-predict proxy tasks that first infer the source of the next behavior and then progressively refine predictions at the app-action level. This design enables unified modeling of cross-source dependencies and fine-grained behavioral dynamics within a single pre-training paradigm. Extensive experiments on large-scale real-world mobile datasets demonstrate that CM-PTM effectively captures users' endogenous interests and consistently delivers significant performance gains on downstream mobile game recommendation tasks.

cs.AI↗

arXiv2026

Concentrated siting of AI data centers drives regional power-system stress under rising global compute demand

The rapid rise of generative artificial intelligence (AI) is driving unprecedented growth in global computational demand, placing increasing pressure on electricity systems. This study introduces an AI-energy coupling framework that combines large language models (LLMs)-based analysis of corporate, policy, and media data with quantitative energy-system modeling to forecast the electricity footprint of AI-driven data centers from 2025 to 2030. Results show that the new AI infrastructure is highly concentrated in North America, Western Europe, and the Asia-Pacific, which together account for more than 90% of projected compute capacity. Aggregate electricity consumption by the six leading firms is projected to increase from roughly 118 TWh in 2024 to between 239 TWh and 295 TWh by 2030, equivalent to about 1% of global power demand. Regions such as Oregon, Virginia, and Ireland may experience high Power Stress Index (PSI) values exceeding 0.25, indicating local grid vulnerability, whereas diversified systems such as those in Texas and Japan can absorb new loads more effectively. These findings demonstrate that AI infrastructure is evolving from a marginal digital service into a structural component of power-system dynamics, underscoring the need for anticipatory planning that aligns computational growth with renewable expansion and grid resilience.

cs.CY↗

arXiv2026

Structured Prompt Optimization for Few-Shot Text Classification via Semantic Alignment in Latent Space

This study addresses the issues of semantic entanglement, unclear label structure, and insufficient feature representation in few-shot text classification, and proposes an optimization framework based on structured prompts to enhance semantic understanding and task adaptation under low-resource conditions. The framework first uses a pretrained language model to encode the input text and obtain basic semantic representations. It then introduces structured prompts composed of multi-dimensional semantic factors and integrates them with text features through a learnable combination mechanism, which forms task-related representations with clear boundaries in the latent space. To further strengthen the consistency between text representations and label semantics, the method constructs a structured label embedding matrix and employs a cross-space alignment mechanism to ensure stable matching between textual features and label attributes. In addition, the model applies prompt orthogonality constraints and a joint optimization objective to maintain independence across different semantic factors in the prompts, allowing the structured prompts to provide transparent and controllable guidance for classification decisions. Three types of sensitivity experiments, including learning rate sensitivity, prompt length sensitivity, and data scale sensitivity, are designed to evaluate the stability and robustness of the framework under different conditions. Experimental results show that the proposed structured prompt optimization framework effectively alleviates semantic conflicts and label ambiguity in few-shot text classification. It significantly improves performance on accuracy, precision, recall, and AUC, and demonstrates strong cross-task applicability.

cs.CL↗

arXiv2026

Symmetric quiver varieties and critical stable envelopes

Symmetric quiver varieties with potentials are natural generalizations of Nakajima quiver varieties, and their equivariant critical cohomologies provide more flexible settings for geometric representation theory and enumerative geometry. In this paper, we study their geometric properties and show that they behave like universally deformed Nakajima quiver varieties. Based on this, we provide a new proof of the existence of critical stable envelopes on them. Following an idea of Nakajima, we give a sheaf theoretic interpretation of critical stable envelopes by the hyperbolic restriction in the affinization of symmetric quiver varieties. The associativity of hyperbolic restrictions implies the triangle lemma of critical stable envelopes.

math.AG↗

arXiv2026

Shifted quantum groups via critical stable envelopes

Given a symmetric quiver with potential, we develop a geometric construction of shifted Yangians acting on the critical cohomologies of antidominantly framed quiver varieties with extended potentials, using the $R$-matrices constructed from critical stable envelopes. We relate such Reshetikhin type Yangians to Drinfeld type Yangians arising from critical cohomological Hall algebras. Several detailed examples, including the trivial, Jordan, and tripled Jordan quivers are explicitly computed. For symmetric quiver varieties with potentials, by using the smallness property of their affinization maps, we derive explicit formulas for quantum multiplication by divisors in terms of Casimir elements of the associated Lie (super)algebras, extending results from Nakajima quiver varieties to the critical setting. A similar formula in the antidominantly framed case is also obtained, which includes Hilbert schemes of points on $\mathbb C^3$ as examples.

math.RT↗

arXiv2025

Stable envelopes for critical loci

This is the first in a sequence of papers devoted to stable envelopes in critical cohomology and critical $K$-theory for symmetric GIT quotients with potentials and related geometries, and their applications to geometric representation theory and enumerative geometry. In this paper, we construct critical stable envelopes and establish their general properties, including compatibility with dimensional reductions, specializations, Hall products, and other geometric constructions. In particular, for tripled quivers with canonical cubic potentials, the critical stable envelopes reproduce those on Nakajima quiver varieties. These set up foundations for applications in subsequent papers.

math.AG↗

arXiv2025

Cluster algebra and quasimap quantum cohomology

We apply the abelianization technique to obtain an explicit ring presentation for the quasimap quantum cohomology of GIT quotients. As an application, for quiver varieties associated with oriented-acyclic quivers, we establish a cluster algebra structure on their equivariant quasimap quantum cohomology rings.

math.AG↗

arXiv2025

IF-VidCap: Can Video Caption Models Follow Instructions?

Although Multimodal Large Language Models (MLLMs) have demonstrated proficiency in video captioning, practical applications require captions that follow specific user instructions rather than generating exhaustive, unconstrained descriptions. Current benchmarks, however, primarily assess descriptive comprehensiveness while largely overlooking instruction-following capabilities. To address this gap, we introduce IF-VidCap, a new benchmark for evaluating controllable video captioning, which contains 1,400 high-quality samples. Distinct from existing video captioning or general instruction-following benchmarks, IF-VidCap incorporates a systematic framework that assesses captions on two dimensions: format correctness and content correctness. Our comprehensive evaluation of over 20 prominent models reveals a nuanced landscape: despite the continued dominance of proprietary models, the performance gap is closing, with top-tier open-source solutions now achieving near-parity. Furthermore, we find that models specialized for dense captioning underperform general-purpose MLLMs on complex instructions, indicating that future work should simultaneously advance both descriptive richness and instruction-following fidelity.

cs.CV↗

arXiv2025

Multi-turn Consistent Image Editing

Many real-world applications, such as interactive photo retouching, artistic content creation, and product design, require flexible and iterative image editing. However, existing image editing methods primarily focus on achieving the desired modifications in a single step, which often struggles with ambiguous user intent, complex transformations, or the need for progressive refinements. As a result, these methods frequently produce inconsistent outcomes or fail to meet user expectations. To address these challenges, we propose a multi-turn image editing framework that enables users to iteratively refine their edits, progressively achieving more satisfactory results. Our approach leverages flow matching for accurate image inversion and a dual-objective Linear Quadratic Regulators (LQR) for stable sampling, effectively mitigating error accumulation. Additionally, by analyzing the layer-wise roles of transformers, we introduce a adaptive attention highlighting method that enhances editability while preserving multi-turn coherence. Extensive experiments demonstrate that our framework significantly improves edit success rates and visual fidelity compared to existing methods.

cs.CV↗

arXiv2024

A degeneration formula of Donaldson-Thomas theory on local Calabi-Yau 4-folds

We define relative Donaldson-Thomas invariants of local log Calabi-Yau 4-folds, under the assumption that the derived Hilbert scheme on the anti-canonical divisor is a derived critical locus. We prove a degeneration formula and apply it to compute zero dimensional invariants on $\mathbb{C}^4$ and on any local curve. This verifies a conjecture proposed by the first author and Kool.

math.AG↗

arXiv2023

Virtual Coulomb branch and vertex functions

We introduce a variant of the $K$-theoretic quantized Coulomb branch constructed by Braverman--Finkelberg--Nakajima, by application of a new virtual intersection theory. In the abelian case, we define Verma modules for such virtual Coulomb branches, and relate them to the moduli spaces of quasimaps into the corresponding Higgs branches. The descendent vertex functions, defined by $K$-theoretic quasimap invariants of the Higgs branch, can be realized as the associated Whittaker functions. The quantum $q$-difference modules and Bethe algebras (analogue of quantum $K$-theory rings) can then be described in terms of the virtual Coulomb branch. As an application, we prove the wall-crossing result for quantum $q$-difference modules under the variation of GIT. Nonabelian cases are also treated via abelianization.

math.AG↗

arXiv2021

3d Mirror Symmetry and Quantum $K$-theory of Hypertoric Varieties

Following the idea of Aganagic--Okounkov \cite{AOelliptic}, we study vertex functions for hypertoric varieties, defined by $K$-theoretic counting of quasimaps from $\mathbb{P}^1$. We prove the 3d mirror symmetry statement that the two sets of $q$-difference equations of a 3d hypertoric mirror pairs are equivalent to each other, with Kähler and equivariant parameters exchanged, and the opposite choice of polarization. Vertex functions of a 3d mirror pair, as solutions to the $q$-difference equations, satisfying particular asymptotic conditions, are related by the elliptic stable envelopes. Various notions of quantum $K$-theory for hypertoric varieties are also discussed.

math.AG↗

arXiv2021

Gromov--Witten theory of $[\mathbb{C}^2/\mathbb{Z}_{n+1}]\times \mathbb{P}^1$

We compute the relative orbifold Gromov-Witten invariants of $[\mathbb{C}^2/\mathbb{Z}_{n+1}]\times \mathbb{P}^1$, with respect to vertical fibers. Via a vanishing property of the Hurwitz-Hodge bundle, 2-point rubber invariants are calculated explicitly using Pixton's formula for the double ramification cycle, and the orbifold quantum Riemann-Roch. As a result parallel to its crepant resolution counterpart for $\mathcal{A}_n$, the GW/DT/Hilb/Sym correspondence is established for $[\mathbb{C}^2/\mathbb{Z}_{n+1}]$. The computation also implies the crepant resolution conjecture for relative orbifold Gromov-Witten theory of $[\mathbb{C}^2/\mathbb{Z}_{n+1}]\times \mathbb{P}^1$.

math.AG↗

arXiv2020

3d Mirror Symmetry and Elliptic Stable Envelopes

We consider a pair of quiver varieties (X;X') related by 3d mirror symmetry, where X =T*Gr(k,n) is the cotangent bundle of the Grassmannian of k-planes of n-dimensional space. We give formulas for the elliptic stable envelopes on both sides. We show an existence of an equivariant elliptic cohomology class on X $\times$ X' (the Mother function) whose restrictions to X and X' are the elliptic stable envelopes of those varieties. This implies, that the restriction matrices of the elliptic stable envelopes for X and X' are equal after transposition and identification of the equivariant parameters on one side with the Kähler parameters on the dual side.

math.AG↗

arXiv2020

Quantum $K$-theory of toric varieties, level structures, and 3d mirror symmetry

We introduce a new version of 3d mirror symmetry for toric stacks, inspired by a 3d $\mathcal{N} = 2$ abelian mirror symmetry construction in physics. Given some toric data, we introduce the $K$-theoretic $I$-function with effective level structure for the associated toric stack. When a particular stability condition is chosen, it restricts to the $I$-function for the particular toric GIT quotient. The mirror of a toric stack is defined by the Gale dual of the original toric data. We then proved the mirror conjecture that the $I$-functions of a mirror pair coincide, under the mirror map, which switches Kähler and equivariant parameters, and maps $q\mapsto q^{-1}$.

math.AG↗

arXiv2019

Three-Dimensional Mirror Self-Symmetry of the Cotangent Bundle of the Full Flag Variety

Let $X$ be a holomorphic symplectic variety with a torus $\mathsf{T}$ action and a finite fixed point set of cardinality $k$. We assume that elliptic stable envelope exists for $X$. Let $A_{I,J}= \operatorname{Stab}(J)|_{I}$ be the $k\times k$ matrix of restrictions of the elliptic stable envelopes of $X$ to the fixed points. The entries of this matrix are theta-functions of two groups of variables: the Kähler parameters and equivariant parameters of $X$. We say that two such varieties $X$ and $X'$ are related by the 3d mirror symmetry if the fixed point sets of $X$ and $X'$ have the same cardinality and can be identified so that the restriction matrix of $X$ becomes equal to the restriction matrix of $X'$ after transposition and interchanging the equivariant and Kähler parameters of $X$, respectively, with the Kähler and equivariant parameters of $X'$. The first examples of pairs of 3d symmetric varieties were constructed in [Rimányi R., Smirnov A., Varchenko A., Zhou Z., arXiv:1902.03677], where the cotangent bundle $T^*\operatorname{Gr}(k,n)$ to a Grassmannian is proved to be a 3d mirror to a Nakajima quiver variety of $A_{n-1}$-type. In this paper we prove that the cotangent bundle of the full flag variety is 3d mirror self-symmetric. That statement in particular leads to nontrivial theta-function identities.

math.AG↗

arXiv2018

Donaldson-Thomas theory of $[\mathbb{C}^2/\mathbb{Z}_{n+1}]\times \mathbb{P}^1$

We study the relative orbifold Donaldson-Thomas theory of $[\mathbb{C}^2/\mathbb{Z}_{n+1}]\times \mathbb{P}^1$. We establish a correspondence between the DT theory relative to 3 fibers to quantum multiplication by divisors in the Hilbert scheme of points on $[\mathbb{C}^2/\mathbb{Z}_{n+1}]$. This determines the whole theory if a further nondegeneracy condition is assumed. The result can also be viewed as a crepant resolution correspondence to the DT theory of $\mathcal{A}_n\times \mathbb{P}^1$.

math.AG↗

arXiv2017

Relative Orbifold Donaldson-Thomas Theory and the Degeneration Formula

We generalize the notion of expanded degenerations and pairs for a simple degeneration or smooth pair to the case of smooth Deligne-Mumford stacks. We then define stable quotients on the classifying stacks of expanded degenerations and pairs and prove the properness of their moduli's. On 3-dimensional smooth projective DM stacks this leads to a definition of relative Donaldson-Thomas invariants and the associated degeneration formula.

math.AG↗