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Zelin Jia

Publications and source records attributed to Zelin Jia.

6 recordsLinked to original sources
arXiv2026

PixelART: Image-to-Layer Decomposition without Latents or Text-to-Image Pretraining

Image-to-layer decomposition converts a flattened image into editable RGBA layers, enabling element-level editing in design workflows. Existing diffusion-based systems typically adapt large pretrained text-to-image (T2I) models and introduce RGBA autoencoders or variable-layer architectural modules. We revisit this design choice and ask whether layer decomposition truly requires these heavyweight components. We introduce PixelART, a pixel-space rectified-flow Transformer trained from scratch for image-to-layer (I2L) decomposition. PixelART directly denoises regional RGBA pixel patches using a single-stream multi-modal diffusion Transformer, avoiding RGBA-VAEs, pretrained T2I backbones, and layer-specific decoders. We identify a key property of the task: high-noise timesteps determine layer assignment and coarse layer organization, while low-noise timesteps mainly refine color, alpha, texture, and boundaries. Based on this observation, we propose a terminal-boosted timestep sampling strategy to increase training coverage in the high-noise layer assignment regime. Trained on 4M multi-layer design templates, PixelART achieves state-of-the-art layer decomposition and composite reconstruction on Design-Multi-Layer-Bench and LICA with over 80% fewer parameters, 98% lower latency, and 85% lower memory than the recent Qwen-Image-Layered model. Ablation experiments show that pixel-space $\mathbf{x}$-prediction, terminal-boosted timestep sampling, and data/model scaling are critical, while T2I pretraining brings marginal benefits to the I2L task.

cs.CV↗
arXiv2026

On the symplectic forms of Groechenig's Higgs moduli over an elliptic curve

Gorsky, Nekrasov, and Rubtsov introduced the moduli space of marked Higgs bundles over an elliptic curve $E$ and identified it with the Hilbert scheme of points on the cotangent bundle. Later, Groechenig constructed four analogous isomorphisms on marked rational curves, of affine Dynkin types $\widetilde D_4$, $\widetilde E_6$, $\widetilde E_7$, and $\widetilde E_8$, for the $Γ$-Hilbert schemes of $T^*E$ for cyclic groups $Γ$ with $|Γ|\in\{2,3,4,6\}$. We prove that the isomorphisms in all five cases are holomorphic symplectomorphisms.

math.AG↗
arXiv2026

The Logarithmic Asymptotic Phenomenon for Generalized Markov-Hurwitz Equations

The purpose of this paper is twofold. First, we introduce a family of generalized Markov-Hurwitz equations, extending classical Markov-Hurwitz equations with additional degree n-1 interaction terms, Gyoda and Matsushita's generalized Markov equations from 3 variables to n variables. Second, we prove a logarithmic asymptotic phenomenon for the positive integer solutions of these equations.

math.NT↗
arXiv2025

Tropicalization and cluster asymptotic phenomenon of generalized Markov equations

The generalized Markov equations are deeply connected with the generalized cluster algebras of Markov type. We construct a deformed Fock-Goncharov tropicalization for the generalized Markov equations and prove that their tropicalized tree structure is essentially the same as that of the classical Euclid tree. We then define the generalized Euclid tree and prove that it converges to the classical Euclid tree up to a scalar multiple. Moreover, by means of cluster mutations, we exhibit an asymptotic phenomenon, up to some limit q, between the logarithmic generalized Markov tree and the classical Euclid tree. A rationality conjecture of q is then put forward. We also propose a generalized Markov uniqueness conjecture for the generalized Markov equations, which illustrates an application of the asymptotic phenomenon.

math.NT↗
arXiv2024

Dynamic Color Assignment for Hierarchical Data

Assigning discriminable and harmonic colors to samples according to their class labels and spatial distribution can generate attractive visualizations and facilitate data exploration. However, as the number of classes increases, it is challenging to generate a high-quality color assignment result that accommodates all classes simultaneously. A practical solution is to organize classes into a hierarchy and then dynamically assign colors during exploration. However, existing color assignment methods fall short in generating high-quality color assignment results and dynamically aligning them with hierarchical structures. To address this issue, we develop a dynamic color assignment method for hierarchical data, which is formulated as a multi-objective optimization problem. This method simultaneously considers color discriminability, color harmony, and spatial distribution at each hierarchical level. By using the colors of parent classes to guide the color assignment of their child classes, our method further promotes both consistency and clarity across hierarchical levels. We demonstrate the effectiveness of our method in generating dynamic color assignment results with quantitative experiments and a user study.

cs.HC↗