arXiv subjects

Zhen Xiong

Publications and source records attributed to Zhen Xiong.

27 records · Page 2Linked to original sources

arXiv2025

Wasserstein complexity penalization priors: a new class of penalizing complexity priors

Penalizing complexity (PC) priors provide a principled framework for reducing model complexity by penalizing the Kullback--Leibler Divergence (KLD) between a ``simple'' base model and a more complex model. However, constructing priors by penalizing the KLD becomes impossible in many cases because the KLD is infinite, and alternative principles often lose interpretability in terms of KLD. We propose a new class of priors, the Wasserstein complexity penalization (WCP) priors, which replace the KLD with the Wasserstein distance in the PC prior framework. WCP priors avoid the issue of infinite model distances and retain interpretability by adhering to adjusted principles. Additionally, we introduce the concept of base measures, removing the parameter dependency on the base model, and extend the framework to joint WCP priors for multiple parameters. These priors can be constructed analytically and we have both analytical and numerical implementations in R programming language. We demonstrate their use in previous PC prior applications and as well as new multivariate settings.

stat.ME↗

arXiv2025

Enhancing LLM Character-Level Manipulation via Divide and Conquer

Large Language Models (LLMs) have demonstrated strong generalization capabilities across a wide range of natural language processing (NLP) tasks. However, they exhibit notable weaknesses in character-level string manipulation, struggling with fundamental operations such as character deletion, insertion, and substitution. These challenges stem primarily from tokenization constraints, despite the critical role of such operations in data preprocessing and code generation. Through systematic analysis, we derive two key insights: (1) LLMs face significant difficulties in leveraging intrinsic token knowledge for character-level reasoning, and (2) atomized word structures can substantially enhance LLMs' ability to process token-level structural information. Building on these insights, we propose Character-Level Manipulation via Divide and Conquer, a novel approach designed to bridge the gap between token-level processing and character-level manipulation. Our method decomposes complex operations into explicit character-level subtasks coupled with controlled token reconstruction phases, leading to significant improvements in accuracy. Without additional training, our method significantly improves accuracies on the $\texttt{Deletion}$, $\texttt{Insertion}$, and $\texttt{Substitution}$ tasks. To support further research, we open-source our implementation and benchmarks.

cs.CL↗

arXiv2025

Enhancing Image Generation Fidelity via Progressive Prompts

The diffusion transformer (DiT) architecture has attracted significant attention in image generation, achieving better fidelity, performance, and diversity. However, most existing DiT - based image generation methods focus on global - aware synthesis, and regional prompt control has been less explored. In this paper, we propose a coarse - to - fine generation pipeline for regional prompt - following generation. Specifically, we first utilize the powerful large language model (LLM) to generate both high - level descriptions of the image (such as content, topic, and objects) and low - level descriptions (such as details and style). Then, we explore the influence of cross - attention layers at different depths. We find that deeper layers are always responsible for high - level content control, while shallow layers handle low - level content control. Various prompts are injected into the proposed regional cross - attention control for coarse - to - fine generation. By using the proposed pipeline, we enhance the controllability of DiT - based image generation. Extensive quantitative and qualitative results show that our pipeline can improve the performance of the generated images.

cs.CV↗

arXiv2024

Skew-Hom-Lie algebras in Semi-Euclidean spaces

In this paper, first we introduce the notion of a skew-Hom-Lie algebra and give some examples. Then we study their representations and give the coboundary operator of skew-Hom-Lie algebras. As an application, there have a skew-Hom-Lie algebra $(R^4_2,[\cdot,\cdot]_θ,P)$ in semi-Euclidean spaces. For the null space of Semi-Euclidean spaces, there have a subset $V^*$ of the null space, and $V^*$ is invariant under the actions of $[\cdot,\cdot]_θ$ and $P$.

math-ph↗

arXiv2023

Covariance-based rational approximations of fractional SPDEs for computationally efficient Bayesian inference

The stochastic partial differential equation (SPDE) approach is widely used for modeling large spatial datasets. It is based on representing a Gaussian random field $u$ on $\mathbb{R}^d$ as the solution of an elliptic SPDE $L^βu = \mathcal{W}$ where $L$ is a second-order differential operator, $2β$ (belongs to natural number starting from 1) is a positive parameter that controls the smoothness of $u$ and $\mathcal{W}$ is Gaussian white noise. A few approaches have been suggested in the literature to extend the approach to allow for any smoothness parameter satisfying $β>d/4$. Even though those approaches work well for simulating SPDEs with general smoothness, they are less suitable for Bayesian inference since they do not provide approximations which are Gaussian Markov random fields (GMRFs) as in the original SPDE approach. We address this issue by proposing a new method based on approximating the covariance operator $L^{-2β}$ of the Gaussian field $u$ by a finite element method combined with a rational approximation of the fractional power. This results in a numerically stable GMRF approximation which can be combined with the integrated nested Laplace approximation (INLA) method for fast Bayesian inference. A rigorous convergence analysis of the method is performed and the accuracy of the method is investigated with simulated data. Finally, we illustrate the approach and corresponding implementation in the R package rSPDE via an application to precipitation data which is analyzed by combining the rSPDE package with the R-INLA software for full Bayesian inference.

stat.ME↗

arXiv2018

Hom-Lie groups of a class of Hom-Lie algebra

In this paper, the definition of Hom-Lie groups is given and one conntected component of Lie group $GL(V)$, which is not a subgroup of $GL(V)$, is a Hom-Lie group. More, we proved that there is a one-to-one relationship between Hom-Lie groups and Hom-Lie algebras $(\gl(V),[\cdot,\cdot]_β,\rm{Ad}_β)$. Next, we also proved that if there is a Hom-Lie group homomorphism, then, there is a morphism between their Hom-Lie algebras. Last, as an application, we use these results on Toda lattice equation.

math.RA↗

arXiv2018

A complement on representations of Hom-Lie algebras

In this paper, we give a new series of coboundary operators of Hom-Lie algebras. And prove that cohomology groups with respect to coboundary operators are isomorphic. Then, we revisit representations of Hom-Lie algebras, and generalize the relation between Lie algebras and their representations to Hom-Lie algebras.

math.RA↗

arXiv2018

Equivalent description of Hom-Lie algebroids

In this paper, we study representations of Hom-Lie algebroids, give some properties of Hom-Lie algebroids and discuss equivalent statements of Hom-Lie algebroids. Then, we prove that two known definitions of Hom-Lie algebroids can be transformed into each other under some conditions.

math.RA↗

arXiv2014

On hom-Lie algebras

In this paper, first we show that $(\g,[\cdot,\cdot],α)$ is a hom-Lie algebra if and only if $(Λ\g^*,α^*,d)$ is an $(α^*,α^*)$-differential graded commutative algebra. Then, we revisit representations of hom-Lie algebras, and show that there are a series of coboundary operators. We also introduce the notion of an omni-hom-Lie algebra associated to a vector space and an invertible linear map. We show that regular hom-Lie algebra structures on a vector space can be characterized by Dirac structures in the corresponding omni-hom-Lie algebra. The underlying algebraic structure of the omni-hom-Lie algebra is a hom-Leibniz algebra, or a hom-Lie 2-algebra.

math-ph↗