arXiv subjects

Yuxu Chen

Publications and source records attributed to Yuxu Chen.

18 recordsLinked to original sources

arXiv2026

The reflective hull of the two-element chain in DCPO: properness, maximal \Gamma-faithfulness, and an internal reflection formula

Let $\DCPO$ be the category of dcpos and Scott-continuous maps, and let $\Rtwo$ be the reflective hull of the two-element chain $2$. We prove that $\Rtwo$ is the least non-discrete proper reflective full subcategory of $\DCPO$. It is closed under limits and Skula-closed sub-dcpos and contains every sober dcpo. We show that $\Rtwo$ is the maximal $\Gamma$-faithful full subcategory of $\DCPO$ that strictly contains weakly dominated dcpos. Finally, we give the concrete construction of $2$-reflection internally by a transfinite iteration and a criterion for reflective full subcategories of $\DCPO$, analogous to the Keimel--Lawson conditions for $T_0$ topological spaces.

math.GN↗

arXiv2026

Finite-valuation approximable structures: a solution to the Jung--Tix problem of probabilistic powerdomains

We introduce the category $\omega{\bf FVA}$ of finite-valuation approximable domains, a full subcategory of continuous domains contained in the category of pointed countably based FS-domains. We prove that $\omega{\bf FVA}$ is Cartesian closed and closed under both the subprobabilistic and probabilistic valuation powerdomains. Hence the valuation monads $\mathcal{V}_{\leq 1}$ and $\mathcal{V}_1$ restrict to $\omega{\bf FVA}$, yielding a positive answer to the category-existence form of the Jung--Tix problem, a long-standing open problem in domain theory since the 1990s. In particular, we develop a new factorization-approximation framework for constructing objects from a given class of known objects or structures. Applying this method to the class of subprobabilistic powerdomains over finite posets, we construct the class $\omega{\bf FVA}$ and show that it is closed under Scott-continuous retracts, finite products, function spaces, $\mathcal{V}_{\leq 1}$ and $\mathcal{V}_1$ monads.

cs.LO↗

arXiv2026

A note on probabilistic powerdomains, RB-domains, and bc-domains

For a finite nonempty poset $F$, the normalized probabilistic powerdomain $\Vone(F)$ is an RB-domain exactly when $F$ is a finite rooted tree. We extend this classification to arbitrary nonempty dcpos from the viewpoint of forbidden structure. The principal-ideal chain condition is expressed by the absence of a lower fork, i.e. a triple $(x,y,t)$ with $x\leq t$, $y\leq t$, and $x\parallel y$. A useful point is that any dcpo $P$ without lower forks is continuous. For normalized valuations the least element remains necessary, and we prove \[ \begin{aligned} \Vone(P)\text{ is RB} \Longleftrightarrow \Vone(P)\text{ is a pointed bc-domain} \Longleftrightarrow P\text{ has a least element and contains no lower fork}. \end{aligned} \] For subprobability and extended valuations, the analogous classifications hold without the pointedness assumption on $P$.

math.GN↗

arXiv2026

Characterizing finite posets whose probabilistic powerdomain are RB-domains

We classify the finite posets whose probabilistic powerdomain is an RB-domain. For a finite nonempty poset $P$, let $\Vone(P)$ be the probability powerdomain of $P$, which is the probability simplex ordered by the stochastic order. We prove that $\Vone(P)$ is an RB-domain if and only if $P$ has a least element and the undirected Hasse graph of $P$ is a tree. Consequently, the probabilistic powerdomain does not preserve RB-domains; the four-point diamond gives a finite counterexample. The proof separates two obstructions. First, if $P$ has no least element, then the face of probability measures supported on the minimal points must be fixed pointwise by every deflation below the identity. Secondly, once a least element exists, the Hasse graph is connected, and a cycle in it makes the local stochastic cone non-simplicial. A Euclidean finite-step cone argument then rules out the finite-valued monotone approximations supplied by the RB property.

math.CO↗

arXiv2026

Cone domains separate FS-domains from RB-domains

Let $C$ be a closed, convex, pointed and generating cone in a finite-dimensional real vector space $V$, and let $ D_C=(-C)\cup\{\bot\}$ be the negative cone with a new least element, ordered by the cone order. Keimel proved that these cone domains are FS-domains and asked whether they are always retracts of bifinite domains. We give a sharp answer: \[D_C\text{ is an RB-domain}\quad\Longleftrightarrow\quad C\text{ is simplicial}. \] Thus every non-simplicial proper cone gives an FS-domain which is not an RB-domain. The proof converts the RB approximation property into finite-valued $C$-isotone approximations of the identity. The analytic obstruction is elementary and finite-dimensional: first in Euclidean space, cone-upper sets are represented, up to null sets, as Lipschitz epigraphs; Rademacher's theorem, Fubini's theorem and integration by parts then force the matrix tested against any finite-valued isotone map to lie in the cone generated by the positive rank-one operators $v\otimes\ell$, $v\in C$, $\ell\in C^*$. If such maps approximate the identity, the identity operator lies in this rank-one cone, which is possible exactly when the cone is simplicial. This answers Keimel's question in the negative for the Lorentz cone and other non-simplicial cones.

math.GN↗

arXiv2026

FS-domains are not always RB-domains

We prove that Lawson's planar closed-disk domain is not an RB-domain. This domain is the dcpo of all closed disks in the Euclidean plane, together with the whole plane as bottom, ordered by reverse inclusion. Since this domain is an FS-domain, it gives a concrete example of an FS-domain which is not an RB-domain, answering negatively the long-standing open problem in domain theory of whether FS-domains and RB-domains are identical.

math.GN↗

arXiv2026

ChLogic: Evaluating Robustness of Logical Reasoning in Chinese Expressions

Large language models perform increasingly well on standardized logical reasoning benchmarks, but whether this ability remains robust beyond English is unclear. We introduce ChLogic, an English--Chinese aligned benchmark that tests whether models preserve logical reasoning performance when the same latent logical structure is expressed in English and diverse Chinese surface realizations. Built from formal logical templates, the benchmark contains three data sets: (i) the General aligned set, derived from 60 General Propositions across nine template families; (ii) the Difficult aligned set, derived from 40 Difficult Problems; and (iii) the Chinese-only set, covering 15 language-specific phenomenon types. Each aligned item pairs one English reference expression with five Chinese realizations. Experiments on Qwen3, Ministral, and GLM models reveal a persistent English--Chinese performance gap. Back-translation from standard Chinese into English often improves performance on the General aligned set, but produces mixed effects on the Difficult aligned set, where Qwen3-32B and GLM-5.1 perform worse after translation. These results indicate that Chinese surface realization, translation artifacts, and model-specific behavior jointly affect multilingual logical reasoning. Overall, ChLogic provides a useful stress test for the robustness of multilingual reasoning.

cs.CL↗

arXiv2026

Directed Convex Powerspaces and Convex Powerdomains

It is known that lower powerdomains preserve and reflect both continuity and quasicontinuity, while the preservation of quasicontinuity by upper and convex powerdomains had long been open. Directed spaces provide a topological extension framework for dcpos. Powerdomains of dcpos can be characterized as the $D$-completions of the corresponding directed powerspaces. Using this observation, the authors proved in 2024 that upper powerdomains do not preserve quasicontinuity. In this paper, we prove that directed convex powerspaces and convex powerdomains do not preserve quasicontinuity, but they do reflect both continuity and quasicontinuity. We also prove that upper powerspaces and upper powerdomains reflect quasicontinuity. Together with the known results for lower and upper powerdomains, these arguments give the complete preservation and reflection profile of the lower, upper and convex powerdomains for continuity and quasicontinuity.

math.GN↗

arXiv2026

NTIRE 2026 The 3rd Restore Any Image Model (RAIM) Challenge: Multi-Exposure Image Fusion in Dynamic Scenes (Track 2)

This paper presents NTIRE 2026, the 3rd Restore Any Image Model (RAIM) challenge on multi-exposure image fusion in dynamic scenes. We introduce a benchmark that targets a practical yet difficult HDR imaging setting, where exposure bracketing must be fused under scene motion, illumination variation, and handheld camera jitter. The challenge data contains 100 training sequences with 7 exposure levels and 100 test sequences with 5 exposure levels, reflecting real-world scenarios that frequently cause misalignment and ghosting artefacts. We evaluate submissions with a leaderboard score derived from PSNR, SSIM, and LPIPS, while also considering perceptual quality, efficiency, and reproducibility during the final review. This track attracted 114 participating teams and received 987 submissions. The winning methods significantly improved the ability to remove artifacts from multi-exposure fusion and recover fine details. The dataset and the code of each team can be found at the repository: https://github.com/qulishen/RAIM-HDR.

cs.CV↗

arXiv2025

ABE-CLIP: Training-Free Attribute Binding Enhancement for Compositional Image-Text Matching

Contrastive Language-Image Pretraining (CLIP) has achieved remarkable performance in various multimodal tasks. However, it still struggles with compositional image-text matching, particularly in accurately associating objects with their corresponding attributes, because its inherent global representation often overlooks fine-grained semantics for attribute binding. Existing methods often require additional training or extensive hard negative sampling, yet they frequently show limited generalization to novel compositional concepts and fail to fundamentally address the drawbacks of global representations. In this paper, we propose ABE-CLIP, a novel training-free Attribute Binding Enhancement method designed to strengthen attribute-object binding in CLIP-like models. Specifically, we employ a Semantic Refinement Mechanism to refine token embeddings for both object and attribute phrases in the text, thereby mitigating attribute confusion and improving semantic precision. We further introduce a Local Token-Patch Alignment strategy that computes similarity scores between refined textual tokens and their most relevant image patches. By aggregating localized similarity scores, ABE-CLIP computes the final image-text similarity. Experiments on multiple datasets demonstrate that ABE-CLIP significantly improves attribute-object binding performance, even surpassing methods that require extensive training.

cs.CV↗

arXiv2025

Reducts of fuzzy contexts: Formal concept analysis vs. rough set theory

We postulate the intuitive idea of reducts of fuzzy contexts based on formal concept analysis and rough set theory. For a complete residuated lattice $L$, it is shown that reducts of $L$-contexts in formal concept analysis are interdefinable with reducts of $L$-contexts in rough set theory via negation if, and only if, $L$ satisfies the law of double negation.

cs.LO↗

arXiv2025

NTIRE 2025 Image Shadow Removal Challenge Report

This work examines the findings of the NTIRE 2025 Shadow Removal Challenge. A total of 306 participants have registered, with 17 teams successfully submitting their solutions during the final evaluation phase. Following the last two editions, this challenge had two evaluation tracks: one focusing on reconstruction fidelity and the other on visual perception through a user study. Both tracks were evaluated with images from the WSRD+ dataset, simulating interactions between self- and cast-shadows with a large number of diverse objects, textures, and materials.

cs.CV↗

arXiv2023

$\mathcal{S}_X$-convergence and locally hypercompact spaces

In this paper, we give a topological version of Scott convergence theorem for locally hypercompact spaces. We introduce the notion of $\mathcal{S}^*_X$-convergence on a $T_0$ topological space $X$, and define the notion of finitely approximated spaces. Monotone determined spaces are natural topological extensions of dcpos. The main results are: (1) A monotone determined space $X$ is a locally hypercompact space iff $\mathcal{S}^*_X$-convergence is topological. (2) For a $T_0$ space $X$, $\mathcal{S}^*_X$-convergence is topological iff $X$ is a finitely approximating space. (3) If the Lawson topology on a monotone determined space $X$ is compact, then $X$ is a dcpo endowed with the Scott topology.

math.GN↗

arXiv2023

Free dcpo-algebras via directed spaces

Directed spaces are natural topological extensions of dcpos in domain theory and form a cartesian closed category. We will show that the D-completion of free algebras over a Scott space $ΣL$, on the context of directed spaces, are exactly the free dcpo-algebras over dcpo $L$, which reveals the close connection between directed powerspaces and powerdomains. By this result, we provide a topological representation of upper, lower and convex powerdomains of dcpos uniformly.

cs.LO↗

arXiv2022

Free algebras over directed spaces

Directed spaces are natural topological extensions of dcpos in domain theory and form a cartesian closed category. In order to model nondeterministic semantics, the power structures over directed spaces were defined through the form of free algebras. We show that free algebras over any directed space exist by the Adjoint Functor Theorem. An c-space (resp.\ b-space) can be characterized as a continuous (resp.\ algebraic) directed space. We show that continuous spaces are just all retracts of algebraic spaces by means of topological ideals, which are generalizations of the rounded ideals. Moreover, by categorical methods, we show that the carrier spaces of free algebras over continuous (resp.\ algebraic) spaces are still continuous (resp.\ algebraic) spaces.

math.CT↗

arXiv2022

Continuity and core compactness of topological spaces

We investigate two approximation relations on a T0 topological space, the n-approximation, and the d-approximation, which are generalizations of the way-below relation on a dcpo. Different kinds of continuous spaces are defined by the two approximations and are all shown to be directed spaces. We show that the continuity of a directed space is very similar to the continuity of a dcpo in many aspects, which indicates that the notion of directed spaces is a suitable topological extension of dcpos.The main results are: (1) A topological space is continuous iff it is a retract of an algebraic space;(2) a directed space X is core compact iff for any directed space Y, the topological product is equal to the categorical product in DTop of X and Y respectively;(3) a directed space is continuous (resp., algebraic, quasicontinuous, quasialgebraic) iff the lattice of its closed subsets is continuous (resp., algebraic, quasicontinuous, quasialgebraic).

math.GN↗

arXiv2022

Monotone determined spaces via $\mathbb{C}$-generated spaces

The category of monotone determined spaces is an extended topological framework for dcpos in domain theory. We first show that monotone determined spaces are exactly the spaces generated by one-point convergence spaces, and then naturally form a convenient Cartesian closed category of $\mathbb{C}$-generated spaces. We then show that monotone determined spaces are not always compact Hausdorff generated, answering the question raised by Ingo Battenfeld in 2013. Moreover, we generalize the notion of monotone determined spaces by introducing $\mathcal{C}$-determined spaces and showing that categories of $\mathcal{C}$-determined spaces correspond to coreflective subcategories of topological spaces. This yields a uniform construction of several convenient categories determined by directed, chain and monotone sequential convergence classes. We finally discuss the relationships among them, including the categories generated by continuous spaces, quasicontinuous spaces and Scott spaces of dcpos.

math.GN↗

arXiv2022

Power structures of directed spaces

Powerdomains in domain theory plays an important role in modeling the semantics of nondeterministic functional programming languages.\ In this paper,\ we extend the notion of powerdomain to the category of directed spaces,\ which is equivalent to the notion of the\ $T_0$\ monotone-determined space\ \cite{EN2009}.\ We define the notion of upper,\ lower and convex powerspace of a directed space by the way of free algebras.\ We show that the upper,\ lower and convex powerspace over any directed space exist and give their concrete structures.\ Generally,\ the upper,\ lower and convex powerspaces of a directed spaces are different from the upper,\ lower and convex powerdomains of a dcpos endowed with the Scott topology and the observationally-induced upper and lower powerspaces introduced by Battenfeld and Schöder in 2015. Keywords: powerdomain,\ directed lower powerspace of directed spaces,\ directed upper powerspace of directed spaces,\ directed convex powerspace of directed spaces,\ observationally-induced lower powerspace,\ observationally-induced lower powerspace

math.GN↗