arXiv subjects

Weifan Wang

Publications and source records attributed to Weifan Wang.

At least 19 recordsLinked to original sources

arXiv2026

All limit points of the largest roots of matching polynomials are determined

The largest matching root $\mu(G)$ of a graph $G$ is that of its matching polynomial. In this paper, all limit points of the largest matching roots of graphs are determined. More precisely, we identify the limit points of the largest matching roots of graphs less than $\tau^{\frac{1}{2}}+\tau^{-\frac{1}{2}}$. For any $\gamma \geq \tau^{\frac{1}{2}}+\tau^{-\frac{1}{2}}$ with $\tau=\frac{\sqrt{5}+1}{2}$, there exists a graph sequence $\{G_i\, |\, i\in \mathbb{N}\}$ such that $\lim\limits_{i \rightarrow \infty}\mu(G_i)=\gamma$.

math.CO↗

arXiv2025

Modeling Rapid Contextual Learning in the Visual Cortex with Fast-Weight Deep Autoencoder Networks

Recent neurophysiological studies have revealed that the early visual cortex can rapidly learn global image context, as evidenced by a sparsification of population responses and a reduction in mean activity when exposed to familiar versus novel image contexts. This phenomenon has been attributed primarily to local recurrent interactions, rather than changes in feedforward or feedback pathways, supported by both empirical findings and circuit-level modeling. Recurrent neural circuits capable of simulating these effects have been shown to reshape the geometry of neural manifolds, enhancing robustness and invariance to irrelevant variations. In this study, we employ a Vision Transformer (ViT)-based autoencoder to investigate, from a functional perspective, how familiarity training can induce sensitivity to global context in the early layers of a deep neural network. We hypothesize that rapid learning operates via fast weights, which encode transient or short-term memory traces, and we explore the use of Low-Rank Adaptation (LoRA) to implement such fast weights within each Transformer layer. Our results show that (1) The proposed ViT-based autoencoder's self-attention circuit performs a manifold transform similar to a neural circuit model of the familiarity effect. (2) Familiarity training aligns latent representations in early layers with those in the top layer that contains global context information. (3) Familiarity training broadens the self-attention scope within the remembered image context. (4) These effects are significantly amplified by LoRA-based fast weights. Together, these findings suggest that familiarity training introduces global sensitivity to earlier layers in a hierarchical network, and that a hybrid fast-and-slow weight architecture may provide a viable computational model for studying rapid global context learning in the brain.

cs.CV↗

arXiv2025

List-recoloring of two classes of planar graphs

For a graph $G$ with a list assignment $L$ and two $L$-colorings $α$ and $β$, an $L$-recoloring sequence from $α$ to $β$ is a sequence of proper $L$-colorings where consecutive colorings differ at exactly one vertex. We prove the existence of such a recoloring sequence in which every vertex is recolored at most a constant number of times under two conditions: (i) $G$ is planar, contains no $3$-cycles or intersecting $4$-cycles, and $L$ is a $6$-assignment; or (ii) the maximum average degree of $G$ satisfies $\mathrm{mad}(G) < \frac{5}{2}$ and $L$ is a $4$-assignment. These results strengthen two theorems previously established by Cranston.

math.CO↗

arXiv2025

CLIP-aware Domain-Adaptive Super-Resolution

This work introduces CLIP-aware Domain-Adaptive Super-Resolution (CDASR), a novel framework that addresses the critical challenge of domain generalization in single image super-resolution. By leveraging the semantic capabilities of CLIP (Contrastive Language-Image Pre-training), CDASR achieves unprecedented performance across diverse domains and extreme scaling factors. The proposed method integrates CLIP-guided feature alignment mechanism with a meta-learning inspired few-shot adaptation strategy, enabling efficient knowledge transfer and rapid adaptation to target domains. A custom domain-adaptive module processes CLIP features alongside super-resolution features through a multi-stage transformation process, including CLIP feature processing, spatial feature generation, and feature fusion. This intricate process ensures effective incorporation of semantic information into the super-resolution pipeline. Additionally, CDASR employs a multi-component loss function that combines pixel-wise reconstruction, perceptual similarity, and semantic consistency. Extensive experiments on benchmark datasets demonstrate CDASR's superiority, particularly in challenging scenarios. On the Urban100 dataset at $\times$8 scaling, CDASR achieves a significant PSNR gain of 0.15dB over existing methods, with even larger improvements of up to 0.30dB observed at $\times$16 scaling.

cs.CV↗

arXiv2025

Differentiable NMS via Sinkhorn Matching for End-to-End Fabric Defect Detection

Fabric defect detection confronts two fundamental challenges. First, conventional non-maximum suppression disrupts gradient flow, which hinders genuine end-to-end learning. Second, acquiring pixel-level annotations at industrial scale is prohibitively costly. Addressing these limitations, we propose a differentiable NMS framework for fabric defect detection that achieves superior localization precision through end-to-end optimization. We reformulate NMS as a differentiable bipartite matching problem solved through the Sinkhorn-Knopp algorithm, maintaining uninterrupted gradient flow throughout the network. This approach specifically targets the irregular morphologies and ambiguous boundaries of fabric defects by integrating proposal quality, feature similarity, and spatial relationships. Our entropy-constrained mask refinement mechanism further enhances localization precision through principled uncertainty modeling. Extensive experiments on the Tianchi fabric defect dataset demonstrate significant performance improvements over existing methods while maintaining real-time speeds suitable for industrial deployment. The framework exhibits remarkable adaptability across different architectures and generalizes effectively to general object detection tasks.

cs.CV↗

arXiv2025

Variable degeneracy of planar graphs without chorded 6-cycles

A cover of a graph $G$ is a graph $H$ with vertex set $V(H) = \bigcup_{v \in V(G)} L_{v}$, where $L_{v} = \{v\} \times [s]$, and the edge set $M = \bigcup_{uv \in E(G)} M_{uv}$, where $M_{uv}$ is a matching between $L_{u}$ and $L_{v}$. A vertex set $T \subseteq V(H)$ is a transversal of $H$ if $|T \cap L_{v}| = 1$ for each $v \in V(G)$. Let $f$ be a nonnegative integer valued function on the vertex-set of $H$. If for any nonempty subgraph $Γ$ of $H[T]$, there exists a vertex $x \in V(H)$ such that $d(x) < f(x)$, then $T$ is called a strictly $f$-degenerate transversal. In this paper, we give a sufficient condition for the existence of strictly $f$-degenerate transversal for planar graphs without chorded $6$-cycles. As a consequence, every planar graph without subgraphs isomorphic to the configurations in Fig. 4 is DP-$4$-colorable.

math.CO↗

arXiv2025

The strong chromatic index of 1-planar graphs

The chromatic index $χ'(G)$ of a graph $G$ is the smallest $k$ for which $G$ admits an edge $k$-coloring such that any two adjacent edges have distinct colors. The strong chromatic index $χ'_s(G)$ of $G$ is the smallest $k$ such that $G$ has an edge $k$-coloring with the condition that any two edges at distance at most 2 receive distinct colors. A graph is 1-planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. In this paper, we show that every graph $G$ with maximum average degree $\bar{d}(G)$ has $χ'_{s}(G)\le (2\bar{d}(G)-1)χ'(G)$. As a corollary, we prove that every 1-planar graph $G$ with maximum degree $Δ$ has $χ'_{\rm s}(G)\le 14Δ$, which improves a result, due to Bensmail et al., which says that $χ'_{\rm s}(G)\le 24Δ$ if $Δ\ge 56$.

math.CO↗

arXiv2024

Single-image reflection removal via self-supervised diffusion models

Reflections often degrade the visual quality of images captured through transparent surfaces, and reflection removal methods suffers from the shortage of paired real-world samples.This paper proposes a hybrid approach that combines cycle-consistency with denoising diffusion probabilistic models (DDPM) to effectively remove reflections from single images without requiring paired training data. The method introduces a Reflective Removal Network (RRN) that leverages DDPMs to model the decomposition process and recover the transmission image, and a Reflective Synthesis Network (RSN) that re-synthesizes the input image using the separated components through a nonlinear attention-based mechanism. Experimental results demonstrate the effectiveness of the proposed method on the SIR$^2$, Flash-Based Reflection Removal (FRR) Dataset, and a newly introduced Museum Reflection Removal (MRR) dataset, showing superior performance compared to state-of-the-art methods.

cs.CV↗

arXiv2024

The Devil is in the Sources! Knowledge Enhanced Cross-Domain Recommendation in an Information Bottleneck Perspective

Cross-domain Recommendation (CDR) aims to alleviate the data sparsity and the cold-start problems in traditional recommender systems by leveraging knowledge from an informative source domain. However, previously proposed CDR models pursue an imprudent assumption that the entire information from the source domain is equally contributed to the target domain, neglecting the evil part that is completely irrelevant to users' intrinsic interest. To address this concern, in this paper, we propose a novel knowledge enhanced cross-domain recommendation framework named CoTrans, which remolds the core procedures of CDR models with: Compression on the knowledge from the source domain and Transfer of the purity to the target domain. Specifically, following the theory of Graph Information Bottleneck, CoTrans first compresses the source behaviors with the perception of information from the target domain. Then to preserve all the important information for the CDR task, the feedback signals from both domains are utilized to promote the effectiveness of the transfer procedure. Additionally, a knowledge-enhanced encoder is employed to narrow gaps caused by the non-overlapped items across separate domains. Comprehensive experiments on three widely used cross-domain datasets demonstrate that CoTrans significantly outperforms both single-domain and state-of-the-art cross-domain recommendation approaches.

cs.IR↗

arXiv2024

Manifold Transform by Recurrent Cortical Circuit Enhances Robust Encoding of Familiar Stimuli

A ubiquitous phenomenon observed throughout the primate hierarchical visual system is the sparsification of the neural representation of visual stimuli as a result of familiarization by repeated exposure, manifested as the sharpening of the population tuning curves and suppression of neural responses at the population level. In this work, we investigated the computational implications and circuit mechanisms underlying these neurophysiological observations in an early visual cortical circuit model. We found that such a recurrent neural circuit, shaped by BCM Hebbian learning, can also reproduce these phenomena. The resulting circuit became more robust against noises in encoding the familiar stimuli. Analysis of the geometry of the neural response manifold revealed that recurrent computation and familiar learning transform the response manifold and the neural dynamics, resulting in enhanced robustness against noise and better stimulus discrimination. This prediction is supported by preliminary physiological evidence. Familiarity training increases the alignment of the slow modes of network dynamics with the invariant features of the learned images. These findings revealed how these rapid plasticity mechanisms can improve contextual visual processing in even the early visual areas in the hierarchical visual system.

q-bio.NC↗

arXiv2023

GARCIA: Powering Representations of Long-tail Query with Multi-granularity Contrastive Learning

Recently, the growth of service platforms brings great convenience to both users and merchants, where the service search engine plays a vital role in improving the user experience by quickly obtaining desirable results via textual queries. Unfortunately, users' uncontrollable search customs usually bring vast amounts of long-tail queries, which severely threaten the capability of search models. Inspired by recently emerging graph neural networks (GNNs) and contrastive learning (CL), several efforts have been made in alleviating the long-tail issue and achieve considerable performance. Nevertheless, they still face a few major weaknesses. Most importantly, they do not explicitly utilize the contextual structure between heads and tails for effective knowledge transfer, and intention-level information is commonly ignored for more generalized representations. To this end, we develop a novel framework GARCIA, which exploits the graph based knowledge transfer and intention based representation generalization in a contrastive setting. In particular, we employ an adaptive encoder to produce informative representations for queries and services, as well as hierarchical structure aware representations of intentions. To fully understand tail queries and services, we equip GARCIA with a novel multi-granularity contrastive learning module, which powers representations through knowledge transfer, structure enhancement and intention generalization. Subsequently, the complete GARCIA is well trained in a pre-training&fine-tuning manner. At last, we conduct extensive experiments on both offline and online environments, which demonstrates the superior capability of GARCIA in improving tail queries and overall performance in service search scenarios.

cs.LG↗

arXiv2022

1-planar graphs are odd 13-colorable

An odd coloring of a graph $G$ is a proper coloring such that any non-isolated vertex in $G$ has a coloring appears odd times on its neighbors. The odd chromatic number, denoted by $χ_o(G)$, is the minimum number of colors that admits an odd coloring of $G$. Petruševski and Škrekovski in 2021 introduced this notion and proved that if $G$ is planar, then $χ_o(G)\le9$ and conjectured that $χ_o(G)\le5$. More recently, Petr and Portier improved $9$ to $8$. A graph is $1$-planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. Cranston, Lafferty and Song showed that every $1$-planar graph is odd $23$-colorable. In this paper, we improved this result and showed that every $1$-planar graph is odd $13$-colorable.

math.CO↗

arXiv2021

Star coloring of sparse graphs

A proper coloring of the vertices of a graph is called a \emph{star coloring} if the union of every two color classes induces a star forest. The star chromatic number $χ_s(G)$ is the smallest number of colors required to obtain a star coloring of $G$. In this paper, we study the relationship between the star chromatic number $χ_s(G)$ and the maximum average degree $\mbox{Mad}(G)$ of a graph $G$. We prove that: (1) If $G$ is a graph with $\mbox{Mad}(G) < \frac{26}{11}$, then $χ_s(G)\leq 4$. (2) If $G$ is a graph with $\mbox{Mad}(G) < \frac{18}{7}$ and girth at least 6, then $χ_s(G)\leq 5$. (3) If $G$ is a graph with $\mbox{Mad}(G) < \frac{8}{3}$ and girth at least 6, then $χ_s(G)\leq 6$. These results are obtained by proving that such graphs admit a particular decomposition into a forest and some independent sets.

math.CO↗

arXiv2020

On the arithmetic-geometric index of graphs

Very recently, the first geometric-arithmetic index $GA$ and arithmetic-geometric index $AG$ were introduced in mathematical chemistry. In the present paper, we first obtain some lower and upper bounds on $AG$ and characterize the extremal graphs. We also establish various relations between $AG$ and other topological indices, such as the first geometric-arithmetic index $GA$, atom-bond-connectivity index $ABC$, symmetric division deg index $SDD$, chromatic number $χ$ and so on. Finally, we present some sufficient conditions of $GA(G)>GA(G-e)$ or $AG(G)>AG(G-e)$ for an edge $e$ of a graph $G$. In particular, for the first geometric-arithmetic index, we also give a refinement of Bollobás-Erdős-type theorem obtained in [3].

math.CO↗

arXiv2020

On $3$-flow-critical graphs

A bridgeless graph $G$ is called $3$-flow-critical if it does not admit a nowhere-zero $3$-flow, but $G/e$ has for any $e\in E(G)$. Tutte's $3$-flow conjecture can be equivalently stated as that every $3$-flow-critical graph contains a vertex of degree three. In this paper, we study the structure and extreme edge density of $3$-flow-critical graphs. We apply structure properties to obtain lower and upper bounds on the density of $3$-flow-critical graphs, that is, for any $3$-flow-critical graph $G$ on $n$ vertices, $$\frac{8n-2}{5}\le |E(G)|\le 4n-10,$$ where each equality holds if and only if $G$ is $K_4$. We conjecture that every $3$-flow-critical graph on $n\ge 7$ vertices has at most $3n-8$ edges, which would be tight if true. For planar graphs, the best possible density upper bound of $3$-flow-critical graphs on $n$ vertices is $\frac{5n-8}{2}$, known from a result of Kostochka and Yancey (JCTB 2014) on vertex coloring $4$-critical graphs by duality.

math.CO↗

arXiv2019

DP-coloring for planar graphs of diameter two

DP-coloring (also known as correspondence coloring) is a generalization of list coloring introduced by Dvourák and Postle (2017). Recently, Huang et al. [https://doi.org/10.1016/j.amc.2019.124562] showed that planar graphs with diameter at most two are $4$-choosable. In this paper, we will prove that planar graphs with diameter at most two are DP-$4$-colorable, which is an extension of the above result.

math.CO↗

arXiv2019

The Extension Degree Conditions for Fractional Factor

In Gao's previous work, the authors determined several graph degree conditions of a graph which admits fractional factor in particular settings. It was revealed that these degree conditions are tight if $b=f(x)=g(x)=a$ for all vertices $x$ in $G$. In this paper, we continue to discuss these degree conditions for admitting fractional factor in the setting that several vertices and edges are removed and there is a difference $Δ$ between $g(x)$ and $f(x)$ for every vertex $x$ in $G$. These obtained new degree conditions reformulate Gao's previous conclusions, and show how $Δ$ acts in the results. Furthermore, counterexamples are structured to reveal the sharpness of degree conditions in the setting $f(x)=g(x)+Δ$.

math.CO↗

arXiv2015

A characterization of L(2, 1)-labeling number for trees with maximum degree 3

An L(2, 1)-labeling of a graph is an assignment of nonnegative integers to the vertices of G such that adjacent vertices receive numbers differed by at least 2, and vertices at distance 2 are assigned distinct numbers. The L(2, 1)-labeling number is the minimum range of labels over all such labeling. It was shown by Griggs and Yeh [Labelling graphs with a condition at distance 2, SIAM J. Discrete Math. 5(1992), 586-595] that the L(2, 1)-labeling number of a tree is either \D+ 1 or \D + 2. In this paper, we give a complete characterization of L(2, 1)-labeling number for trees with maximum degree 3.

math.CO↗