arXiv subjects

Xueliang Li

Publications and source records attributed to Xueliang Li.

At least 19 recordsLinked to original sources

arXiv2026

ChebBooster: A Training-Free Approach for Efficient Diffusion Transformer Inference via Chebyshev-Inspired Extrapolation

Diffusion Transformers (DiTs) have shown strong performance in high-fidelity image generation, but their sampling process remains computationally intensive due to full model execution at every timestep. While cache-based acceleration has been explored to mitigate inference cost, naive reuse schemes suffer from low accuracy over long intervals, and Taylor-series-based extrapolation methods often face instability caused by Runge oscillations. In this paper, we propose ChebBooster, a training-free extrapolation framework based on Chebyshev polynomial theory that achieves stable and efficient acceleration for DiTs. Specifically, we adopt the Barycentric formulation to evaluate Chebyshev approximants with high numerical stability and minimal overhead, and further decouple the extrapolation into an offline weight precomputation phase and a lightweight online application stage. Extensive experiments across three representative DiT-based models, including DiT-XL/2, PixArt-$\Sigma$, and FLUX.1-dev, demonstrate that ChebBooster achieves consistent improvements in visual quality and inference efficiency, reaching up to $3.68\times$ latency speedup and $5.12\times$ FLOPs reduction, outperforming existing training-free baselines under diverse generation tasks and resolutions.

cs.LG↗

arXiv2026

Memory-Efficient Training-Free Acceleration of Diffusion Transformers with BaryCache

Diffusion Transformers achieve high-fidelity image and video generation, but their iterative sampling remains expensive, for each denoising step requires large matrix operations. Existing cache-based acceleration reduces redundant computation yet increases the VRAM footprint by storing intermediate states, which can directly constrain inference batch size. In this work, we propose a training-free acceleration method that performs stepwise forecasting for DiT sampling using a Barycentric Extrapolator. By leveraging barycentric extrapolation, our predictor is numerically stable and alleviates oscillatory artifacts analogous to the Runge phenomenon during forward forecasting. Across extensive experiments on both image and video generation, our approach provides a favorable trade-off between memory usage and perceptual quality, while delivering up to 3.30x end-to-end sampling speedup compared with baseline DiT inference.

cs.CV↗

arXiv2026

PreferRec: Learning and Transferring Pareto Preferences for Multi-objective Re-ranking

Multi-objective re-ranking has become a critical component of modern multi-stage recommender systems, as it tasked to balance multiple conflicting objectives such as accuracy, diversity, and fairness. Existing multi-objective re-ranking methods typically optimize aggregate objectives at the item level using static or handcrafted preference weights. This design overlooks that users inherently exhibit Pareto-optimal preferences at the intent level, reflecting personalized trade-offs among objectives rather than fixed weight combinations. Moreover, most approaches treat re-ranking task for each user as an isolated problem, and repeatedly learn the preferences from scratch. Such a paradigm not only incurs high computational cost, but also ignores the fact that users often share similar preference trade-off structures across objectives. Inspired by the existence of homogeneous multi-objective optimization spaces where Pareto-optimal patterns are transferable, we propose PreferRec, a novel framework that explicitly models and transfers Pareto preferences across users. Specifically, PreferRec is built upon three tightly coupled components: Preference-Aware Pareto Learning aims to capture user intrinsic trade-offs among multiple conflicting objectives at the intent level. By learning Pareto preference representations from re-ranking populations, this component explicitly models how users prioritize different objectives under diverse contexts. Knowledge-Guided Transfer facilitates efficient cross-user knowledge transfer by distilling shared optimization patterns across homogeneous optimization spaces. The transferred knowledge is then used to guide solution selection and personalized re-ranking, biasing the optimization process toward high-quality regions of the Pareto front while preserving user-specific preference characteristics.

cs.IR↗

arXiv2026

TaleBot: A Tangible AI Companion to Support Children in Co-creative Storytelling for Resilience Cultivation

Resilience is a key factor affecting children's mental wellbeing and future development. Yet, limited HCI research has explored how to help children build resilience through adversarial experiences. Informed by a formative study with elementary school teachers and professional psychologists, we design TaleBot, an AI-empowered system that supports children to co-create stories about overcoming everyday adversities tailored to their personal situations. We evaluated the system with 12 elementary children in school counseling rooms under teacher guidance and conducted reflective interviews with parents upon the Child-AI co-created stories. The findings show that TaleBot encourages children in self-expression of feelings and thoughts, creating opportunities for teachers to provide personalized support and for parents to better understand the profound impact of family communication on children's mental wellbeing. We conclude with design implications for using generative AI to support children's mental health education and interventions across school and family contexts.

cs.HC↗

arXiv2026

FuturePrism: Supporting Adolescence in Collaborative Storytelling to Cope with Future Uncertainty

FuturePrism is a GenAI-empowered collaborative storytelling system designed to scaffold adolescents to navigate future life challenges. Adolescents often suffer from anxiety related to future uncertainty for lacking the executive function to develop concrete pathways. Operationalizing Snyder's Hope Theory, the system utilizes a triadic role-play mechanics to externalize cognitive processes through four narrative chapters: The Goal, The Opportunity, The Challenge, and The Agency. An evaluation workshop with 20 adolescents demonstrated that FuturePrism significantly enhances momentary hope levels, particularly in the Agency dimension. Participants reported high levels of narrative immersion and positive feedback towards system usability. Participants also confirmed that the AI-scaffolded collaborative storytelling empowered them to develop positive attitudes towards future challenges.

cs.HC↗

arXiv2026

RIGA-Fold: A General Framework for Protein Inverse Folding via Recurrent Interaction and Geometric Awareness

Protein inverse folding, the task of predicting amino acid sequences for desired structures, is pivotal for de novo protein design. However, existing GNN-based methods typically suffer from restricted receptive fields that miss long-range dependencies and a "single-pass" inference paradigm that leads to error accumulation. To address these bottlenecks, we propose RIGA-Fold, a framework that synergizes Recurrent Interaction with Geometric Awareness. At the micro-level, we introduce a Geometric Attention Update (GAU) module where edge features explicitly serve as attention keys, ensuring strictly SE(3)-invariant local encoding. At the macro-level, we design an attention-based Global Context Bridge that acts as a soft gating mechanism to dynamically inject global topological information. Furthermore, to bridge the gap between structural and sequence modalities, we introduce an enhanced variant, RIGA-Fold*, which integrates trainable geometric features with frozen evolutionary priors from ESM-2 and ESM-IF via a dual-stream architecture. Finally, a biologically inspired ``predict-recycle-refine'' strategy is implemented to iteratively denoise sequence distributions. Extensive experiments on CATH 4.2, TS50, and TS500 benchmarks demonstrate that our geometric framework is highly competitive, while RIGA-Fold* significantly outperforms state-of-the-art baselines in both sequence recovery and structural consistency.

cs.LG↗

arXiv2026

The local antimagic (total) chromatic numbers of firecracker graphs and edge-corona product graphs

Let G=(V(G),E(G)) be a connected simple graph with n vertices and m edges. A bijection f from the edge set of G to [m] is called a local antimagic labeling of G, if for any two adjacent vertices u and v in G, the sums of the weights of the edges associated with u and v ,respectively, are different. Similarly, A bijection g from the union of edge set and vertex set of G to [n+m] is called a local antimagic total labeling of G, if for any two adjacent vertices u and v in G, The sum of the weight of u and the weights of its incident edges differs from that of v. Obviously, any local antimagic (total) labeling induces a proper vertex-coloring of G when every vertex v is assigned the color w(v)(w_t(v)). The local antimagic (total) chromatic number of G, denoted by X_la(G)(X_lat(G)) , is defined as the minimum number of colors taken over all colorings induced by local antimagic (total) labelings of G. In this paper, we present the local antimagic (total) chromatic number of firecracker graph F_n,k, obtained by the concatenation of n k-stars by linking one leaf from each. Then we give the local antimagic chromatic number of the edge-corona product of two graphs G and H, where the graph is constructed by taking one copy of G and |E(G)| disjoint copies of H one-to-one assigned to each edge of G, and for every edge uv of G, joining u and v to every vertex of the copy of H associated to uv. For the graph studied here, G is a star S_k or a double star S_k1,k2, and H is an empty graph with r vertices or a complete graph K_2.

math.CO↗

arXiv2025

On Neutral Edge Sets in Anti-Ramsey Numbers

The anti-Ramsey number of a graph $G$, introduced by Erd\H{o}s et al.\ in 1975, is the maximum number of colors in an edge-coloring of the complete graph $K_n$ that avoids a rainbow copy of $G$. We call a subset of edges of $G$ \emph{neutral} for the anti-Ramsey number if removing them does not alter the anti-Ramsey number of $G$. Let $k$, $t$, and $n$ be positive integers, and consider $G = kP_4 \cup tP_2$. Assume $S \subseteq E(G)$ consists of internal edges of the $P_4$ components in $G$. It is known that $S$ is neutral when $t \geq k+1 \geq 2$ and $n \geq 8k + 2t - 4$. In this paper, we identify values of $k \geq t$ such that, for all $n$ in a specific subinterval of $[8k + 2t - 4, \infty)$, $S$ remains neutral. Since the anti-Ramsey numbers for matchings are well understood, our results provide a complete determination of the anti-Ramsey number for $G$ under these conditions. Based on our findings, we conjecture that this neutrality may extend to the general case $t \geq 1$, $k \geq 1$, and $n \geq 4k + 2t$, but not when $t = 0$, $k \geq 2$, and $n \geq 4k$.

math.CO↗

arXiv2025

On the Anti-Ramsey Number Under Edge Deletion

According to a study by Erd\H{o}s et al. in 1975, the anti-Ramsey number of a graph $G$, denoted as $AR(n, G)$, is defined as the maximum number of colors that can be used in an edge-coloring of the complete graph $K_n$ without creating a rainbow copy of $G$. In this paper, we investigate the anti-Ramsey number under edge deletion and demonstrate that both decreasing and unchanging are possible outcomes. For three non-negative integers $k$, $t$, and $n$, let $G = kP_4 \cup tP_2$. Let $E'$ be a subset of the edge set $E(G)$ such that every endpoint of these edges has a degree of two in $G$. We prove that if one of the conditions (i) $t \geq k + 1 \geq 2$ and $n \geq 8k + 2t - 4$; (ii) $k, t \geq 1$ and $n = 4k + 2t$; (iii) $k = 1$, $t \geq 1$, and $n \geq 2t + 4$, occurs then the behavior of the anti-Ramsey number remains consistent when the edges in $E'$ are removed from $G$, i.e., $AR(n, G) = AR(n, G - E')$. However, this is not the case when $k \geq 2$, $t = 0$, and $n=4k$. As a result, we calculate $AR(kP_4 \cup tP_2)$ for the cases: (i) $t \geq k + 1 \geq 2$ and $n \geq 8k + 2t - 4$; (ii) $k, t \geq 1$ and $n = 4k + 2t$; (iii) $k = 1$, $t \geq 0$, and $n \geq 2t + 4$; (iv) $k \geq 1$, $t = 0$, and $n = 4k$.

math.CO↗

arXiv2025

Anti-Ramsey Numbers for Spanning Linear Forests of 3-Vertex Paths and Matchings

A subgraph in an edge-colored graph is called rainbow if all its edges have distinct colors. For a graph $G$ and an integer $n$, the anti-Ramsey number $AR(n,G)$ is the maximum number of colors in an edge-coloring of $K_n$ that contains no rainbow copy of $G$. We study $AR(n, kP_3 \cup tP_2)$, where $kP_3 \cup tP_2$ is the linear forest of $k$ disjoint paths on three vertices and a matching of size $t$. Recently, Jie and Jin [Discrete Appl. Math. 386 (2026) 30-57] determined this number for $k\geq 2$, $t\geq\frac{k^2-3k+4}{2}$ and $n=2t+3k$. Here we solve the spanning case $n=3k+2t$ for all $k\ge1$, $t\ge2$ with no extra restrictions.

math.CO↗

arXiv2025

On the local metric dimension of $K_5$-free graphs

Let $ G $ be a graph with order $ n(G) \geq 5 $, local metric dimension $ \dim_l(G) $, and clique number $ \omega(G) $. In this paper, we investigate the local metric dimension of $ K_5 $-free graphs and prove that $ \dim_l(G) \leq \lfloor\frac{2}{3}n(G)\rfloor $ when $ \omega(G) = 4 $. As a consequence of this finding, along with previous publications, we establish that if $ G $ is a $ K_5 $-free graph, then $ \dim_l(G) \leq \lfloor\frac{2}{5}n(G)\rfloor $ when $ \omega(G) = 2 $, $ \dim_l(G) \leq \lfloor\frac{1}{2}n(G)\rfloor $ when $ \omega(G) = 3 $, and $ \dim_l(G) \leq \lfloor\frac{2}{3}n(G)\rfloor $ when $ \omega(G) = 4 $. Notably, these bounds are sharp for planar graphs. These results for graphs with a clique number less than or equal to 4 provide a positive answer to the conjecture stating that if $ n(G) \geq \omega(G) + 1 \geq 4 $, then $ \dim_l(G) \leq \left( \frac{\omega(G) - 2}{\omega(G) - 1} \right)n(G) $.

math.CO↗

arXiv2025

Intertwining local (adjacency) metric dimension with the clique number of a graph

Let $G$ be a simple connected graph with order $ n(G)$, local metric dimension $ {\rm dim}_l(G)$, local adjacency metric dimension $ {\rm dim}_{A,l}(G)$, and clique number $ \omega(G)$, where $G\not\cong K_{n(G)}$ and $\omega(G)\geq3$. It is proved that $ {\rm dim}_{A,l}(G) \leq \left\lfloor \left(\frac{\omega(G) - 2}{\omega(G) - 1}\right)n(G)\right\rfloor$. Consequently, the conjecture asserting that the latter expression is an upper bound for ${\rm dim}_l(G)$ is confirmed. It is important to note that there are infinitely many graphs that satisfy the equalities.

math.CO↗

arXiv2025

On the local metric dimension of $K_4$-free graphs

Let $G$ be a graph of order $ n(G) $, local metric dimension $ \dim_l(G) $, and clique number $ \omega(G) $. It has been conjectured that if $ n(G) \geq \omega(G) + 1 \geq 4 $, then $ \dim_l(G) \leq \left( \frac{\omega(G) - 2}{\omega(G) - 1} \right) n(G) $. In this paper the conjecture is confirmed for the case $ \omega(G) = 3 $. Consequently, a problem regarding the local metric dimension of planar graphs is also resolved.

math.CO↗

arXiv2025

The maximum spectral radius of $\theta_{2,2,3}$-free graphs with given size

A theta graph $\theta_{r,p,q}$ is the graph obtained by connecting two distinct vertices with three internally disjoint paths of length $r,p,q$, where $q\geq p\geq r\geq1$ and $p\geq2$. A graph is $\theta_{r,p,q}$-free if it does not contain $\theta_{r,p,q}$ as a subgraph. The maximum spectral radius of $\theta_{1,p,q}$-free graphs with given size has been determined for any $q\geq p\geq2$. Zhai, Lin and Shu [Spectral extrema of graphs with fixed size: cycles and complete bipartite graphs, European J. Combin. 95 (2021) 103322] characterized the extremal graph with the maximum spectral radius of $\theta_{2,2,2}$-free graphs having $m$ edges. In this paper, we consider the maximum spectral radius of $\theta_{2,2,3}$-free graphs with size $m$ and characterize the extremal graph.

math.CO↗

arXiv2025

A Dual-Directional Context-Aware Test-Time Learning for Text Classification

Text classification assigns text to predefined categories. Traditional methods struggle with complex structures and long-range dependencies. Deep learning with recurrent neural networks and Transformer models has improved feature extraction and context awareness. However, these models still trade off interpretability, efficiency and contextual range. We propose the Dynamic Bidirectional Elman Attention Network (DBEAN). DBEAN combines bidirectional temporal modeling and self-attention. It dynamically weights critical input segments and preserves computational efficiency.

cs.CL↗

arXiv2025

On Maximum Induced Forests of the Balanced Bipartite Graphs

The decycling number $\nabla(G)$ of a graph $G$ is the minimum number of vertices that must be removed to eliminate all cycles in $G$. The forest number $f(G)$ is the maximum number of vertices that induce a forest in $G$. So $\nabla(G) + f(G) = |V(G)|$. For the Cartesian product $T \,\square\, T'$ of trees $T$ and $T'$ it is proved that $\nabla(S_n \,\square\, S_{n'}) \leq \nabla(T \,\square\, T')$, thus resolving the conjecture of Wang and Wu asserting that $f(T \,\square\, T') \leq f(S_n \,\square\, S_{n'})$. It is shown that $\nabla(T \,\square\, T') \ge\min\{ |V(T)|,|V(T')|\} - 1$ and the equality cases characterized. For prisms over trees, it is proved that $\nabla(T\,\square\, K_2) = \alpha'(T)$, and for arbitrary graphs $G_1$ and $G_2$, it is proved that $\nabla(G_1 \,\square\, G_2) \geq \alpha'(G_1) \alpha'(G_2)$, where $\alpha'$ is the matching number.

math.CO↗

arXiv2024

Interplay between the local metric dimension and the clique number of a graph

The local metric dimension ${\rm dim}_l$ in relation to the clique number $\omega$ is investigated. It is proved that if $\omega(G)\leq n(G)-3$, then ${\rm dim}_l(G) \leq n(G)-3$ and the graphs attaining the bound classified. Moreover, the graphs $G$ with ${\rm dim}_l(G) = n(G)-3$ are listed (with no condition on the clique number). It is proved that if $\omega(G)=n(G)-2$, then $n(G)-4 \leq {\rm dim}_l(G)\leq n(G)-3$, and all graphs are divided into two groups depending on which of the options applies. The conjecture asserting that for any graph $G$ we have ${\rm dim}_l(G) \leq \left[(\omega(G)-2)/(\omega(G)-1)\right] \cdot n(G)$ is proved for all graphs with $\omega(G)\in\{n(G)-1,n(G)-2,n(G)-3\}$. A negative answer is given for the problem whether every planar graph fulfills the inequality ${\rm dim}_l(G) \leq \lceil (n(G)+1)/2 \rceil$.

math.CO↗

arXiv2024

Spectral radius of graphs of given size with forbidden a fan graph $F_6$

Let $F_k=K_1\vee P_{k-1}$ be the fan graph on $k$ vertices. A graph is said to be $F_k$-free if it does not contain $F_k$ as a subgraph. Yu et al. in [arXiv:2404.03423] conjectured that for $k\geq2$ and $m$ sufficiently large, if $G$ is an $F_{2k+1}$-free or $F_{2k+2}$-free graph, then $\lambda(G)\leq \frac{k-1+\sqrt{4m-k^2+1}}{2}$ and the equality holds if and only if $G\cong K_k\vee\left(\frac{m}{k}-\frac{k-1}{2}\right)K_1$. Recently, Li et al. in [arXiv:2409.15918] showed that the above conjecture holds for $k\geq 3$. The only left case is for $k=2$, which corresponds to $F_5$ or $F_6$. Since the case of $F_5$ was solved by Yu et al. in [arXiv:2404.03423] and Zhang and Wang in [On the spectral radius of graphs without a gem, Discrete Math. 347 (2024) 114171]. So, one needs only to deal with the case of $F_6$. In this paper, we solve the only left case by determining the maximum spectral radius of $F_6$-free graphs with size $m\geq 88$, and the corresponding extremal graph.

math.CO↗