arXiv subjects

Jiadong Wu

Publications and source records attributed to Jiadong Wu.

8 recordsLinked to original sources

arXiv2026

A reduction principle for non-$r$-partite spectral extremal problems, with a complete multipartite classification

A graph is non-$r$-partite if its chromatic number exceeds $r$. For an edge-color-critical graph $F$ with $χ(F)=r+1$, let $\mathrm{ex}_{r+1,ρ}(n,F)$ be the maximum adjacency spectral radius among non-$r$-partite $F$-free graphs of order $n$, and let $\mathrm{EX}_{r+1,ρ}(n,F)$ and $\mathrm{EX}_{r+1}(n,F)$ be the families of such graphs attaining, respectively, this maximum spectral radius and the maximum number of edges $\mathrm{ex}_{r+1}(n,F)$. Fang and Lin conjectured that $\mathrm{EX}_{r+1,ρ}(n,F)\subseteq\mathrm{EX}_{r+1}(n,F)$ for every such $F$ and all large $n$. We prove a reduction principle: if $F$ is \emph{$s$-embeddable} and $\mathrm{ex}_{r+1}(n,F)=|E(T_{n,r})|-\lfloor n/r\rfloor+2(s-1)$, where $T_{n,r}$ is the Turán graph, then the inclusion holds and, moreover, the spectral extremal graph is unique. The reduction replaces the spectral problem by an edge-counting one, and its proof rests on a direct comparison of secular functions together with a second-order residual refinement of the Rayleigh principle. We then determine the spectral extremal graphs for all edge-color-critical complete multipartite forbidden graphs. For $F=K_{1,1,t_3,\ldots,t_{r+1}}$ with $t_3,\ldots,t_{r+1}\ge 2$ we show \[ \mathrm{ex}_{r+1}(n,F)=|E(T_{n,r})|-\Bigl\lfloor\frac nr\Bigr\rfloor+2(t_{\min}-1), \qquad t_{\min}:=\min\{t_3,\ldots,t_{r+1}\}, \] for all sufficiently large $n$, and we identify the unique spectral extremal graph; in particular $\mathrm{EX}_{r+1,ρ}(n,F)\subseteq\mathrm{EX}_{r+1}(n,F)$. The endpoint $t_3=1$ lies outside the embeddability framework and is treated by a separate argument: for $F=K_{1,1,1,t_4,\ldots,t_{r+1}}$ with $r\ge3$, the unique non-$r$-partite spectral extremal graph is $Y_r(n)$, obtained through a saturation reduction followed by the spectral refinement of Turán's theorem. The complete graph $K_{r+1}$ and the complete split graph $B_{r,q}$

math.CO↗

arXiv2026

DRAINCODE: Stealthy Energy Consumption Attacks on Retrieval-Augmented Code Generation via Context Poisoning

Large language models (LLMs) have demonstrated impressive capabilities in code generation by leveraging retrieval-augmented generation (RAG) methods. However, the computational costs associated with LLM inference, particularly in terms of latency and energy consumption, have received limited attention in the security context. This paper introduces DrainCode, the first adversarial attack targeting the computational efficiency of RAG-based code generation systems. By strategically poisoning retrieval contexts through a mutation-based approach, DrainCode forces LLMs to produce significantly longer outputs, thereby increasing GPU latency and energy consumption. We evaluate the effectiveness of DrainCode across multiple models. Our experiments show that DrainCode achieves up to an 85% increase in latency, a 49% increase in energy consumption, and more than a 3x increase in output length compared to the baseline. Furthermore, we demonstrate the generalizability of the attack across different prompting strategies and its effectiveness compared to different defenses. The results highlight DrainCode as a potential method for increasing the computational overhead of LLMs, making it useful for evaluating LLM security in resource-constrained environments. We provide code and data at https://github.com/DeepSoftwareAnalytics/DrainCode.

cs.SE↗

arXiv2026

The signless Laplacian spectral Turán problems for hypergraphs

Let $\mathcal{H}=(V, E)$ be an $r$-uniform hypergraph on $n$ vertices. The signless Laplacian spectral radius of $\mathcal{H}$ is defined as the maximum modulus of the eigenvalues of the tensor $\mathcal{Q}(\mathcal{H})=\mathcal{D}(\mathcal{H})+\mathcal{A}(\mathcal{H})$, where $\mathcal{D}(\mathcal{H})$ and $\mathcal{A}(\mathcal{H})$ are the degree diagonal tensor and the adjacency tensor of $\mathcal{H}$, respectively. In this paper, we establish a general theorem that extends the spectral Turán result of Keevash, Lenz and Mubayi [SIAM J. Discrete Math., 28 (4) (2014)] to the setting of signless Laplacian spectral Turán problems. We prove that if a family $\mathcal{F}$ of $r$-uniform hypergraphs is degree-stable with respect to a family $\mathcal{H}_n$ of $r$-uniform hypergraphs and its extremal constructions satisfy certain natural assumptions, then the signless Laplacian spectral Turán problem for $\mathcal{F}$ can be effectively reduced to the corresponding problem restricted to the family $\mathcal{H}_n$. As a concrete application, we completely determine the extremal hypergraph that maximizes the signless Laplacian spectral radius among all Fano plane-free $3$-uniform hypergraphs, showing that the unique extremal hypergraph is the balanced complete bipartite $3$-uniform hypergraph.

math.CO↗

arXiv2025

The $α$-spectral Turán type problems for graphs

For $0 \leq α< 1$, the $α$-spectral radius of a graph $G$ is defined as the largest eigenvalue of $A_α(G)=αD(G)+(1-α)A(G)$, where $D(G)$ and $A(G)$ are the diagonal matrix of degrees and adjacency matrix of $G$, respectively. A graph is called color-critical if it contains an edge whose deletion reduces its chromatic number. The celebrated Erdős-Stone-Simonovits theorem asserts that $ \mathrm{ex}(n,\mathcal{F})=\left(1-\frac{1}{χ(\mathcal{F})-1}+o(1)\right)\frac{n^2}{2},$ where $χ(\mathcal{F})$ is the chromatic number of $\mathcal{F}$. Nikiforov and Zheng et al. established the adjacency spectral and signless Laplacian spectral versions of this theorem, respectively. In this paper, we present the $α$-spectral version of this theorem, which unifies the aforementioned results. Furthermore, we characterize the $α$-spectral extremal graphs for color-critical graphs, thereby extending the existing results on adjacency spectral and signless Laplacian spectral extremal graphs for such graphs.

math.CO↗

arXiv2025

Spectral extremal problems for degenerate graphs

A family of graphs is called degenerate if it contains at least one bipartite graph. In this paper, we investigate the spectral extremal problems for a degenerate family of graphs $\mathcal{F}$. By employing covering and independent covering of graphs, we establish a spectral stability result for $\mathcal{F}$. Using this stability result, we prove two general theorems that characterize spectral extremal graphs for a broad class of graph families $\mathcal{F}$ and imply several new and known results. Meanwhile, we establish the correlation between extremal graphs and spectral extremal graphs for $\mathcal{F}$.

math.CO↗

arXiv2024

Spectral Extremal Graphs of Planar Graphs with Fixed Size

Tait and Tobin [J. Combin. Theory Ser. B 126 (2017) 137--161] determined the unique spectral extremal graph over all outerplanar graphs and the unique spectral extremal graph over all planar graphs when the number of vertices is sufficiently large. In this paper we consider the spectral extremal problems of outerplanar graphs and planar graphs with fixed number of edges. We prove that the outerplanar graph on $m \geq 64$ edges with the maximum spectral radius is $S_m$, where $S_m$ is a star with $m$ edges. For planar graphs with $m$ edges, our main result shows that the spectral extremal graph is $K_2 \vee \frac{m-1}{2} K_1$ when $m$ is odd and sufficiently large, and $K_1 \vee (S_{\frac{m-2}{2}} \cup K_1)$ when $m$ is even and sufficiently large. Additionally, we obtain spectral extremal graphs for path, cycle and matching in outerplanar graphs and spectral extremal graphs for path, cycle and complete graph on $4$ vertices in planar graphs.

math.CO↗

arXiv2019

Cooperation on the monte carlo rule Prison's dilemma game on the grid

In this paper, we investigate the prison's dilemma game with monte carlo rule in the view of the idea of the classic Monte Carlo method on the grid. Monte carlo rule is an organic combination of the current dynamic rules of individual policy adjustment, which not only makes full use of information but also reflects the individual's bounded rational behavior and the ambivalence between the pursuit of high returns and high risks. In addition, it also reflects the individual's behavioral execution preferences. The implementation of monte carlo rule brings an extremely good result, higher cooperation level and stronger robustness are achieved by comparing with the unconditional imitation rule, replicator dynamics rule and fermi rule. When analyse the equilibrium density of cooperators as a function of the temptation to defect, it appears a smooth transition between the mixed state of coexistence of cooperators and defectors and the pure state of defectors when enhancing the temptation, which can be perfectly characterized by the trigonometric behavior instead of the power-law behavior discovered in the pioneer's work. When discuss the relationship between the temptation to defect and the average returns of cooperators and defectors, it is found that cooperators' average returns is almost a constant throughout the whole temptation parameter ranges while defectors' decreases as the growth of temptation. Additionally, the insensitivity of cooperation level to the initial density of cooperators and the sensitivity to the social population have been both demonstrated.

cs.GT↗

arXiv2015

Maximum a Posteriori Adaptation of Network Parameters in Deep Models

We present a Bayesian approach to adapting parameters of a well-trained context-dependent, deep-neural-network, hidden Markov model (CD-DNN-HMM) to improve automatic speech recognition performance. Given an abundance of DNN parameters but with only a limited amount of data, the effectiveness of the adapted DNN model can often be compromised. We formulate maximum a posteriori (MAP) adaptation of parameters of a specially designed CD-DNN-HMM with an augmented linear hidden networks connected to the output tied states, or senones, and compare it to feature space MAP linear regression previously proposed. Experimental evidences on the 20,000-word open vocabulary Wall Street Journal task demonstrate the feasibility of the proposed framework. In supervised adaptation, the proposed MAP adaptation approach provides more than 10% relative error reduction and consistently outperforms the conventional transformation based methods. Furthermore, we present an initial attempt to generate hierarchical priors to improve adaptation efficiency and effectiveness with limited adaptation data by exploiting similarities among senones.

cs.LG↗