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Liping Zhang

Publications and source records attributed to Liping Zhang.

At least 19 recordsLinked to original sources
arXiv2026

A New Perspective on Optimal Power Flow: From Control Theory to Numerical Optimization

The optimal power flow (OPF) problem is a classical non-convex optimization problem with nonlinear constraints and multiple potential solutions. Existing methods often fail to find the global optimal solution, motivating the development of a method to identify multiple local solutions. This paper applies the optimal control principle to solve the OPF problem, aiming to systematically explore all feasible solutions within a single run. We first handle the constraints in the OPF problem using the penalty method and the Lagrange multiplier, and then reformulate it as an optimal control problem. The connection between the two problems is established by the maximum principle. Moreover, a numerical algorithm is proposed to solve this optimal control problem. The state trajectory of the system can rapidly and stably converge to the solution of the OPF problem. By designing the initial control sequence, the proposed method can successfully find multiple solutions and escape local solutions. Finally, simulations were conducted on several representative test systems to validate the potential of the proposed method in identifying multiple solutions for non-convex problems.

math.OC↗
arXiv2026

Supersaturation thresholds for expanded color-critical graphs

For a $k$-uniform hypergraph $L$, let $h_L(n,q)$ be the minimum number of copies of $L$ in an $n$-vertex $k$-graph with $\mathrm{ex}(n,L)+q$ edges. Let $t_L(n,q)$ be the minimum number of copies obtained by adding $q$ edges to an extremal $L$-free $k$-graph. A graph is color-critical if deleting a suitable edge decreases its chromatic number. Let $\mathcal K_k(F)$ be the expanded graph obtained by adding $k-2$ new vertices to each edge of $F$, with disjoint sets of new vertices for distinct edges. Mubayi proved that, for every clique $K_r$ with $r\ge4$ and fixed $ q>0$, $ h_{\mathcal K_3(K_r)}(n,q)\ge qt_{\mathcal K_3(K_r)}(n,1)$ for every sufficiently large $n$. Pikhurko and Yilma later proved that, for every color-critical graph $F$, there is a constant $ε_F>0$ such that $h_{F}(n,q)=t_{F}(n,q)$ for every sufficiently large $n$ and $1\le q\leε_F n$. We extend this equality to expanded color-critical graphs. Let $d>k\ge3$. For every color-critical graph $F$ with $χ(F)=d+1$, there is a constant $ε>0$ such that $ h_{\mathcal K_k(F)}(n,q)=t_{\mathcal K_k(F)}(n,q)$ for every sufficiently large $n$ and $1\le q\leεn^{k-1}$. Let $q_L(n)$ be the largest integer $q$ such that $h_L(n,s)=t_L(n,s)$ for every integer $1\le s\le q$. We give a sufficient condition for $q_L(n)=Θ_L(n^{k-1})$ and an explicit family satisfying it. We also give a different sufficient condition under which $q_L(n)=Ω_L(n^{k-1/2})$ and an explicit family satisfying it. \noindent \emph{Keywords.} Supersaturation; extremal graph; color-critical graph; chromatic number; expanded graph; hypergraph.

math.CO↗
arXiv2026

Complete counterexamples to Mubayi's supersaturation conjecture for graphs

For a graph $F$, its extremal number ${\rm ex}(n,F)$ and extremal graphs denote the maximum number of edges in $F$-free graphs and the graphs attaining this maximum, respectively. Let $h_F(n,q)$ be the minimum number of copies of $F$ in an $n$-vertex graph with ${\rm ex}(n,F)+q$ edges, and let $t_F(n,q)$ denote the corresponding minimum obtained by adding $q$ edges to an extremal graph. Mubayi (2013) conjectured that for every non-$r$-partite stable $r$-uniform hypergraph $F$ with $r\ge 2$, $h_F(n,q)\ge q\cdot t_F(n,1)$ holds for all sufficiently large $n$ and all integers $q\ge 1$. In this paper, we prove that Mubayi's conjecture fails in a stronger sense. For every integer $d\ge 2$, we construct a family of non-$d$-partite stable graphs $F$ such that $h_F(n,q)< q\cdot t_F(n,1)$ for all $1\le q\le O\bigl(n^{4/ 3}\bigr)$. In particular, these examplesis completely refute Mubayi's conjecture. \noindent\emph{Key words}: extremal graph; supersaturation; chromatic number.

math.CO↗
arXiv2026

Convergence Rates of Factorized Gradient Descent for Overparameterized Asymmetric Matrix Sensing with Balancing Regularization

We study factorized gradient descent (FGD) for overparameterized asymmetric matrix sensing with the balancing regularizer $\frac18\|L^\top L-R^\top R\|_F^2$. An exact indefinite lifting of the population objective decomposes the dynamics of FGD into positive, negative, and null spectral subspaces. The first two components have linear restoring terms, whereas the null component contracts only quadratically. For independent isotropic sub-Gaussian sensing matrices and independent centered sub-Gaussian noise with scale proxy $σ$, we prove the local bound \[ \|L_tR_t^\top-X^\star\|_2 \lesssim\max\left\{\frac{1}{ηt+1/σ_r}, κσ\sqrt{\frac{d_1+d_2}{n}}\right\}, \] under a sufficiently small initialization error, the number of linear measurements $n\gtrsimκ^2(d_1+d_2)\max\{k^2,σ^2/σ_r^2\}$, and step size $η\lesssimσ_1^{-1}$. Here $σ_1$ and $σ_r$ are the largest and smallest nonzero singular values of the target $X^\star\in \mathbb{R}^{d_1\times d_2}$ respectively, and $κ=σ_1/σ_r$. Furthermore, a population trajectory was constructed to have tight product error $Θ(1/t)$. These results provide a local rate characterization for ordinary gradient descent for overparameterized asymmetric matrix sensing with balancing regularizer.

math.OC↗
arXiv2026

Connectivity keeping pendant extensions of paths in $k$-connected triangle-free graphs

Motivated by Mader's conjecture on connectivity keeping trees, we study the corresponding problem in triangle-free graphs. For positive integers $k,m$, we first prove that every $k$-connected triangle-free graph $G$ with $δ(G)\geq k+\left \lceil \frac{m}{2} \right \rceil $ contains a path $P$ of order $m$ such that $G-V(P)$ remains $k$-connected. Moreover, if $κ(G)=k$, then for every end $F$ of $G$ and every vertex $v\in F$, the path $P$ can be chosen in $G[F]$ with $v$ as an endvertex. If $κ(G)\geq k+1$, then any vertex of $G$ can be chosen as an endvertex of $P$. This result confirms the conjecture of Luo, Tian and Wu on connectivity keeping trees in bipartite graphs for all paths, and it also sharpens Fujita's path theorem to the optimal minimum degree bound. For an integer $i$ with $1\leq i\leq m-1$, let $P_m^+(i)$ denote the tree obtained from a path of order $m-1$ by adding one pendant vertex adjacent to its $i$th vertex. Let $(X,Y)$ be the bipartition of $P_m^+(i)$. We further prove that every $k$-connected triangle-free graph $G$ with $δ(G)\geq k+\max\{|X|,|Y|\}$ contains a subgraph $T\cong P_m^+(i)$ such that $G-V(T)$ remains $k$-connected. The minimum degree bound is sharp, and the result confirms the bipartite conjecture for all pendant extensions of paths.

math.CO↗
arXiv2026

TACoS: Weakly Supervised Learning of Two-Dimensional Materials from Scribble Annotations to Precise Segmentation

The precise pixel-level localization of 2D material flakes is crucial for high-throughput screening. However, traditional fully supervised methods rely on dense annotations, which are costly and time-consuming, severely limiting the practical deployment of segmentation models. This paper proposes TACoS, a specialized scribble segmentation framework tailored for 2D materials. First, we design a unified framework that integrates semi-supervised consistency learning with structured tree energy constraints. This framework comprises two core components: an unlabeled weak-strong distribution alignment module and a tree energy regularization module. The former employs cosine consistency constraints to enhance prediction alignment across views. Meanwhile, the latter utilizes minimum spanning trees to establish pixel affinity relationships and generate structure-aware soft pseudo labels for online semantic guidance. Next, we introduce asymmetric regional contrast learning. This approach fuses high-confidence predictions from the weak augmentation branch with scribbles to form augmented labels, and construct category prototypes in the representation space. Simultaneously, we prioritize contrastive constraints on challenging pixels in boundary-unlabeled regions. This strategy enhances intra-class cohesion and inter-class separation at the representation level, effectively reducing category confusion in low-contrast edges and complex backgrounds. Experiments conducted on the constructed graphene and MoS2 datasets demonstrate that our method TACoS achieves over 96% of fully supervised performance using less than 0.6% annotated data. Furthermore, it exhibits superior structural coherence and boundary stability in scenarios with weakly contrasting edges and complex backgrounds, providing an efficient and scalable solution for automated high-throughput screening of 2D material flakes.

cs.CV↗
arXiv2026

Herschel: Continuous Optimization of Production LLM Inference through On-Demand Profiling

Model-as-a-service platforms call for continuous optimization as complex serving conditions expose inefficiencies missed before deployment. Detailed always-on profiling can incur substantial overhead, while lightweight collection omits information needed for diagnosis. We present Herschel, a continuous optimization system for production large language model (LLM) inference. Our key insight is that adaptive, on-demand profiling can provide rich full-stack evidence without continuous collection. Herschel safely attaches to and detaches from selected running processes without engine changes or restarts, and adapts coverage as investigations reveal missing evidence. Herschel reconstructs operator executions and cross-process dependencies to identify inefficiency mechanisms and suggest solutions using applicable reference fixes. AI agents implement and test engine and kernel changes under controlled conditions that preserve the triggering workload and dependencies, with expert review before deployment. Controlled tests show active-collection overhead below 0.5% for time to first token and 7% for time per output token. Bounded windows, typically 30 s, avoid the continuous cost of always-on tracing. Over six months, Herschel collected approximately 17,000 traces across over 120 model variants and more than 10 accelerator types, identifying inefficiency patterns in 23% of the traces. Representative findings guide widely deployed optimizations, including restructured synchronization, removal of unused computation, and improved operator implementations.

cs.OS↗
arXiv2026

Rainbow Berge Hamiltonicity in edge-colored random $k$-uniform hypergraphs

Let $H \sim H^{k}_c(n,p)$ be an edge-colored random $k$-uniform hypergraph on the vertex set $[n]$, where each edge $e \in \binom{[n]}{k}$ is included independently with probability $p$ and is uniformly and independently assigned a color from the color set $[c]$. For $k = 2$, Ferber and Krivelevich (2016) established that if $c = (1+o(1))n$ and $p = (\log n + \log \log n + ω(n))/n$, then with high probability the edge-colored random graph $H \sim H^2_c(n,p)$ contains a rainbow Hamilton Berge cycle. Subsequently, Bal, Berkowitz, Devlin, and Schacht (2021) determined the threshold for the appearance of a (non-rainbow) Hamilton Berge cycle in random $k$-uniform hypergraphs. In this paper, we generalize the results to all integers $k \ge 3$. We prove that if $c = (1+o(1))n$ and $p = (k-1)! \frac{\log n + \log\log n + ω(n)}{n^{k-1}}$, then with high probability $H \sim H^{k}_c(n,p)$ contains a rainbow Hamilton Berge cycle. Furthermore, both conditions on $c$ and $p$ are asymptotically tight. \noindent\emph{Key words:} Rainbow subgraph, Hamiltonicity, Berge cycle, Random hypergraph.

math.CO↗
arXiv2026

Weave: Fine-Grained Dynamic SM Scheduling in an MoE Megakernel for Compute-Communication Overlap

Mixture-of-Experts (MoE) inference under expert parallelism (EP) turns each MoE layer into a distributed computation with costly dispatch and combine communication. State-of-the-art systems reduce this cost through communication-computation overlap, splitting the GPU's SMs for communication and computation respectively. However, this approach still leaves GPU resources wasted along two dimensions. Spatially, the best SM split is determined by each layer's routing result and varies across layers and GPUs, so fixed policies mismatch the workload and waste either NVLink bandwidth or compute throughput. Temporally, complex MoE data dependencies introduce bubbles that leave SMs idle. We present Weave, to our knowledge the first MoE overlap system that performs fine-grained dynamic SM scheduling - deciding per layer and per GPU by routing results at runtime. Once routing completes, each layer's communication and computation volumes become known; Weave exploits this predictability through a lightweight cost model running inside the persistent megakernel: a spatial scheduler partitions SMs into communication workers and computation workers to match the communication/computation throughput ratio, and a temporal scheduler coordinates the two worker groups to minimize SM idleness. On 4x H100 SXM GPUs across six mainstream MoE models, Weave achieves a 2.89x geometric-mean MoE-layer speedup and a 1.33x geometric-mean end-to-end speedup over five state-of-the-art baselines.

cs.DC↗
arXiv2026

KREX: Concurrent Kernel Benchmarking on Shared GPUs via Region-Granular Exclusivity

LLM agents automate GPU kernel optimization by repeatedly composing candidates and measuring their duration on real GPUs. Existing systems preserve measurement fidelity by reserving a GPU for an entire agent session or benchmarking command. However, this results in poor utilization because only a small fraction of command execution requires exclusive GPU access. Sharing GPUs could recover this idle capacity, but introduces contention that compromises measurement fidelity and misdirects the agent's search. We present KREX, a runtime for concurrent kernel agent benchmarking with region-granular exclusivity. KREX lets agents mark critical regions involving timing-sensitive operations within a benchmarking command. The runtime then enforces exclusivity within marked regions and allows concurrent execution outside them, achieving high throughput while preserving measurement fidelity. To enforce in-region exclusivity, KREX blocks new competing GPU submissions and drains outstanding work before freezing sibling processes and isolating CPU cores, protecting both GPU execution and the host threads that drive measurements. To maximize off-region concurrency, KREX reuses GPU contexts in persistent context processes to avoid repeated, node-wide serialized context creation. We evaluate KREX on NVIDIA and AMD GPUs. Compared with command-granular exclusivity baselines, KREX delivers up to $3.4\times$ the benchmarking throughput with a negligible p95 timing inflation of $0.30\%$, $1.58\%$, and $3.90\%$ for kernels longer than 10 ms, 1 ms, and 0.1 ms, respectively.

cs.DC↗
arXiv2026

A Bondy-type theorem for rainbow pancyclicity in graph systems

We establish a Hamiltonian-to-pancyclic analogue of Bondy's theorem for graph systems under an aggregate degree condition. Let $\G=(G_1,\ldots,G_n)$ be a graph system on a common $n$-vertex set $V$, and write $δ(v)=\min_{i\in[n]}d_{G_i}(v)$. If $\G$ contains a rainbow Hamilton cycle and \[ \sum_{v\in V}δ(v)\ge \left\lceil\frac{n^2}{2}\right\rceil-1, \] then $\G$ is rainbow pancyclic, unless $n$ is even and every member is the same balanced complete bipartite graph. For even $n$ the threshold is exact at the integer level. Unlike the usual transversal Dirac- or Ore-type hypotheses, our condition is not layerwise: the member attaining $δ(v)$ may depend on $v$, and some vertices may have $δ(v)<n/2$. Relative to a fixed rainbow Hamilton cycle, we count shortcuts whose colors are released by the Hamilton arcs they replace. A missing cycle length forces complementary shortcut supports to cross-intersect. A counting gap settles even shortening, while equality or near equality in odd shortening yields a distance-two exchange whose orbits force the balanced bipartite obstruction. At the lower integer threshold an exact defect identity shows that only one or two units of slack are available. \noindent\textbf{Keywords:} graph system; rainbow cycle; pancyclicity; Hamilton cycle; extremal graph theory.

math.CO↗
arXiv2026

Connectivity keeping pendant extensions of paths in $k$-connected graphs and triangle-free graphs

Motivated by Mader's conjecture on connectivity keeping trees, we study trees obtained from paths by adding one pendant vertex, as well as related problems in triangle-free graphs. For an integer $m$ and $1\leq i\leq m-1$, let $P_m^+(i)$ denote the tree obtained from a path of order $m-1$ by adding one pendant vertex adjacent to its $i$th vertex. We prove that, for positive integers $k,m,1\leq i\leq m-1$, every $k$-connected graph $G$ with $δ(G)\geq \lfloor \frac{3k}{2}\rfloor+m-1$ contains a subgraph $T\cong P_m^+(i)$ such that $κ(G-V(T))\geq k$. This confirms Mader's conjecture for all pendant extensions of paths. For highly connected triangle-free graphs, a connectivity keeping result for paths was obtained in [J. Combin. Theory Ser. B, 174 (2025), 190-206]. Let $(X,Y)$ be the bipartition of $P_m^+(i)$. We further prove that every $k$-connected triangle-free graph $G$ with $δ(G)\geq k+\max\{|X|,|Y|\}+[P_m^+(i)\text{ is bad}]$ contains a subgraph $T\cong P_m^+(i)$ such that $κ(G-V(T))\geq k$, where we use Iverson's convention for $[P_m^+(i)\text{ is bad}]$. This extends the corresponding result for paths to pendant extensions of paths.

math.CO↗
arXiv2026

Deep Divide-and-Reduce in Symbolic Regression

Symbolic regression (SR) aims to discover underlying mathematical expressions from data while preserving interpretability. Most existing learning-based SR methods primarily optimize expressions from observations without explicitly exploiting their structural mathematical properties. AI Feynman introduced a complementary paradigm that leverages such properties to recursively decompose complex expressions, but its decomposition criteria cover only restricted structural forms and its treatment of nested composition can require brute-force search over candidate sub-expressions. Building on this paradigm, we propose Deep Divide-and-Reduce in Symbolic Regression (DDRSR), a mathematically grounded framework that systematically generalizes expression decomposition and variable reduction. DDRSR extends translational symmetry to coefficient- and exponent-interfered forms, enables variable separation under overlapping variables and additive constant offsets, and generalizes the identification of nested compositional structures. We further characterize an intrinsic non-identifiability limitation of decomposition when no effective variable separation is induced. Experiments across multiple symbolic regression algorithms and benchmark datasets show that DDRSR identifies a broader range of decomposable structures than AI Feynman and overall improves downstream regression accuracy and exact-expression recovery.

cs.LG↗
arXiv2026

Rank-Adaptive and Linearly Convergent Frank--Wolfe Method over Spectrahedron via Nonconvex Oracle

For Frank--Wolfe (FW) methods for convex optimization over the spectrahedron, it remains open whether a block-update variant can be linearly convergent when the update rank never exceeds the (unknown) optimal rank $r^*$ at each iteration. Existing block and spectral FW methods require an update rank at least $r^*$---and typically prior knowledge of $r^*$---to obtain a linear rate. This paper develops a rank-adaptive FW method whose update ranks satisfy $\widehat{r}_t\le r_t\le r^*$ at every iteration and which converges linearly after a finite burn-in under quadratic growth and strict complementarity, the two conditions commonly used in spectral FW analyses. The method is built on two designs. The first is a nonconvex spectral oracle, motivated by the geometric connection between the simplex and the spectrahedron; it yields a thresholding rank $r_t$ of the current iterate and a closed-form low-rank solution. Computing $r_t$ exactly, however, requires a full eigendecomposition. The second introduces the efficient rank $\widehat{r}_t$ of the current iterate, a cheap surrogate that inherits the optimality properties of the spectral oracle. The algorithm switches between the thresholding rank and the efficient rank so that the actual FW update uses $\widehat{r}_t$, keeps the per-iteration cost comparable to standard FW, and eventually identifies $r^*$. These results close the gap between low-rank efficiency and fast convergence for Frank--Wolfe methods over the spectrahedron. Numerical experiments demonstrate the advantage of the proposed method.

math.OC↗
arXiv2026

Exchange Policy Optimization Algorithm for Semi-Infinite Safe Reinforcement Learning

Safe reinforcement learning (RL) aims to optimize long-term performance while adhering to safety requirements. However, many practical applications involve an infinite number of constraints, forming semi-infinite safe RL (SI-safe RL). Such scenarios typically appear when safety conditions must be enforced across an entire continuous parameter space, such as ensuring adequate resource distribution at every spatial location. Existing approaches typically tackle these continuous constraints through naive spatial discretization or stochastic sampling. Such methods inherently suffer from residual violations or provide only probabilistic safety guarantees. Therefore, no current framework can handle infinitely many constraints to provide reliable safety certificates. In this paper, we propose exchange policy optimization (EPO), an algorithmic framework that achieves optimal policy performance with provably bounded safety guarantees. EPO operates by iteratively solving safe RL subproblems restricted to a finite constraint set, adaptively adjusting the active set through constraint expansion and deletion. Specifically, at each iteration, constraints violating a predefined tolerance are added to refine the policy, while those with zero Lagrange multipliers are removed after the policy update. This exchange rule limits the subproblem complexity to ensure computational tractability while driving policy convergence. Theoretically, we establish that, under mild assumptions, EPO achieves finite convergence to a policy that both ensures the optimal reward performance and keeps the global constraint violation within the prescribed tolerance. Furthermore, we derive an upper bound on the required number of iterations and quantify the gap between the obtained policy and the true optimum.

cs.LG↗
arXiv2026

Momentum as Residual-Driven Multiplier Correction for Deep Learning Optimization

Momentum-based optimizers are widely used in modern deep learning, yet the relations among momentum recursion, update geometry, and acceleration remain only partially understood. We develop an $\textbf{A}$DMM-$\textbf{I}$nspired $\textbf{M}$omentum (AIM) framework based on residual-penalty variable splitting, which interprets momentum as a multiplier-like correction driven by the splitting residual. AIM recovers the exponential moving average of gradients from an ADMM-style multiplier update and separates two mechanisms that are usually intertwined in practical optimizers: the residual penalty determines the update geometry, whereas the approximation of the objective-related subproblem determines the acceleration form. Building on AIM, we propose $\textbf{R}$elativistic $\textbf{A}$daptive gradient $\textbf{D}$escent with $\textbf{A}$ccelerated $\textbf{R}$esidual (RADAR), which combines relativistic adaptive geometry, decoupled residual correction, and second-order momentum filtering to improve the update direction and momentum estimation. We establish stochastic convergence through a variance-perturbed Lyapunov drift analysis. Experiments on supervised vision learning, language modeling, and reinforcement learning show that RADAR achieves consistent improvements over strong adaptive optimizer baselines.

cs.LG↗
arXiv2026

The Bounded-VC chromatic thresholds of graphs

For a graph $H$, the chromatic threshold $δ_χ(H)$ is the infimum of $c>0$ such that the chromatic number of every $n$-vertex $H$-free graph with minimum degree at least $cn$ is bounded by a constant depending only on $H$ and $c$. Allen, Böttcher, Griffiths, Kohayakawa, and Morris proved that if $χ(H)=r\geq 3$, then $δ_χ(H)\in\{\frac{r-3}{r-2}, \frac{2r-5}{2r-3}, \frac{r-2}{r-1}\}$. Liu, Shangguan, Skokan, and Xu introduced the bounded-VC chromatic threshold $\text{VC}(H)$ by restricting the host graphs to have bounded VC-dimension. We determine this parameter for graph $H$ with $χ(H)\ge 3$. More precisely, let $\mathcal{M}(H)$ be the decomposition family of an $r$-chromatic graph $H$, then \[ \text{VC}(H)= \begin{cases} \dfrac{r-3}{r-2},&\text{if $\mathcal{M}(H)$ contains a forest},\\[4pt] \dfrac{r-2}{r-1},&\text{otherwise}. \end{cases} \]

math.CO↗
arXiv2026

Bifrost: Empowering Pretrained Language Model with Fallibility Representation for Log-Based Fault Diagnosis

Log-based fault diagnosis is crucial for runtime debugging and maintenance. Existing fault diagnosis methods use language models pre-trained on natural language (PLMs) for log representation. However, system faults are reflected in the multi-level structure of system logs. PLMs pre-trained on natural language struggle to comprehensively capture multi-level fault information, failing to meet the requirements of fault diagnosis. We refer to this information as fallibility representations. To address this problem, we propose a novel log representation learning method, Bifrost. It draws inspiration from the log analysis experience of Site Reliability Engineers and meticulously designs strategies based on self-supervised contrastive learning to learn the fallibility representations of logs. Across three public systems and one industrial ML-as-a-Service system, the log representations produced by Bifrost outperform existing PLMs by average margins of 9.83% in F1 for anomaly detection, 18.28% in HR@k for root cause localization, and 20.88% in Macro-F1 for fault identification.

cs.SE↗