arXiv subjects

Liping Zhang

Publications and source records attributed to Liping Zhang.

At least 19 recordsLinked to original sources

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

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 $p = (\log n + \log \log n + \omega(n))/n$, 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 $p = (k-1)! \frac{\log n + \log\log n + \omega(n)}{n^{k-1}}$, 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

The Bounded-VC chromatic thresholds of graphs

For a graph $H$, the chromatic threshold $\delta_\chi(H)$ 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, B\"ottcher, Griffiths, Kohayakawa, and Morris proved that if $\chi(H)=r\geq 3$, then $\delta_{\chi}(H)\in\{\frac{r-3}{r-2}, \frac{2r-5}{2r-3}, \frac{r-2}{r-1}\}$. 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 $\chi(H)\ge 3$. 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

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

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↗

arXiv2026

Are LLM-Generated GPU Kernels Production-Ready? A Trace-Driven Benchmark and Optimization Agent

Existing GPU kernel generation benchmarks draw problems from synthetic or curated sources that diverge from deployed workloads. We present Atrex-Bench, a benchmark whose 30 operators and 440 shapes are sampled directly from full-cluster production inference traces of compute-limited, memory-rich GPUs. Each problem carries an importance weight derived from its share of observed GPU time, weighted by application card-hours and computed separately for the serving phases in which it runs, together with a per-problem roofline ceiling, so the aggregate score emphasizes the kernels that consume the most serving time. Evaluating six frontier coding agents on Atrex-Bench shows that even the best vanilla model reaches only ${\sim}10\%$ of the hardware roofline on production operators; and correctness alone overstates capability, since much of the apparent pass rate comes from PyTorch fallbacks rather than kernels the model wrote. To close this gap, we co-release Atrex-Kernel-Agent (AKA), a profile-driven kernel-optimization agent that combines iterative measure-revise search, optimization dropout for escaping stalled search contexts, and a layered GPU-optimization knowledge base (298 reference-kernel files and 244 optimization-knowledge documents, plus external upstream reference projects for API/ISA lookup). In a controlled case study, the agent converts zero-FlyDSL fallbacks into real kernels that match or exceed hand-tuned production baselines.

cs.AI↗

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

Convergence Analysis of the Restarted Moving-Anchored Extra-Gradient Method in the Absence of Local Lipschitz Continuity

In this paper, we introduce the moving-anchored extra-gradient (MAEG) method for solving monotone inclusion problems involving the sum of a continuous monotone operator and a maximal monotone operator. Notably, the distance from the anchor point to the solution set is designed to be monotonically non-increasing. Under Lipschitz continuity of the forward operator, MAEG attains an $\mathcal{O}(1/k)$ non-asymptotic iteration complexity, and when a positive anchor-update parameter is used, it further achieves an $o(1/k)$ asymptotic rate. Furthermore, leveraging the specific behavior of the anchor point, we propose a tailored restart strategy. We demonstrate that this strategy ensures convergence even in the absence of local Lipschitz continuity, while preserving the original iteration complexity guarantees whenever the Lipschitz condition holds.

math.OC↗

arXiv2026

Factorized low-rank matrix recovery problem, Schatten-$q$ quasi-norm, Error bound for critical point, Kurdyka-\L ojasiewicz property, Inexact proximal alternating linearized minimization

The Schatten-$q$ quasi-norm is a widely used nonconvex rank surrogate and matrix factorization is an effective approach to reduce computational cost. In this paper, we consider the equivalent group-sparse factorized reformulation of Schatten-$q$ norm regularized low-rank matrix recovery problem. Though this factorized model exhibits favorable performance, two issues remain: (i) the error bound of critical points is unexplored; (ii) the proximal operator of $\|\cdot\|_2^q$ lacks a closed-form solution for general $q$, limiting algorithms to adopt fixed $q$ like $1/2$ or $2/3$. This paper addresses both issues. We investigate the properties of critical points for the factorized problem and show that, compared to nuclear norm, the Schatten-$q$ norm implicitly endows critical points with column orthogonality. From this insight, we introduce the notion of S-critical points under mild conditions that ensure column orthogonality with easily operable criterion for identifying. We show that global optimal points must be S-critical points and we derive an error bound between S-critical points and the true matrix. We further present an inexact proximal alternating linearized minimization method for the factorized problem, along with practically computable inexact proximal operator for $\|\cdot\|_2^q$ and criteria to find solutions satisfying inexactness conditions, and we establish the whole sequence convergence and a convergence rate guarantee under Kurdyka--\L ojasiewicz condition. Moreover, we prove that the factorized model with least-squares loss has KL exponent $1/2$ at S-critical points, then the iteration converges linearly under suitable condition. Extensive numerical experiments validate the effectiveness of our algorithm and confirm the theoretical properties of the factorized model.

math.OC↗

arXiv2026

Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry

Owing to the effectiveness of Tensor Train (TT) decomposition in managing high-order tensors, low-rank tensor completion within the TT-format has emerged as a prominent research focus. In this paper, we leverage the left-orthogonal property of the TT-decomposition to construct a novel quotient manifold and introduce a family of admissible Riemannian metrics. Within this geometric framework, we propose a new approach to constructing retractions compatible with the quotient structure, realized via two novel retractions based on recursive polar and QR decompositions that respect the recursive orthogonalization structure of the TT format. We then derive Riemannian gradient descent and conjugate gradient methods to solve the tensor completion problem. Theoretically, our approach streamlines the horizontal projection by reducing the number of unknowns per block from a quadratic dependence on the TT-ranks to a near-half scaling, thereby enhancing computational efficiency over conventional quotient-based methods. Numerical experiments demonstrate that the proposed algorithms achieve reconstruction accuracy comparable to state-of-the-art TT-based geometric methods.

math.NA↗

arXiv2026

ChatSR: Multimodal Large Language Models for Scientific Formula Discovery

Current multimodal large language models (MLLMs) are mainly focused on the understanding and processing of perceptual modalities such as images and videos, while their capability for scientific data understanding remains insufficient. To this end, we propose ChatSR, a novel multimodal large language model tailored for scientific data understanding. ChatSR treats scientific data as a new modality analogous to visual content and, through carefully designed encoders and modality alignment mechanisms, maps scientific data into a representation space that can be processed by large language models, enabling the model to grasp the structural characteristics and underlying regularities of scientific data. Building on this foundation, ChatSR further exploits the rich domain knowledge and strong reasoning abilities of large language models to emulate a knowledgeable human scientist: based on user-specified prior constraints and preferences expressed (such as requirements on periodicity, symmetry, etc.), it automatically generates mathematical formulas that not only accurately fit the observed data but also conform to domain priors, thereby characterizing the latent laws embodied in scientific data and promoting the automation of scientific discovery. Experiments on 13 datasets show that ChatSR achieves state-of-the-art performance on traditional symbolic regression benchmarks. In addition, ChatSR exhibits a promising zero-shot ability to understand and utilize types of prior knowledge that are not present in its training data.

cs.AI↗

arXiv2026

GESR: A Genetic Programming-Based Symbolic Regression Method with Gene Editing

Mathematical formulas serve as a language through which humans communicate with nature. Discovering mathematical laws from scientific data to describe natural phenomena has been a long-standing pursuit of humanity for centuries. In the field of artificial intelligence, this challenge is known as the symbolic regression problem. Among existing symbolic regression approaches, Genetic Programming (GP) based on evolutionary algorithms remains one of the most classical and widely adopted methods. GP simulates the evolutionary process across generations through genetic mutation and crossover. However, mutations and crossovers in GP are entirely random. While this randomness effectively mimics natural evolution, it inevitably produces both beneficial and detrimental variations. If there existed a metaphorical `God` capable of foreseeing which genetic mutations or crossovers would yield superior outcomes and performing targeted gene editing accordingly, the efficiency of evolution could be substantially improved. Motivated by this idea, we propose in this paper a symbolic regression approach based on gene editing, termed GESR. In GESR, we trained two "hands of God" (two BERT models). Among them, the first leverages the BERT's masked language modeling capability to guide the mutation of genes (expression symbols). The other BERT model guides the crossover of individual genes by predicting the crossover point. Experimental results demonstrate that GESR significantly improves computational efficiency compared with traditional GP algorithms and achieves strong overall performance across multiple symbolic regression tasks.

cs.AI↗

arXiv2026

Augmented Lagrangian Multiplier Network for State-wise Safety in Reinforcement Learning

Safety is a primary challenge in real-world reinforcement learning (RL). Formulating safety requirements as state-wise constraints has become a prominent paradigm. Handling state-wise constraints with the Lagrangian method requires a distinct multiplier for every state, necessitating neural networks to approximate them as a multiplier network. However, applying standard dual gradient ascent to multiplier networks induces severe training oscillations. This is because the inherent instability of dual ascent is exacerbated by network generalization -- local overshoots and delayed updates propagate to adjacent states, further amplifying policy fluctuations. Existing stabilization techniques are designed for scalar multipliers, which are inadequate for state-dependent multiplier networks. To address this challenge, we propose an augmented Lagrangian multiplier network (ALaM) framework for stable learning of state-wise multipliers. ALaM consists of two key components. First, a quadratic penalty is introduced into the augmented Lagrangian to compensate for delayed multiplier updates and establish the local convexity near the optimum, thereby mitigating policy oscillations. Second, the multiplier network is trained via supervised regression toward a dual target, which stabilizes training and promotes convergence. Theoretically, we show that ALaM guarantees multiplier convergence and thus recovers the optimal policy of the constrained problem. Building on this framework, we integrate soft actor-critic (SAC) with ALaM to develop the SAC-ALaM algorithm. Experiments demonstrate that SAC-ALaM outperforms state-of-the-art safe RL baselines in both safety and return, while also stabilizing training dynamics and learning well-calibrated multipliers for risk identification.

cs.LG↗

arXiv2026

PipeWeave: Synergizing Analytical and Learning Models for Unified GPU Performance Prediction

The rapid expansion of Transformer-based large language models has dramatically increased the need for high-performance GPUs. As a result, there is growing demand for fast, accurate, and widely generalizable GPU performance models to support next-generation hardware selection and system-level exploration. However, current data-driven methods are limited, exhibiting poor generalization across hardware and inadequate modeling of complex production-level kernels common in modern inference stacks. To address these issues, we present PipeWeave, a unified GPU modeling framework. This approach first employs an analytical model to quantify a given kernel's demands on the GPU's heterogeneous instruction pipelines. These analytical features are then fed into a machine learning (ML) model to capture complex cross-pipeline interactions and resource dependencies, enabling high-fidelity performance prediction. Our evaluation across 11 GPU types from four generations of major architectures on two widely-used serving systems demonstrates that PipeWeave delivers high fidelity and strong generalizability. It achieves accurate predictions, with only 6.1% average error at the kernel level and 8.5% for end-to-end inference -- reducing the error of state-of-the-art methods by 6.7x and 4.4x, respectively. We also demonstrate PipeWeave's value "beyond simulation" by utilizing its performance ceiling to diagnose implementation shortcomings and guide the optimization of a production fused MoE Triton kernel, achieving up to 1.7x speedup. Code is available https://github.com/zksainx/pipeweave.

cs.PF↗

arXiv2026

On the Optimization Landscape of Observer-based Dynamic Linear Quadratic Control

Understanding the optimization landscape of linear quadratic regulation (LQR) problems is fundamental to the design of efficient reinforcement learning solutions. Recent work has made significant progress in characterizing the landscape of static output-feedback control and linear quadratic Gaussian (LQG) control. For LQG, much of the analysis leverages the separation principle, which allows the controller and estimator to be designed independently. However, this simplification breaks down when the gradients with respect to the estimator and controller parameters are inherently coupled, leading to a more intricate analysis. This paper investigates the optimization landscape of observer-based dynamic output-feedback control of LQR problems. We derive the optimal observer-controller pair in settings where transient quadratic performance cannot be neglected. Our analysis reveals that, in general, the combination of the standard LQR controller and the observer that minimizes the trace of the accumulated estimation error covariance does not correspond to a stationary point of the overall closed-loop performance objective. Moreover, we derive a pair of discrete-time Sylvester equations with symmetric structure, both involving the same set of matrix elements, that characterize the stationary point of the observer-based dynamic LQR problem. These equations offer analytical insight into the structure of the optimality conditions and provide a foundation for developing numerical policy gradient methods aimed at learning complex controllers that rely on reconstructed state information.

eess.SY↗

arXiv2026

WaveTune: Wave-aware Bilinear Modeling for Efficient GPU Kernel Auto-tuning

The rapid adoption of Large Language Models (LLMs) has made GPU inference efficiency an increasingly critical system concern. The runtime of LLM workloads is largely dominated by tile-based kernels, particularly General Matrix Multiplications (GEMMs). Although these kernels are highly optimized, their performance remains sensitive to a large space of runtime parameters, such as tile sizes and pipeline stages. The interaction between these parameters and hardware resources leads to a non-convex optimization landscape. Existing approaches to parameter configuration -- including search-based auto-tuning, heuristic rules, and learned cost models -- face a fundamental trade-off between performance optimality and runtime efficiency. In this paper, we present WaveTune, a wave-aware framework for runtime kernel auto-tuning. First, we introduce a unified mapping method to handle input diversity and decompose the configuration space to manage high dimensionality. Second, we develop an analytical wave-aware bilinear model that accurately predicts kernel latency. Third, we design a sparse sampling scheme based on wave structures and a lightweight dual-table retrieval mechanism to minimize runtime overhead. As a result, WaveTune enables precise and efficient runtime configuration for GPU kernels. Across three representative kernels and five GPU architectures, WaveTune consistently achieves near-optimal kernel performance, delivering up to 1.83x kernel-level speedup and up to 1.33x end-to-end TTFT reduction, while reducing runtime decision overhead by five orders of magnitude compared to exhaustive search. These results demonstrate that WaveTune effectively eliminates the traditional trade-off between configuration latency and execution optimality, providing a practical and robust solution for high-performance LLM inference.

cs.PF↗

arXiv2026

LegoDiffusion: Micro-Serving Text-to-Image Diffusion Workflows

Text-to-image generation executes a diffusion workflow comprising multiple models centered on a base diffusion model. Existing serving systems treat each workflow as an opaque monolith, provisioning, placing, and scaling all constituent models together, which obscures internal dataflow, prevents model sharing, and enforces coarse-grained resource management. In this paper, we make a case for micro-serving diffusion workflows with LegoDiffusion, a system that decomposes a workflow into loosely coupled model-execution nodes that can be independently managed and scheduled. By explicitly managing individual model inference, LegoDiffusion unlocks cluster-scale optimizations, including per-model scaling, model sharing, and adaptive model parallelism. Collectively, LegoDiffusion outperforms existing diffusion workflow serving systems, sustaining up to 3x higher request rates and tolerating up to 8x higher burst traffic.

cs.DC↗

arXiv2026

Distributed Optimal Consensus of Nonlinear Multi-Agent Systems

In this paper, the optimal consensus problem for general nonlinear multi-agent systems is studied, where both leaderless and leader-follower cases are considered in a unified framework. The key idea is to convert consensus problems into optimal control problems where the objective of each agent with nonlinear dynamics is to design the control input minimizing the global consensus cost function. Compared with the existing distributed consensus control for nonlinear multi-agent systems, we propose a distributed optimal consensus algorithm based on the optimal control principle (OCP) method, and two enhanced algorithms are developed under the model predictive control (MPC) framework,these two algorithms demonstrate broader applicability when handling general nonlinear multi-agent systems. Moreover, the convergence and superlinear convergence rate of the proposed algorithms are rigorously analyzed. Numerical simulations demonstrate the effectiveness of the proposed algorithms.

math.OC↗