arXiv subjects

Wei Jiang

Publications and source records attributed to Wei Jiang.

At least 19 recordsLinked to original sources

arXiv2026

High-order parametric local discontinuous Galerkin methods for anisotropic curve-shortening flows

We propose a family of high-order local discontinuous Galerkin (LDG) methods, built on a parametric representation and coupled with a semi-implicit backward Euler time discretization, for isotropic and anisotropic curve-shortening flows. The spatial LDG formulation introduces auxiliary variables and carefully designed numerical fluxes which inherit the underlying variational structure. We prove unconditional energy dissipation for the semidiscrete scheme and establish energy dissipation and well-posedness for the fully discrete scheme under certain assumptions. For $P^k$ approximations, the LDG method achieves high-order spatial convergence; extensive numerical experiments confirm optimal $(k+1)$-order accuracy when the surface energy is isotropic or weakly anisotropic. Compared to classical parametric finite element methods (PFEM), the proposed LDG schemes do not need to rely on good mesh distributions or auxiliary symmetrized surface energy matrices for strongly anisotropic surface energy cases, and remain numerically stable on severely degraded meshes that typically cause PFEMs failure. This intrinsic stability enables effective capture of complex geometric evolution and sharp corner singularities produced by strong anisotropy. The approach thus provides a flexible and reliable framework for the numerical simulation of a broader class of geometric flows.

math.NA↗

arXiv2026

Optimal Regret for Communication-Efficient Decentralized Online Learning

In this paper, we investigate decentralized online convex optimization with compressed communication, where $n$ learners over a network jointly minimize a sequence of global loss functions based only on their local losses and compressed messages from their neighbors. The best known regret bounds for this problem are $O(ω^{-1/2}nρ^{-1}\sqrt{T\ln n})$ and $O(ω^{-1}nρ^{-2}\ln n\ln T)$ for convex and strongly convex loss functions, respectively, where $ρ\in(0,1)$ is the spectral gap of the communication matrix and $ω\in(0,1]$ is the compression quality factor. Compared with the corresponding lower bounds of $Ω(ω^{-1/2}nρ^{-1/4}\sqrt{T})$ and $Ω(ω^{-1}nρ^{-1/2}\ln T)$, these upper bounds exhibit polynomial gaps in their dependence on $ρ^{-1}$. To close these gaps, we first develop Ascent-gossip, which combines an online compression strategy with a Chebyshev recursion and attains a faster consensus rate than existing compressed gossip methods. Furthermore, by adopting Ascent-gossip, we propose an online algorithm that achieves optimal regret bounds of $\widetilde O(ω^{-1/2}nρ^{-1/4}\sqrt{T})$ and $\widetilde O(ω^{-1}nρ^{-1/2}\ln T)$ for convex and strongly convex loss functions, respectively. Up to logarithmic factors in $n$ and $ρ^{-1}$, these results match the lower bounds in terms of $T$, $n$, $ρ$, and $ω$.

cs.LG↗

arXiv2026

A minimizing-movement framework for parametric finite element approximation of anisotropic curve shortening flows

We propose a minimizing-movement framework for constructing parametric finite element methods (PFEMs) for anisotropic curve shortening flows. The cornerstone is an admissible modified energy: a smooth, convex, and iteration-dependent surrogate that majorizes the original anisotropic energy and agrees with it at the current iterate. For any fixed finite element degree $n\geq1$ and any positive surface energy density $γ\in C^2(\mathbb{S}^1)$, the unconstrained one-step problem has a unique solution for any time-step size whenever the parametric derivative of the current discrete curve does not vanish on any mesh element. It also satisfies a one-step discrete energy dissipation inequality. It therefore preserves the variational structure of the underlying $L^2$-gradient flow. The framework recovers a variational interpretation of Dziuk's isotropic scheme and applies directly to the weak anisotropies. For strong anisotropies, a convex splitting removes the weak-anisotropy restriction on the original density. A scalar constraint further extends the framework to area-preserving flows. Numerical experiments exhibit approximately the expected convergence for smooth isotropic and weakly anisotropic examples. They also confirm energy dissipation and area preservation. In the strongly anisotropic regime, the computations produce sharp facet-like profiles but reveal mesh-scale oscillations under the grid refinement.

math.NA↗

arXiv2026

Kinetic Sectors and Nonequilibrium Dynamics in the $δ$-Ising Model

We introduce and analyze the $δ$-Ising model, a kinetic Ising ferromagnet in which single-spin flips are accepted when their energy change does not exceed a tunable threshold. Varying the field and threshold opens or closes local flip channels, dividing parameter space into kinetic sectors, each governed by a fixed Markov transition operator. We prove that the dynamics retains global spin-inversion symmetry exactly when up and down spins have equal numbers of open channels. In one such sector on a periodic chain of length $L$, unbiased random initial states therefore reach the field-aligned and antifield states with probability $1/2$ each. Closing a single channel leaves both states absorbing but makes the probability of ordering against the field decay as $(2/π)^L$. Parameter sweeps correspond to ordered products of sector operators, which separate reaching a state from holding it, so hysteresis appears when a state is reached and released at different sector boundaries. We also show how increasing the system size can induce a Mpemba-like reversal, allowing a state with more misaligned spins to reach the final ordered state sooner on average. On a periodic chain, this reversal arises because the mean absorption time grows logarithmically with system size for many short domains but linearly for a single macroscopic domain, and it disappears when the bulk flip channel is opened. These findings show how a simple, intuitive rule for Ising dynamics links local kinetic constraints to field response, memory, and relaxation within a unified framework.

cond-mat.stat-mech↗

arXiv2026

Symmetry Inheritance and Exact Mirror Symmetry Reduction for Electric Field Vector Wave Problems with PEC Boundaries

A symmetry-inheritance and exact domain-reduction framework is developed for the second-order vector wave equation of the electric field in bounded domains with a perfect electric conductor (PEC) boundary and general spatially varying anisotropic media. Orthogonal group actions on polar vectors, axial vectors, and second-order constitutive tensors are used to derive the transformed curl--curl equation and PEC trace directly from the original boundary-value problem. Under unique solvability, the common symmetry group of the problem data is inherited by the electric field. When the symmetry group of the electromagnetic medium admits a mirror symmetry, an arbitrary impressed current can be decomposed by the associated reflection projectors into mirror-even and mirror-odd components. The corresponding full-domain fields inherit the respective parities, and their exact restriction to one half-domain yields a perfect magnetic conductor (PMC) condition for the even field and a PEC condition for the odd field. The original problem is therefore represented exactly by two independent reduced-domain problems. A symmetry-compatible first-family Nédélec discretization preserves this decomposition at the discrete level. Analytical and numerical results verify the symmetry-inheritance theory, the exact PEC/PMC reduced-domain formulations, and the discrete reconstruction for constant and spatially varying anisotropic conductive media under both symmetric and asymmetric excitations.

math.NA↗

arXiv2026

S-PASS: Star-Topology Pinching-Antenna Systems with Pipelined Antenna Pre-Positioning

Pinching-antenna systems (PASS) flexibly reconfigure the wireless channel by positioning dielectric antennas along a waveguide near each user. Releasing and re-attaching an antenna, however, is a mechanical operation orders of magnitude slower than electronic switching, wasting much transmission time. Existing designs generally assume instant reconfiguration, neglect the mechanical latency, or keep the antenna fixed. This paper proposes S-PASS, a star architecture of waveguides sharing one radio-frequency chain through a switch, and pipelined antenna pre-positioning (PAP), a time-division protocol in which idle waveguides pre-position their antennas for their next users while one transmits. It derives in closed form the scheduling efficiency, the number of waveguides beyond which the latency costs no transmission time, and the latency up to which PAP outperforms fixed placement. Analytical and numerical results show that this latency grows with each added waveguide, and users at the outer ends of the waveguides gain most.

cs.IT↗

arXiv2026

Variance Reduction with Delayed Feedback for Non-Convex Optimization

We study variance reduction for non-convex optimization when gradient evaluations return with a delay. The server can update the parameter while earlier evaluations remain unfinished. We first analyze an ordered recursive momentum estimator for stochastic optimization. Under average smoothness and bounded variance, its oracle complexity is $O(1+σ^2ε^{-2}+LΔ_f(1+σ/ε+τ)ε^{-2})$, where the target is an expected squared gradient norm of at most $ε^2$ and $τ$ bounds the feedback delay. We next study finite sums with $n$ components and obtain $O(n+LΔ_f(\sqrt n+\min\{τ,n-1\})ε^{-2})$ evaluations. An asynchronous snapshot variant continues updating during full-gradient computations under an explicit bound on their completion time. For the stochastic method, we further replace a maximum-delay bound by a bound on the weighted amount of missing feedback.

math.OC↗

arXiv2026

Revisiting Smoothed Online Learning: Competitive Ratio, Dynamic Regret with Switching Cost, and Best of Both Worlds

We revisit smoothed online learning and develop algorithms with improved competitive ratios, optimal dynamic regret with switching cost, and best-of-both-worlds guarantees. Surprisingly, minimizing the hitting cost alone is $\max(1,\frac{2}α)$-competitive for $α$-polyhedral functions under the $\ell_2$-norm switching cost and $1+\frac{4}λ$-competitive for $λ$-quadratic growth functions under the squared $\ell_2$-norm switching cost, significantly improving existing guarantees. The polyhedral bound is tight for this naive algorithm, and we establish a matching lower bound for $α\geq1$. For convex $λ$-quadratic growth hitting costs, minimizing a suitably weighted sum of hitting and squared $\ell_2$-norm switching costs yields a competitive ratio of $1+\frac{2}{\sqrtλ}$. For dynamic regret with the $\ell_2$-norm switching cost, we develop Smoothed Ader (SAder), which achieves the optimal $O(\sqrt{T(1+P_T)})$ rate in the standard online convex optimization setting, where $P_T$ is the comparator's path-length. Its lookahead version removes the bounded-gradient assumption, and a matching lower bound establishes optimality in this setting. Finally, for convex hitting costs on a bounded convex domain, we develop UDNP to aggregate any two experts in the lookahead setting under both switching costs. Its additional cumulative cost is at most $O(1)$ relative to the first expert and $O(\sqrt{T\log T})$ relative to the second, yielding best-of-both-worlds guarantees without bounded gradients.

cs.LG↗

arXiv2026

Causal Value Attribution of Marketing Labels in LLM-Generated Ads: A Deconfounder Approach

As AI-generated content becomes commoditized, economic value increasingly shifts from final artifacts to the upstream expertise used to specify inputs that steer LLM generation. Yet organizations lack methods for valuing this expertise and identifying which individual skills or configurations causally improve performance. This study examines generative marketing, where structured expert labels serve as skill primitives conditioning LLM-generated advertisements. Estimating their causal effects is difficult because outcomes reflect stochastic LLM mediation, high-dimensional label interactions, and multimodal confounding. This study proposes D-VAE (Deconfounder Variational Autoencoder), a counterfactual-inference framework integrating a multi-treatment deconfounder with causal representation learning. D-VAE recovers causally disentangled expert-labeling logic and derives PAC-based bounds on omitted-variable bias from single-treatment confounders. Applied to 29,177 foundation-makeup ad creatives, D-VAE outperforms state-of-the-art benchmarks. A field experiment shows that recommended configurations increase engagement by 32.7% and perform statistically indistinguishably from human experts, while a simulation study confirms causal attribution under complex confounding and treatment interactions. Overall, the study shifts value assessment from AI-generated products to skills, providing a foundation for pricing and optimizing AI-augmented skill portfolios.

cs.AI↗

arXiv2026

No One-Size-Fits-All: Adaptive Code Editing with Feature-Based Strategy Selection

Large language models have shown strong potential in automating code editing (CE) tasks, yet most existing systems rely on a fixed CE strategy (i.e., one-step, search-replace, and plan-apply) across diverse scenarios. In practice, CE tasks vary widely in code context, edit locality, and semantic complexity, causing no single strategy to perform consistently well. Moreover, systematic studies on the relationship between strategies and CE tasks remain scarce, limiting further optimization of LLM-based code editing strategies. To address this gap, we construct CEBench, comprising 500 real-world CE tasks curated from SWE-bench. Then we compare three representative CE strategies (one-step, search-replace, plan-apply). Our study reveals two key findings: (1) each strategy exhibits distinct advantages for specific CE tasks, with no universal optimality; (2) strategy effectiveness is significantly influenced by four core task features: total lines of code, modification type, modification scope, and task type. Motivated by these findings, we propose Ace, an adaptive code editing framework that dynamically selects optimal CE strategies based on task features. Unlike classifier-based or instruction-prompting approaches, Ace employs a fine-tuned LLM that learns feature-strategy mappings from empirical data to recommend strategies with interpretable rationales. Extensive experiments on our CEBench-verified show that Ace outperforms state-of-the-art baselines: it boosts Pass@1 by 21.7% while reducing token consumption by 27.3% compared to the best baseline (AutoCodeRover). Our strategy selector achieves 72.6% selection accuracy with 69.9% rationale accuracy (Cohen's Kappa = 0.807), providing transparent and trustworthy decision-making for developers.

cs.SE↗

arXiv2026

Memory-Efficient Subspace Optimization with Residual Correction: From Momentum SGD to Muon

Memory-efficient subspace optimization has emerged as a practical approach to reducing the memory cost of LLM training while preserving optimization performance. Previous algorithms typically rely on the leading singular subspace of stochastic gradients, yet the gradient noise may dominate the subspace in later training stages and can prevent convergence. To overcome this limitation, we adopt a residual correction framework, which maintains the optimizer states in the subspace and adds the orthogonal residual gradient to the parameter update. We first integrate this scheme into momentum SGD to develop SMRC, which attains an $O(T^{-1/4})$ convergence rate for a fixed orthonormal basis, matching that of full-space momentum SGD. Our analysis introduces a subspace virtual iterate to resolve the coupling between the momentum and the residual correction. Furthermore, we extend SMRC to a multi-stage variant which periodically recomputes bases to track the evolving dominant subspace and retains the same rate. Since each basis refresh breaks the consistency of the virtual iterates, we devise a boundary correction approach that aligns them across stages. Beyond momentum SGD, we incorporate our framework into Muon and propose PMRC, which applies the matrix sign to the projected momentum. Through a weighted momentum tracking analysis that accounts for the residual gradient, we establish an $O(T^{-1/4})$ convergence rate for PMRC, which matches the rate of full-space Muon. We also design a multi-stage PMRC with periodically refreshed bases, which maintains a convergence rate of the same order. Extensive experimental results confirm the effectiveness and efficiency of our algorithms.

cs.LG↗

arXiv2026

Last-Iterate Convergence of Clipped SGD with Linear Decay

In this paper, we study the last-iterate convergence of clipped stochastic gradient descent under heavy-tailed noise. We assume that the stochastic gradients are unbiased and that the noise has a bounded central $p$-th moment, where $1<p\le2$. For smooth convex objectives, a linearly decreasing learning rate gives a high-probability error bound of order $O(LR^2\log(1/δ)/T+σR(\log(1/δ)/T)^{(p-1)/p})$. We further establish last-iterate guarantees for nonsmooth composite objectives and smooth composite objectives with proximal updates. In addition, when a causal adversary replaces at most $q$ gradients, the same clipped update achieves a bound with $\log(1/δ)$ replaced by $\log(1/δ)+q$. The corresponding lower bounds for the clean and corrupted oracle models are also provided.

cs.LG↗

arXiv2026

Adaptive Variance Reduction without Knowing Oracle Smoothness

Variance reduction improves the convergence rate of stochastic non-convex optimization under the average smoothness condition. Existing adaptive variance reduction methods are especially designed for average smoothness and do not adapt to standard smoothness. In this paper, we study how one algorithm can adapt to these two settings and the noiseless setting without knowing the smoothness constants or the variance bound. Given the gradient budget $T$, we develop a two-phase method. The first phase compares two independent gradients and switches to normalized momentum when their difference exceeds a threshold. This phase provides both a candidate with standard smooth and noiseless guarantees and also ensures a bounded expected function gap for the second variance reduction phase. The resulting rates are $O(T^{-1/3})$ under average smoothness, $O(T^{-1/4})$ under standard smoothness, and $O(T^{-1/2})$ without noise. When $T$ is unknown, we propose a method with two paths that attain the corresponding rates with logarithmic factors in the stochastic settings. Here, we use a variance reduction path to deal with average smoothness and employ the AdaGrad-Norm for standard smoothness and noiseless setting. Neither method restarts from the initial point or requires a growing number of oracle calls in each round.

math.OC↗

arXiv2026

CHASE: Channel-Aligned Structure Exploitation for Geometry-Aware Model Engineering

Geometric and Spectral Alignment (GSA) characterizes trained networks through spectral concentration, physical-channel alignment, support structure, and changes in singular bases. In this paper, we propose CHASE (Channel-Aligned Structure Exploitation) to use these structures in practical model design. CHASE covers six applications across model modification, reconfiguration, and compression. CORA, COEC, and CORAM apply GSA to parameter-efficient finetuning, structured-pruning compensation, and model merging. We further develop three new methods. CAGA uses GSA to identify multi-head attention heads that can share a KV representation and constructs the shared key and value heads through geometric alignment and low-rank subspace extraction. SAKV uses GSA to determine which adjacent layers can share a low-rank KV-cache representation and the retained rank for each layer group. CAPS uses GSA spectral structure to group output neurons and selects retained input channels separately for each group. Results from CORA, COEC, and CORAM establish the effectiveness of GSA for adaptation, pruning compensation, and model merging. Experiments on CAGA show that geometric shared-head construction substantially improves MHA-to-GQA conversion, and SAKV and CAPS improve over representative baselines for KV-cache compression and structured pruning. These results show that the structures identified by GSA can be used directly to design methods for a range of model operations.

cs.LG↗

arXiv2026

Implict-Explicit Runge-Kutta schemes for geometric flows

We propose a one-step implicit-explicit (IMEX) Runge-Kutta framework for high-order time integration of geometric flows. Starting from the Dziuk and Deckelnick-Dziuk parametric finite element formulations of curve shortening flow, we recast the spatially semidiscrete equations as systems of ordinary differential equations and construct second- and third-order schemes. Each stage requires only a linear solve. The key ingredient is a reduced-coefficient structure that allows the variational problem at each stage to be posed on the geometry generated by the preceding stage. The Runge-Kutta stages thus supply the required prediction geometry without a separate prediction procedure. The resulting schemes require no additional starting values. The framework also extends directly to the Barrett-Garcke-Nürnberg formulations of mean curvature flow and surface diffusion for curves and surfaces. Numerical experiments support the designed orders of temporal convergence and indicate that suitable coefficient choices yield mesh quality comparable to that of the corresponding first-order methods.

math.NA↗

arXiv2026

Multiple Access in Pinching-Antenna Systems: A Survey, Impairment Analysis, and Evaluation

Pinching-antenna systems attach dielectric pinches to a waveguide, creating line-of-sight radiation points within a few meters of any user. The pinches on one waveguide, however, radiate the same signal, unlike a conventional array, where each element transmits a dedicated signal. Separating the signals of multiple users therefore becomes challenging and requires a new perspective on multiple access. Most existing studies rest on an idealized model, and no survey examines the access schemes under realistic impairments. This article surveys multiple access in pinching-antenna systems and organizes fifty-six works into a unified taxonomy by spatial degrees of freedom. The users of one waveguide can be separated only in time, frequency, power, or guided mode, while multiple waveguides add the space domain. The article then identifies the impairments critical to this separation, which perturb the effective channel, leak interference across orthogonal resources, or couple the pinches on the uplink, and summarizes them in an impairment-versus-method map. A unified evaluation of time-, frequency-, power-, and space-domain access under identical channel and impairment models reveals that the degradation is method specific. The analytical and numerical results give insight into multiple access in these systems and provide a basis for its impairment-aware design, a necessary step toward their adoption in practical networks.

cs.IT↗

arXiv2026

Better Convergence Guarantees for Sign-Based Momentum Methods

This paper presents an improved analysis for sign-based methods with momentum updates. Traditional sign-based methods obtain a convergence rate of $\mathcal{O}(T^{-1/4})$ under the separable smoothness assumption, but they typically require large batch sizes or assume unimodal symmetric stochastic noise. To address these limitations, we demonstrate that signSGD with momentum can achieve the same convergence rate using constant batch sizes without additional assumptions. We also establish a convergence rate under the $l_2$-smoothness condition, improving upon the result of prior work by a factor of $\mathcal{O}(d^{1/2})$, where $d$ is the problem dimension. Furthermore, we explore sign-based methods in distributed settings and show that the proposed methods yield convergence rates of $\mathcal{O}\left( d^{1/2}T^{-1/2} + dn^{-1/2} \right)$ and $\mathcal{O}\left(d^{1/4}T^{-1/4}\right)$, which outperform the previous results of $\mathcal{O}\left( dT^{-1/4} + dn^{-1/2} \right)$ and $\mathcal{O}\left( d^{3/8}T^{-1/8} \right)$, respectively. Numerical experiments also validate the effectiveness of the proposed methods.

math.OC↗

arXiv2026

From Switching to Dynamic Regret: A Simple Reduction via Unbiased Random Sequences

In non-stationary online learning, dynamic regret has attracted increasing attention as a measure of how well an online learner performs against a time-varying comparator sequence. Despite considerable advances, attaining optimal bounds for strongly convex and exp-concave losses often involves intricate analysis. In this paper, we present a \textit{simple} framework that reduces dynamic regret minimization to switching regret minimization. As a result, we can derive dynamic regret bounds by using off-the-shelf algorithms with switching regret guarantees. The key idea of our reduction is to construct, for \textit{any} comparator sequence, an auxiliary random sequence that is unbiased at each round, with the controlled variance and a manageable number of switches. Combining this construction with suitable surrogate losses, we can decompose dynamic regret into the expected switching regret against the random sequence and its controlled variance. Theoretically, for strongly convex and exp-concave losses, we establish the $\widetilde{O}(T^{1/3}P_T^{2/3})$ dynamic regret bounds, where $T$ denotes the time horizon and $P_T$ denotes the path-length of the comparator sequence. Moreover, for general convex losses, the same reduction also recovers the $O(\sqrt{T(1+P_T)})$ dynamic regret bound. Notably, all our findings match the minimax optimal results for these three types of losses, highlighting the versatility of our proposed framework.

cs.LG↗