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Zhiqiang Gao

Zhiqiang Gao appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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Machine Learning math.PR Artificial Intelligence Computation and Language math.CA math.FA

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preprint2026arXiv

Fix the Loss, Not the Radius: Rethinking the Adversarial Perturbation of Sharpness-Aware Minimization

Sharpness-Aware Minimization (SAM) improves generalization by minimizing the worst-case loss within a fixed parameter-space radius neighborhood. SAM and its variants mainly rely on a first-order linearized surrogate, while flat minima are inherently a second-order (curvature) notion.We revisit this mismatch and propose Loss-Equated SAM (LE-SAM), which inverts the traditional SAM mechanism that fixed perturbation radius with a fixed loss-space budget,effectively removing gradient-norm-dominated learning signals and shifting optimization toward curvature-dominated terms. Extensive experiments across diverse benchmarks and tasks demonstrate the strong generalization ability of LESAM that consistently outperforms SAM and even its variants, achieving the state-of-the-art performance.

preprint2026arXiv

Rethinking Loss Reweighting for Imbalance Learning as an Inverse Problem: A Neural Collapse Point of View

Loss reweighting is a widely used strategy for long-tailed classification, but existing reweighting strategies often rely on heuristics and rarely define a well-specified target. Inspired by Neural Collapse (NC), the ideal simplex Equiangular Tight Frame (ETF) terminal geometry suggests equal per-class average loss as a reasonable target for reweighting. Based on the ideal equal loss objective, we consider loss reweighting as an inverse problem and propose an inverse-view reweighting strategy that infers class weights dynamically to match this ideal objective. Empirically, NC metrics suggest our method can effectively reduce the loss imbalance coefficient and closer alignment with NC geometry while consistently outperforming strong long-tailed baselines on different datasets.

preprint2022arXiv

A Higher-Order Semantic Dependency Parser

Higher-order features bring significant accuracy gains in semantic dependency parsing. However, modeling higher-order features with exact inference is NP-hard. Graph neural networks (GNNs) have been demonstrated to be an effective tool for solving NP-hard problems with approximate inference in many graph learning tasks. Inspired by the success of GNNs, we investigate building a higher-order semantic dependency parser by applying GNNs. Instead of explicitly extracting higher-order features from intermediate parsing graphs, GNNs aggregate higher-order information concisely by stacking multiple GNN layers. Experimental results show that our model outperforms the previous state-of-the-art parser on the SemEval 2015 Task 18 English datasets.

preprint2015arXiv

Exact convergence rates in central limit theorems for a branching random walk with a random environment in time

Chen [Ann. Appl. Probab. {\bf 11} (2001), 1242--1262] derived exact convergence rates in a central limit theorem and a local limit theorem for a supercritical branching Wiener process.We extend Chen's results to a branching random walk under weaker moment conditions. For the branching Wiener process, our results sharpen Chen's by relaxing the second moment condition used by Chen to a moment condition of the form $ \E X (\ln^+X )^{1+λ}< \infty$. In the rate functions that we find for a branching random walk, we figure out some new terms which didn't appear in Chen's work.The results are established in the more general framework, i.e. for a branching random walk with a random environment in time.The lack of the second moment condition for the offspring distribution and the fact that the exponential moment does not exist necessarily for the displacements make the proof delicate; the difficulty is overcome by a careful analysis of martingale convergence using a truncating argument. The analysis is significantly more awkward due to the appearance of the random environment.

preprint2013arXiv

Stable laws and spectral gap properties for affine random walks

We consider a general multidimensional affine recursion with corresponding Markov operator $P$ and a unique $P$-stationary measure. We show spectral gap properties on Hölder spaces for the corresponding Fourier operators and we deduce convergence to stable laws for the Birkhoff sums along the recursion. The parameters of the stable laws are expressed in terms of basic quantities depending essentially on the matricial multiplicative part of $P$. Spectral gap properties of $P$ and homogeneity at infinity of the $P$-stationary measure play an important role in the proofs.

preprint2012arXiv

Criterions of Wiener type for minimally thin sets and rarefied sets associated with the stationary Schrödinger operator in a cone

In the paper we give some criterions for a-minimally thin sets and a-rarefied sets associated with the stationary Schrödinger operator at a fixed Martin boundary point or {\infty} with respect to a cone. Moreover, we show that a positive superfunction on a cone behaves regularly outside a-rarefied set. Finally we illustrate the relation between a-minimally thin set and a-rarefied set in a cone.

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