arXiv subjects

Shuainan Liu

Publications and source records attributed to Shuainan Liu.

3 recordsLinked to original sources

arXiv2026

Beyond Local Edits: Embedding-Virtualized Knowledge for Broader Evaluation and Preservation of Model Editing

Knowledge editing methods for large language models are commonly evaluated using predefined benchmarks that assess edited facts together with a limited set of related or neighboring knowledge. While effective, such evaluations remain confined to finite, dataset-bounded samples, leaving the broader impact of editing on the model's knowledge system insufficiently understood. To address this gap, we introduce Embedding-Virtualized Knowledge (EVK) that characterizes model knowledge through controlled perturbations in embedding space, enabling the exploration of a substantially broader and virtualized knowledge region beyond explicit data annotations. Based on EVK, we construct an embedding-level evaluation benchmark EVK-Bench that quantifies potential knowledge drift induced by editing, revealing effects that are not captured by conventional sample-based metrics. Furthermore, we propose a plug-and-play EVK-Align module that constrains embedding-level knowledge drift during editing and can be seamlessly integrated into existing editing methods. Experiments demonstrate that our approach enables more comprehensive evaluation while significantly improving knowledge preservation without sacrificing editing accuracy.

cs.CL↗

arXiv2025

Privacy Loss of Noise Perturbation via Concentration Analysis of A Product Measure

Noise perturbation is one of the most fundamental approaches for achieving $(\epsilon,\delta)$-differential privacy (DP) guarantees when releasing the result of a query or function $f(\cdot)\in\mathbb{R}^M$ evaluated on a sensitive dataset $\mathbf{x}$. In this approach, calibrated noise $\mathbf{n}\in\mathbb{R}^M$ is used to obscure the difference vector $f(\mathbf{x})-f(\mathbf{x}')$, where $\mathbf{x}'$ is known as a neighboring dataset. A DP guarantee is obtained by studying the tail probability bound of a privacy loss random variable (PLRV), defined as the Radon-Nikodym derivative between two distributions. When $\mathbf{n}$ follows a multivariate Gaussian distribution, the PLRV is characterized as a specific univariate Gaussian. In this paper, we propose a novel scheme to generate $\mathbf{n}$ by leveraging the fact that the perturbation noise is typically spherically symmetric (i.e., the distribution is rotationally invariant around the origin). The new noise generation scheme allows us to investigate the privacy loss from a geometric perspective and express the resulting PLRV using a product measure, $W\times U$; measure $W$ is related to a radius random variable controlling the magnitude of $\mathbf{n}$, while measure $U$ involves a directional random variable governing the angle between $\mathbf{n}$ and the difference $f(\mathbf{x})-f(\mathbf{x}')$. We derive a closed-form moment bound on the product measure to prove $(\epsilon,\delta)$-DP. Under the same $(\epsilon,\delta)$-DP guarantee, our mechanism yields a smaller expected noise magnitude than the classic Gaussian noise in high dimensions, thereby significantly improving the utility of the noisy result $f(\mathbf{x})+\mathbf{n}$. To validate this, we consider convex and non-convex empirical risk minimization (ERM) problems in high dimensional space and apply the proposed product noise to achieve privacy.

cs.CR↗

arXiv2023

Physics-Informed Kernel Function Neural Networks for Solving Partial Differential Equations

This paper proposed a novel radial basis function neural network (RBFNN) to solve various partial differential equations (PDEs). In the proposed RBF neural networks, the physics-informed kernel functions (PIKFs), which are derived according to the governing equations of the considered PDEs, are used to be the activation functions instead of the traditional RBFs. Similar to the well-known physics-informed neural networks (PINNs), the proposed physics-informed kernel function neural networks (PIKFNNs) also include the physical information of the considered PDEs in the neural network. The difference is that the PINNs put this physical information in the loss function, and the proposed PIKFNNs put the physical information of the considered governing equations in the activation functions. By using the derived physics-informed kernel functions satisfying the considered governing equations of homogeneous, nonhomogeneous, transient PDEs as the activation functions, only the boundary/initial data are required to train the neural network. Finally, the feasibility and accuracy of the proposed PIKFNNs are validated by several benchmark examples referred to high-wavenumber wave propagation problem, infinite domain problem, nonhomogeneous problem, long-time evolution problem, inverse problem, spatial structural derivative diffusion model, and so on.

math.NA↗