Bo Jiang

Ziyan Zhang, Bo Jiang, Jin Tang

Parameter-Efficient Fine-Tuning (PEFT) method has emerged as a dominant paradigm for adapting pre-trained GNN models to downstream tasks. However, existing PEFT methods usually exhibit significant vulnerability to various noise and attacks on graph topology and node attributes/features. To address this issue, for the first time, we propose integrating adversarial learning into graph prompting and develop a novel Adversarial Graph Prompting (AGP) framework to achieve robust graph fine-tuning. Our AGP has two key aspects. First, we propose the general problem formulation of AGP as a min-max optimization problem and develop an alternating optimization scheme to solve it. For inner maximization, we propose Joint Projected Gradient Descent (JointPGD) algorithm to generate strong adversarial noise. For outer minimization, we employ a simple yet effective module to learn the optimal node prompts to counteract the adversarial noise. Second, we demonstrate that the proposed AGP can theoretically address both graph topology and node noise. This confirms the versatility and robustness of our AGP fine-tuning method across various graph noise. Note that, the proposed AGP is a general method that can be integrated with various pre-trained GNN models to enhance their robustness on the downstream tasks. Extensive experiments on multiple benchmark tasks validate the robustness and effectiveness of AGP method compared to state-of-the-art methods.

Ruofeng Yang, Yongcan Li, Bo Jiang et al.

Recently, diffusion models have achieved a great performance with a small dataset of size $n$ and a fast optimization process. However, the estimation error of diffusion models suffers from the curse of dimensionality $n^{-1/D}$ with the data dimension $D$. Since images are usually a union of low-dimensional manifolds, current works model the data as a union of linear subspaces with Gaussian latent and achieve a $1/\sqrt{n}$ bound. Though this modeling reflects the multi-manifold property, the Gaussian latent can not capture the multi-modal property of the latent manifold. To bridge this gap, we propose the mixture subspace of low-rank mixture of Gaussian (MoLR-MoG) modeling, which models the target data as a union of $K$ linear subspaces, and each subspace admits a mixture of Gaussian latent ($n_k$ modals with dimension $d_k$). With this modeling, the corresponding score function naturally has a mixture of expert (MoE) structure, captures the multi-modal information, and contains nonlinear property. We first conduct real-world experiments to show that the generation results of MoE-latent MoG NN are much better than MoE-latent Gaussian score. Furthermore, MoE-latent MoG NN achieves a comparable performance with MoE-latent Unet with $10 \times$ parameters. These results indicate that the MoLR-MoG modeling is reasonable and suitable for real-world data. After that, based on such MoE-latent MoG score, we provide a $R^4\sqrt{Σ_{k=1}^Kn_k}\sqrt{Σ_{k=1}^Kn_kd_k}/\sqrt{n}$ estimation error, which escapes the curse of dimensionality by using data structure. Finally, we study the optimization process and prove the convergence guarantee under the MoLR-MoG modeling. Combined with these results, under a setting close to real-world data, this work explains why diffusion models only require a small training sample and enjoy a fast optimization process to achieve a great performance.