Shih-Hsin Wang

Fan Jia, Yuhao Huang, Shih-Hsin Wang et al.

Flow matching-based generative models have been integrated into the plug-and-play image restoration framework, and the resulting plug-and-play flow matching (PnP-Flow) model has achieved some remarkable empirical success for image restoration. However, the theoretical understanding of PnP-Flow lags its empirical success. In this paper, we derive a continuous limit for PnP-Flow, resulting in a stochastic differential equation (SDE) surrogate model of PnP-Flow. The SDE model provides two particular insights to improve PnP-Flow for image restoration: (1) It enables us to quantify the error for image restoration, informing us to improve step scheduling and regularize the Lipschitz constant of the neural network-parameterized vector field for error reduction. (2) It informs us to accelerate off-the-shelf PnP-Flow models via extrapolation, resulting in a rescaled version of the proposed SDE model. We validate the efficacy of the SDE-informed improved PnP-Flow using several benchmark tasks, including image denoising, deblurring, super-resolution, and inpainting. Numerical results show that our method significantly outperforms the baseline PnP-Flow and other state-of-the-art approaches, achieving superior performance across evaluation metrics.

Shih-Hsin Wang, Justin Baker, Cory Hauck et al.

The pioneering work of Oono and Suzuki [ICLR, 2020] and Cai and Wang [arXiv:2006.13318] initializes the analysis of the smoothness of graph convolutional network (GCN) features. Their results reveal an intricate empirical correlation between node classification accuracy and the ratio of smooth to non-smooth feature components. However, the optimal ratio that favors node classification is unknown, and the non-smooth features of deep GCN with ReLU or leaky ReLU activation function diminish. In this paper, we propose a new strategy to let GCN learn node features with a desired smoothness -- adapting to data and tasks -- to enhance node classification. Our approach has three key steps: (1) We establish a geometric relationship between the input and output of ReLU or leaky ReLU. (2) Building on our geometric insights, we augment the message-passing process of graph convolutional layers (GCLs) with a learnable term to modulate the smoothness of node features with computational efficiency. (3) We investigate the achievable ratio between smooth and non-smooth feature components for GCNs with the augmented message-passing scheme. Our extensive numerical results show that the augmented message-passing schemes significantly improve node classification for GCN and some related models.