Neural diffusion on graphs is a novel class of graph neural networks that has attracted increasing attention recently. The capability of graph neural partial differential equations (PDEs) in addressing common hurdles of graph neural networks (GNNs), such as the problems of over-smoothing and bottlenecks, has been investigated but not their robustness to adversarial attacks. In this work, we explore the robustness properties of graph neural PDEs. We empirically demonstrate that graph neural PDEs are intrinsically more robust against topology perturbation as compared to other GNNs. We provide insights into this phenomenon by exploiting the stability of the heat semigroup under graph topology perturbations. We discuss various graph diffusion operators and relate them to existing graph neural PDEs. Furthermore, we propose a general graph neural PDE framework based on which a new class of robust GNNs can be defined. We verify that the new model achieves comparable state-of-the-art performance on several benchmark datasets.

Despite the rapid advance of 3D-aware image synthesis, existing studies usually adopt a mixture of techniques and tricks, leaving it unclear how each part contributes to the final performance in terms of generality. Following the most popular and effective paradigm in this field, which incorporates a neural radiance field (NeRF) into the generator of a generative adversarial network (GAN), we build a well-structured codebase, dubbed Carver, through modularizing the generation process. Such a design allows researchers to develop and replace each module independently, and hence offers an opportunity to fairly compare various approaches and recognize their contributions from the module perspective. The reproduction of a range of cutting-edge algorithms demonstrates the availability of our modularized codebase. We also perform a variety of in-depth analyses, such as the comparison across different types of point feature, the necessity of the tailing upsampler in the generator, the reliance on the camera pose prior, etc., which deepen our understanding of existing methods and point out some further directions of the research work. We release code and models here to facilitate the development and evaluation of this field.