Few-shot knowledge graph (KG) completion task aims to perform inductive reasoning over the KG: given only a few support triplets of a new relation ./(e.g., (chop, ./,

This paper proposes a new easy-to-implement parameter-free gradient-based optimizer: DoWG (Distance over Weighted Gradients). We prove that DoWG is efficient--matching the convergence rate of optimally tuned gradient descent in convex optimization up to a logarithmic factor without tuning any parameters, and universal--automatically adapting to both smooth and nonsmooth problems. While popular algorithms following the AdaGrad framework compute a running average of the squared gradients to use for normalization, DoWG maintains a new distance-based weighted version of the running average, which is crucial to achieve the desired properties. To complement our theory, we also show empirically that DoWG trains at the edge of stability, and validate its effectiveness on practical machine learning tasks.

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.

A.1 Multiple data matrices A combinatorial optimization problem can be presented with multiple (f) relationship features between two groups of items. In FFSP, for example, a production cost could be different for each process that one has to take into account for scheduling in addition to the processing time for each pair of the job and the machine. When there are f number of matrices that need to be encoded (D1, D2, ..., Df), MatNet can be easily expended to accommodate such problems by using the mixed-score attention shown in Figure A.1 instead of the one in Figure 2(b). "Trainable element-wise function" block in Figure A.1 is now an MLP with f + 1 input nodes and 1 output node. A.2 Alternative encoding sequences Equation (2) in the main text describes the application of FA and FB in the graph attentional layer of MatNet that happens in parallel.