Inthis paper,we theoretically extend spectral-based graph convolution todigraphs and deriveasimplified form usingpersonalizedPageRank. Specifically,we present theDigraph Inception Convolutional Networks(DiGCN) whichutilizes digraph convolution andkth-order proximity to achievelarger receptivefields and learn multi-scale features in digraphs.

Several approaches to predictive uncertainty quantification have been introduced in recent years, considering uncertainty inaBayesian sense [2,7,18]aswell asfrom afrequentist'spoint ofview [15,5,34].

Note that, because the number of basis vectors parameterized by62 the imaginary coefficients is smaller,there are four gaps in Fig. S2. The results ofthis experiment are illustrated inFig. Because the eigendecomposition ofID is isotropic, we can see that the logistic regression has no159 directional bias.160 8 Example3(Single hidden-layer neural network). Surprisingly, both algorithms yield very similar results, but the algorithm based on the191 eigendecomposition ofthegradient covariance isnumerically much more stable. Meanwhile, thegradient covariance onlyrequires information about firstorder gradients195 and these are orders of magnitudes larger than the second derivatives.

In machine learning, given a finite set of samples, there are usually multiple solutions that can perfectly fit the training data, but theinductive biasof a learning algorithm selects and prioritizes those solutions that agree with itsaprioriassumptions [1,2].

The issue of distribution shifts is emerging as a critical concern in graph representation learning.