Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability and Generalization of Graph Convolutional Neural Networks   Inspired by convolutional neural networks on 1D and 2D data, graph
convolutional neural networks (GCNNs) have been developed for various learning
tasks on graph data, and have shown superior performance on real-world
datasets. Despite their success, there is a dearth of theoretical explorations
of GCNN models such as their generalization properties. In this paper, we take
a first step towards developing a deeper theoretical understanding of GCNN
models by analyzing the stability of single-layer GCNN models and deriving
their generalization guarantees in a semi-supervised graph learning setting. In
particular, we show that the algorithmic stability of a GCNN model depends upon
the largest absolute eigenvalue of its graph convolution filter. Moreover, to
ensure the uniform stability needed to provide strong generalization
guarantees, the largest absolute eigenvalue must be independent of the graph
size. Our results shed new insights on the design of new & improved graph
convolution filters with guaranteed algorithmic stability. We evaluate the
generalization gap and stability on various real-world graph datasets and show
that the empirical results indeed support our theoretical findings. To the best
of our knowledge, we are the first to study stability bounds on graph learning
in a semi-supervised setting and derive generalization bounds for GCNN models.

8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom