194 research outputs found
Rethinking the Expressive Power of GNNs via Graph Biconnectivity
Designing expressive Graph Neural Networks (GNNs) is a central topic in
learning graph-structured data. While numerous approaches have been proposed to
improve GNNs in terms of the Weisfeiler-Lehman (WL) test, generally there is
still a lack of deep understanding of what additional power they can
systematically and provably gain. In this paper, we take a fundamentally
different perspective to study the expressive power of GNNs beyond the WL test.
Specifically, we introduce a novel class of expressivity metrics via graph
biconnectivity and highlight their importance in both theory and practice. As
biconnectivity can be easily calculated using simple algorithms that have
linear computational costs, it is natural to expect that popular GNNs can learn
it easily as well. However, after a thorough review of prior GNN architectures,
we surprisingly find that most of them are not expressive for any of these
metrics. The only exception is the ESAN framework (Bevilacqua et al., 2022),
for which we give a theoretical justification of its power. We proceed to
introduce a principled and more efficient approach, called the Generalized
Distance Weisfeiler-Lehman (GD-WL), which is provably expressive for all
biconnectivity metrics. Practically, we show GD-WL can be implemented by a
Transformer-like architecture that preserves expressiveness and enjoys full
parallelizability. A set of experiments on both synthetic and real datasets
demonstrates that our approach can consistently outperform prior GNN
architectures.Comment: ICLR 2023 notable top-5%; 58 pages, 11 figure
Quantum Algorithm for Maximum Biclique Problem
Identifying a biclique with the maximum number of edges bears considerable
implications for numerous fields of application, such as detecting anomalies in
E-commerce transactions, discerning protein-protein interactions in biology,
and refining the efficacy of social network recommendation algorithms. However,
the inherent NP-hardness of this problem significantly complicates the matter.
The prohibitive time complexity of existing algorithms is the primary
bottleneck constraining the application scenarios. Aiming to address this
challenge, we present an unprecedented exploration of a quantum computing
approach. Efficient quantum algorithms, as a crucial future direction for
handling NP-hard problems, are presently under intensive investigation, of
which the potential has already been proven in practical arenas such as
cybersecurity. However, in the field of quantum algorithms for graph databases,
little work has been done due to the challenges presented by the quantum
representation of complex graph topologies. In this study, we delve into the
intricacies of encoding a bipartite graph on a quantum computer. Given a
bipartite graph with n vertices, we propose a ground-breaking algorithm qMBS
with time complexity O^*(2^(n/2)), illustrating a quadratic speed-up in terms
of complexity compared to the state-of-the-art. Furthermore, we detail two
variants tailored for the maximum vertex biclique problem and the maximum
balanced biclique problem. To corroborate the practical performance and
efficacy of our proposed algorithms, we have conducted proof-of-principle
experiments utilizing IBM quantum simulators, of which the results provide a
substantial validation of our approach to the extent possible to date
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