Stability Properties of Graph Neural Networks

Gama, Fernando; Bruna, Joan; Ribeiro, Alejandro

doi:10.1109/tsp.2020.3026980

Cited by 164 publications

(167 citation statements)

References 39 publications

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“…(1)] and of the GCNN [cf. (8)] are recently linked with their ability to be robust to perturbations [17], [24]. Next, we investigate this property for consensus and observe that GCNNs have a better transference to unseen graphs compared with the FIR filter (1).…”

Section: Methodsmentioning

confidence: 98%

“…Employing instead a GCNN with filters of the form in (1) does not require the GSO eigendecomposition, a fixed labeling, and it is better transferable to unseen graphs than the linear graph filter [17].…”

Section: B Consensus As Graph Signal Filteringmentioning

confidence: 99%

“…By having the FIR graph filter as their integral part, GCNNs link directly to finite-time consensus if the activation functions leave unaffected the distributed implementation. The coupling graph filter-activation function also facilitates the transferability of GCNNs to graphs that deviate slightly from the ones they were trained on [17]. The main research question we address is how do GCNNs behave for distributed finite-time consensus.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Towards Finite-Time Consensus with Graph Convolutional Neural Networks

Iancu

Isufi

2021

2020 28th European Signal Processing Conference (EUSIPCO)

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Section: Methodsmentioning

confidence: 98%

Section: B Consensus As Graph Signal Filteringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Towards Finite-Time Consensus with Graph Convolutional Neural Networks

Iancu

Isufi

2021

2020 28th European Signal Processing Conference (EUSIPCO)

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“…They do not require full knowledge of the graph, but only of their immediate neighbors. Thus, the distributed implementation scales seamlessly to the graph filtering operation [20]. We fundamentally use (3) as a mathematical framework that offers a condensed description of the communication exchanges that happen in a network.…”

Section: Wide Component: Bank Of Graph Filtersmentioning

confidence: 99%

“…Therefore, we oftentimes need to adapt to (slightly) new data structures. GNNs have been shown to be resilient to changes, as proven by the properties of permutation equivariance and stability [19,20]. While these properties guarantee transference, we can further improve the performance by leveraging online learning approaches.…”

Section: Introductionmentioning

confidence: 99%

Wide and Deep Graph Neural Networks with Distributed Online Learning

Gao

Ribeiro

Gama

2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Graph neural networks (GNNs) learn representations from network data with naturally distributed architectures, rendering them well-suited candidates for decentralized learning. Oftentimes, this decentralized graph support changes with time due to link failures or topology variations. These changes create a mismatch between the graphs on which GNNs were trained and the ones on which they are tested. Online learning can be used to retrain GNNs at testing time, overcoming this issue. However, most online algorithms are centralized and work on convex problems (which GNNs rarely lead to). This paper proposes the Wide and Deep GNN (WD-GNN), a novel architecture that can be easily updated with distributed online learning mechanisms. The WD-GNN comprises two components: the wide part is a bank of linear graph filters and the deep part is a GNN. At training time, the joint architecture learns a nonlinear representation from data. At testing time, the deep part (nonlinear) is left unchanged, while the wide part is retrained online, leading to a convex problem. We derive convergence guarantees for this online retraining procedure and further propose a decentralized alternative. Experiments on the robot swarm control for flocking corroborate theory and show potential of the proposed architecture for distributed online learning.

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