Transferable Graph Neural Networks on Large-Scale Stochastic Graphs

Ruiz, Luana; Chamon, Luiz F. O.; Ribeiro, Alejandro

doi:10.1109/ieeeconf53345.2021.9723298

Cited by 7 publications

(5 citation statements)

References 12 publications

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“…In future work, we will investigate more general classes of cellular sheaves that approximate unions of manifolds (perhaps representing multiple classes) or, more generally, stratified spaces [42], [43]. We believe our perspective on tangent bundle neural networks could shed further light on challenging problems in graph neural networks such as heterophily [29], over-squashing [44], or transferability [45]- [47]. Finally,we plan to tackle more sophisticated tasks such as robot coordination with our proposed architectures.…”

Section: Discussionmentioning

confidence: 99%

Tangent Bundle Convolutional Learning: from Manifolds to Cellular Sheaves and Back

Battiloro¹,

Wang²,

Riess³

et al. 2023

Preprint

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In this work we introduce a convolution operation over the tangent bundle of Riemann manifolds in terms of exponentials of the Connection Laplacian operator. We define tangent bundle filters and tangent bundle neural networks (TNNs) based on this convolution operation, which are novel continuous architectures operating on tangent bundle signals, i.e. vector fields over the manifolds. Tangent bundle filters admit a spectral representation that generalizes the ones of scalar manifold filters, graph filters and standard convolutional filters in continuous time. We then introduce a discretization procedure, both in the space and time domains, to make TNNs implementable, showing that their discrete counterpart is a novel principled variant of the very recently introduced sheaf neural networks. We formally prove that this discretized architecture converges to the underlying continuous TNN. Finally, we numerically evaluate the effectiveness of the proposed architecture on various learning tasks, both on synthetic and real data.

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Section: Discussionmentioning

confidence: 99%

Tangent Bundle Convolutional Learning: from Manifolds to Cellular Sheaves and Back

Battiloro¹,

Wang²,

Riess³

et al. 2023

Preprint

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“…It is well-known that GNN models have an unprecedented capability to generalize over graph-structured data [38], [39]. In the context of scaling to larger graphs, it is also known that GNNs keep good generalization capabilities as long as the spectral properties of graphs are similar to those seen during training [40]. In our particular case, the internal message passing architecture of RouteNet-F generalizes accurately to graphs with similar structures (e.g., a similar number of queues at output ports, or a similar number of flows aggregated in queues).…”

Section: Scaling To Larger Network: Scale-independent Featuresmentioning

confidence: 99%

RouteNet-Fermi: Network Modeling With Graph Neural Networks

Ferriol-Galmés¹,

Paillissé²,

Suárez‐Varela³

et al. 2023

IEEE/ACM Trans. Networking

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Network models are an essential block of modern networks. For example, they are widely used in network planning and optimization. However, as networks increase in scale and complexity, some models present limitations, such as the assumption of Markovian traffic in queuing theory models, or the high computational cost of network simulators. Recent advances in machine learning, such as Graph Neural Networks (GNN), are enabling a new generation of network models that are datadriven and can learn complex non-linear behaviors. In this paper, we present RouteNet-Fermi, a custom GNN model that shares the same goals as Queuing Theory, while being considerably more accurate in the presence of realistic traffic models. The proposed model predicts accurately the delay, jitter, and packet loss of a network. We have tested RouteNet-Fermi in networks of increasing size (up to 300 nodes), including samples with mixed traffic profiles -e.g., with complex non-Markovian modelsand arbitrary routing and queue scheduling configurations. Our experimental results show that RouteNet-Fermi achieves similar accuracy as computationally-expensive packet-level simulators and scales accurately to larger networks. Our model produces delay estimates with a mean relative error of 6.24% when applied to a test dataset of 1,000 samples, including network topologies one order of magnitude larger than those seen during training. Finally, we have also evaluated RouteNet-Fermi with measurements from a physical testbed and packet traces from a real-life network.

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“…AGGR{ • } indicates a generic permutation invariant aggregation function, while N (i) refers to the set of neighbors of node i, each associated to an edge with weight a ji . Models of this type are fully inductive, in the sense that they can be used to make predictions for networks and time windows different from those they have been trained on, provided a certain level of similarity (e.g., homogenous sensors) between source and target node sets [15]. Among the different implementations of this general framework, we can distinguish between time-then-space (TTS) and time-and-space (T&S) models by following the terminology of previous works [16,17].…”

Section: Forecasting With Stgnnsmentioning

confidence: 99%

Taming Local Effects in Graph-based Spatiotemporal Forecasting

Cini¹,

Marisca²,

Zambon³

et al. 2023

Preprint

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Spatiotemporal graph neural networks have shown to be effective in time series forecasting applications, achieving better performance than standard univariate predictors in several settings. These architectures take advantage of a graph structure and relational inductive biases to learn a single (global) inductive model to predict any number of the input time series, each associated with a graph node. Despite the gain achieved in computational and data efficiency w.r.t. fitting a set of local models, relying on a single global model can be a limitation whenever some of the time series are generated by a different spatiotemporal stochastic process. The main objective of this paper is to understand the interplay between globality and locality in graph-based spatiotemporal forecasting, while contextually proposing a methodological framework to rationalize the practice of including trainable node embeddings in such architectures. We ascribe to trainable node embeddings the role of amortizing the learning of specialized components. Moreover, embeddings allow for 1) effectively combining the advantages of shared message-passing layers with node-specific parameters and 2) efficiently transferring the learned model to new node sets. Supported by strong empirical evidence, we provide insights and guidelines for specializing graph-based models to the dynamics of each time series and show how this aspect plays a crucial role in obtaining accurate predictions.

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Transferable Graph Neural Networks on Large-Scale Stochastic Graphs

Cited by 7 publications

References 12 publications

Tangent Bundle Convolutional Learning: from Manifolds to Cellular Sheaves and Back

Tangent Bundle Convolutional Learning: from Manifolds to Cellular Sheaves and Back

RouteNet-Fermi: Network Modeling With Graph Neural Networks

Taming Local Effects in Graph-based Spatiotemporal Forecasting

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