Neural Network for Graphs: A Contextual Constructive Approach
Abstract
This paper presents a new approach for learning in structured domains (SDs) using a constructive neural network for graphs (NN4G). The new model allows the extension of the input domain for supervised neural networks to a general class of graphs including both acyclic/cyclic, directed/undirected labeled graphs. In particular, the model can realize adaptive contextual transductions, learning the mapping from graphs for both classification and regression tasks. In contrast to previous neural networks for structures that had a recursive dynamics, NN4G is based on a constructive feedforward architecture with state variables that uses neurons with no feedback connections. The neurons are applied to the input graphs by a general traversal process that relaxes the constraints of previous approaches derived by the causality assumption over hierarchical input data. Moreover, the incremental approach eliminates the need to introduce cyclic dependencies in the definition of the system state variables. In the traversal process, the NN4G units exploit (local) contextual information of the graphs vertices. In spite of the simplicity of the approach, we show that, through the compositionality of the contextual information developed by the learning, the model can deal with contextual information that is incrementally extended according to the graphs topology. The effectiveness and the generality of the new approach are investigated by analyzing its theoretical properties and providing experimental results.
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In 2009, Micheli et al. first addressed graph mutual dependency by architecturally composite nonrecursive layers while inheriting ideas of message passing from RecGNNs.
“In 2009, Micheli et al. [24] first addressed graph mutual dependency by architecturally composite nonrecursive layers while inheriting ideas of message passing from RecGNNs.”
From A Comprehensive Survey on Graph Neural Networks (2021) · cites this paper as [24]
NN4G performs graph convolutions by summing up a node's neighborhood information directly.
“NN4G performs graph convolutions by summing up a node's neighborhood information directly.”
From A Comprehensive Survey on Graph Neural Networks (2021) · cites this paper as [24]
NN4G is the first work towards spatial-based ConvGNNs.
“Neural Network for Graphs (NN4G) [24], proposed in parallel with GNN*, is the first work towards spatial-based ConvGNNs.”
From A Comprehensive Survey on Graph Neural Networks (2021) · cites this paper as [24]
NN4G uses the unnormalized adjacency matrix, which may potentially cause hidden node states to have extremely different scales.
“One difference is that NN4G uses the unnormalized adjacency matrix which may potentially cause hidden node states to have extremely different scales.”
From A Comprehensive Survey on Graph Neural Networks (2021) · cites this paper as [24]
Distinctively different from RecGNNs, NN4G learns graph mutual dependency through a compositional neural architecture with independent parameters at each layer.
“Distinctively different from RecGNNs, NN4G learns graph mutual dependency through a compositional neural architecture with independent parameters at each layer.”
From A Comprehensive Survey on Graph Neural Networks (2021) · cites this paper as [24]
Micheli proves that a finite number of spatial graph convolutional layers exists such that for each node v, the receptive field of node v covers all nodes in the graph.
“Micheli [24] prove that a finite number of spatial graph convolutional layers exists such that for each node v ∈ V the receptive field of node v covers all nodes in the graph.”
From A Comprehensive Survey on Graph Neural Networks (2021) · cites this paper as [24]
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- Authors
- Micheli, A.
- Affiliations
- University of Pisa (IT)
- Corresponding author
- Micheli, A.
- ORCID
- Micheli, A.
- Venue
- IEEE Transactions on Neural Networks
- Published
- 2009-03
- Volume
- 20
- Issue
- 3
- Pages
- 498-511
- ISSN
- 1045-9227 (ISSN-L)
- 1941-0093
- OpenAlex
- W2139906443
- Cited by
- 639
- References
- 49
- Citations by year
- 2026: 31 · 2025: 76 · 2024: 91 · 2023: 93 · 2022: 97 · 2021: 107 · 2020: 76 · 2019: 12 · 2018: 12 · 2017: 2 · 2016: 7 · 2015: 6 · 2014: 6 · 2013: 8 · 2012: 6
- FWCI
- 5.40
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Transactions on Neural Networks (publishedVersion)
- PubMed (publishedVersion)
- CINECA IRIS Institutial research information system (University of Pisa) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Advanced Graph Neural Networks
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Graph Theory and Algorithms
- Keywords
- structured domains, constructive neural networks, contextual information, graph classification, graph regression, incremental learning, cyclic graphs, directed and undirected graphs, supervised learning
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