# Edge-Wise Graph-Instructed Neural Networks

arXiv: https://arxiv.org/abs/2409.08023 · HTML: https://mlsanity.com/paper/2409.08023/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 21 references that are in the map.
- First posted on arXiv 12 Sep 2024.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Long Range Graph Benchmark](https://mlsanity.com/paper/2206.08164/) (2022)
- [Geometric Deep Learning on Molecular Representations](https://mlsanity.com/paper/2107.12375/) (2021)
- [Simplifying approach to Node Classification in Graph Neural Networks](https://mlsanity.com/paper/2111.06748/) (2021)
- [A graph convolutional autoencoder approach to model order reduction for parametrized PDEs](https://mlsanity.com/paper/2305.08573/) (2023)
- [GINNs: Graph-Informed Neural Networks for Multiscale Physics](https://mlsanity.com/paper/2006.14807/) (2020)
- [Analyzing Modularity Maximization in Approximation, Heuristic, and Graph Neural Network Algorithms for Community Detection](https://mlsanity.com/paper/2310.10898/) (2023)
- [Graph-Instructed Neural Networks for Sparse Grid-Based Discontinuity Detectors](https://mlsanity.com/paper/2401.13652/) (2024)

## Built on by (most cited first, 1 of 1)

- [Graph-Instructed Neural Networks for parametric problems with varying boundary conditions](https://mlsanity.com/paper/2603.08304/) (2026)

## Abstract (arXiv)

The problem of multi-task regression over graph nodes has been recently approached through Graph-Instructed Neural Network (GINN), which is a promising architecture belonging to the subset of message-passing graph neural networks. In this work, we discuss the limitations of the Graph-Instructed (GI) layer, and we formalize a novel edge-wise GI (EWGI) layer. We discuss the advantages of the EWGI layer and we provide numerical evidence that EWGINNs perform better than GINNs over some graph-structured input data, like the ones inferred from the Barabasi-Albert graph, and improve the training regularization on graphs with chaotic connectivity, like the ones inferred from the Erdos-Renyi graph.