mlsanityData to 7 Oct 2026

Pyramidal Reservoir Graph Neural Network

arXiv 2104.04710 ↗First posted 10 Apr 2021cs.LG cs.NE stat.MLcited by 10

Not on the map. Why?

Abstract (arXiv)

We propose a deep Graph Neural Network (GNN) model that alternates two types of layers. The first type is inspired by Reservoir Computing (RC) and generates new vertex features by iterating a non-linear map until it converges to a fixed point. The second type of layer implements graph pooling operations, that gradually reduce the support graph and the vertex features, and further improve the computational efficiency of the RC-based GNN. The architecture is, therefore, pyramidal. In the last layer, the features of the remaining vertices are combined into a single vector, which represents the graph embedding. Through a mathematical derivation introduced in this paper, we show formally how graph pooling can reduce the computational complexity of the model and speed-up the convergence of the dynamical updates of the vertex features. Our proposed approach to the design of RC-based GNNs offers an advantageous and principled trade-off between accuracy and complexity, which we extensively demonstrate in experiments on a large set of graph datasets.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 21 of its 48 references that are in the map. First posted on arXiv 10 Apr 2021.

Builds on

21 of 48 references.

References · 21

  1. 2018How Powerful are Graph Neural Networks?cited by 4,355
  2. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
  3. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
  4. 2013Spectral Networks and Locally Connected Networks on Graphscited by 1,097
  5. 2019Deep Equilibrium Modelscited by 603
  6. 2019Graph U-Netscited by 489
  7. 2019Self-Attention Graph Poolingcited by 421
  8. 2016Learning Convolutional Neural Networks for Graphscited by 314
  9. 2015Diffusion-Convolutional Neural Networkscited by 268
  10. 2019A Fair Comparison of Graph Neural Networks for Graph Classificationcited by 244
  11. 2017CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filterscited by 203
  12. 2019Graph Neural Networks with convolutional ARMA filterscited by 185
9 more
  1. 2017SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernelscited by 160
  2. 2020Multiscale Deep Equilibrium Modelscited by 149
  3. 2019A Gentle Introduction to Deep Learning for Graphscited by 107
  4. 2019Fast and Deep Graph Neural Networkscited by 35
  5. 2019Hierarchical Representation Learning in Graph Neural Networks with Node Decimation Poolingcited by 30
  6. 2013A Multiscale Pyramid Transform for Graph Signalscited by 15
  7. 2019A Non-Negative Factorization approach to node pooling in Graph Convolutional Neural Networkscited by 14
  8. 2018On Filter Size in Graph Convolutional Networkscited by 3
  9. 2020Ring Reservoir Neural Networks for Graphscited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 3; 2024: 2; 2025: 3; 2026: 1.

10 papers.

  1. 2023The expressive power of pooling in Graph Neural Networkscited by 35
  2. 2023Graph-based Time Series Clustering for End-to-End Hierarchical Forecastingcited by 16
  3. 2024Attending to Topological Spaces: The Cellular Transformercited by 11
  4. 2022Total Variation Graph Neural Networkscited by 7
  5. 2024MaxCutPool: differentiable feature-aware Maxcut for pooling in graph neural networkscited by 5
  6. 2023Neuromorphic Imaging and Classification with Graph Learningcited by 3
  7. 2025BN-Pool: Bayesian Nonparametric Pooling for Graphscited by 2
  8. 2025Torch Geometric Pool: the PyTorch library for pooling in Graph Neural Networkscited by 2
  9. 2025A Spectral Interpretation of Redundancy in a Graph Reservoircited by 1
  10. 2026Reservoir-Based Graph Convolutional Networkscited by 0