# Pooling Strategies for Simplicial Convolutional Networks

arXiv: https://arxiv.org/abs/2210.05490 · HTML: https://mlsanity.com/paper/2210.05490/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 26 references that are in the map.
- First posted on arXiv 11 Oct 2022.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [Weisfeiler and Lehman Go Cellular: CW Networks](https://mlsanity.com/paper/2106.12575/) (2021)
- [Simplicial Neural Networks](https://mlsanity.com/paper/2010.03633/) (2020)
- [Towards Sparse Hierarchical Graph Classifiers](https://mlsanity.com/paper/1811.01287/) (2018)
- [Topological Signal Processing over Simplicial Complexes](https://mlsanity.com/paper/1907.11577/) (2019)
- [Graph Convolutional Networks with EigenPooling](https://mlsanity.com/paper/1904.13107/) (2019)
- [Random Walks on Simplicial Complexes and the normalized Hodge 1-Laplacian](https://mlsanity.com/paper/1807.05044/) (2018)
- [Hierarchical Graph Pooling with Structure Learning](https://mlsanity.com/paper/1911.05954/) (2019)
- [Understanding Pooling in Graph Neural Networks](https://mlsanity.com/paper/2110.05292/) (2021)
- [Cell Complex Neural Networks](https://mlsanity.com/paper/2010.00743/) (2020)
- [Simplicial Attention Networks](https://mlsanity.com/paper/2204.09455/) (2022)
- [Simplicial Convolutional Neural Networks](https://mlsanity.com/paper/2110.02585/) (2021)
- [Cell Attention Networks](https://mlsanity.com/paper/2209.08179/) (2022)
- [Simplicial Attention Neural Networks](https://mlsanity.com/paper/2203.07485/) (2022)
- [Finite Impulse Response Filters for Simplicial Complexes](https://mlsanity.com/paper/2103.12587/) (2021)

## Built on by (most cited first, 5 of 5)

- [Graph Neural Networks in Histopathology: Emerging Trends and Future Directions](https://mlsanity.com/paper/2406.12808/) (2024)
- [Advancing Graph Neural Networks with HL-HGAT: A Hodge-Laplacian and Attention Mechanism Approach for Heterogeneous Graph-Structured Data](https://mlsanity.com/paper/2403.06687/) (2024)
- [NervePool: A Simplicial Pooling Layer](https://mlsanity.com/paper/2305.06315/) (2023)
- [SC-MAD: Mixtures of Higher-order Networks for Data Augmentation](https://mlsanity.com/paper/2309.07453/) (2023)
- [TopoU-Net: a U-Net architecture for topological domains](https://mlsanity.com/paper/2605.10091/) (2026)

## Abstract (arXiv)

The goal of this paper is to introduce pooling strategies for simplicial convolutional neural networks. Inspired by graph pooling methods, we introduce a general formulation for a simplicial pooling layer that performs: i) local aggregation of simplicial signals; ii) principled selection of sampling sets; iii) downsampling and simplicial topology adaptation. The general layer is then customized to design four different pooling strategies (i.e., max, top-k, self-attention, and separated top-k) grounded in the theory of topological signal processing. Also, we leverage the proposed layers in a hierarchical architecture that reduce complexity while representing data at different resolutions. Numerical results on real data benchmarks (i.e., flow and graph classification) illustrate the advantage of the proposed methods with respect to the state of the art.