Pooling Strategies for Simplicial Convolutional Networks

TL;DR

This paper introduces novel pooling strategies for simplicial convolutional neural networks, enabling hierarchical data representation and improved performance on flow and graph classification tasks.

Contribution

It presents a general formulation for simplicial pooling layers and designs four specific strategies based on topological signal processing theory.

Findings

Proposed pooling methods outperform existing techniques on benchmark datasets.

Hierarchical architecture reduces complexity while maintaining accuracy.

Effective in flow and graph classification tasks.

Abstract

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.