Pooling Strategies for Simplicial Convolutional Networks

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...

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Bibliographic Details
Published inICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) pp. 1 - 5
Main Authors Cinque, Domenico Mattia, Battiloro, Claudio, Di Lorenzo, Paolo
Format Conference Proceeding
LanguageEnglish
Published IEEE 04.06.2023
Subjects
Benchmark testing
Complexity theory
Computer architecture
Microprocessors
Network topology
Neural networks
pooling
simplicial neural networks
topological deep learning
Topological signal processing
Topology
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Summary: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.
ISSN:2379-190X
DOI:10.1109/ICASSP49357.2023.10096866