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.

Pooling strategies for simplicial convolutional networks / Cinque, Domenico Mattia; Battiloro, Claudio; Di Lorenzo, Paolo. - (2023), pp. 1-5. (Intervento presentato al convegno 48th IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2023 tenutosi a Rhodes; Greece) [10.1109/ICASSP49357.2023.10096866].

Pooling strategies for simplicial convolutional networks

Cinque, Domenico Mattia;Battiloro, Claudio;Di Lorenzo, Paolo
2023

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.
2023
48th IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2023
topological signal processing; topological deep learning; simplicial neural networks; pooling
04 Pubblicazione in atti di convegno::04b Atto di convegno in volume
Pooling strategies for simplicial convolutional networks / Cinque, Domenico Mattia; Battiloro, Claudio; Di Lorenzo, Paolo. - (2023), pp. 1-5. (Intervento presentato al convegno 48th IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2023 tenutosi a Rhodes; Greece) [10.1109/ICASSP49357.2023.10096866].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1687995
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