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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.","url_abs":"https://arxiv.org/abs/2104.04710v1","url_pdf":"https://arxiv.org/pdf/2104.04710v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"pyramidal-reservoir-graph-neural-network","repo_url":"https://github.com/FilippoMB/Benchmark_dataset_for_graph_classification","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"pyramidal-reservoir-graph-neural-network","repo_url":"https://github.com/FilippoMB/Pyramidal-Reservoir-Graph-Nerual-Networks","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"computational-efficiency","task_name":"Computational Efficiency"},{"task_slug":"graph-embedding","task_name":"Graph Embedding"},{"task_slug":"graph-neural-network","task_name":"Graph Neural Network"}],"methods":[{"method_slug":"graph-neural-network","method_name":"Graph Neural Network"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2104.04710","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2104.04710"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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