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We propose a novel information-theoretic approach that addresses this fundamental challenge through R\u00e9nyi entropy optimization. Our method quantifies and maximizes the diversity of node representations across network layers using kernel density estimation with Gaussian kernels. By formulating a graph-structured entropy regularization term that respects the underlying topology, we encourage networks to maintain discriminative features while preserving essential structural information. This approach integrates seamlessly with existing GNN architectures, requiring minimal modifications to the training procedure. Extensive experiments on ten benchmark datasets demonstrate that our R\u00e9nyi entropy regularization consistently improves performance across multiple GNN variants, with average gains of 1.89% and particularly significant improvements on heterophilic graphs exceeding 2.5%. Our depth analysis shows that the method extends viable network depth from 2\u20133 layers to 8\u201310 layers, effectively countering the homogenization tendency of deep GNNs and establishing a principled foundation for more expressive graph neural networks.<\/jats:p>","DOI":"10.1007\/s10044-026-01701-3","type":"journal-article","created":{"date-parts":[[2026,6,13]],"date-time":"2026-06-13T08:42:25Z","timestamp":1781340145000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Preserving node representation diversity in deep graph neural networks through R\u00e9nyi entropy regularization"],"prefix":"10.1007","volume":"29","author":[{"given":"Ahmed","family":"Begga","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Francisco","family":"Escolano","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Miguel \u00c1ngel","family":"Lozano","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,13]]},"reference":[{"key":"1701_CR1","unstructured":"Defferrard M, Bresson X, Vandergheynst P (2016) Convolutional neural networks on graphs with fast localized spectral filtering. 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