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However, traditional Graph Neural Network models often overlook this frequency diversity, applying uniform filtering and layer fusion strategies that fail to capture cross-layer complementarity. We propose AMN-ARMA, a frequency-adaptive representation learning framework that models each layer as operating in a distinct spectral regime. It combines adaptive ARMA (AutoRegressive Moving Average) filters tailored to layer-specific frequency responses with multi-band, entropy-regularized attention to ensure balanced and interpretable integration. We further introduce a training objective that encourages frequency specialization across layers while maintaining both intra- and inter-layer consistency. Experiments on three real-world AMN datasets demonstrate that AMN-ARMA achieves up to 1.8% improvement in cross-layer link prediction and 2.6% gain in clustering quality, while maintaining robustness to structural perturbations and spectral noise. Spectral analyses reveal that AMN layers indeed operate in complementary frequency bands, and that the learned filters adapt accordingly\u2013validating the framework design motivation and theoretical underpinnings.<\/jats:p>","DOI":"10.1007\/s10618-026-01248-1","type":"journal-article","created":{"date-parts":[[2026,8,8]],"date-time":"2026-08-08T04:10:44Z","timestamp":1786162244000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Representation learning for attributed multiplex networks: a graph signal processing approach using adaptive ARMA filters"],"prefix":"10.1007","volume":"40","author":[{"given":"Zhenguo","family":"Xu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jun","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Irene","family":"Moulitsas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,8,8]]},"reference":[{"issue":"4","key":"1248_CR1","doi-asserted-by":"publisher","first-page":"1624","DOI":"10.1109\/TKDE.2023.3305809","volume":"36","author":"K Abdous","year":"2023","unstructured":"Abdous K, Mrabah N, Bouguessa M (2023) Hierarchical aggregations for high-dimensional multiplex graph embedding. 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