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While link prediction has been widely explored in multi-layer networks, it is typically treated as an isolated technical problem, often missing its broader implications for network structure and the mechanisms driving edge formation. In this article, we investigate the extent to which network layers exhibit shared generative regularities. By examining the alignment of latent representations across layers, we assess the similarity of their underlying mechanisms and leverage this alignment to improve predictive performance. To facilitate this, we introduce a new metric,\n                    <jats:italic toggle=\"yes\">\n                      <jats:underline>C<\/jats:underline>\n                    <\/jats:italic>\n                    ross-\n                    <jats:italic toggle=\"yes\">\n                      <jats:underline>L<\/jats:underline>\n                    <\/jats:italic>\n                    ayer\n                    <jats:italic toggle=\"yes\">\n                      <jats:underline>G<\/jats:underline>\n                    <\/jats:italic>\n                    enerative\n                    <jats:underline>\n                      <jats:italic toggle=\"yes\">C<\/jats:italic>\n                    <\/jats:underline>\n                    onsistency (\n                    <jats:sc>CLGC<\/jats:sc>\n                    ), which quantitatively captures the degree of structural and generative alignment between network layers.\n                    <jats:sc>CLGC<\/jats:sc>\n                    is grounded in the shared-latent space framework, positing that layers generated by similar mechanisms will produce compatible latent representations. To realize this approach, we present\n                    <jats:sc>SupportNet<\/jats:sc>\n                    \u2013\n                    <jats:italic toggle=\"yes\">\n                      <jats:underline>Support<\/jats:underline>\n                    <\/jats:italic>\n                    prediction and consistency analysis in multi-layer\n                    <jats:italic toggle=\"yes\">\n                      <jats:underline>Net<\/jats:underline>\n                    <\/jats:italic>\n                    works\u2013a GCN-based model augmented with adversarial training to effectively learn robust shared-latent space representations. These representations support both accurate link prediction and interpretable evaluation of cross-layer generative consistency. Experiments on real-world multi-layer networks demonstrate that\n                    <jats:sc>SupportNet<\/jats:sc>\n                    delivers strong link prediction results improving AUC by 17.47%, AP by 40.41% and AUPR by 39.59% on the Kapferer dataset, while\n                    <jats:sc>CLGC<\/jats:sc>\n                    reveals significant patterns of structural and generative alignment among layers.\n                  <\/jats:p>\n                  <jats:p\/>\n                  <jats:p\/>\n                  <jats:p\/>","DOI":"10.1145\/3798056","type":"journal-article","created":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T11:54:03Z","timestamp":1772193243000},"page":"1-24","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Generative Regularities in Multi-Layer Networks: A Shared-Latent Space Representation Approach"],"prefix":"10.1145","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-8862-8664","authenticated-orcid":false,"given":"Ruohan","family":"Yang","sequence":"first","affiliation":[{"name":"College of Informatics, Key Laboratory of Smart Farming for Agricultural Animals, Engineering Research Center of Intelligent Technology for Agriculture, Ministry of Education, Huazhong Agricultural University","place":["Wuhan, China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9365-4817","authenticated-orcid":false,"given":"Muhammad Asif","family":"Ali","sequence":"additional","affiliation":[{"name":"Division of Computer, Electrical and Mathematical Sciences and Engineering, King Abdullah University of Science and Technology","place":["Thuwal, Saudi Arabia"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-1423-9165","authenticated-orcid":false,"given":"Anyu","family":"Xue","sequence":"additional","affiliation":[{"name":"College of Informatics, Key Laboratory of Smart Farming for Agricultural Animals, Engineering Research Center of Intelligent Technology for Agriculture, Ministry of Education, Huazhong Agricultural University","place":["Wuhan, China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3162-2350","authenticated-orcid":false,"given":"Huan","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Informatics, Key Laboratory of Smart Farming for Agricultural Animals, Engineering Research Center of Intelligent Technology for Agriculture, Ministry of Education, Huazhong Agricultural University","place":["Wuhan, China"]},{"name":"Division of Computer, Electrical and Mathematical Sciences and Engineering, King Abdullah University of Science and Technology","place":["Wuhan, China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1139-8654","authenticated-orcid":false,"given":"Junyang","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Computer Science and Software Engineering, Shenzhen University","place":["Shenzhen, China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4908-0243","authenticated-orcid":false,"given":"Di","family":"Wang","sequence":"additional","affiliation":[{"name":"Division of Computer, Electrical and Mathematical Sciences and Engineering, King Abdullah University of Science and Technology","place":["Thuwal, Saudi Arabia"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2026,4,14]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"crossref","unstructured":"Amir Mahdi Abdolhosseini-Qomi Seyed Hossein Jafari Amirheckmat Taghizadeh Naser Yazdani Masoud Asadpour and Maseud Rahgozar. 2020. 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