{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/linear-or-non-linear-that-is-the-question","title":"Linear, or Non-Linear, That is the Question!","arxiv_id":"2111.07265","date":"2021-11-14","proceeding":null,"authors":["Taeyong Kong","Taeri Kim","Jinsung Jeon","Jeongwhan Choi","Yeon-Chang Lee","Noseong Park","Sang-Wook Kim"],"abstract":"There were fierce debates on whether the non-linear embedding propagation of GCNs is appropriate to GCN-based recommender systems. It was recently found that the linear embedding propagation shows better accuracy than the non-linear embedding propagation. Since this phenomenon was discovered especially in recommender systems, it is required that we carefully analyze the linearity and non-linearity issue. In this work, therefore, we revisit the issues of i) which of the linear or non-linear propagation is better and ii) which factors of users/items decide the linearity/non-linearity of the embedding propagation. We propose a novel Hybrid Method of Linear and non-linEar collaborative filTering method (HMLET, pronounced as Hamlet). In our design, there exist both linear and non-linear propagation steps, when processing each user or item node, and our gating module chooses one of them, which results in a hybrid model of the linear and non-linear GCN-based collaborative filtering (CF). The proposed model yields the best accuracy in three public benchmark datasets. Moreover, we classify users/items into the following three classes depending on our gating modules' selections: Full-Non-Linearity (FNL), Partial-Non-Linearity (PNL), and Full-Linearity (FL). We found that there exist strong correlations between nodes' centrality and their class membership, i.e., important user/item nodes exhibit more preferences towards the non-linearity during the propagation steps. To our knowledge, we are the first who design a hybrid method and report the correlation between the graph centrality and the linearity/non-linearity of nodes. All HMLET codes and datasets are available at: https://github.com/qbxlvnf11/HMLET.","url_abs":"https://arxiv.org/abs/2111.07265v2","url_pdf":"https://arxiv.org/pdf/2111.07265v2.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":"linear-or-non-linear-that-is-the-question","repo_url":"https://github.com/jeongwhanchoi/HMLET","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"linear-or-non-linear-that-is-the-question","repo_url":"https://github.com/qbxlvnf11/hmlet","is_official":0,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"collaborative-filtering","task_name":"Collaborative Filtering"},{"task_slug":"recommendation-systems","task_name":"Recommendation Systems"}],"methods":[{"method_slug":"gcn","method_name":"GCN"},{"method_slug":"gumbel-softmax","method_name":"Gumbel Softmax"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2111.07265","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2111.07265"}},"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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