{"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/neural-eigenfunctions-are-structured","title":"Neural Eigenfunctions Are Structured Representation Learners","arxiv_id":"2210.12637","date":"2022-10-23","proceeding":null,"authors":["Zhijie Deng","Jiaxin Shi","Hao Zhang","Peng Cui","Cewu Lu","Jun Zhu"],"abstract":"This paper introduces a structured, adaptive-length deep representation called Neural Eigenmap. Unlike prior spectral methods such as Laplacian Eigenmap that operate in a nonparametric manner, Neural Eigenmap leverages NeuralEF to parametrically model eigenfunctions using a neural network. We show that, when the eigenfunction is derived from positive relations in a data augmentation setup, applying NeuralEF results in an objective function that resembles those of popular self-supervised learning methods, with an additional symmetry-breaking property that leads to \\emph{structured} representations where features are ordered by importance. We demonstrate using such representations as adaptive-length codes in image retrieval systems. By truncation according to feature importance, our method requires up to $16\\times$ shorter representation length than leading self-supervised learning ones to achieve similar retrieval performance. We further apply our method to graph data and report strong results on a node representation learning benchmark with more than one million nodes.","url_abs":"https://arxiv.org/abs/2210.12637v3","url_pdf":"https://arxiv.org/pdf/2210.12637v3.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":"neural-eigenfunctions-are-structured","repo_url":"https://github.com/thudzj/NEigenmaps","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"contrastive-learning","task_name":"Contrastive Learning"},{"task_slug":"data-augmentation","task_name":"Data Augmentation"},{"task_slug":"feature-importance","task_name":"Feature Importance"},{"task_slug":"image-retrieval","task_name":"Image Retrieval"},{"task_slug":"linear-probe-classification","task_name":"Linear-Probe Classification"},{"task_slug":"representation-learning","task_name":"Representation Learning"},{"task_slug":"retrieval","task_name":"Retrieval"},{"task_slug":"self-supervised-learning","task_name":"Self-Supervised Learning"},{"task_slug":"transfer-learning","task_name":"Transfer Learning"}],"methods":[{"method_slug":"contrastive-learning","method_name":"Contrastive Learning"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2210.12637","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}