{"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/a-geometric-framework-for-neural-feature","title":"Neural Feature Learning in Function Space","arxiv_id":"2309.10140","date":"2023-09-18","proceeding":null,"authors":["Xiangxiang Xu","Lizhong Zheng"],"abstract":"We present a novel framework for learning system design with neural feature extractors. First, we introduce the feature geometry, which unifies statistical dependence and feature representations in a function space equipped with inner products. This connection defines function-space concepts on statistical dependence, such as norms, orthogonal projection, and spectral decomposition, exhibiting clear operational meanings. In particular, we associate each learning setting with a dependence component and formulate learning tasks as finding corresponding feature approximations. We propose a nesting technique, which provides systematic algorithm designs for learning the optimal features from data samples with off-the-shelf network architectures and optimizers. We further demonstrate multivariate learning applications, including conditional inference and multimodal learning, where we present the optimal features and reveal their connections to classical approaches.","url_abs":"https://arxiv.org/abs/2309.10140v3","url_pdf":"https://arxiv.org/pdf/2309.10140v3.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":"a-geometric-framework-for-neural-feature","repo_url":"https://github.com/xiangxiangxu/nfe","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"density-ratio-estimation","task_name":"Density Ratio Estimation"},{"task_slug":"learning-semantic-representations","task_name":"Learning Semantic Representations"},{"task_slug":"representation-learning","task_name":"Representation Learning"},{"task_slug":"statistical-independence-testing","task_name":"statistical independence testing"}],"methods":[{"method_slug":"1d-cnn","method_name":"1D CNN"},{"method_slug":"adam","method_name":"Adam"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2309.10140","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}