{"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/manifold-contrastive-learning-with","title":"Manifold Contrastive Learning with Variational Lie Group Operators","arxiv_id":"2306.13544","date":"2023-06-23","proceeding":null,"authors":["Kion Fallah","Alec Helbling","Kyle A. Johnsen","Christopher J. Rozell"],"abstract":"Self-supervised learning of deep neural networks has become a prevalent paradigm for learning representations that transfer to a variety of downstream tasks. Similar to proposed models of the ventral stream of biological vision, it is observed that these networks lead to a separation of category manifolds in the representations of the penultimate layer. Although this observation matches the manifold hypothesis of representation learning, current self-supervised approaches are limited in their ability to explicitly model this manifold. Indeed, current approaches often only apply augmentations from a pre-specified set of \"positive pairs\" during learning. In this work, we propose a contrastive learning approach that directly models the latent manifold using Lie group operators parameterized by coefficients with a sparsity-promoting prior. A variational distribution over these coefficients provides a generative model of the manifold, with samples which provide feature augmentations applicable both during contrastive training and downstream tasks. Additionally, learned coefficient distributions provide a quantification of which transformations are most likely at each point on the manifold while preserving identity. We demonstrate benefits in self-supervised benchmarks for image datasets, as well as a downstream semi-supervised task. In the former case, we demonstrate that the proposed methods can effectively apply manifold feature augmentations and improve learning both with and without a projection head. In the latter case, we demonstrate that feature augmentations sampled from learned Lie group operators can improve classification performance when using few labels.","url_abs":"https://arxiv.org/abs/2306.13544v1","url_pdf":"https://arxiv.org/pdf/2306.13544v1.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":"manifold-contrastive-learning-with","repo_url":"https://github.com/kfallah/manifold-contrastive","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"contrastive-learning","task_name":"Contrastive Learning"},{"task_slug":"representation-learning","task_name":"Representation Learning"},{"task_slug":"self-supervised-learning","task_name":"Self-Supervised Learning"}],"methods":[{"method_slug":"contrastive-learning","method_name":"Contrastive Learning"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}