{"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/group-invariance-stability-to-deformations","title":"Group Invariance, Stability to Deformations, and Complexity of Deep Convolutional Representations","arxiv_id":"1706.03078","date":"2017-06-09","proceeding":null,"authors":["Alberto Bietti","Julien Mairal"],"abstract":"The success of deep convolutional architectures is often attributed in part\nto their ability to learn multiscale and invariant representations of natural\nsignals. However, a precise study of these properties and how they affect\nlearning guarantees is still missing. In this paper, we consider deep\nconvolutional representations of signals; we study their invariance to\ntranslations and to more general groups of transformations, their stability to\nthe action of diffeomorphisms, and their ability to preserve signal\ninformation. This analysis is carried by introducing a multilayer kernel based\non convolutional kernel networks and by studying the geometry induced by the\nkernel mapping. We then characterize the corresponding reproducing kernel\nHilbert space (RKHS), showing that it contains a large class of convolutional\nneural networks with homogeneous activation functions. This analysis allows us\nto separate data representation from learning, and to provide a canonical\nmeasure of model complexity, the RKHS norm, which controls both stability and\ngeneralization of any learned model. In addition to models in the constructed\nRKHS, our stability analysis also applies to convolutional networks with\ngeneric activations such as rectified linear units, and we discuss its\nrelationship with recent generalization bounds based on spectral norms.","url_abs":"http://arxiv.org/abs/1706.03078v4","url_pdf":"http://arxiv.org/pdf/1706.03078v4.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":"group-invariance-stability-to-deformations","repo_url":"https://github.com/albietz/ckn_kernel","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"generalization-bounds","task_name":"Generalization Bounds"}],"methods":[],"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}