{"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/topological-parallax-a-geometric","title":"Topological Parallax: A Geometric Specification for Deep Perception Models","arxiv_id":null,"date":"2023-09-21","proceeding":"NeurIPS 2023 11","authors":[],"abstract":"For safety and robustness of AI systems, we introduce _topological parallax_ as a \ntheoretical and computational tool that compares a trained model to a reference dataset to determine whether they have similar multiscale geometric structure. \n\nOur proofs and examples show that this geometric similarity between dataset and model is essential \nto trustworthy interpolation and perturbation, and we conjecture that this new concept will add value to the current debate regarding the unclear relationship between \"overfitting\"' and \"generalization'' in applications of deep-learning. \n\nIn typical deep-learning applications, an explicit geometric description of the model is\nimpossible, but parallax can estimate topological features (components, cycles, voids, etc.)\nin the model by examining the effect on the Rips complex of geodesic distortions using the reference dataset.\nThus, parallax indicates whether the model shares similar multiscale geometric features with the dataset.\n\nParallax presents theoretically via topological data analysis [TDA] as a bi-filtered persistence module,\nand the key properties of this module are stable under perturbation of the reference dataset.","url_abs":"https://openreview.net/forum?id=SthlUe5xDP","url_pdf":"https://openreview.net/pdf?id=SthlUe5xDP","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":"topological-parallax-a-geometric","repo_url":"https://gitlab.com/geomdata/topological-parallax","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}