{"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/hyperplane-arrangements-of-trained-convnets","title":"Hyperplane Arrangements of Trained ConvNets Are Biased","arxiv_id":"2003.07797","date":"2020-03-17","proceeding":null,"authors":["Matteo Gamba","Stefan Carlsson","Hossein Azizpour","Mårten Björkman"],"abstract":"We investigate the geometric properties of the functions learned by trained ConvNets in the preactivation space of their convolutional layers, by performing an empirical study of hyperplane arrangements induced by a convolutional layer. We introduce statistics over the weights of a trained network to study local arrangements and relate them to the training dynamics. We observe that trained ConvNets show a significant statistical bias towards regular hyperplane configurations. Furthermore, we find that layers showing biased configurations are critical to validation performance for the architectures considered, trained on CIFAR10, CIFAR100 and ImageNet.","url_abs":"https://arxiv.org/abs/2003.07797v2","url_pdf":"https://arxiv.org/pdf/2003.07797v2.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":"hyperplane-arrangements-of-trained-convnets","repo_url":"https://github.com/magamba/hp_arrangements","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"GPL-3.0"}}],"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}