{"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/regular-polytope-networks","title":"Regular Polytope Networks","arxiv_id":"2103.15632","date":"2021-03-29","proceeding":"IEEE Transactions on Neural Networks and Learning Systems 2021 3","authors":["Federico Pernici","Matteo Bruni","Claudio Baecchi","Alberto del Bimbo"],"abstract":"Neural networks are widely used as a model for classification in a large variety of tasks. Typically, a learnable transformation (i.e. the classifier) is placed at the end of such models returning a value for each class used for classification. This transformation plays an important role in determining how the generated features change during the learning process. In this work, we argue that this transformation not only can be fixed (i.e. set as non-trainable) with no loss of accuracy and with a reduction in memory usage, but it can also be used to learn stationary and maximally separated embeddings. We show that the stationarity of the embedding and its maximal separated representation can be theoretically justified by setting the weights of the fixed classifier to values taken from the coordinate vertices of the three regular polytopes available in $\\mathbb{R}^d$, namely: the $d$-Simplex, the $d$-Cube and the $d$-Orthoplex. These regular polytopes have the maximal amount of symmetry that can be exploited to generate stationary features angularly centered around their corresponding fixed weights. Our approach improves and broadens the concept of a fixed classifier, recently proposed in \\cite{hoffer2018fix}, to a larger class of fixed classifier models. Experimental results confirm the theoretical analysis, the generalization capability, the faster convergence and the improved performance of the proposed method. Code will be publicly available.","url_abs":"https://arxiv.org/abs/2103.15632v1","url_pdf":"https://arxiv.org/pdf/2103.15632v1.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":"regular-polytope-networks","repo_url":"https://github.com/matteo-bruni/regular-polytope-networks","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"regular-polytope-networks","repo_url":"https://github.com/aimagelab/mammoth","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2103.15632","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2103.15632"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/aimagelab/mammoth","reach":{"status":"ok","spdx":"MIT"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/matteo-bruni/regular-polytope-networks","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":1},"by_repo_kind":{},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":1,"samples":[{"code_sha256_prefix":"e2a98c6a53ded11f","entry":"validate","repo":null,"repo_kind":null,"path":null,"file_url":null,"link_basis":"identical_code_first_harvested_elsewhere","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":null,"inline_ok":false,"mcp_get_code":{"code_sha256":"e2a98c6a53ded11f"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}