{"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/extrapolation-and-learning-equations","title":"Extrapolation and learning equations","arxiv_id":"1610.02995","date":"2016-10-10","proceeding":null,"authors":["Georg Martius","Christoph H. Lampert"],"abstract":"In classical machine learning, regression is treated as a black box process\nof identifying a suitable function from a hypothesis set without attempting to\ngain insight into the mechanism connecting inputs and outputs. In the natural\nsciences, however, finding an interpretable function for a phenomenon is the\nprime goal as it allows to understand and generalize results. This paper\nproposes a novel type of function learning network, called equation learner\n(EQL), that can learn analytical expressions and is able to extrapolate to\nunseen domains. It is implemented as an end-to-end differentiable feed-forward\nnetwork and allows for efficient gradient based training. Due to sparsity\nregularization concise interpretable expressions can be obtained. Often the\ntrue underlying source expression is identified.","url_abs":"http://arxiv.org/abs/1610.02995v1","url_pdf":"http://arxiv.org/pdf/1610.02995v1.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":"extrapolation-and-learning-equations","repo_url":"https://github.com/KristofPusztai/EQL","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1610.02995","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1610.02995"}},"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/KristofPusztai/EQL","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":3},"by_repo_kind":{"listed":{"samples":3,"ran":0,"repositories":1}},"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":0,"samples":[{"code_sha256_prefix":"6274de91a7106166","entry":"cos","repo":"KristofPusztai/EQL","repo_kind":"listed","path":"EQL/layer.py","file_url":"https://github.com/KristofPusztai/EQL/blob/HEAD/EQL/layer.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"6274de91a7106166"}},{"code_sha256_prefix":"6527abf32fde9819","entry":"identity","repo":"KristofPusztai/EQL","repo_kind":"listed","path":"EQL/layer.py","file_url":"https://github.com/KristofPusztai/EQL/blob/HEAD/EQL/layer.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"6527abf32fde9819"}},{"code_sha256_prefix":"208d7252063b9790","entry":"sin","repo":"KristofPusztai/EQL","repo_kind":"listed","path":"EQL/layer.py","file_url":"https://github.com/KristofPusztai/EQL/blob/HEAD/EQL/layer.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"208d7252063b9790"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}