{"id":13426957,"url":"https://github.com/Ranlot/single-parameter-fit","last_synced_at":"2025-03-15T22:30:58.551Z","repository":{"id":37591887,"uuid":"183765906","full_name":"Ranlot/single-parameter-fit","owner":"Ranlot","description":"Real numbers, data science and chaos: How to fit any dataset with a single parameter","archived":false,"fork":false,"pushed_at":"2022-11-22T08:49:16.000Z","size":6635,"stargazers_count":645,"open_issues_count":11,"forks_count":58,"subscribers_count":16,"default_branch":"master","last_synced_at":"2024-10-28T05:13:13.299Z","etag":null,"topics":["chaos-theory","goodness-of-fit","machine-learning"],"latest_commit_sha":null,"homepage":"","language":"Jupyter Notebook","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/Ranlot.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null}},"created_at":"2019-04-27T11:46:51.000Z","updated_at":"2024-09-07T13:35:32.000Z","dependencies_parsed_at":"2023-01-20T21:19:07.238Z","dependency_job_id":null,"html_url":"https://github.com/Ranlot/single-parameter-fit","commit_stats":null,"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Ranlot%2Fsingle-parameter-fit","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Ranlot%2Fsingle-parameter-fit/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Ranlot%2Fsingle-parameter-fit/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Ranlot%2Fsingle-parameter-fit/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/Ranlot","download_url":"https://codeload.github.com/Ranlot/single-parameter-fit/tar.gz/refs/heads/master","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":243801600,"owners_count":20350105,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["chaos-theory","goodness-of-fit","machine-learning"],"created_at":"2024-07-31T00:01:49.382Z","updated_at":"2025-03-15T22:30:53.528Z","avatar_url":"https://github.com/Ranlot.png","language":"Jupyter Notebook","funding_links":[],"categories":["Jupyter Notebook"],"sub_categories":[],"readme":"### Real numbers, data science and chaos: How to fit any dataset with a single parameter\n##### *All details and more examples can be found in the accompanying [arXiv:1904.12320](https://arxiv.org/abs/1904.12320) paper (also hosted [here](1904.12320.pdf)).*\n\n[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/Ranlot/single-parameter-fit/master)\n\nWe show how any dataset of any modality (time-series, images, sound...) can be approximated by a well-behaved \n(continuous, differentiable...) scalar function with a single real-valued parameter:\n\n\u003cp align=\"center\"\u003e\n\u003cimg src=\"resources/decodingFunction.png\" width=\"200\"/\u003e\n\u003c/p\u003e\n\nBuilding upon elementary concepts from chaos theory, we adopt a pedagogical approach demonstrating how to adjust\nthis parameter in order to achieve arbitrary precision fit to all samples of the data.\nTargeting an audience of data scientists with a taste for the curious and unusual, the results presented here\nexpand on previous similar observations regarding expressiveness power and generalization of machine learning models.\n\n\u003cp align=\"center\"\u003e\n\u003cimg src=\"resources/generatedAnimals/elephant.png\" width=\"200\"/\u003e\n\u003cimg src=\"resources/generatedAnimals/bird.png\" width=\"200\"/\u003e\n\u003cimg src=\"resources/generatedAnimals/turtle.png\" width=\"200\"/\u003e\n\u003cimg src=\"resources/generatedAnimals/fish.png\" width=\"200\"/\u003e\n\u003c/p\u003e\n\nAs a real number, the parameter \u0026alpha; is non-terminating and its capacity to encode an infinite amount of information is used to translate any arbitrary dataset into\na single numerical value.\n\n\u003cp align=\"center\"\u003e\n\u003cimg src=\"resources/alphaEncoding.png\" width=\"230\"/\u003e\n\u003c/p\u003e\n\nAs such, there is no reason to expect this model to provide any kind of generalization to data outside of its training samples as demonstrated by the time series below:\n\n\u003cp align=\"center\"\u003e\n\u003cimg src=\"resources/timeSeries/generalization.png\" width=\"430\"/\u003e\n\u003c/p\u003e\n\n\u003cp align=\"center\"\u003e\n\u003cimg src=\"resources/timeSeries/alphaValue.png\" width=\"700\"/\u003e\n\u003c/p\u003e\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2FRanlot%2Fsingle-parameter-fit","html_url":"https://awesome.ecosyste.ms/projects/github.com%2FRanlot%2Fsingle-parameter-fit","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2FRanlot%2Fsingle-parameter-fit/lists"}