{"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/quantifying-emergent-behavior-of-autonomous","title":"Quantifying Emergent Behavior of Autonomous Robots","arxiv_id":"1510.01495","date":"2015-10-06","proceeding":null,"authors":["Georg Martius","Eckehard Olbrich"],"abstract":"Quantifying behaviors of robots which were generated autonomously from\ntask-independent objective functions is an important prerequisite for objective\ncomparisons of algorithms and movements of animals. The temporal sequence of\nsuch a behavior can be considered as a time series and hence complexity\nmeasures developed for time series are natural candidates for its\nquantification. The predictive information and the excess entropy are such\ncomplexity measures. They measure the amount of information the past contains\nabout the future and thus quantify the nonrandom structure in the temporal\nsequence. However, when using these measures for systems with continuous states\none has to deal with the fact that their values will depend on the resolution\nwith which the systems states are observed. For deterministic systems both\nmeasures will diverge with increasing resolution. We therefore propose a new\ndecomposition of the excess entropy in resolution dependent and resolution\nindependent parts and discuss how they depend on the dimensionality of the\ndynamics, correlations and the noise level. For the practical estimation we\npropose to use estimates based on the correlation integral instead of the\ndirect estimation of the mutual information using the algorithm by Kraskov et\nal. (2004) which is based on next neighbor statistics because the latter allows\nless control of the scale dependencies. Using our algorithm we are able to show\nhow autonomous learning generates behavior of increasing complexity with\nincreasing learning duration.","url_abs":"http://arxiv.org/abs/1510.01495v1","url_pdf":"http://arxiv.org/pdf/1510.01495v1.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":"quantifying-emergent-behavior-of-autonomous","repo_url":"https://github.com/georgmartius/behavior-quant","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series","task_name":"Time Series Analysis"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}