[{"publication_identifier":{"eissn":["2835-8279"]},"article_processing_charge":"Yes","dataavailabilitystatement":"The data that support the findings of this article are not\r\npublicly available. The data are available from the authors\r\nupon reasonable request.","month":"06","doi":"10.1103/48k2-cw3b","PlanS_conform":"1","_id":"22248","title":"Learning by Training: Emergent physical memory from cyclically tuning disordered sphere packings","intvolume":"         4","year":"2026","corr_author":"1","author":[{"full_name":"Zu, Mengjie","id":"26dd9e7c-e86a-11eb-a854-82ac731c9ae2","first_name":"Mengjie","last_name":"Zu"},{"last_name":"Goodrich","first_name":"Carl Peter","id":"EB352CD2-F68A-11E9-89C5-A432E6697425","orcid":"0000-0002-1307-5074","full_name":"Goodrich, Carl Peter"}],"date_updated":"2026-07-06T07:28:45Z","publisher":"American Physical Society","researchdata_availability":"upon request","status":"public","publication":"PRX Life","article_type":"original","citation":{"ista":"Zu M, Goodrich CP. 2026. Learning by Training: Emergent physical memory from cyclically tuning disordered sphere packings. PRX Life. 4(2), 023029.","ama":"Zu M, Goodrich CP. Learning by Training: Emergent physical memory from cyclically tuning disordered sphere packings. <i>PRX Life</i>. 2026;4(2). doi:<a href=\"https://doi.org/10.1103/48k2-cw3b\">10.1103/48k2-cw3b</a>","chicago":"Zu, Mengjie, and Carl Peter Goodrich. “Learning by Training: Emergent Physical Memory from Cyclically Tuning Disordered Sphere Packings.” <i>PRX Life</i>. American Physical Society, 2026. <a href=\"https://doi.org/10.1103/48k2-cw3b\">https://doi.org/10.1103/48k2-cw3b</a>.","short":"M. Zu, C.P. Goodrich, PRX Life 4 (2026).","ieee":"M. Zu and C. P. Goodrich, “Learning by Training: Emergent physical memory from cyclically tuning disordered sphere packings,” <i>PRX Life</i>, vol. 4, no. 2. American Physical Society, 2026.","apa":"Zu, M., &#38; Goodrich, C. P. (2026). Learning by Training: Emergent physical memory from cyclically tuning disordered sphere packings. <i>PRX Life</i>. American Physical Society. <a href=\"https://doi.org/10.1103/48k2-cw3b\">https://doi.org/10.1103/48k2-cw3b</a>","mla":"Zu, Mengjie, and Carl Peter Goodrich. “Learning by Training: Emergent Physical Memory from Cyclically Tuning Disordered Sphere Packings.” <i>PRX Life</i>, vol. 4, no. 2, 023029, American Physical Society, 2026, doi:<a href=\"https://doi.org/10.1103/48k2-cw3b\">10.1103/48k2-cw3b</a>."},"oa_version":"Published Version","file":[{"relation":"main_file","file_name":"2026_PRXLife_Zu.pdf","file_size":2758728,"creator":"dernst","checksum":"e2d13c30bf9c036951fd2ba3455cf72a","date_updated":"2026-07-06T07:24:43Z","success":1,"access_level":"open_access","date_created":"2026-07-06T07:24:43Z","file_id":"22251","content_type":"application/pdf"}],"das_tickbox":"1","supplementarymaterial":"no","ddc":["570"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"CaGo"}],"has_accepted_license":"1","date_published":"2026-06-18T00:00:00Z","file_date_updated":"2026-07-06T07:24:43Z","volume":4,"publication_status":"published","type":"journal_article","OA_type":"gold","language":[{"iso":"eng"}],"OA_place":"publisher","quality_controlled":"1","DOAJ_listed":"1","day":"18","issue":"2","scopus_import":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"article_number":"023029","date_created":"2026-07-05T22:01:37Z","fulldoi":"https://doi.org/10.1103/48k2-cw3b","acknowledgement":"We thank Nathan Keim, Aayush Desai, Nicholas Barton,\r\nand Gašper Tkacik for important and stimulating discussions. ˇ\r\nThe work was funded by the Institute of Science and Technology Austria.","oa":1,"abstract":[{"text":"Many living and artificial systems improve their fitness or performance by adapting to changing environments or diverse training data. However, it remains unclear how environmental variation shapes adaptation, what is learned, and when memory of past conditions is retained. Here we show how cyclic environmental change can produce robust memory. Using a model athermal disordered solid trained by inverse design to attain target elastic properties over a prescribed range, we find that the system evolves toward a marginally absorbing manifold (MAM), meaning that training is reversible within the training range but not beyond it, which encodes a memory of that range. We further propose a general mechanism for MAM formation and memory encoding based on discontinuities in the gradient of the trained quantity. These results provide a simple, broadly applicable physical framework for how adaptive systems learn under changing environments and retain memory of past conditions.","lang":"eng"}]}]