{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T01:26:22Z","timestamp":1769563582693,"version":"3.49.0"},"reference-count":0,"publisher":"IOS Press","isbn-type":[{"value":"9781643686448","type":"electronic"}],"license":[{"start":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T00:00:00Z","timestamp":1769472000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,1,27]]},"abstract":"<jats:p>This paper introduces a novel mathematical framework for adaptive neural transfer functions that dynamically reconfigure input-output state spaces based on structural gradients. Unlike traditional weight-centric approaches, our Adaptive State-Space Transfer Function (ASSTF) enables neurons to evolve their topology during learning and inference. We formalize continuous gradient-driven dimensionality adaptation, establish theoretical guarantees for state-space continuity and Lyapunov stability, and present a regularized bilevel optimization scheme. This framework provides a mathematical foundation for adaptive neurons that transcend weight-centric learning.<\/jats:p>","DOI":"10.3233\/faia251675","type":"book-chapter","created":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T13:19:34Z","timestamp":1769519974000},"source":"Crossref","is-referenced-by-count":0,"title":["Mathematical Framework to Enable Adaptive Neuron Transitions"],"prefix":"10.3233","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-2569-5919","authenticated-orcid":false,"given":"Bentley Yusen","family":"Lin","sequence":"first","affiliation":[{"name":"Safeware Technologies Inc., Ltd"}]}],"member":"7437","container-title":["Frontiers in Artificial Intelligence and Applications","Fuzzy Systems and Data Mining XI"],"original-title":[],"link":[{"URL":"https:\/\/ebooks.iospress.nl\/pdf\/doi\/10.3233\/FAIA251675","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T13:19:34Z","timestamp":1769519974000},"score":1,"resource":{"primary":{"URL":"https:\/\/ebooks.iospress.nl\/doi\/10.3233\/FAIA251675"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,27]]},"ISBN":["9781643686448"],"references-count":0,"URL":"https:\/\/doi.org\/10.3233\/faia251675","relation":{},"ISSN":["0922-6389","1879-8314"],"issn-type":[{"value":"0922-6389","type":"print"},{"value":"1879-8314","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,27]]}}}