20.500.12556/RUL-182908 Iskanje morfizmov z gradientnim spustom magistrsko delo Finding morphisms with gradient descent V delu predstavimo metodo iskanja nerazcepnih upodobitev končnih grup z gradientnim spustom. Preslikave med končnimi grupami in matrikami predstavimo z vektorji v evklidskem prostoru in definiramo nenegativno funkcijo izgube, ki doseže nič natanko v nerazcepnih unitarnih upodobitvah. Predstavimo povezavo med gradientnim spustom in reševanjem diferencialnih enačb. Vsako nerazcepno upodobitev izrazimo kot limito gradientnega toka gladke funkcije z ugodnimi začetnimi parametri in preučujemo numerične rezultate za ciklične in diedrske grupe. Metodo razširimo na iskanje delovanj in izomorfizmov grafov. Definiramo gladko družino porazdelitev nad preslikavami končnih množic in maksimiziramo verjetnost, da je slučajna preslikava morfizem. Definiramo gladko družino porazdelitev nad tabelo inverzij, ki ponuja alternativo Sinkhornovemu algoritmu. A method for finding irreducible representations of finite groups using gradient descent is presented. Mappings between finite groups and matrices are represented as vectors in Euclidean space and a non-negative loss function is defined, which is zero exactly at irreducible unitary representations. The connection between gradient descent and solving differential equations is presented. Each irreducible representation is expressed as a limit of the gradient flow of a smooth function with suitable initial parameters. Numerical results for cyclic and dihedral groups are studied. The method is extended to finding actions and graph isomorphisms via a smooth family of distributions over mappings of finite sets. A smooth family of distributions over the inversion table is defined, offering an alternative to the Sinkhorn algorithm. gradientni spust upodobitve izomorfizmi grafov delovanja ta bela inverzij gradient descent representations graph isomorphisms actions inver sion table true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2026-05-28 08:15:09 2026-05-28 08:15:17 2026-05-29 08:01:42 0000-00-00 00:00:00 2026 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.6 160331 279477507 21638.pdf 21638.pdf 1 4B4AA7904DC85689CBDC8CC8DA284CCE 687fe4ae468a8ae7d1ccd47faa64e72e4ac66f17898a71f0b89aa82d04e897a4 42b0ed6d-5a5c-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=234559 Fakulteta za matematiko in fiziko 0 0 0