An optimization-based equilibrium measure describes fixed points of non-equilibrium dynamics: application to edge of chaos

Communications in Theoretical Physics, Год журнала: 2024, Номер 77(3), С. 035601 - 035601

Опубликована: Сен. 29, 2024

Abstract Understanding neural dynamics is a central topic in machine learning, non-linear physics, and neuroscience. However, the are non-linear, stochastic particularly non-gradient, i.e., driving force cannot be written as gradient of potential. These features make analytic studies very challenging. The common tool path integral approach or dynamical mean-field theory. Still, drawback that one has to solve integro-differential equations, which computationally expensive no closed-form solutions general. From associated Fokker–Planck equation, steady-state solution generally unknown. Here, we treat searching for fixed points an optimization problem, construct approximate potential related speed dynamics, find ground state this equivalent running Langevin dynamics. Only zero temperature limit, can distribution original achieved. resultant stationary exactly follows canonical Boltzmann measure. Within framework, quenched disorder intrinsic networks averaged out by applying replica method, leads naturally order parameters non-equilibrium steady states. Our theory reproduces well-known result edge-of-chaos. Furthermore, characterizing continuous transition derived, explained fluctuations responses method thus opens door analytically studying fixed-point landscape deterministic high dimensional

Язык: Английский

Local-contrastive-learning machine with both generalization and adversarial robustness: A statistical physics analysis

Science China Physics Mechanics and Astronomy, Год журнала: 2024, Номер 68(1)

Опубликована: Ноя. 5, 2024

Язык: Английский