Kinetic energy in random recurrent neural networks
Kinetic energy in random recurrent neural networks
The relationship between unstable fixed points and chaotic dynamics in high-dimensional neural dynamics remains elusive. In this work, we investigate the kinetic energy distribution of random recurrent neural networks by combining dynamical mean-field theory with extensive numerical simulations. We find that the average kinetic energy shifts continuously from zero to a positive value at a critical value of coupling variance (synaptic gain), with a power-law behavior close to the critical point. The steady-state activity distribution is further calculated by the theory and compared with simulations on finite-size systems. This study provides a first step toward understanding the landscape of kinetic energy, which may reflect the structure of phase space for the non-equilibrium dynamics.
Li-Ru Zhang、Haiping Huang
计算技术、计算机技术自动化基础理论
Li-Ru Zhang,Haiping Huang.Kinetic energy in random recurrent neural networks[EB/OL].(2025-08-07)[2025-08-18].https://arxiv.org/abs/2508.04983.点此复制
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