We investigate a mean-field model of interacting synapses on a directed neural network. Our interest lies in the slow adaptive dynamics of synapses, which are driven by the fast dynamics of the neurons they connect. Cooperation is modelled from the usual Hebbian perspective, while competition is modelled by an original polarity-driven rule. The emergence of a critical manifold culminating in a tricritical point is crucially dependent on the presence of synaptic competition. This leads to a universal $1/t$ power-law relaxation of the mean synaptic strength along the critical manifold and an equally universal $1/\sqrt{t}$ relaxation at the tricritical point, to be contrasted with the exponential relaxation that is otherwise generic. In turn, this leads to the natural emergence of long- and short-term memory from different parts of parameter space in a synaptic network, which is the most novel and important result of our present investigations.
Synaptic shot-noise triggers fast and slow global oscillations in balanced neural networks
Institute of Continuous Media Mechanics, Ural Branch of RAS（连续介质力学研究所，俄罗斯科学院乌拉尔分院）；Perm State University（彼尔姆国立大学）；Stem Cell and Brain Research Institute U1208（干细胞与脑研究所U1208）；CNRS（法国国家科学研究中心）
Emergent Slow Thinking in LLMs as Inverse Tree Freezing
Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥微尺度物质科学国家实验室）；Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China（中国科学技术大学合肥微尺度物质科学国家实验室和现代物理系）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院基础物理与数学科学学院）；DP Technology（DP技术）；Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Key Laboratory of Quantum Theory and Applications of MoE, Gansu Provincial Research Center for Basic Disciplines of Quantum Physics, Lanzhou University（兰州理论物理中心、甘肃省理论物理重点实验室、教育部量子理论与应用重点实验室、甘肃省量子物理基础学科省重点实验室、兰州大学）；AI for Science Institute, Beijing（北京人工智能科学研究院）
