… the mean-field limit of a model of biological neuron networks … map outside of a generalized
mean-field scaling. We propose a … addresses the challenges of sparse interacting graphs/…

… are insufficient to describe many real-world networks such as power law graphs. Our paper
… solutions for sparse network problems. This especially includes power law networks which …

… on sparse directed networks with a random structure. By generalizing dynamical mean-field
theory to sparse … Our general solution applies to key models in the study of neural networks, …

… The emphasis given in this context was on sparse controls, meaning that we consider …
We design a sparse control u to drive the whole population of m+N individuals to a given …

… networks are sparse, meaning that d ≪ 1. The transition to collective behavior in such sparse
networks … in both dense and sparse complex networks, considering systems that evolve …

… 2.3), whereas we demonstrate that mean-field neural network can improve the rate to O(…
-sparse parity problem beyond the kernel regime, and showed that 2-layer ReLU neural network …

… In this case, we introduce the mean field E ž "ei and the corresponding standard deviation E.
The … For small K, the mean field is constant in the thermodynamic limit, revealing a so-called …

… For this reason, we model the control action by means of a vector field g[µ], … Admissible
controls satisfy the following continuous sparse space constraint: we assume to act only on a …

… Mean field game (MFG) theory has enjoyed rapid development and widespread application
… form of a graph or network. This is the purview of the broad field of network games, and we …

… By means of an exact mean field theory for populations of heterogeneous, … sparse
synchronization are governed by exactly the same mean field equations as deterministic networks …