4 papers
Geometric Dyson Brownian Motions and the Free Log-Normal Limit for a Non-Square Gaussian Matrix Product
Mufan Li, Jaume de Dios Pont, Mihai Nica +1
We study the squared singular value spectrum of a non-square product of independent real Gaussian matrices, equivalently the feature covariance spectrum of a deep linear neural net…
Acceleration of Gossip Algorithms through the Euler-Poisson-Darboux Equation
Raphaël Berthier, Mufan Bill Li
Gossip algorithms and their accelerated versions have been studied exclusively in discrete time on graphs. In this work, we take a different approach, and consider the scaling limi…
Sampling from the Mean-Field Stationary Distribution
Yunbum Kook, Matthew S. Zhang, Sinho Chewi +2
We study the complexity of sampling from the stationary distribution of a mean-field SDE, or equivalently, the complexity of minimizing a functional over the space of probability m…
Differential Equation Scaling Limits of Shaped and Unshaped Neural Networks
Mufan Bill Li, Mihai Nica
Recent analyses of neural networks with shaped activations (i.e. the activation function is scaled as the network size grows) have led to scaling limits described by differential e…