5 citations · 19 across the 11 of their papers we have counts for
7 papers · 1 filter
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…
Depthwise Hyperparameter Transfer in Residual Networks: Dynamics and Scaling Limit
Blake Bordelon, Lorenzo Noci, Mufan Bill Li +2
The cost of hyperparameter tuning in deep learning has been rising with model sizes, prompting practitioners to find new tuning methods using a proxy of smaller networks. One such…
The Shaped Transformer: Attention Models in the Infinite Depth-and-Width Limit
Lorenzo Noci, Chuning Li, Mufan Bill Li +4
In deep learning theory, the covariance matrix of the representations serves as a proxy to examine the network's trainability. Motivated by the success of Transformers, we study th…
The Neural Covariance SDE: Shaped Infinite Depth-and-Width Networks at Initialization
Mufan Bill Li, Mihai Nica, Daniel M. Roy
The logit outputs of a feedforward neural network at initialization are conditionally Gaussian, given a random covariance matrix defined by the penultimate layer. In this work, we…
The Future is Log-Gaussian: ResNets and Their Infinite-Depth-and-Width Limit at Initialization
Mufan Bill Li, Mihai Nica, Daniel M. Roy
Theoretical results show that neural networks can be approximated by Gaussian processes in the infinite-width limit. However, for fully connected networks, it has been previously s…
Higher Order Generalization Error for First Order Discretization of Langevin Diffusion
Mufan Bill Li, Maxime Gazeau
We propose a novel approach to analyze generalization error for discretizations of Langevin diffusion, such as the stochastic gradient Langevin dynamics (SGLD). For an toleranc…
Riemannian Langevin Algorithm for Solving Semidefinite Programs
Mufan Bill Li, Murat A. Erdogdu
We propose a Langevin diffusion-based algorithm for non-convex optimization and sampling on a product manifold of spheres. Under a logarithmic Sobolev inequality, we establish a gu…