517 citations · 580 across the 9 of their papers we have counts for
10 papers
Limiting fluctuation and trajectorial stability of multilayer neural networks with mean field training
Huy Tuan Pham, Phan-Minh Nguyen
The mean field (MF) theory of multilayer neural networks centers around a particular infinite-width scaling, where the learning dynamics is closely tracked by the MF limit. A rando…
Global Convergence of Three-layer Neural Networks in the Mean Field Regime
Huy Tuan Pham, Phan-Minh Nguyen
In the mean field regime, neural networks are appropriately scaled so that as the width tends to infinity, the learning dynamics tends to a nonlinear and nontrivial dynamical limit…
Analysis of feature learning in weight-tied autoencoders via the mean field lens
Phan-Minh Nguyen
Autoencoders are among the earliest introduced nonlinear models for unsupervised learning. Although they are widely adopted beyond research, it has been a longstanding open problem…
A Note on the Global Convergence of Multilayer Neural Networks in the Mean Field Regime
Huy Tuan Pham, Phan-Minh Nguyen
In a recent work, we introduced a rigorous framework to describe the mean field limit of the gradient-based learning dynamics of multilayer neural networks, based on the idea of a…
A Rigorous Framework for the Mean Field Limit of Multilayer Neural Networks
Phan-Minh Nguyen, Huy Tuan Pham
We develop a mathematically rigorous framework for multilayer neural networks in the mean field regime. As the network's widths increase, the network's learning trajectory is shown…
Mean Field Limit of the Learning Dynamics of Multilayer Neural Networks
Phan-Minh Nguyen
Can multilayer neural networks -- typically constructed as highly complex structures with many nonlinearly activated neurons across layers -- behave in a non-trivial way that yet s…
A Mean Field View of the Landscape of Two-Layers Neural Networks
Song Mei, Andrea Montanari, Phan-Minh Nguyen
Multi-layer neural networks are among the most powerful models in machine learning, yet the fundamental reasons for this success defy mathematical understanding. Learning a neural…
State Evolution for Approximate Message Passing with Non-Separable Functions
Raphael Berthier, Andrea Montanari, Phan-Minh Nguyen
Given a high-dimensional data matrix , Approximate Message Passing (AMP) algorithms construct sequences of vectors ${\boldsymbol u}^t\in{…
On Capacity Formulation with Stationary Inputs and Application to a Bit-Patterned Media Recording Channel Model
Phan-Minh Nguyen, Marc A. Armand
In this correspondence, we illustrate among other things the use of the stationarity property of the set of capacity-achieving inputs in capacity calculations. In particular, as a…
Capacity of the Energy Harvesting Channel with a Finite Battery
Dor Shaviv, Phan-Minh Nguyen, Ayfer Ozgur
We consider an energy harvesting channel, in which the transmitter is powered by an exogenous stochastic energy harvesting process , such that , which ca…