82 citations · 212 across the 6 of their papers we have counts for
6 papers
Stochastic Modified Equations and Dynamics of Stochastic Gradient Algorithms I: Mathematical Foundations
Qianxiao Li, Cheng Tai, Weinan E
We develop the mathematical foundations of the stochastic modified equations (SME) framework for analyzing the dynamics of stochastic gradient algorithms, where the latter is appro…
A Mean-Field Optimal Control Formulation of Deep Learning
Weinan E, Jiequn Han, Qianxiao Li
Recent work linking deep neural networks and dynamical systems opened up new avenues to analyze deep learning. In particular, it is observed that new insights can be obtained by re…
Maximum Principle Based Algorithms for Deep Learning
Qianxiao Li, Long Chen, Cheng Tai +1
The continuous dynamical system approach to deep learning is explored in order to devise alternative frameworks for training algorithms. Training is recast as a control problem and…
Noisy Hegselmann-Krause Systems: Phase Transition and the 2R-Conjecture
Chu Wang, Qianxiao Li, Weinan E +1
The classic Hegselmann-Krause (HK) model for opinion dynam- ics consists of a set of agents on the real line, each one instructed to move, at every time step, to the mass center of…
Stochastic modified equations and adaptive stochastic gradient algorithms
Qianxiao Li, Cheng Tai, Weinan E
We develop the method of stochastic modified equations (SME), in which stochastic gradient algorithms are approximated in the weak sense by continuous-time stochastic differential…
Well-Posedness of the Limiting Equation of a Noisy Consensus Model in Opinion Dynamics
Bernard Chazelle, Quansen Jiu, Qianxiao Li +1
This paper establishes the global well-posedness of the nonlinear Fokker-Planck equation for a noisy version of the Hegselmann-Krause model. The equation captures the mean-field be…