Related Experiment Video
Updated: Sep 14, 2026

Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels
Published on: September 8, 2016
Convergence Analysis of Controlled Particle Systems Arising in Deep Learning: From Finite to Infinite Sample Size
Huafu Liao1, Alpár R Mészáros2, Chenchen Mou3
1School of Mathematical Sciences, Dalian University of Technology, Dalian, China.
Abstract:
This paper deals with a class of neural SDEs and studies the limiting behavior of the associated sampled optimal control problems as the sample size grows to infinity. The neural SDEs with N samples can be linked to the N-particle systems with centralized control. We analyze the Hamilton-Jacobi-Bellman equation corresponding to the N-particle system and establish regularity results which are uniform in N. The uniform regularity estimates are obtained by the stochastic maximum principle and the analysis of a backward stochastic Riccati equation. Using these uniform regularity results, we show the convergence of the minima of the objective functionals and optimal parameters of the neural SDEs as the sample size N tends to infinity. The limiting objects can be identified with suitable functions defined on the Wasserstein space of Borel probability measures. Furthermore, quantitative convergence rates are also obtained.
Related Concept Videos
Convergence of Sequences
Introduction to Infinite Series
Partial Sums and Series Convergence
Comparison Tests
Limits with Oscillating Discontinuities
Convolution: Math, Graphics, and Discrete Signals
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
