7 papers
Demystifying Lipschitz verification: positive matrices, negative results
Simon Kuang, Yuezhu Xu, S. Sivaranjani +1
The global Lipschitz constant of a neural network is related to robustness and generalization, yet unlike in many classical models, it is not plainly legible from the parameters. T…
Exact Gaussian Moment Matching for Residual Networks: a Second-Order Method
Simon Kuang, Xinfan Lin
We study the problem of propagating the mean and covariance of a general multivariate Gaussian distribution through a deep (residual) neural network using layer-by-layer moment mat…
Instrumental variables system identification with consistency
Simon Kuang, Xinfan Lin
Instrumental variables (eliminate the bias that afflicts least-squares identification of dynamical systems through noisy data, yet traditionally relies on external instruments that…
Assumed Density Filtering and Smoothing with Neural Network Surrogate Models
Simon Kuang, Xinfan Lin
The Kalman filter and Rauch-Tung-Striebel (RTS) smoother are optimal for state estimation in linear dynamic systems. With nonlinear systems, the challenge consists in how to propag…
Incremental stability in and : classification and synthesis
Simon Kuang, Xinfan Lin
All Lipschitz dynamics with the weak infinitesimal contraction (WIC) property can be expressed as a Lipschitz nonlinear system in proportional negative feedback -- this statement,…
Debiasing Continuous-time Nonlinear Autoregressions
Simon Kuang, Xinfan Lin
We study how to identify a class of continuous-time nonlinear systems defined by an ordinary differential equation affine in the unknown parameter. We define a notion of asymptotic…