7 papers
Input-to-State Stability Implications in Contraction Theory
Yu Kawano, Francesco Bullo
For nonlinear control systems on normed vector spaces, we characterize an incremental input-to-state stability (ISS) type property in which the overshoot constant multiplies both t…
Predictive Coding with Bayesian Priors via Proximal Gradients
Francesco Bullo
We recast predictive coding as continuous-time proximal gradient descent applied to a regularized maximum-a-posteriori (MAP) objective. We study first a single-level problem and th…
A Nonlinear Separation Principle via Contraction Theory: Applications to Neural Networks, Control, and Learning
Anand Gokhale, Anton V. Proskurnikov, Yu Kawano +1
This paper establishes a nonlinear separation principle based on contraction theory and derives sharp stability conditions for recurrent neural networks (RNNs). First, we introduce…
Contracting Neural Networks: Sharp LMI Conditions with Applications to Integral Control and Deep Learning
Anand Gokhale, Anton V. Proskurnikov, Yu Kawano +1
This paper studies contractivity of firing-rate and Hopfield recurrent neural networks. We derive sharp LMI conditions on the synaptic matrices that characterize contractivity of b…
Contractivity of Multi-Stage Runge-Kutta Dynamics
Yu Kawano, Francesco Bullo
Many control, optimization, and learning algorithms rely on discretizations of continuous-time contracting systems, where preservation of contractivity under numerical integration…
Regular Pairings for Non-quadratic Lyapunov Functions and Contraction Analysis
Anton V. Proskurnikov, Francesco Bullo
Recent studies on stability and contractivity have highlighted the importance of semi-inner products, which we refer to as pairings, associated with general norms. A pairing is a b…