Approximation properties of neural ODEs
We study the approximation properties of neural ordinary differential equations (neural ODEs) in the space of continuous functions. Since a neural ODE requires input and output dimensions to be the same, while input and output dimensions of a continuous function are generally different, we need to embed an input into …
Improving the robustness of neural ODEs with minimal weight perturbation
We propose a method to enhance the stability of a neural ordinary differential equation (neural ODE) by reducing the maximum error growth subsequent to a perturbation of the initial value. Since the stability depends on the logarithmic norm of the Jacobian matrix associated with the neural ODE, we control the …
Contractivity of neural ODEs: an eigenvalue optimization problem
Mathematics of Computation, vol. 95, pp. 293–319, 2026
We propose a novel methodology to solve a key eigenvalue optimization problem which arises in the contractivity analysis of neural ODEs. When looking at contractivity properties of a one layer weight-tied neural ODE $\dot{u}(t)=σ(Au(t)+b)$ (with $u,b \in {\mathbb R}^n$, $A$ is a given $n \times n$ matrix, $σ: {\mathbb …