Abstract: Ordinary differential equation (ODE)-based neural networks, such as the now well-known Neural ODE framework, have recently drawn increasing attention. These approaches treat a system of ODEs as a “continuous-depth” component within a neural network architecture. In this talk, I will explore the expressive power of ODE-based neural networks in a broad setting that includes manifold domains, shedding light on how continuous-time dynamics enrich their representational abilities. In addition, I will discuss learnability aspects from a statistical learning theory perspective, addressing questions of generalization and capacity. Time permitting, I will also consider the computational demands associated with training and evaluating these ODE-based models, highlighting both their potential advantages and practical challenges.