On Non-asymptotic Theory of Recurrent Neural Networks in Temporal Point Processes

Temporal point process (TPP) is an important tool for modeling and predicting irregularly timed events across various domains. Recently, the recurrent neural network (RNN)-based TPPs have shown practical advantages over traditional parametric TPP models. However, in the current literature, it remains nascent in understanding neural TPPs from theoretical viewpoints. In this paper, we establish the excess risk bounds of RNN-TPPs under many well-known TPP settings. We especially show that an RNN-TPP with no more than four layers can achieve vanishing generalization errors. Our technical contributions include the characterization of the complexity of the multi-layer RNN class, the construction of $\tanh$ neural networks for approximating dynamic event intensity functions, and the truncation technique for alleviating the issue of unbounded event sequences. Our results bridge the gap between TPP's application and neural network theory.

Terrestrial Locomotion of PogoX: From Hardware Design to Energy Shaping and Step-to-step Dynamics Based Control

We present a novel controller design on a robotic locomotor that combines an aerial vehicle with a spring-loaded leg. The main motivation is to enable the terrestrial locomotion capability on aerial vehicles so that they can carry heavy loads: heavy enough that flying is no longer possible, e.g., when the thrust-to-weight ratio (TWR) is small. The robot is designed with a pogo-stick leg and a quadrotor, and thus it is named as PogoX. We show that with a simple and lightweight spring-loaded leg, the robot is capable of hopping with TWR $<1$. The control of hopping is realized via two components: a vertical height control via control Lyapunov function-based energy shaping, and a step-to-step (S2S) dynamics based horizontal velocity control that is inspired by the hopping of the Spring-Loaded Inverted Pendulum (SLIP). The controller is successfully realized on the physical robot, showing dynamic terrestrial locomotion of PogoX which can hop at variable heights and different horizontal velocities with robustness to ground height variations and external pushes.