Boundary-Aware Neural Point-to-Point Set Evolution for Interactive Trajectory Prediction

Abstract

Trajectory prediction in multi-agent settings requires models that can handle complex interactions under real-world sensing constraints, such as partial observations and temporal irregularities. This thesis presents a unified framework for interactive trajectory prediction that is grounded in deep mathematical theory and realized in a series of practical highly parallelized neural architectures. We establish a theoretical foundation built on universality theorems for set-equivariant functions and the unique decomposition of the spatio-temporal symmetry group, which provide a principled justification for our encoder designs. We translate this theory into a practical system through three signature characteristics: boundary awareness, addressed with a data type classification and loss function; causal-pointwise equivariance, implemented via multi-stage encoders and a JIT-compatible data processing pipeline; and continuous-time dynamics, realized with adaptive causal convolutions and Neural ODE decoders. Our final model, implemented in JAX, is a VAE that demonstrates significant parameter efficiency. Experimental results on standard benchmarks show that our models are competitive with state-of-the-art methods. Furthermore, we demonstrate that our final architecture successfully handles the more challenging task of multi-horizon prediction from partial trajectories, offering a robust and flexible solution for real-world forecasting.