ORBITER: Conflict-Aware Decision-Making for Agentic Last-Mile Delivery

Last-mile delivery aims to handle dynamically arriving orders with couriers while modeling complex spatial and temporal correlations. Recent learning-based methods model spatiotemporal dependencies among orders to predict courier service sequences, but leave next-order decision making unexplained. Describing the current delivery state in language allows LLMs to reason explicitly about the spatial, temporal, and behavioral cues behind an individual decision. As direct predictors, however, LLMs remain sensitive to task presentation and often produce unreliable decisions. To address these challenges, we introduce ORBITER, an agentic Order Arbiter for next-order decision-making in last-mile delivery. ORBITER models courier service through decision points, each containing the courier's spatiotemporal state and visible orders and exposing local trade-offs for modeling and verification. Fixed proposers rank the candidates, and a structured report identifies where their rankings disagree. The LLM uses task-specific tools to gather evidence on the leading alternatives, while an independent critic checks the resulting decision against that evidence. We conduct extensive evaluations on data in four cities, where ORBITER outperforms existing state-of-the-art baselines by up to 9.2% on average showing its effectiveness.

Liquid Neural Networks as a Drop-in Continuous-Time Deformation Field for Dynamic 3D Gaussian Splatting

Deformable 3D Gaussian Splatting (D-3DGS) re-constructs dynamic scenes from monocular video by deforming a canonical set of 3D Gaussians through a positional-encoded MLP of frame time t. Although fitted to a continuous variable, the MLP couples no two values of t in its architecture and effectively predicts discrete per-frame offsets, leaving temporal smoothness to emerge only as a byproduct of optimisation. We redesign the deformation field as a stack of Closed-form Continuous-time (CfC) cells, a Liquid Neural Network (LNN), that is the closed-form solution of the Liquid Time-constant ODE while preserving every other part of the D-3DGS pipeline. Each cell exposes a sigmoidal time gate that interpolates between two candidate hidden states, baking a learned smooth response to t into the loss landscape without invoking any numerical solver. On the eight D-NeRF and seven NeRF-DS scenes the liquid field matches or exceeds the MLP baseline in aggregate, with its largest gains concentrated on the scenes with the most high-frequency articulated motion. The result is a near-zero-friction architectural design that turns the discrete MLP deformation field into an explicit continuous-time function of t.