SlotODE: Slot Trajectory Separation for Collision Reduction

Object-Centric Learning (OCL) aims to decompose a scene into slot representations corresponding to individual objects, and Slot Attention is a representative framework that iteratively updates these slots. However, how slot representations evolve across updates and whether they maintain separation remain unclear. For clarity, we define slot-state collision as the case in which initially different slot representations become identical during iterative updates, so that the collided slots can no longer maintain different representations for different objects. To address this problem, we propose SlotODE, which formulates iterative slot updates as an ordinary differential equation (ODE). Instead of directly predicting the next slot representations, SlotODE learns a vector field that defines the time derivatives of the slot representations. Our theoretical analysis shows that SlotODE prevents slot-state collision over any finite update interval, and further derives an explicit lower bound on pairwise slot separation. In experiments, SlotODE significantly improves object discovery performance across OCL benchmarks. In-depth analyses demonstrate the impact of the ODE formulation and its components, and the robustness of the learned vector field across different ODE solvers and numbers of update steps.