Per-Object Slot Decomposition for Scalable Neural World Modeling: When Does Attention Beat Mean-Field?

We investigate the inductive biases required for neural networks to learn multi-object physical dynamics and generalize to long-horizon prediction. We propose SlotCTM, an object-centric architecture combining per-object computational slots with CTM recurrence. Our central finding is a density-dependent crossover between GNN attention and mean-field aggregation, consistent with classical mean-field theory. Under partial observation at N=12, GNN attention exhibits initialization-sensitive instability: with one seed it diverges catastrophically (MSE=334), yet with another it converges to MSE=0.029, beating mean-field (0.033). Shannon entropy analysis confirms attention oversquashing at high density. DuoNeural AI Research Lab, April 2026.