# Per-atom Message-Passing Depth Allocation

Molecular properties depend on chemical structure at different ranges, yet graph neural networks usually fix one propagation depth for every atom. PRISM turns each atom's own encoded features into a bounded scalar that positions a unimodal distribution over retained message-passing states, so the allocated depth is analytically tractable and moves monotonically with that scalar. Under matched scaffold partitions and tuning budgets, PRISM trained from scratch reaches the lowest or tied-lowest mean error on ESOL and FreeSolv, and on a pre-trained GIN it improves on last-layer readout on four of six endpoints.

Molecular properties depend on chemical structure at different ranges, yet graph neural networks usually fix one propagation depth for every atom. PRISM turns each atom's own encoded features into a bounded scalar that positions a unimodal distribution over retained message-passing states, so the allocated depth is analytically tractable and moves monotonically with that scalar. Under matched scaffold partitions and tuning budgets, PRISM trained from scratch reaches the lowest or tied-lowest mean error on ESOL and FreeSolv, and on a pre-trained GIN it improves on last-layer readout on four of six endpoints.