Stateful inverted dropout for the compile path — sibling of dropout_op that explicitly threads an MPSGraph-Philox state tensor as a second input and returns (y, state_out).

In eager mode the function delegates to dropout_op for the actual masking (so the result distribution matches the standard dropout op identically) and returns a clone of state_in as the state-out tensor — Lucid's eager Generator already advances per call, so the state buffer is purely a placeholder that exists for the trace recording. Suppresses any nested tracer recording from the inner dropout_op call so the trace contains exactly one "dropout_stateful" op node (not a nested "dropout" underneath it).

In the compile path the matching MPSGraph emitter consumes the captured op node by calling randomTensorWithShape — the 2-output stateful Philox API — using state_in to seed the RNG and binding the new state to state_out. Across dispatches the state buffer is rotated by the executable (either as an in/out feed pair or promoted to an MPSGraph variable via compile_generic_fused_step_with_vars), giving genuinely per-dispatch varying masks where the stateless seed-only path produces dispatch-deterministic ones.