Macroscopic Feynman Cycles and Poisson--Kingman Universality in Bose Condensation

What the math gives to ML

The paper provides a constructive family of conditioned completely random measures whose ranked atom masses are Poisson–Dirichlet only in the constant-profile case, while a visible low-energy spectrum changes the mass profile and therefore the partition law. This is transferable as a principled heavy-tailed capacity prior for sparse mixture-of-experts routing: instead of forcing equal expert loads or using an unstructured Dirichlet target, route toward a sampled Poisson–Kingman allocation with controllable numbers of large and small experts. The nonconstant profile offers a knob for preventing both expert collapse and artificial uniformity, while conditioning on total mass directly matches the fixed token-budget constraint. The initial implementation should use the sampled partition only as a detached load-balancing target, making the method easy to compare against Switch-style auxiliary losses.