Diverse Construction of Sidon Sets with Generative Flow Networks

Sidon sets — subsets of [n] with all pairwise sums distinct — admit many structurally different maximum-size solutions, making the family Mn of maximum Sidon sets in [n] a clean benchmark for diverse combinatorial construction under a sharp global constraint. We cast maximum-Sidon- set construction as a sequential GFlowNet with ordered trajectories and exact feasibility mask- ing, and study three ingredients chosen to remain applicable when Mn cannot be enumerated: a number-theoretic transformer encoding modular, Fourier, and sum-conflict structure; an adherence loss over a partial catalogue of maximum sets at the target; and behavioural cloning transfer- ring from sizes n < n⋆ to an unseen n⋆. At n∈{30,50}the number-theoretic backbone con- sistently dominates MLP and vanilla-transformer baselines, isolating inductive bias as the domi- nant source of gain. At n = 80 scratch training collapses; BC-initialized fine-tuning reaches cov- erage ≈0.83 of M80, and a 30 →···→80 cur- riculum reaches 0.77 without using the n = 80 catalogue. The same recipe is designed to ex- tend to n∈{200,500}, where Mn is no longer enumerable.