# Pinning Decomposition

For categorical distributions with local dependence modeled by low-order Markov random fields, the work introduces a pinning decomposition of the discrete score, builds a weight-sharing neural score learner combined with tau-leaping into an end-to-end sampling procedure, derives optimal sampling guarantees from finite data with explicit dependence on vocabulary size, MRF interaction order, and sample size, and reports numerical experiments on Potts, Ising, and tree-structured models where weight-sharing score networks outperform fully connected ones for sampling long sequences.

For categorical distributions with local dependence modeled by low-order Markov random fields, the work introduces a pinning decomposition of the discrete score, builds a weight-sharing neural score learner combined with tau-leaping into an end-to-end sampling procedure, derives optimal sampling guarantees from finite data with explicit dependence on vocabulary size, MRF interaction order, and sample size, and reports numerical experiments on Potts, Ising, and tree-structured models where weight-sharing score networks outperform fully connected ones for sampling long sequences.