Discrete Adjoint Schrödinger Bridge Sampler
This work addresses the problem of efficient discrete sampling for researchers in machine learning, representing an incremental extension of existing methods to new domains.
The paper tackled the challenge of learning discrete neural samplers by extending adjoint matching and adjoint Schrödinger bridge sampler to discrete spaces, achieving competitive sample quality with significant improvements in training efficiency and scalability.
Learning discrete neural samplers is challenging due to the lack of gradients and combinatorial complexity. While stochastic optimal control (SOC) and Schrödinger bridge (SB) provide principled solutions, efficient SOC solvers like adjoint matching (AM), which excel in continuous domains, remain unexplored for discrete spaces. We bridge this gap by revealing that the core mechanism of AM is $\mathit{state}\text{-}\mathit{space~agnostic}$, and introduce $\mathbf{discrete~ASBS}$, a unified framework that extends AM and adjoint Schrödinger bridge sampler (ASBS) to discrete spaces. Theoretically, we analyze the optimality conditions of the discrete SB problem and its connection to SOC, identifying a necessary cyclic group structure on the state space to enable this extension. Empirically, discrete ASBS achieves competitive sample quality with significant advantages in training efficiency and scalability.