Conditional Total Correlation and the Serial Depth of Adaptive Parallel Sampling
Read the original on arXiv Computation and Language →The paper introduces a new framework for adaptive parallel sampling of discrete vectors, where a deterministic policy reveals coordinates round‑by‑round based on previously observed values and samples the remaining coordinates from their exact conditional marginals. The authors prove an exact identity linking the forward Kullback‑Leibler divergence of any policy to the expected conditional total correlation accumulated during the sampling process, establishing conditional total correlation as the precise information cost of within‑round parallelism. Using this identity, they derive zero‑error schedules for finite‑order Markov chains, characterize the serial depth of Bernoulli walks, and demonstrate separations between different reveal orders, permutation strategies, and string structures, thereby revealing how conditional dependence governs parallelizability. whyItMatters":"The results provide a principled, information‑theoretic measure of parallel sampling efficiency that can guide the design of decoding rules for masked diffusion models and other generative systems."
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