Conditional Total Correlation and the Serial Depth of Adaptive Parallel Sampling

What the math gives to ML

The paper provides an exact information-theoretic cost for parallel revealing: the forward KL error incurred by sampling a set of coordinates independently equals the conditional total correlation of that set, accumulated over adaptive rounds. This turns decoding-order selection into a measurable scheduling problem rather than a heuristic confidence-ranking problem: coordinates can be revealed together when their conditional dependence is low, while strongly dependent coordinates should be serialized. The most direct neural-network transfer is a dependency-aware masked diffusion decoder that selects reveal batches by minimizing estimated conditional total correlation subject to a desired amount of parallelism.