A note on shifting distributions via Poisson races
arXiv:2608.26996
2026
Sampling
1 ideas extracted · analyzed Aug 29, 2026
What the math gives to ML
The paper gives a constructive method for transforming iid samples from a proposal distribution P into an exact sample from a target distribution Q by selecting an index in the proposal stream. Its transferable asset is a Poisson race whose expected logarithmic search cost is bounded by KL divergence plus a total-variation correction, with a matching information-theoretic lower bound. This suggests adaptive-compute sampling for neural networks: use a cheap proposal model to generate candidates and a weighted race to select a candidate distributed according to an expensive target model. The method is most promising for categorical generation, posterior sampling, and teacher-guided inference when the proposal is close to the target.
Ideas from this paper
Unverified
2026
Replace repeated rejection sampling from a neural proposal P with a Poisson race that selects one proposal candidate with exactly the target distribution Q. Candidate i receives a Poisson arrival time A_i and race score A_i divided by Q(X_i)/P(X_i); the smallest score wins. When Q is close to P in KL divergence, the selected index has low expected logarithmic rank, providing an adaptive compute budget instead of a fixed number of candidates.
Useful6/10
Difficulty5/10
Novelty6/10