arXiv:2608.18392 2026 Regularization 1 ideas extracted · analyzed Sep 1, 2026
The paper gives an exact worst-case chance constraint for a sum of independent nonnegative random variables when only their individual means are known. The transferable asset is not a generic concentration bound: it reduces an infinite-dimensional distributional optimization to the finite minimum of explicit product expressions. A neural-network use is a distributionally robust compute or loss-budget regularizer: model per-component stochastic costs, estimate only their means, and optimize the theorem's certified probability that total cost stays below a target.
Use Samuels' exact lower bound as a differentiable certificate for the probability that a random neural-network cost remains below a hard budget, under independent nonnegative component costs and known means. This can regularize stochastic MoE loads, activation memory, dynamic depth, or per-example loss decompositions without assuming variances or bounded support.