A Proof of the Novak--Woźniakowski Conjecture: Optimal Polynomial Tractability Exponents for the Inverse Star Discrepancy

What the math gives to ML

The paper turns uniform coverage of points in a high-dimensional cube into a finite collection of anchored-box integration errors, using an explicit transfer lemma and normalized indicator functions. This suggests a concrete regularizer for neural representations or minibatches: penalize deviations between empirical and population mass in randomly sampled lower-orthant boxes, rather than relying only on pairwise distances or covariance matching. The useful asset is the dimension-aware discrepancy interpretation, together with the expansion of coordinate indicator products into anchored boxes, which gives a computable certificate for low-order feature correlations. The approach is most plausible for latent-space coverage, contrastive batches, generative-model support coverage, or learned token embeddings, using small coordinate subsets to avoid exponential coefficient growth.