Sample-Conditional Mixtures of Entropy Estimators for Short Sequences Under a Uniform Marginal Null

Entropy estimation from short samples recurs in symmetric cryptography, where the reference distribution is uniform by design and no single estimator in the considered classical comparison set minimizes mean squared error (MSE) across the full range of ratios n/k. We introduce the adaptive sample-conditional entropy diagnostic (ASED), in which a compact network trained offline maps a frequency-of-frequencies descriptor of the sample to convex mixture weights over six classical estimators, at a cost of O(n+k). We prove an oracle inequality bounding the excess risk of such a mixture by the L1 error of its weights and fixed-alphabet consistency for every simplex-valued weighting rule, independently of the distribution used to train the weights. Under the uniform-null protocol, ASED attains an integrated MSE of 1.7×10−3 for bytes, compared with 3.8×10−2 for James–Stein shrinkage, a reduction that depends materially on the aggregation scheme: 95.4% for summed or averaged MSE across sample sizes versus 24% for the mean of per-size ratios. Both figures are reported together throughout, and neither is presented as the headline; the entire advantage is confined to the undersampled regime n