Fast independence tests without permutations

Independence testing is bottlenecked by permutation calibration—you need to shuffle your data hundreds of times to set a threshold. This paper adapts recent martingale theory to build two new test statistics (mHSIC and mdHSIC) whose null distributions are always standard normal, eliminating permutations entirely. On synthetic data up to 500 dimensions, both match the power of permutation-calibrated tests while running 25–60× faster, with no sample splits required for the first variant.