Distribution-Preserving Fragmentation Augmentation

Integrate this at the input or intermediate-feature augmentation stage of a CNN, U-Net, neural cellular automaton, or spatial graph network. For a tensor X with shape C by H by W, select one channel or a learned scalar mask M. Threshold it into an active set, preserve the active values, and replace the active set by n separated components with the same total pixel count. Choose n from {2, 4, 8}, place equal-area components inside an envelope expanded by a factor gamma, and copy the original active amplitude α. Apply the transformation with probability p while keeping the original label. Pseudocode: mask = (X[c] > tau); A = mask.sum(); n = sample({2,4,8}); E = place_equal_components(area=A, envelope=gamma * bounding_box(mask), n=n); X_aug[c] = alpha * E + X[c] * (1-mask). The preserved mathematical quantities are the value distribution, active measure R_1, fragmentation count n, and envelope scale R_2. Estimate tau from feature quantiles and choose gamma and p on a validation split. First test on MNIST or CIFAR-10 with a small CNN and synthetic objects whose connectedness varies. Compare ordinary augmentation, histogram-preserving pixel shuffling, and structured fragmentation at equal compute. Measure clean accuracy, accuracy under object splitting, calibration, and performance as n increases. Success means improved accuracy on fragmented layouts without degrading compact-layout accuracy, together with lower prediction variance across spatial arrangements having the same activation histogram.