K-ABENA: K-Adaptive Backpropagation with Error-based N-exclusion Algorithm

The paper introduces K-ABENA, a selective backpropagation framework that excludes a fraction of low-loss samples while correcting selection bias through defensive-mixture sampling and Horvitz–Thompson inverse-probability weighting. It proves design-unbiased gradient estimation for the canonical version, gives a non-convex SGD convergence guarantee, and quantifies the bias of a self-normalized variant. In experiments, compensated K-ABENA saves 28–54% of per-epoch gradient computation on several tabular datasets. Under 0.17% class imbalance, it reaches 0.9991 test AUC versus 0.9998 for full-batch SGD, while uncompensated variants obtain only 0.53–0.62.