[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84863-en":3,"doc-seo-84863-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},84863,8796095461564,"Liam","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","K-ABENA K-Adaptive Backpropagation with Error-based N-exclusion Algorithm","K-ABENA introduces a selective gradient computation framework that lowers per-iteration training cost by excluding a fraction of low-loss (“minor”) observations from the backward pass. The canonical v3 design uses a defensive-mixture sampling strategy over the minor set combined with Horvitz–Thompson inverse-probability reweighting, providing a design-unbiased gradient estimator and a self-normalized practical variant with bias shrinking as O(1/m). It proves O(1/√T) non-convex SGD convergence with an explicit residual-bias term, and shows uncompensated loss-based selection prevents convergence under imbalance or noise.","arXiv :2607 .05903v 1 [ cs .LG] 7 Jul 2026  \nK-ABENA: K-Adaptive Backpropagation with Error-based  \nN-exclusion Algorithm  \nCompensated Loss-Based Sample Exclusion with Unbiased Gradient Estimation  \nJean-Fran¸cois Bonbhel  \nNeuroSoft IA, Qu´ebec City, Canada | YekoElite University, Brazzaville, Republic of Congo UN AI Governance Expert Network (UN PNAI)—Member since 2021  \n[bonbhel@yekoelite.com](bonbhel@yekoelite.com)  \nJuly 2026  \nAbstract  \nWe present K-ABENA (K-Adaptive Backpropagation with Error-based N-exclusion Algorithm), a selective gradient computation framework that reduces per-iteration training cost by excluding a fraction of low-loss (“minor”) observations from the backward pass. Its canonical form (v3) combines a defensive-mixture sampling design over the minor set with Horvitz–Thompson inverse-probability reweighting, yielding a design-unbiased Horvitz–Thompson gradient estimator (Lemma 2) and whose self-normalized practical variant carries a bias of order O(1/m) with an explicit constant (Lemma 3) . We prove an O(1/ √T ) non-convex convergence guarantee for SGD under the estimator, with an additive term that quantifies the residual bias (Theorem 1) . We further prove that uncompensated loss-based selection—a family that includes OHEM, SBP, and the two earlier K-ABENA variants—admits no stationary point at any minimizer where its selection bias is bounded away from zero (Proposition 2), and we quantify this failure empirically: at 0.17% class imbalance, uncompensated variants reach test AUC 0.53–0.62 versus 0.9998 for full-batch SGD, while the compensated estimator attains 0 .9991 at identical 28 .4% compute savings. On real datasets (Breast Cancer, Digits, Wine, Diabetes) the compensated estimator is statistically indistinguishable from full-batch SGD (paired permutation tests, p ≥ 0.5; Section 7) while saving 28–54% of per-epoch gradient computation. A biased “regularized mode”(the earlier half-domain variant) is retained as an option with a proven exact bias decomposition (Lemma 5) and quantified contraindications: it collapses to 0.386 accuracy under 40% label noise (baseline: 0.832) and to 0.53 AUC under extreme imbalance. Every advantage and every limitation reported in this paper is either proved or measured; all experiments are CPU-scale (NumPy/scikit-learn) and their scope is stated explicitly.  \n1 Introduction  \nIn large-scale empirical risk minimization, a substantial fraction of per-iteration computation is spent on observations the model has already learned: their per-sample losses are small, their gradients are small, and their marginal contribution to the descent direction is limited. Selectivebackpropagation methods exploit this observation by skipping the backward pass for low-loss samples [6, 12], but they share a structural defect: the retained subset is correlated with the loss, so the resulting gradient is a biased estimator of the full-batch gradient. In benign regimes the bias is small relative to the signal and these methods work well; we show in Section 5 that in adverse regimes — extreme class imbalance, heavy label noise—the bias does not merely degrade performance but structurally prevents convergence to the minimizer, and we prove this as Proposition 2.  \nThis paper develops K-ABENA, whose canonical estimator (referred to as v3) resolves the defect using a century-old idea from survey sampling [5]: any sampling design with known, strictly positive inclusion probabilities admits an unbiased estimator of a population total via inverse-probability weighting. K-ABENA v3 samples retained minors from the entire minor set under a defensive mixture design [10] and reweights them accordingly. The result occupies a design point that, to our knowledge, none of the established selective or reweighting methods occupies: per-iteration compute reduction with an (exactly or near-) unbiased gradient. Hardselection methods (OHEM [12], SBP [6]) save compute but are biased; soft-reweighting methods (F","cbCaivV91x5LRXkV","https://ap.wps.com/l/cbCaivV91x5LRXkV","pdf",348888,1,13,"English","en",105,"# Abstract\n# 1 Introduction\n## Contributions","[{\"question\":\"What problem does K-ABENA address in selective backpropagation?\",\"answer\":\"Selective backpropagation skips the backward pass for low-loss samples to save compute, but the retained subset correlates with loss, creating a biased gradient. K-ABENA targets this bias while still reducing backward computation.\"},{\"question\":\"How does the canonical K-ABENA (v3) reduce gradient bias?\",\"answer\":\"It samples retained “minor” observations using a defensive-mixture design and applies Horvitz–Thompson inverse-probability reweighting. This yields a design-unbiased estimator, and a self-normalized variant with bias that decreases on the order of O(1/m).\"},{\"question\":\"What does the paper show about uncompensated loss-based selection?\",\"answer\":\"Uncompensated selection methods cannot have a stationary point at a minimizer when the selection bias remains bounded away from zero. Experiments indicate large performance degradation under class imbalance, while the compensated estimator restores near full-batch performance.\"}]",1784198893,33,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"k-abena-k-adaptive-backpropagation-with-error-based-n-exclusion-algorithm","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/k-abena-k-adaptive-backpropagation-with-error-based-n-exclusion-algorithm/84863/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does K-ABENA address in selective backpropagation?","Question",{"text":75,"@type":76},"Selective backpropagation skips the backward pass for low-loss samples to save compute, but the retained subset correlates with loss, creating a biased gradient. K-ABENA targets this bias while still reducing backward computation.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the canonical K-ABENA (v3) reduce gradient bias?",{"text":80,"@type":76},"It samples retained “minor” observations using a defensive-mixture design and applies Horvitz–Thompson inverse-probability reweighting. This yields a design-unbiased estimator, and a self-normalized variant with bias that decreases on the order of O(1/m).",{"name":82,"@type":73,"acceptedAnswer":83},"What does the paper show about uncompensated loss-based selection?",{"text":84,"@type":76},"Uncompensated selection methods cannot have a stationary point at a minimizer when the selection bias remains bounded away from zero. Experiments indicate large performance degradation under class imbalance, while the compensated estimator restores near full-batch performance.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":45,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":45,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":45,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":45,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":45,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]