arXiv:2608.23859 2026 Training 1 ideas extracted · analyzed Aug 29, 2026
The paper identifies a precise condition under which an accumulated point score is not merely a heuristic but a sufficient statistic for ordinal match outcomes: complementary outcome points must sum to a constant, and outcome probabilities must follow an adjacent-categories ordinal model whose slope parameters are those points. This provides a principled way to compress repeated pairwise ordinal observations into scalar scores without discarding likelihood-relevant information. A transferable neural-network use is to replace arbitrary ordinal target encodings with constant-sum score encodings and an ordinal likelihood whose log-odds slopes are tied to those scores. The approach is most relevant to preference learning, recommender systems, ranking models, and graph-based pairwise prediction under repeated or imbalanced comparisons.
Use a constant-sum point vector to encode ordered pairwise outcomes and train a neural scorer with an adjacent-categories ordinal likelihood whose slope parameters are tied to those points. The accumulated point score is then a theoretically motivated compressed statistic for repeated comparisons, rather than an arbitrary regression target or one-hot label.