arXiv：cs.AI· Saad Alqithami·· 4 小时前
Soft Tournament Equilibrium：非传递性成对比较的可微集合值推理
Soft Tournament Equilibrium: Differentiable Set-Valued Inference for Non-Transitive Pairwise Comparisons
AI 导读
Soft Tournament Equilibrium（STE）是一种可微层，用于从互惠成对概率中推断 Top-Cycle（TC）和 Uncovered-Set（UC），通过归一化 log-sum-exp 可达性与覆盖计算给出平滑分数。
正文
Abstract:Soft Tournament Equilibrium (STE) is a differentiable layer for Top-Cycle (TC) and Uncovered-Set (UC) inference from reciprocal pair probabilities. Normalized log-sum-exp reachability and covering give smooth scores with approximation, perturbation, and margin-recovery bounds. We distinguish structural supervision, posterior uncertainty, and the final set decision through controlled synthetic studies and reconstruction of recorded ordinal profiles. Matched-epoch training improves F1 under a common structural readout, but a separate equal-budget soft-UC comparison does not demonstrate an advantage. A prospective equal-budget hard-UC study improves selective F1 at 24 alternatives from 0.6327/0.6292 for ordinary/relational native heads to 0.6676, while exact recovery remains only 1.16%. On 36 human profiles held out by source, a separate exploratory comparison favors Jeffreys posterior inference over learned independent-edge and mixture distributions in native expected-F1 decoding (0.8742 versus 0.8704/0.8366). Only three references are non-singleton selective cores. Completion certificates and full-depth TC diagnostics clarify additional identification, smoothing, and computational limits. The evidence supports conditional synthetic overlap gains, while preserving the soft-set null and the absence of a demonstrated learning advantage over strong count-based human-profile controls.
| Comments: | Expanded empirical evaluation with native count/posterior controls and complete supporting proofs; disclosed and excluded an invalid secondary mixture decoder diagnostic |
| Subjects: | Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Multiagent Systems (cs.MA) |
| Cite as: | arXiv:2604.04328 [cs.AI] |
| (or arXiv:2604.04328v4 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2604.04328 arXiv-issued DOI via DataCite |
Submission history
From: Saad Alqithami [view email]
[v1]
Mon, 6 Apr 2026 00:40:14 UTC (93 KB)
[v2]
Tue, 7 Apr 2026 10:00:10 UTC (93 KB)
[v3]
Tue, 5 May 2026 14:08:00 UTC (278 KB)
[v4]
Wed, 7 Oct 2026 20:02:59 UTC (230 KB)
来源：arXiv：cs.AI · arxiv.org