人机交互中多智能体互补性的树形式化框架（arXiv 论文）
Tree-Based Formalization of Multi-Agent Complementarity in Human-AI Interactions
AI 导读
一篇 arXiv 论文提出基于有根平面二叉树的数学框架，刻画多智能体人机交互中的互补性，即人机组合超过其组成个体基准的表现。论文证明四项结果：线性池化下协议树为全局权重单纯形内部提供双射坐标系；平方损失回归的最优线性池化权重；选择器协议无法相对 pointwise-min 基准实现互补性；以及端点单调损失下二元分类无法实现互补性。该框架为分析多智能体预测子过程奠定了数学基础。
正文 · 原文
Abstract:Predictive tasks constitute subprocedures within human--AI interactions (HAIs) involving professionals and AI systems. Complementarity occurs when an HAI outperforms a benchmark defined by its constituent agents. Existing formalizations, however, focus on a single human and a single AI, leaving multi-agent interactions insufficiently characterized. We introduce a tree-based mathematical framework for multi-agent complementarity. Ordered agent-role configurations decorate the leaves of rooted planar binary trees and local aggregation rules generate protocol outputs evaluated against either a best-average or a pointwise-min benchmark. We establish four results. First, under linear pooling, every protocol tree provides a bijective coordinate system for the interior of the simplex of global leaf weights. Arbitrary trees with the same ordered leaves admit output- and complementarity-preserving reparameterizations, realized locally through path-independent Tamari rotations. However, HAI constraints can violate admissibility preservation between equivalent protocols. Second, for regression under squared loss, we characterize complementarity through residual correction and derive optimal linear-pooling weights. We also characterize protocol-indifference loci under identical local parameters. Third, selector-based protocols cannot achieve complementarity relative to the pointwise-min benchmark, independently of task and loss. Fourth, in binary classification, HAIs cannot achieve complementarity under endpoint-monotone losses and the pointwise-min benchmark, with an analogous obstruction for multiclass cross-entropy. Numerical illustrations examine the main claims. We provide a mathematical foundation for analyzing multi-agent predictive subprocedures within HAIs, establishing a first step toward understanding how interaction, aggregation, and real-world constraints affect HAI performance.
| Comments: | Improved exposition and manuscript organization, including a new figure outlining the paper's structure. Added a section examining how real-world constraints on human-AI interaction protocols affect admissibility and protocol equivalence under linear pooling. 28 pages, 8 figures |
| Subjects: | Artificial Intelligence (cs.AI); Combinatorics (math.CO) |
| Cite as: | arXiv:2606.04779 [cs.AI] |
| (or arXiv:2606.04779v3 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2606.04779 arXiv-issued DOI via DataCite |
Submission history
From: Andrea Ferrario [view email]
[v1]
Wed, 3 Jun 2026 12:02:19 UTC (1,613 KB)
[v2]
Sat, 25 Jul 2026 11:58:07 UTC (1,616 KB)
[v3]
Thu, 12 Nov 2026 13:53:35 UTC (1,610 KB)
来源：arXiv cs.AI · arxiv.org