Tree-Based Formalization of Multi-Agent Complementarity in Human-AI Interactions

arXiv:2606.04779v2 Announce Type: replace Abstract: Complementarity is the case in which a human--AI interaction (HAI) outperforms the best prediction benchmark available among its members. Although this idea is central in HAI research, formal work on complementarity remains limited. Existing frameworks do not model how agents' predictions compose into workflow-sensitive multi-agent protocols. We close this gap by introducing a tree-based formalization of complementarity in multi-agent HAI. An HAI protocol is represented by an ordered agent-role configuration together with a rooted planar binary tree whose leaves are decorated by prediction vectors. A local binary composition rule is evaluated recursively along the tree, yielding a tree-relative complementarity functional relative to a pointwise-min benchmark. We prove four results. First, selector-based HAIs, including reliance, cannot achieve complementarity regardless of task, loss, or prediction quality. Second, in regression under squared loss, complementarity is equivalent to Euclidean distance minimization from the ground-truth vector; for $N=2$, the optimal linear-pooling weight has a closed form and a residual-correction interpretation. Third, under linear local composition, every protocol tree defines a barycentric coordinate chart on the simplex of leaf weights; Tamari-cover reparameterizations of protocol trees preserve complementarity, and for all $N$, any two Tamari paths with the same initial and terminal trees preserve the protocol output and complementarity. Fourth, in binary classification, no internal local composition can achieve complementarity under endpoint-monotone losses, including standard Bregman and many finite Bernoulli $f$-divergence losses; an analogous obstruction holds for multiclass aggregation under cross-entropy. In summary, our framework shows that complementarity is attainable in multi-agent regression, but obstructed in classification.

Abstract:Complementarity is the case in which a human--AI interaction (HAI) outperforms the best prediction benchmark available among its members. Although this idea is central in HAI research, formal work on complementarity remains limited. Existing frameworks do not model how agents' predictions compose into workflow-sensitive multi-agent protocols. We close this gap by introducing a tree-based formalization of complementarity in multi-agent HAI. An HAI protocol is represented by an ordered agent-role configuration together with a rooted planar binary tree whose leaves are decorated by prediction vectors. A local binary composition rule is evaluated recursively along the tree, yielding a tree-relative complementarity functional relative to a pointwise-min benchmark. We prove four results. First, selector-based HAIs, including reliance, cannot achieve complementarity regardless of task, loss, or prediction quality. Second, in regression under squared loss, complementarity is equivalent to Euclidean distance minimization from the ground-truth vector; for $N=2$, the optimal linear-pooling weight has a closed form and a residual-correction interpretation. Third, under linear local composition, every protocol tree defines a barycentric coordinate chart on the simplex of leaf weights; Tamari-cover reparameterizations of protocol trees preserve complementarity, and for all $N$, any two Tamari paths with the same initial and terminal trees preserve the protocol output and complementarity. Fourth, in binary classification, no internal local composition can achieve complementarity under endpoint-monotone losses, including standard Bregman and many finite Bernoulli $f$-divergence losses; an analogous obstruction holds for multiclass aggregation under cross-entropy. In summary, our framework shows that complementarity is attainable in multi-agent regression, but obstructed in classification.

31 pages, 10 figures. Improved notation and added Figure 8 w.r.t. the original submission

Artificial Intelligence (cs.AI); Combinatorics (math.CO)

arXiv:2606.04779 [cs.AI]

(or arXiv:2606.04779v2 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2606.04779 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

analiza aiqbench

Tree-Based Formalization of Multi-Agent Complementarity in Human-AI Interactions

Subiecte conexe