This paper explores the value of network node connections, particularly in the context of AI agent networks. We model the net value of connection as a function of coordination-group size and derive the properties that an optimal collaboration protocol must have. We introduce ANet Patu-1, a self-organizing consensus protocol that continuously reforms its coalitions, adaptively riding the upper envelope of all three connection regimes at $O(1)$ parallel consensus rounds.
To measure value without opinion grading, we score the emergent protocol by formally specifying it and deriving its complexity, akin to how distributed algorithms are analyzed. Two results follow:
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Emergence: A crowd of the cheapest model, when heterogeneous, starts weak but its collective value compounds with $N$ and overtakes that of a far stronger homogeneous model, marking a scaling law for collaboration rather than for mere scale.
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Reflexivity: A heterogeneous network, given only its own problem and no design hints, converges on ANet Patu-1 itself, reconstructing the high-dimensional law that governs its own connective value.
This research provides a new perspective on understanding collaboration among AI agents, emphasizing the profound impact of connection methods on network value.
Blogger's Review: The introduction of ANet Patu-1 not only illustrates the complexity of network connections but also lays a crucial theoretical foundation for future adaptive protocol designs, especially in heterogeneous network environments. This study has significant potential applications in optimizing and collaborating within multi-agent systems.