# ANet Patu-1: The Value of Connection in the Agent Network

arXiv: https://arxiv.org/abs/2607.15053 · HTML: https://mlsanity.com/paper/2607.15053/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 20 references that are in the map.
- First posted on arXiv 16 Jul 2026.

## Builds on (most cited first, 4 of 4)

- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [MetaGPT: Meta Programming for A Multi-Agent Collaborative Framework](https://mlsanity.com/paper/2308.00352/) (2023)
- [CAMEL: Communicative Agents for "Mind" Exploration of Large Language Model Society](https://mlsanity.com/paper/2303.17760/) (2023)

## Abstract (arXiv)

The Internet taught us that the value of a network depends on how its nodes connect: broadcast stars scale as V!propto!N (Sarnoff), fully-connected meshes as N2 (Metcalfe), and group-forming networks as 2N (Reed). We ask the analogous question for networks of AI agents. We model the net value of connection as a function of coordination-group size, derive from it the properties an optimal collaboration protocol must have, and introduce ANet Patu-1 -- a self-organizing consensus protocol in which the network continuously re-forms its own coalitions, adaptively riding the upper envelope of all three regimes at O(1) parallel consensus rounds. To measure value without opinion-grading, we score an emergent protocol by formally specifying it and deriving its complexity, the way distributed algorithms are analyzed. Two results follow. (i)~Emergence -- a crowd of the cheapest model, when heterogeneous, starts weak but its collective value compounds with N and overtakes a crowd of a far stronger model that is homogeneous: a crossover that marks a scaling law for collaboration rather than for scale. (ii)~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.