On the Reliability of Networks of AI Agents: Density Evolution, Stopping Sets, and Architecture Optimization

Computer Science > Multiagent Systems [Submitted on 16 Jun 2026] Title:On the Reliability of Networks of AI Agents: Density Evolution, Stopping Sets, and Architecture Optimization View PDFAbstract:Modern AI systems increasingly solve a task not with a single model call but with several imperfect agents working together: some propose pieces of a solution, others verify them, and the results are combined. These systems often outperform any single model, yet it is rarely clear why they succeed or when they will fail. We model such a system as message passing on a sparse graph, the structure that underlies low-density parity-check (LDPC) codes, and extend the density-evolution machinery of coding theory to this richer setting. In our model a task is a set of coupled binary subclaims, and an agent architecture is a sparse, role-typed factor graph whose check nodes are noisy Boolean verifier nodes, each computing a local Boolean function of the subclaims it touches. Three distinct failure modes, all modeled as erasures (an agent abstaining, a verifier returning no usable output, and a message lost between two agents), propagate as the agents exchange set-valued messages. The check agents combine these messages by a single logical-forcing rule that specializes to XOR, AND, OR, implication, and Horn constraints. This is more than a relabeling of LDPC theory: the verifier functions are nonlinear and value-asymmetric, and the three failure modes do not reduce to a single effective channel, so they require new threshold, finite-length, and converse results rather than a direct reuse of parity-check density evolution. We prove a density-evolution theorem that predicts the asymptotic fraction of unresolved subclaims on random role-typed architectures, with an extension to deterministic, locally tree-like graph sequences. The XOR case recovers the classical LDPC recursion on the binary erasure channel (BEC); the AND case exposes an asymmetry between positive and negative verifier certificates. Current browse context: cs.MA References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators 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.