How a Belief Spreads Across AI Agents: The arXiv Paper

How the experiment was designed

On 2 October 2026 Tathagata Banerjee and Nima Moghaddas filed an 18-page, 6-figure paper^[1], accepted at the NeurIPS 2026 workshop on the theoretical foundations of agentic systems (FAST).

The literature on social contagion usually starts from a hypothesis: it fixes a rule for how an individual adopts a belief, then derives population behaviour from that rule. The authors reverse the order. They first measure adoption inside language agents, then look at the collective dynamics that come out of it.

The object of measurement is one precise probability: the probability that an agent accepts a statement, given the number of peers who hold it.

This arXiv paper on large language models calls that curve the adoption kernel. It finds the curve sigmoid. The sigmoid shape is the signature of complex contagion, the class of diffusion that requires reinforcement from several sources at once.

The sigmoid curve and the two regimes

A linear curve would say something reassuring: every additional peer adds the same push, and the total effect grows in proportion.

The sigmoid says something else. Below a certain share of supporters the push stays almost flat, around the threshold it climbs sharply, beyond the threshold it saturates.

The difference weighs on the design of multi-agent systems. Under simple contagion an isolated voice stays isolated, and error dilutes within the group. Under complex contagion the system has two regimes, and the jump between them depends on how many peers speak together at the same moment.

The threshold varies, and it varies legibly. It responds to three factors the authors state explicitly: the plausibility of the statement, the reliability of the source, the disposition of the agent.

The first factor concerns content, the second the channel, the third the internal state of the receiving model.

Three factors, one dimension: coherence

The finest step in the work concerns the reduction. The three sources of the threshold prove well approximated by a single effective dimension, which the authors propose reading as coherence between the incoming belief and the beliefs already held by the agent.

Three dials become one. The agent's prior explains almost the whole threshold.

The practical reach is concrete: a statement coherent with the prior passes with few supporters, a dissonant statement requires a wide majority.

The evidence therefore shows that resistance to the spread of a false statement depends on the alignment between that statement and what the agent already holds to be true. Model accuracy on the single task enters the account second. A system populated by agents with similar priors becomes homogeneous ground, where a belief coherent with that shared prior travels at a low threshold.

The network changes diffusion

From measurement on the single agent the authors move to the population. In a system of AI agents, diffusion advances further on clustered networks than on random ones.

The result confirms the class. Simple, epidemic-type contagion runs better along the long shortcuts of a random network, where a single contact suffices to transmit. Complex contagion requires reinforcement from several neighbours at once, and tight clusters supply it naturally.

The point touches a widespread architecture. Specialising agent teams by function creates dense subgroups, with many internal links and few towards the outside.

That shape, chosen for reasons of competence and cost, raises the probability that a belief born in one subgroup becomes the consensus of the entire system. Topology thus joins the design variables, alongside the chosen model and the prompt.

Cascade window and self-sustaining consensus

The collective dynamics show two further properties, both measured in the work.

The first is a cascade window that bifurcates: inside a parameter interval the system has two stable outcomes, and small initial variations select which of the two is realised.

The second is a hysteretic consensus that sustains itself. The authors sum it up in a sharp sentence: consensus proves far harder to remove than to create.

Hysteresis has a precise meaning. Once the threshold is crossed, the population stays in the new state even when initial conditions return to the starting point. The return path follows a different curve from the outbound one.

The cost of restoration after a cascade therefore exceeds the cost of containment before the threshold. The measurement describes a system with memory, where the state reached weighs on subsequent states.

Risk leaves the single model

Evaluation of AI systems today turns on the accuracy of the single model. A benchmark measures one agent at a time, under fixed and repeatable conditions.

The evidence from this work describes a different object: a population dynamic with threshold, bifurcation and state memory. Two variables a per-model score leaves out are network topology and the coherence of priors.

Compound arithmetic makes the distance concrete. An agent reliable 90% of the time across five independent steps closes the compound task at 59%: error accumulates along the chain.

The work adds a second, lateral channel of accumulation: the error that passes between peers.

The strand is growing. A recent survey, «LLMs for Social Network Modeling: From Network Generation to Dynamic Processes», covers the dual use of language models to generate networks and to simulate dynamic processes (Pith^[2]). The full text of the contagion paper remains open, with PDF, experimental HTML and TeX source, also on alphaXiv^[3].

What stays outside, and what changes for decision makers

The declared perimeter stays narrow. The measurement concerns language agents in an environment built by the authors, with statements, sources and dispositions under the experimenter's control.

The document passes a workshop review, lighter than a journal review. Extension to a fleet of agents in production stays outside the limits the authors set.

Where the data is silent, this desk stays silent: the shape of the curve and the reduction to one dimension are measured, the numerical width of the threshold in a real system remains an open matter.

For an investment committee the diagnosis is legible. Spending concentrated on model accuracy covers one part of the risk; the other part lives in the structure of the agent population.

For a head of data analytics the work indicates which traces are needed: who held which statement, in front of how many peers, at which point in the network, with which prior. A per-agent output log leaves that chain invisible.

For a board the thesis the data supports concerns risk internal to the collective: trust in the single model and trust in the group of models remain two distinct measures.