Cascades in LLM agent networks become predictable, but only if each agent is measured with its follower count

Networked LLM agents produce information cascades whose reach depends on both the network structure and the post, and an individual agent's sharing decision depends on its own local situation in a way no single response curve captures. Earlier prediction work placed agents in well-mixed populations where everyone sees everyone, measured one response curve, and assumed it did not depend on the agent's position in the network. Across four contested political posts, the seed fraction needed to trigger a global cascade varies by a factor of 2.6 between posts on BA networks and 3.5 on ER networks, so both post and network structure matter.

The sharing probability depends on the number of contacts itself, not only on the fraction of contacts who have shared: agents with more contacts need a lower sharing fraction before sharing becomes more likely than not. Classic threshold models assume either a fixed fraction threshold or a fixed count threshold, and neither includes a drift with contact count. At the same fraction, an agent seeing 2 of 10 contacts share almost never shares, while one seeing 20 of 100 shares far more often; at large contact counts the midpoint of the response falls with contact count by similar amounts across the four posts.

The response measured by contact count, fed into mean-field theory of network cascades, predicts the cascades of full LLM simulations, including whether they spread and the tipping seed fraction. Responses that ignore contact count, read either as a fraction or as a count, mispredict cascades, and the direction of the error depends on the post content. Across three network types (ER and BA) and four posts, the theory matches the full simulations; once the response is measured, the cascade on any network follows without further queries to the language model.

The error from ignoring contact count can be written analytically, but it does not factor into network statistics times a single number for the response, so it cannot be corrected after the fact from network statistics. If the error factorized, a correction factor computed from the network would replace the contact-count-resolved measurement. On networks rewired step by step to raise heterogeneity at fixed mean degree, the error grows monotonically with heterogeneity, is zero on a regular graph and reaches a finite range at the largest heterogeneity; on the same network, errors for different posts differ by about a factor of two while the single number describing response deviation differs little between posts.

The conclusions rest on a single open-weight model, mistral:7b, one prompt template and four contested political posts, with agents that have only a minimal persona and no memory; the networks are synthetic, locally tree-like ER and BA graphs. The authors propose refining the response step by step to per-persona and history-dependent policies until prediction and simulation agree, but that extension is not carried out in this setting.

The authors note that the gun-rights post differs from the other three at low contact count, and whether that difference survives rewording has not been tested; the police-defunded post, and to a lesser extent migration-must-be-limited, spreads slightly earlier in the full simulations than its response predicts; the first-order error expansion overestimates the largest error by about a third on ER networks and does not apply on BA networks or for gun-right on the sparse ER network; real social networks are often clustered, where the tree theory loses accuracy.