Forge: An Agentic System for ERGM Specification and Interpretation in Social Networks

Abstract

Exponential Random Graph Models (ERGMs) provide a statistical framework for testing hypotheses about how ties form using network structure and node attributes. Their usefulness depends on model specification, which often requires researchers to repeatedly propose models, fit them, check how well they reproduce the observed network, and revise them when they do not. We present Forge (Formation-Oriented Reasoning with Guarded ERGMs), an agentic system that performs this process using a language model and external statistical tools. Given an observed network and a domain description, Forge proposes hypotheses about tie formation, translates them into candidate ERGM specifications, evaluates them statistically, refines the best candidate using goodness-of-fit feedback, and returns a human-readable interpretation of the final model. On 16 benchmark networks, Forge improves on the best baseline on 13 networks and matches it on the other three, with a median 24.8% improvement in goodness of fit. On 60 controlled networks with known generating specifications, Forge achieves exact specification recovery in 78.3% of cases and attains 90.8% term-level F1. These results show that Forge can reduce the manual trial-and-error involved in ERGM specification while making the process more reproducible and keeping model selection grounded in statistical evidence.

arXiv comment11 pages, 4 figures. Substantially revised manuscript with updated framing, expanded experiments on 16 benchmark networks, and a controlled recovery study on 60 networks