Relational Minds and Differentiated Worlds: A Neural Network Model of Multiplex Self

• In Event: Recent Advances in Mathematical Sociology

Abstract

This paper advances a relational theory of mind in which the self emerges from internalized models of “particular others” rather than from an abstract “generalized other.” Drawing on insights from George Herbert Mead, we formalize the distinction between the “I” and the “me” as a computational architecture in which evaluative responses are indexed to “particular others” with whom one interacts. We model agents as multiplex neural networks that jointly process expressive content and social identity, which allows for alter-specific mappings between stimuli and evaluations. Each agent is implemented as a feedforward neural network with separate subnets for expression and identity, integrated to produce probabilistic evaluative outputs. Learning proceeds via a sign-based update rule, capturing incremental and directionally bounded belief revision. Social interaction is modeled as iterative exchange: agents communicate expressions with attached evaluations, infer partners’ mappings, and update their own parameters accordingly. Using simulation experiments, we demonstrate that multiplex cognition sustains social differentiation even in well-connected networks. A control condition that disables identity-based multiplex cognition produces uniform convergence. Rather than treating fragmentation as a byproduct of network topology, the results show polarization and differentiation as endogenous consequences of relationally structured cognition. Society, on this account, is reproduced within cognition itself.

Authors

• Yongren Shi, University of Arizona

• Jeffrey Shen, University of Arizona