DYNAPIN: Mechanism-pluratistic dynamics profiling fro interpretable node classification

Node classification is a core graph-learning task for citation, hyperlink, purchase, and political-interaction networks, where accurate predictions are valuable only when the learned graph behavior can also be read. Existing graph neural and diffusion models improve message passing, scalability, uncertainty modeling, and non-homophilous learning, but their embeddings rarely state the mechanism by which a node responds to graph-mediated influence. Inspired by recent progress in neural symbolic regression, we introduce DynaPIN (Dynamics-informed profile learning for interpretable node classification), a mechanism-pluralistic framework that uses opinion-dynamics equations as a symbolic hypothesis space for graph classification. DynaPIN constructs graph-induced opinion evolution signals, fits each node with a Candidate Mechanism Bank covering neighbor diffusion, self-retention, selective interaction, and attraction–repulsion, and converts fitted parameters, validation errors, and Soft Mechanism Evidence into a Mechanism Fingerprint. The fingerprint supports downstream classification, while the same fitted quantities instantiate a Soft Equation Lens for mechanism discovery. Experiments on three opinion-oriented voting datasets and five general node-classification benchmarks show that DynaPIN remains competitive on voting graphs and achieves leading or near-leading Macro-F1 on citation, co-purchase, and hyperlink benchmarks. More importantly, the Soft Equation Lens reveals a repeated non-consensus grammar: fitted graph responses concentrate on selective nonlinear coupling and attraction–repulsion-like patterns, with dataset-specific mixtures rather than one universal smoothing law. These results establish opinion dynamics as a predictive and equation-readable mechanism language for interpretable graph representation learning.