# Interaction Graph

This work models multiple generative models that consume each other's synthetic data as nodes in a directed weighted graph, derives sufficient conditions for local asymptotic stability of the retraining dynamics via the Jacobian and a comparison matrix, and gives an upper bound on system diversity at the fixed point, showing that stability is jointly governed by local amplification factors and graph propagation while synthetic-data consumption induces a topology-dependent smoothing effect that contracts inter-model heterogeneity; experiments on an 8-mode Gaussian dataset and CIFAR-10 across several generative model classes and interaction topologies align with the theoretical predictions.

This work models multiple generative models that consume each other's synthetic data as nodes in a directed weighted graph, derives sufficient conditions for local asymptotic stability of the retraining dynamics via the Jacobian and a comparison matrix, and gives an upper bound on system diversity at the fixed point, showing that stability is jointly governed by local amplification factors and graph propagation while synthetic-data consumption induces a topology-dependent smoothing effect that contracts inter-model heterogeneity; experiments on an 8-mode Gaussian dataset and CIFAR-10 across several generative model classes and interaction topologies align with the theoretical predictions.

The study presents AlloPool, a graph neural network framework that combines temporal attention with iterative edge pooling to learn minimal, time-evolving residue interaction networks from equilibrium and non-equilibrium molecular dynamics trajectories, reconstructing trajectories at sub-angstrom RMSD across Pin1, the GAIN mechanosensor domain, dopamine D2 and beta-1 adrenergic receptors, the SdrG adhesin, PDZ3, and the Engrailed homeodomain, and using those networks to map allosteric pathways, predict ligand pharmacology, mechanical loading states, and mutation effects.

The study presents AlloPool, a graph neural network framework that combines temporal attention with iterative edge pooling to learn minimal, time-evolving residue interaction networks from equilibrium and non-equilibrium molecular dynamics trajectories, reconstructing trajectories at sub-angstrom RMSD across Pin1, the GAIN mechanosensor domain, dopamine D2 and beta-1 adrenergic receptors, the SdrG adhesin, PDZ3, and the Engrailed homeodomain, and using those networks to map allosteric pathways, predict ligand pharmacology, mechanical loading states, and mutation effects.