# Stability Margin

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 work introduces the first framework that explicitly disentangles prompt dependence into prompt ambiguity (inter-user variability) and local sensitivity (interaction imprecision): a mixture density network models the image-conditioned distribution of plausible prompts and quantifies ambiguity by the trace of its covariance, while a stability margin captures the minimal perturbation under measurement noise needed to induce a mask change; evaluated on two female pelvic T2-weighted MRI datasets, UT-EndoMRI (81 patients with endometriosis, uterus segmentation) and MOGaMBO (94 patients with locally advanced cervical cancer, bladder segmentation), with MobileSAM and MedSAM, the two metrics correlate significantly and negatively with Dice, correlate little with each other, and conditional samp

The work introduces the first framework that explicitly disentangles prompt dependence into prompt ambiguity (inter-user variability) and local sensitivity (interaction imprecision): a mixture density network models the image-conditioned distribution of plausible prompts and quantifies ambiguity by the trace of its covariance, while a stability margin captures the minimal perturbation under measurement noise needed to induce a mask change; evaluated on two female pelvic T2-weighted MRI datasets, UT-EndoMRI (81 patients with endometriosis, uterus segmentation) and MOGaMBO (94 patients with locally advanced cervical cancer, bladder segmentation), with MobileSAM and MedSAM, the two metrics correlate significantly and negatively with Dice, correlate little with each other, and conditional samp