Long time behaviour of generative models

The proliferation of generative models, combined with pretraining on web-scale data, raises a crucial question: what happens when these models are trained on their own generated outputs? Recent investigations have hinted that such models would create loops that would lead to a phenomenon called model collapse, under which the performance progressively degrades with each model-data feedback iteration until fitted models become useless.

The goal of this project is to rigorously define at the mathematic level these systems and phenomena, and to study them by means of tools from probability theory (e.g. Markov chains), stochastic calculus (SDEs theory) and functional analysis. The theoretical study will be corroborated by extensive numerical experiments geared towards potential applications in e.g. image-generation and finance.