A theoretical basis for model collapse in recursive training

Our analysis will draw heavily upon the three topics in probability theory mentioned above. We briefly summarize the relevant results here. These can be found respectively, in [3] (see also [12] for a more extensive treatment), [11], and [2] (see also [9] for a more extensive treatment), respectively. A. Convergence of probability measures: Let S be a Polish space, i.e., a separable topological space with its topology compatible with a complete metric. Let B denote its Borel σ -field, i.e., the smallest σ -field containing its open sets.