Criticality in Dissimilar Decomposition and Undersampling of Random Datasets with Anomalies

A new arXiv paper (2609.13201v1) models AI-generated text and images as anomalies linked to main data points and derives bounds on the minimum size of a strongly dissimilar decomposition of random datasets using redundancy graphs and iteration techniques. The authors report a phase transition in which that minimum size is determined by the main data points when anomalies are few but is taken over by the anomalies above a certain threshold, and they establish a size criticality result for strong similarity of a randomly undersampled dataset. The work is framed around the effect of AI-generated data on batch decompositions and the performance of future LLMs trained on such datasets.

arXiv:2609.13201v1 Announce Type: new Abstract: Training datasets for upcoming LLMs would include a significant amount of AI text/image data generated from current LLMs. In such a scenario, it is important to understand how this affects batch decompositions and thereby, the performance of the resultant new LLM. In this paper, we consider AI generated data as anomalies linked" to main data points and study decomposition and undersampling properties of the overall random dataset. We use redundancy graphs and iteration techniques to obtain bounds for the minimum size of a strongly dissimilar SD decomposition and demonstrate a phase transition phenomena, wherein the minimum size is essentially determined by the \emph{main} data points when the number of anomalies is small and is taken" over by the anomalies above a certain threshold. We also establish a size criticality result for the strong similarity of a randomly undersampled dataset and illustrate our results with examples involving categorical datasets, whose overall space size is much larger than the size of the dataset.