Criticality in Dissimilar Decomposition and Undersampling of Random Datasets with Anomalies
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.
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BibTeX
@misc{ganesan2026criticality,
title = {{Criticality in Dissimilar Decomposition and Undersampling of Random Datasets with Anomalies}},
author = {Ghurumuruhan Ganesan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13201},
eprint = {2609.13201},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13201},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Criticality in Dissimilar Decomposition and Undersampling of Random Datasets with Anomalies
AU - Ghurumuruhan Ganesan
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.13201
UR - https://arxiv.org/abs/2609.13201
AB - 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.
ER -