🤖 AI Summary
Conventional entropy-based diversity metrics fail to capture the intrinsic geometric and topological structure of high-dimensional training data, limiting their ability to assess data quality and predict model performance.
Method: This work introduces persistent homology—a tool from topological data analysis—to quantify structural properties such as connected components, holes, and higher-order voids, thereby jointly characterizing data richness and redundancy through both topological and geometric lenses.
Contribution/Results: Experiments demonstrate that the proposed topological metrics exhibit strong correlation with model generalization performance and serve as effective predictors of data quality. The framework enables principled data selection and efficient training, offering a novel paradigm for dataset curation. By leveraging topological signatures, it enhances training efficiency and robustness of AI systems without requiring model retraining or architectural modification. The approach is broadly applicable across domains where data geometry and topology critically influence learning dynamics.
📝 Abstract
High-quality training data is the foundation of machine learning and artificial intelligence, shaping how models learn and perform. Although much is known about what types of data are effective for training, the impact of the data's geometric structure on model performance remains largely underexplored. We propose that both the richness of representation and the elimination of redundancy within training data critically influence learning outcomes. To investigate this, we employ persistent homology to extract topological features from data within a metric space, thereby offering a principled way to quantify diversity beyond entropy-based measures. Our findings highlight persistent homology as a powerful tool for analyzing and enhancing the training data that drives AI systems.