# Predict Training Data Quality via Its Geometry in Metric Space

arXiv: https://arxiv.org/abs/2510.15970 · HTML: https://mlsanity.com/paper/2510.15970/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 31 references that are in the map.
- First posted on arXiv 12 Oct 2025.

## Builds on (most cited first, 12 of 12)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [The Vendi Score: A Diversity Evaluation Metric for Machine Learning](https://mlsanity.com/paper/2210.02410/) (2022)
- [Data Augmentation Can Improve Robustness](https://mlsanity.com/paper/2111.05328/) (2021)
- [DDXPlus: A New Dataset For Automatic Medical Diagnosis](https://mlsanity.com/paper/2205.09148/) (2022)
- [Learning metrics for persistence-based summaries and applications for graph classification](https://mlsanity.com/paper/1904.12189/) (2019)
- [Representation Matters: Assessing the Importance of Subgroup Allocations in Training Data](https://mlsanity.com/paper/2103.03399/) (2021)
- [Automatically Identifying Complaints in Social Media](https://mlsanity.com/paper/1906.03890/) (2019)
- [Metric Space Magnitude for Evaluating the Diversity of Latent Representations](https://mlsanity.com/paper/2311.16054/) (2023)
- [Data Representativity for Machine Learning and AI Systems](https://mlsanity.com/paper/2203.04706/) (2022)
- [Fill In The Gaps: Model Calibration and Generalization with Synthetic Data](https://mlsanity.com/paper/2410.10864/) (2024)
- [Protoformer: Embedding Prototypes for Transformers](https://mlsanity.com/paper/2206.12710/) (2022)

## Abstract (arXiv)

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.