# Logifold: A Geometrical Foundation of Ensemble Machine Learning

arXiv: https://arxiv.org/abs/2407.16177 · HTML: https://mlsanity.com/paper/2407.16177/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 26 references that are in the map.
- First posted on arXiv 23 Jul 2024.

## Builds on (most cited first, 10 of 10)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [A Unified Theory of Diversity in Ensemble Learning](https://mlsanity.com/paper/2301.03962/) (2023)
- [A Review of Adversarial Attack and Defense for Classification Methods](https://mlsanity.com/paper/2111.09961/) (2021)
- [Less Is More: A Comprehensive Framework for the Number of Components of Ensemble Classifiers](https://mlsanity.com/paper/1709.02925/) (2017)
- [Efficient Adaptive Ensembling for Image Classification](https://mlsanity.com/paper/2206.07394/) (2022)
- [A logifold structure on measure space](https://mlsanity.com/paper/2405.05492/) (2024)
- [Towards a Systematic Approach to Design New Ensemble Learning Algorithms](https://mlsanity.com/paper/2402.06818/) (2024)

## Abstract (arXiv)

We present a local-to-global and measure-theoretical approach to understanding datasets. The core idea is to formulate a logifold structure and to interpret network models with restricted domains as local charts of datasets. In particular, this provides a mathematical foundation for ensemble machine learning. Our experiments demonstrate that logifolds can be implemented to identify fuzzy domains and improve accuracy compared to taking average of model outputs. Additionally, we provide a theoretical example of a logifold, highlighting the importance of restricting to domains of classifiers in an ensemble.