# Sheaves as a Framework for Understanding and Interpreting Model Fit

arXiv: https://arxiv.org/abs/2105.10414 · HTML: https://mlsanity.com/paper/2105.10414/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 13 references that are in the map.
- First posted on arXiv 21 May 2021.

## Builds on (most cited first, 6 of 6)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [No Subclass Left Behind: Fine-Grained Robustness in Coarse-Grained Classification Problems](https://mlsanity.com/paper/2011.12945/) (2020)
- [Fruit recognition from images using deep learning](https://mlsanity.com/paper/1712.00580/) (2017)
- [Fuzzy Simplicial Networks: A Topology-Inspired Model to Improve Task Generalization in Few-shot Learning](https://mlsanity.com/paper/2009.11253/) (2020)

## Built on by (most cited first, 5 of 5)

- [Copresheaf Topological Neural Networks: A Generalized Deep Learning Framework](https://mlsanity.com/paper/2505.21251/) (2025)
- [Prospects for inconsistency detection using large language models and sheaves](https://mlsanity.com/paper/2401.16713/) (2024)
- [Quantum-Like Contextuality in Large Language Models](https://mlsanity.com/paper/2412.16806/) (2024)
- [A Topological-Framework to Improve Analysis of Machine Learning Model Performance](https://mlsanity.com/paper/2107.04714/) (2021)
- [Disentangling Hyperedges through the Lens of Category Theory](https://mlsanity.com/paper/2510.16289/) (2025)

## Abstract (arXiv)

As data grows in size and complexity, finding frameworks which aid in interpretation and analysis has become critical. This is particularly true when data comes from complex systems where extensive structure is available, but must be drawn from peripheral sources. In this paper we argue that in such situations, sheaves can provide a natural framework to analyze how well a statistical model fits at the local level (that is, on subsets of related datapoints) vs the global level (on all the data). The sheaf-based approach that we propose is suitably general enough to be useful in a range of applications, from analyzing sensor networks to understanding the feature space of a deep learning model.