# Clustering-Based Interpretation of Deep ReLU Network

arXiv: https://arxiv.org/abs/2110.06593 · HTML: https://mlsanity.com/paper/2110.06593/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 16 references that are in the map.
- First posted on arXiv 13 Oct 2021.

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

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [Methods for Interpreting and Understanding Deep Neural Networks](https://mlsanity.com/paper/1706.07979/) (2017)
- [Gradients of Counterfactuals](https://mlsanity.com/paper/1611.02639/) (2016)
- [Expressiveness of Rectifier Networks](https://mlsanity.com/paper/1511.05678/) (2015)

## Built on by (most cited first, 1 of 1)

- [REALM: Regime-Switching, Explainable, and Activation-Induced Linear Models](https://mlsanity.com/paper/2609.32141/) (2026)

## Abstract (arXiv)

Amongst others, the adoption of Rectified Linear Units (ReLUs) is regarded as one of the ingredients of the success of deep learning. ReLU activation has been shown to mitigate the vanishing gradient issue, to encourage sparsity in the learned parameters, and to allow for efficient backpropagation. In this paper, we recognize that the non-linear behavior of the ReLU function gives rise to a natural clustering when the pattern of active neurons is considered. This observation helps to deepen the learning mechanism of the network; in fact, we demonstrate that, within each cluster, the network can be fully represented as an affine map. The consequence is that we are able to recover an explanation, in the form of feature importance, for the predictions done by the network to the instances belonging to the cluster. Therefore, the methodology we propose is able to increase the level of interpretability of a fully connected feedforward ReLU neural network, downstream from the fitting phase of the model, without altering the structure of the network. A simulation study and the empirical application to the Titanic dataset, show the capability of the method to bridge the gap between the algorithm optimization and the human understandability of the black box deep ReLU networks.