# Functional Network: A Novel Framework for Interpretability of Deep Neural Networks

arXiv: https://arxiv.org/abs/2205.11702 · HTML: https://mlsanity.com/paper/2205.11702/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 60 references that are in the map.
- First posted on arXiv 24 May 2022.

## Builds on (most cited first, 17 of 17)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [On the Expressive Power of Deep Neural Networks](https://mlsanity.com/paper/1606.05336/) (2016)
- [What Is One Grain of Sand in the Desert? Analyzing Individual Neurons in Deep NLP Models](https://mlsanity.com/paper/1812.09355/) (2018)
- [Topology of deep neural networks](https://mlsanity.com/paper/2004.06093/) (2020)
- [Deep Neural Networks Reveal a Gradient in the Complexity of Neural Representations across the Brain's Ventral Visual Pathway](https://mlsanity.com/paper/1411.6422/) (2014)
- [The Bayesian Case Model: A Generative Approach for Case-Based Reasoning and Prototype Classification](https://mlsanity.com/paper/1503.01161/) (2015)
- [Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology](https://mlsanity.com/paper/1812.09764/) (2018)
- [Deep Neural Networks Rival the Representation of Primate IT Cortex for Core Visual Object Recognition](https://mlsanity.com/paper/1406.3284/) (2014)
- [Understanding the Disharmony between Dropout and Batch Normalization by Variance Shift](https://mlsanity.com/paper/1801.05134/) (2018)
- [Batch Normalization Increases Adversarial Vulnerability and Decreases Adversarial Transferability: A Non-Robust Feature Perspective](https://mlsanity.com/paper/2010.03316/) (2020)
- [Topological Measurement of Deep Neural Networks Using Persistent Homology](https://mlsanity.com/paper/2106.03016/) (2021)
- [Learning-Induced Autonomy of Sensorimotor Systems](https://mlsanity.com/paper/1403.6034/) (2014)
- [On The Robustness of a Neural Network](https://mlsanity.com/paper/1707.08167/) (2017)

## Built on by (most cited first, 2 of 2)

- [Addressing caveats of neural persistence with deep graph persistence](https://mlsanity.com/paper/2307.10865/) (2023)
- [Artificial Structure Function Search: Preserving Artificial Functional Connectivity for Structured Pruning](https://mlsanity.com/paper/2609.24401/) (2026)

## Abstract (arXiv)

The layered structure of deep neural networks hinders the use of numerous analysis tools and thus the development of its interpretability. Inspired by the success of functional brain networks, we propose a novel framework for interpretability of deep neural networks, that is, the functional network. We construct the functional network of fully connected networks and explore its small-worldness. In our experiments, the mechanisms of regularization methods, namely, batch normalization and dropout, are revealed using graph theoretical analysis and topological data analysis. Our empirical analysis shows the following: (1) Batch normalization enhances model performance by increasing the global e ciency and the number of loops but reduces adversarial robustness by lowering the fault tolerance. (2) Dropout improves generalization and robustness of models by improving the functional specialization and fault tolerance. (3) The models with dierent regularizations can be clustered correctly according to their functional topological dierences, re ecting the great potential of the functional network and topological data analysis in interpretability.