# Modular Representation of Layered Neural Networks

arXiv: https://arxiv.org/abs/1703.00168 · HTML: https://mlsanity.com/paper/1703.00168/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2017.

## Built on by (most cited first, 12 of 12)

- [Toward Transparent AI: A Survey on Interpreting the Inner Structures of Deep Neural Networks](https://mlsanity.com/paper/2207.13243/) (2022)
- [Understanding the Dynamics of DNNs Using Graph Modularity](https://mlsanity.com/paper/2111.12485/) (2021)
- [Clustering units in neural networks: upstream vs downstream information](https://mlsanity.com/paper/2203.11815/) (2022)
- [Neural Network Module Decomposition and Recomposition](https://mlsanity.com/paper/2112.13208/) (2021)
- [Modular Federated Learning](https://mlsanity.com/paper/2209.03090/) (2022)
- [Modularity in Deep Learning: A Survey](https://mlsanity.com/paper/2310.01154/) (2023)
- [Studying Cross-cluster Modularity in Neural Networks](https://mlsanity.com/paper/2502.02470/) (2025)
- [Modularity is the Bedrock of Natural and Artificial Intelligence](https://mlsanity.com/paper/2602.18960/) (2026)
- [Learning to Transfer with von Neumann Conditional Divergence](https://mlsanity.com/paper/2108.03531/) (2021)
- [Training Neural Networks for Modularity aids Interpretability](https://mlsanity.com/paper/2409.15747/) (2024)
- [Neural Sculpting: Uncovering hierarchically modular task structure in neural networks through pruning and network analysis](https://mlsanity.com/paper/2305.18402/) (2023)
- [RDSA: A Robust Deep Graph Clustering Framework via Dual Soft Assignment](https://mlsanity.com/paper/2410.21745/) (2024)

## Abstract (arXiv)

Layered neural networks have greatly improved the performance of various applications including image processing, speech recognition, natural language processing, and bioinformatics. However, it is still difficult to discover or interpret knowledge from the inference provided by a layered neural network, since its internal representation has many nonlinear and complex parameters embedded in hierarchical layers. Therefore, it becomes important to establish a new methodology by which layered neural networks can be understood. In this paper, we propose a new method for extracting a global and simplified structure from a layered neural network. Based on network analysis, the proposed method detects communities or clusters of units with similar connection patterns. We show its effectiveness by applying it to three use cases. (1) Network decomposition: it can decompose a trained neural network into multiple small independent networks thus dividing the problem and reducing the computation time. (2) Training assessment: the appropriateness of a trained result with a given hyperparameter or randomly chosen initial parameters can be evaluated by using a modularity index. And (3) data analysis: in practical data it reveals the community structure in the input, hidden, and output layers, which serves as a clue for discovering knowledge from a trained neural network.