# Enhancing Explainability of Neural Networks through Architecture Constraints

arXiv: https://arxiv.org/abs/1901.03838 · HTML: https://mlsanity.com/paper/1901.03838/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jan 2019.

## Built on by (most cited first, 29 of 29)

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- [PiML Toolbox for Interpretable Machine Learning Model Development and Diagnostics](https://mlsanity.com/paper/2305.04214/) (2023)
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- [Attention Visualizer Package: Revealing Word Importance for Deeper Insight into Encoder-Only Transformer Models](https://mlsanity.com/paper/2308.14850/) (2023)
- [On the Relationship Between Interpretability and Explainability in Machine Learning](https://mlsanity.com/paper/2311.11491/) (2023)
- [FAME: Introducing Fuzzy Additive Models for Explainable AI](https://mlsanity.com/paper/2504.07011/) (2025)
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- [Less Discriminatory Alternative and Interpretable XGBoost Framework for Binary Classification](https://mlsanity.com/paper/2410.19067/) (2024)
- [Using Decision Tree as Local Interpretable Model in Autoencoder-based LIME](https://mlsanity.com/paper/2204.03321/) (2022)
- [Are Logistic Models Really Interpretable?](https://mlsanity.com/paper/2406.13427/) (2024)
- [Linear Iterative Feature Embedding: An Ensemble Framework for Interpretable Model](https://mlsanity.com/paper/2103.09983/) (2021)
- [Rethinking Log Odds: Linear Probability Modelling and Expert Advice in Interpretable Machine Learning](https://mlsanity.com/paper/2211.06360/) (2022)
- [Analyzing User Characteristics of Hate Speech Spreaders on Social Media](https://mlsanity.com/paper/2310.15772/) (2023)
- [Use of Parallel Explanatory Models to Enhance Transparency of Neural Network Configurations for Cell Degradation Detection](https://mlsanity.com/paper/2404.11311/) (2024)
- [An Interpretable Deep Learning Model for General Insurance Pricing](https://mlsanity.com/paper/2509.08467/) (2025)
- [Sample-wise Constrained Learning via a Sequential Penalty Approach with Applications in Image Processing](https://mlsanity.com/paper/2601.16812/) (2026)
- [Wrong Operator or Blind Design? A Post-Training Diagnostic for Physics-Informed Coefficient Learning](https://mlsanity.com/paper/2608.16925/) (2026)

## Abstract (arXiv)

Prediction accuracy and model explainability are the two most important objectives when developing machine learning algorithms to solve real-world problems. The neural networks are known to possess good prediction performance, but lack of sufficient model interpretability. In this paper, we propose to enhance the explainability of neural networks through the following architecture constraints: a) sparse additive subnetworks; b) projection pursuit with orthogonality constraint; and c) smooth function approximation. It leads to an explainable neural network (xNN) with the superior balance between prediction performance and model interpretability. We derive the necessary and sufficient identifiability conditions for the proposed xNN model. The multiple parameters are simultaneously estimated by a modified mini-batch gradient descent method based on the backpropagation algorithm for calculating the derivatives and the Cayley transform for preserving the projection orthogonality. Through simulation study under six different scenarios, we compare the proposed method to several benchmarks including least absolute shrinkage and selection operator, support vector machine, random forest, extreme learning machine, and multi-layer perceptron. It is shown that the proposed xNN model keeps the flexibility of pursuing high prediction accuracy while attaining improved interpretability. Finally, a real data example is employed as a showcase application.