# Characterizing the Decision Boundary of Deep Neural Networks

arXiv: https://arxiv.org/abs/1912.11460 · HTML: https://mlsanity.com/paper/1912.11460/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Dec 2019.

## Built on by (most cited first, 30 of 32)

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- [MANO: Exploiting Matrix Norm for Unsupervised Accuracy Estimation Under Distribution Shifts](https://mlsanity.com/paper/2405.18979/) (2024)
- [Understanding Deep Learning via Decision Boundary](https://mlsanity.com/paper/2206.01515/) (2022)
- [Boundary-Aware Uncertainty for Feature Attribution Explainers](https://mlsanity.com/paper/2210.02419/) (2022)
- [SoK: Unintended Interactions among Machine Learning Defenses and Risks](https://mlsanity.com/paper/2312.04542/) (2023)
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- [ASAT: Adaptively Scaled Adversarial Training in Time Series](https://mlsanity.com/paper/2108.08976/) (2021)
- [How to Explain Neural Networks: an Approximation Perspective](https://mlsanity.com/paper/2105.07831/) (2021)
- [The Missing Margin: How Sample Corruption Affects Distance to the Boundary in ANNs](https://mlsanity.com/paper/2302.06925/) (2023)
- [Improving classifier decision boundaries using nearest neighbors](https://mlsanity.com/paper/2310.03927/) (2023)
- [Guidelines For The Choice Of The Baseline in XAI Attribution Methods](https://mlsanity.com/paper/2503.19813/) (2025)
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- [Heating up decision boundaries: isocapacitory saturation, adversarial scenarios and generalization bounds](https://mlsanity.com/paper/2101.06061/) (2021)
- [Extracting Global Dynamics of Loss Landscape in Deep Learning Models](https://mlsanity.com/paper/2106.07683/) (2021)
- [Certainty Volume Prediction for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2111.02901/) (2021)
- [The Vanishing Decision Boundary Complexity and the Strong First Component](https://mlsanity.com/paper/2211.16209/) (2022)
- [Linking in Style: Understanding learned features in deep learning models](https://mlsanity.com/paper/2409.16865/) (2024)
- [MMARD: Improving the Min-Max Optimization Process in Adversarial Robustness Distillation](https://mlsanity.com/paper/2503.06559/) (2025)
- [Epsilon-Neighborhood Decision-Boundary Governed Estimation (EDGE) of 2D Black Box Classifier Functions](https://mlsanity.com/paper/2504.09733/) (2025)
- [Decision Potential Surface: A Theoretical and Practical Approximation of Large Language Model Decision Boundary](https://mlsanity.com/paper/2510.03271/) (2025)

## Abstract (arXiv)

Deep neural networks and in particular, deep neural classifiers have become an integral part of many modern applications. Despite their practical success, we still have limited knowledge of how they work and the demand for such an understanding is evergrowing. In this regard, one crucial aspect of deep neural network classifiers that can help us deepen our knowledge about their decision-making behavior is to investigate their decision boundaries. Nevertheless, this is contingent upon having access to samples populating the areas near the decision boundary. To achieve this, we propose a novel approach we call Deep Decision boundary Instance Generation (DeepDIG). DeepDIG utilizes a method based on adversarial example generation as an effective way of generating samples near the decision boundary of any deep neural network model. Then, we introduce a set of important principled characteristics that take advantage of the generated instances near the decision boundary to provide multifaceted understandings of deep neural networks. We have performed extensive experiments on multiple representative datasets across various deep neural network models and characterized their decision boundaries. The code is publicly available at https://github.com/hamidkarimi/DeepDIG/.