# Abstraction and Symbolic Execution of Deep Neural Networks with Bayesian Approximation of Hidden Features

arXiv: https://arxiv.org/abs/2103.03704 · HTML: https://mlsanity.com/paper/2103.03704/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 42 references that are in the map.
- First posted on arXiv 5 Mar 2021.

## Builds on (most cited first, 23 of 23)

- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [The Secret Sharer: Evaluating and Testing Unintended Memorization in Neural Networks](https://mlsanity.com/paper/1802.08232/) (2018)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Does Learning Require Memorization? A Short Tale about a Long Tail](https://mlsanity.com/paper/1906.05271/) (2019)
- [DeepXplore: Automated Whitebox Testing of Deep Learning Systems](https://mlsanity.com/paper/1705.06640/) (2017)
- [Safety Verification of Deep Neural Networks](https://mlsanity.com/paper/1610.06940/) (2016)
- [Evaluating the Robustness of Neural Networks: An Extreme Value Theory Approach](https://mlsanity.com/paper/1801.10578/) (2018)
- [Reachability Analysis of Deep Neural Networks with Provable Guarantees](https://mlsanity.com/paper/1805.02242/) (2018)
- [DLFuzz: Differential Fuzzing Testing of Deep Learning Systems](https://mlsanity.com/paper/1808.09413/) (2018)
- [Concolic Testing for Deep Neural Networks](https://mlsanity.com/paper/1805.00089/) (2018)
- [Feature-Guided Black-Box Safety Testing of Deep Neural Networks](https://mlsanity.com/paper/1710.07859/) (2017)
- [Testing Deep Neural Networks](https://mlsanity.com/paper/1803.04792/) (2018)
- [Outside the Box: Abstraction-Based Monitoring of Neural Networks](https://mlsanity.com/paper/1911.09032/) (2019)
- [Runtime Monitoring Neuron Activation Patterns](https://mlsanity.com/paper/1809.06573/) (2018)
- [A Game-Based Approximate Verification of Deep Neural Networks with Provable Guarantees](https://mlsanity.com/paper/1807.03571/) (2018)
- [How does Weight Correlation Affect the Generalisation Ability of Deep Neural Networks](https://mlsanity.com/paper/2010.05983/) (2020)
- [Analyzing Deep Neural Networks with Symbolic Propagation: Towards Higher Precision and Faster Verification](https://mlsanity.com/paper/1902.09866/) (2019)
- [A Safety Framework for Critical Systems Utilising Deep Neural Networks](https://mlsanity.com/paper/2003.05311/) (2020)
- [Into the Unknown: Active Monitoring of Neural Networks](https://mlsanity.com/paper/2009.06429/) (2020)
- [Coverage Guided Testing for Recurrent Neural Networks](https://mlsanity.com/paper/1911.01952/) (2019)
- [Provably-Robust Runtime Monitoring of Neuron Activation Patterns](https://mlsanity.com/paper/2011.11959/) (2020)
- [Symbolic Execution for Deep Neural Networks](https://mlsanity.com/paper/1807.10439/) (2018)
- [Reliability Validation of Learning Enabled Vehicle Tracking](https://mlsanity.com/paper/2002.02424/) (2020)

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

- [A Survey of Safety and Trustworthiness of Large Language Models through the Lens of Verification and Validation](https://mlsanity.com/paper/2305.11391/) (2023)

## Abstract (arXiv)

Intensive research has been conducted on the verification and validation of deep neural networks (DNNs), aiming to understand if, and how, DNNs can be applied to safety critical applications. However, existing verification and validation techniques are limited by their scalability, over both the size of the DNN and the size of the dataset. In this paper, we propose a novel abstraction method which abstracts a DNN and a dataset into a Bayesian network (BN). We make use of dimensionality reduction techniques to identify hidden features that have been learned by hidden layers of the DNN, and associate each hidden feature with a node of the BN. On this BN, we can conduct probabilistic inference to understand the behaviours of the DNN processing data. More importantly, we can derive a runtime monitoring approach to detect in operational time rare inputs and covariate shift of the input data. We can also adapt existing structural coverage-guided testing techniques (i.e., based on low-level elements of the DNN such as neurons), in order to generate test cases that better exercise hidden features. We implement and evaluate the BN abstraction technique using our DeepConcolic tool available at https://github.com/TrustAI/DeepConcolic.