# Prioritizing Corners in OoD Detectors via Symbolic String Manipulation

arXiv: https://arxiv.org/abs/2205.07736 · HTML: https://mlsanity.com/paper/2205.07736/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 27 references that are in the map.
- First posted on arXiv 16 May 2022.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [DeepXplore: Automated Whitebox Testing of Deep Learning Systems](https://mlsanity.com/paper/1705.06640/) (2017)
- [Training independent subnetworks for robust prediction](https://mlsanity.com/paper/2010.06610/) (2020)
- [Efficient and Scalable Bayesian Neural Nets with Rank-1 Factors](https://mlsanity.com/paper/2005.07186/) (2020)
- [Model-based Exploration of the Frontier of Behaviours for Deep Learning System Testing](https://mlsanity.com/paper/2007.02787/) (2020)
- [Outside the Box: Abstraction-Based Monitoring of Neural Networks](https://mlsanity.com/paper/1911.09032/) (2019)
- [Quantitative Projection Coverage for Testing ML-enabled Autonomous Systems](https://mlsanity.com/paper/1805.04333/) (2018)
- [Towards Safety Verification of Direct Perception Neural Networks](https://mlsanity.com/paper/1904.04706/) (2019)
- [Combinatorial Testing for Deep Learning Systems](https://mlsanity.com/paper/1806.07723/) (2018)
- [Customizable Reference Runtime Monitoring of Neural Networks using Resolution Boxes](https://mlsanity.com/paper/2104.14435/) (2021)

## Built on by (most cited first, 3 of 3)

- [A Survey of Safety and Trustworthiness of Large Language Models through the Lens of Verification and Validation](https://mlsanity.com/paper/2305.11391/) (2023)
- [What, Indeed, is an Achievable Provable Guarantee for Learning-Enabled Safety Critical Systems](https://mlsanity.com/paper/2307.11784/) (2023)
- [BAM: Box Abstraction Monitors for Real-time OoD Detection in Object Detection](https://mlsanity.com/paper/2403.18373/) (2024)

## Abstract (arXiv)

For safety assurance of deep neural networks (DNNs), out-of-distribution (OoD) monitoring techniques are essential as they filter spurious input that is distant from the training dataset. This paper studies the problem of systematically testing OoD monitors to avoid cases where an input data point is tested as in-distribution by the monitor, but the DNN produces spurious output predictions. We consider the definition of "in-distribution" characterized in the feature space by a union of hyperrectangles learned from the training dataset. Thus the testing is reduced to finding corners in hyperrectangles distant from the available training data in the feature space. Concretely, we encode the abstract location of every data point as a finite-length binary string, and the union of all binary strings is stored compactly using binary decision diagrams (BDDs). We demonstrate how to use BDDs to symbolically extract corners distant from all data points within the training set. Apart from test case generation, we explain how to use the proposed corners to fine-tune the DNN to ensure that it does not predict overly confidently. The result is evaluated over examples such as number and traffic sign recognition.