# Negative Selection Approach to support Formal Verification and Validation of BlackBox Models' Input Constraints

arXiv: https://arxiv.org/abs/2209.01411 · HTML: https://mlsanity.com/paper/2209.01411/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 20 references that are in the map.
- First posted on arXiv 3 Sep 2022.

## Builds on (most cited first, 6 of 6)

- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Formal Security Analysis of Neural Networks using Symbolic Intervals](https://mlsanity.com/paper/1804.10829/) (2018)
- [NNV: The Neural Network Verification Tool for Deep Neural Networks and Learning-Enabled Cyber-Physical Systems](https://mlsanity.com/paper/2004.05519/) (2020)
- [Parallelization Techniques for Verifying Neural Networks](https://mlsanity.com/paper/2004.08440/) (2020)
- [Driver Identification Based on Vehicle Telematics Data using LSTM-Recurrent Neural Network](https://mlsanity.com/paper/1911.08030/) (2019)
- [Negative Selection Algorithm Research and Applications in the last decade: A Review](https://mlsanity.com/paper/2105.06109/) (2021)

## Built on by (most cited first, 2 of 2)

- [Volatility in Certainty (VC): A Metric for Detecting Adversarial Perturbations During Inference in Neural Network Classifiers](https://mlsanity.com/paper/2511.11834/) (2025)
- [Upper Bounds on the Generalization Error of Deep Learning Models via Local Robustness and Stability](https://mlsanity.com/paper/2606.16883/) (2026)

## Abstract (arXiv)

Generating unsafe sub-requirements from a partitioned input space to support verification-guided test cases for formal verification of black-box models is a challenging problem for researchers. The size of the search space makes exhaustive search computationally impractical. This paper investigates a meta-heuristic approach to search for unsafe candidate sub-requirements in partitioned input space. We present a Negative Selection Algorithm (NSA) for identifying the candidates' unsafe regions within given safety properties. The Meta-heuristic capability of the NSA algorithm made it possible to estimate vast unsafe regions while validating a subset of these regions. We utilize a parallel execution of partitioned input space to produce safe areas. The NSA based on the prior knowledge of the safe regions is used to identify candidate unsafe region areas and the Marabou framework is then used to validate the NSA results. Our preliminary experimentation and evaluation show that the procedure finds candidate unsafe sub-requirements when validated with the Marabou framework with high precision.