Building on VeriX (Verified eXplainability, arXiv:2212.01051), a system for producing optimal verified explanations for machine learning models, we present VeriX+, which significantly improves both the size and the generation time of formal explanations. We introduce a bound propagation-based sensitivity technique to improve the size, and a binary search-based traversal with confidence ranking for improving time -- the two techniques are orthogonal and can be used independently or together. We also show how to adapt the QuickXplain algorithm to our setting to provide a trade-off between size and time. Experimental evaluations on standard benchmarks demonstrate significant improvements on both metrics, e.g., a size reduction of 38% on the GTSRB dataset and a time reduction of 90% on MNIST. We demonstrate that our approach is scalable to transformers and real-world scenarios such as autonomous aircraft taxiing and sentiment analysis. We conclude by showcasing several novel applications of formal explanations.
@article{arxiv.2409.03060,
title = {Efficiently Computing Compact Formal Explanations},
author = {Min Wu and Xiaofu Li and Haoze Wu and Clark Barrett},
journal= {arXiv preprint arXiv:2409.03060},
year = {2025}
}