Building on VeriX (Verified eXplainability, arXiv:2212.01051), a system for producing optimal verified explanations for machine learning model outputs, we present VeriX+, which significantly improves both the size and the generation time of verified 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 (Junker 2004) 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 also explore applications of our verified explanations and show that explanation size is a useful proxy for both incorrectness detection and out-of-distribution detection.
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