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AI's widespread integration has led to neural networks (NN) deployment on edge and similar limited-resource platforms for safety-critical scenarios. Yet, NN's fragility raises concerns about reliable inference. Moreover, constrained platforms demand compact networks. This study introduces VeriCompress, a tool that automates the search and training of compressed models with robustness guarantees. These models are well-suited for safety-critical applications and adhere to predefined architecture and size limitations, making them deployable on resource-restricted platforms. The method trains models 2-3 times faster than the state-of-the-art approaches, surpassing them by average accuracy and robustness gains of 15.1 and 9.8 percentage points, respectively. When deployed on a resource-restricted generic platform, these models require 5-8 times less memory and 2-4 times less inference time than models used in verified robustness literature. Our comprehensive evaluation across various model architectures and datasets, including MNIST, CIFAR, SVHN, and a relevant pedestrian detection dataset, showcases VeriCompress's capacity to identify compressed verified robust models with reduced computation overhead compared to current standards. This underscores its potential as a valuable tool for end users, such as developers of safety-critical applications on edge or Internet of Things platforms, empowering them to create suitable models for safety-critical, resource-constrained platforms in their respective domains. 

The ability of Deep Neural Networks to approximate highly complex functions is the key to their success. This benefit, however, often comes at the cost of a large model size, which challenges their deployment in resource-constrained environments. To limit this issue, pruning techniques can introduce sparsity in the models, but at the cost of accuracy and adversarial robustness. This paper addresses these critical issues and introduces Deadwooding, a novel pruning technique that exploits a Lagrangian Dual method to encourage model sparsity while retaining accuracy and ensuring robustness. The resulting model is shown to significantly outperform the state-of-the-art studies in measures of robustness and accuracy.