It has been shown that a neural network's Lipschitz constant can be leveraged to derive robustness guarantees, to improve generalizability via regularization or even to construct invertible networks. Therefore, a number of methods varying in the tightness of their bounds and their computational cost have been developed to approximate the Lipschitz constant for different classes of networks. However, comparatively little research exists on methods for exact computation, which has been shown to be NP-hard. Nonetheless, there are applications where one might readily accept the computational cost of an exact method. These applications could include the benchmarking of new methods or the computation of robustness guarantees for small models on sensitive data. Unfortunately, existing exact algorithms restrict themselves to only ReLU-activated networks, which are known to come with severe downsides in the context of Lipschitz-constrained networks. We therefore propose a generalization of the LipBaB algorithm to compute exact Lipschitz constants for arbitrary piecewise linear neural networks and $p$-norms. With our method, networks may contain traditional activations like ReLU or LeakyReLU, activations like GroupSort or the related MinMax and FullSort, which have been of increasing interest in the context of Lipschitz constrained networks, or even other piecewise linear functions like MaxPool.

Large Language Models (LLMs) have achieved impressive performance across diverse natural language processing tasks, but their growing power also amplifies potential risks such as jailbreak attacks that circumvent built-in safety mechanisms. Existing defenses including input paraphrasing, multi step evaluation, and safety expert models often suffer from high computational costs, limited generalization, or rigid workflows that fail to detect subtle malicious intent embedded in complex contexts. Inspired by cognitive science findings on human decision making, we propose SafeBehavior, a novel hierarchical jailbreak defense mechanism that simulates the adaptive multistage reasoning process of humans. SafeBehavior decomposes safety evaluation into three stages: intention inference to detect obvious input risks, self introspection to assess generated responses and assign confidence based judgments, and self revision to adaptively rewrite uncertain outputs while preserving user intent and enforcing safety constraints. We extensively evaluate SafeBehavior against five representative jailbreak attack types including optimization based, contextual manipulation, and prompt based attacks and compare it with seven state of the art defense baselines. Experimental results show that SafeBehavior significantly improves robustness and adaptability across diverse threat scenarios, offering an efficient and human inspired approach to safeguarding LLMs against jailbreak attempts.