mPOLICE：深度神经网络中多区域仿射约束的可证明强制执行
mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks
AI总结：
mPOLICE通过为每个不相交凸区域分配不同神经元激活模式并逐层优化参数，将POLICE推广至多区域仿射约束的可证明强制执行，在安全强化学习、3D形状表示和流体模拟中验证有效，且推理无额外开销。
摘要：
深度神经网络越来越多地用于安全关键领域，如机器人技术和科学建模，在这些领域中，严格遵守输出约束至关重要。像POLICE这样的方法，专为单一凸区域设计，在扩展到多个不相交区域时面临挑战，常常导致约束违反或跨区域的不期望的仿射行为。本文提出mPOLICE，一种将POLICE推广到可证明地在多个不相交凸区域上强制执行仿射约束的新方法。其核心是，mPOLICE为每个受约束区域分配不同的神经元激活模式，实现局部仿射行为并避免意外泛化。这是通过网络参数的逐层优化来实现的。此外，我们引入了一种训练算法，将mPOLICE纳入常规深度学习流程，通过周期性符号模式强制来平衡任务特定性能与约束执行。我们通过跨多种应用的实验验证了mPOLICE的灵活性和有效性，包括安全关键强化学习、带几何约束的隐式3D形状表示，以及带边界条件执行的流体动力学模拟。重要的是，mPOLICE在推理期间不产生运行时开销，使其成为深度神经网络中约束处理的实用且可靠的解决方案。
英文摘要：
Deep neural networks are increasingly used in safety-critical domains such as robotics and scientific modeling, where strict adherence to output constraints is essential. Methods like POLICE, which are tailored for single convex regions, face challenges when extended to multiple disjoint regions, often leading to constraint violations or unwanted affine behavior across regions. This paper proposes mPOLICE, a new approach that generalizes POLICE to provably enforce affine constraints over multiple disjoint convex regions. At its core, mPOLICE assigns distinct neuron activation patterns to each constrained region, enabling localized affine behavior and avoiding unintended generalization. This is implemented through a layer-wise optimization of the network parameters. Additionally, we introduce a training algorithm that incorporates mPOLICE into conventional deep learning pipelines, balancing task-specific performance with constraint enforcement using periodic sign pattern enforcement. We validate the flexibility and effectiveness of mPOLICE through experiments across various applications, including safety-critical reinforcement learning, implicit 3D shape representation with geometric constraints, and fluid dynamics simulations with boundary condition enforcement. Importantly, mPOLICE incurs no runtime overhead during inference, making it a practical and reliable solution for constraint handling in deep neural networks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
