PREMAP：一种统一的神经网络原像近似框架
PREMAP: A Unifying PREiMage APproximation Framework for Neural Networks
AI总结：
PREMAP提出一种统一的神经网络原像近似框架，通过参数化线性松弛与迭代划分，高效生成多面体输出集的上下近似，显著提升高维图像分类任务的验证效率与可扩展性。
摘要：
大多数神经网络验证方法侧重于对像（即给定输入集的输出集）进行界定。这可用于例如检查神经网络预测对输入有界扰动的鲁棒性。然而，验证关于原像（即满足输出属性的输入集）的性质，需要在输入空间中进行抽象。我们提出了一个通用的原像抽象框架，该框架可对任意多面体输出集生成下近似和上近似。我们的框架采用廉价的参数化线性松弛神经网络，并结合一种随时细化程序，该程序通过分割输入特征和神经元来迭代地划分输入区域。我们方法的效果依赖于精心设计的启发式方法和优化目标，以实现近似体积的快速改进。我们在一系列任务上评估了我们的方法，与最先进的技术相比，在高维输入图像分类任务上展示了效率和可扩展性的显著提升。此外，我们展示了在定量验证和鲁棒性分析中的应用，为前者提供了一种健全且完备的算法，并为后者提供了健全的定量结果。
英文摘要：
Most methods for neural network verification focus on bounding the image, i.e., set of outputs for a given input set. This can be used to, for example, check the robustness of neural network predictions to bounded perturbations of an input. However, verifying properties concerning the preimage, i.e., the set of inputs satisfying an output property, requires abstractions in the input space. We present a general framework for preimage abstraction that produces under- and over-approximations of any polyhedral output set. Our framework employs cheap parameterised linear relaxations of the neural network, together with an anytime refinement procedure that iteratively partitions the input region by splitting on input features and neurons. The effectiveness of our approach relies on carefully designed heuristics and optimization objectives to achieve rapid improvements in the approximation volume. We evaluate our method on a range of tasks, demonstrating significant improvement in efficiency and scalability to high-input-dimensional image classification tasks compared to state-of-the-art techniques. Further, we showcase the application to quantitative verification and robustness analysis, presenting a sound and complete algorithm for the former and providing sound quantitative results for the latter.
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