提出新方法在高维空间高效估算神经网络输入区域，保证结果可靠性。
On the Probabilistic Learnability of Compact Neural Network Preimage Bounds
- 用随机决策树集成生成满足输出属性的输入区域
- 理论证明区域纯度与覆盖范围有统计保障
- 适合需要可靠、可扩展预像近似的人工智能研究者
尽管近期已发展出可证明的神经网络预像边界计算方法，但其可扩展性受问题#P难性的根本限制。本文采用新的概率视角，旨在提供高置信度保证且误差有界的解法。我们研究了基于自助采样和随机化的方法，以捕捉高维空间中的复杂模式，包括满足给定输出属性的输入区域。具体地，提出$ exttt{RF-ProVe}$方法，利用一组随机决策树生成满足目标输出属性的候选输入区域，并通过主动重采样进行优化。理论推导提供了区域纯度与全局覆盖的正式统计保证，为精确求解器无法扩展的情形下，提供了一种实用且可扩展的紧凑预像逼近方案。
原文摘要 · Abstract (English)
Although recent provable methods have been developed to compute preimage bounds for neural networks, their scalability is fundamentally limited by the #P-hardness of the problem. In this work, we adopt a novel probabilistic perspective, aiming to deliver solutions with high-confidence guarantees and bounded error. To this end, we investigate the potential of bootstrap-based and randomized approaches that are capable of capturing complex patterns in high-dimensional spaces, including input regions where a given output property holds. In detail, we introduce $\textbf{R}$andom $\textbf{F}$orest $\textbf{Pro}$perty $\textbf{Ve}$rifier ($\texttt{RF-ProVe}$), a method that exploits an ensemble of randomized decision trees to generate candidate input regions satisfying a desired output property and refines them through active resampling. Our theoretical derivations offer formal statistical guarantees on region purity and global coverage, providing a practical, scalable solution for computing compact preimage approximations in cases where exact solvers fail to scale.
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