Branch and Bound Methods for Neural Network Verification

本项目主要属于EPSRC“理论计算机科学”研究领域。然而，还有许多其他的研究领域也与我的项目相关，如“人工智能技术”，“图像和视觉计算”，以及在较小程度上的“自然语言处理”。尽管深度学习最近在各种科学领域取得了成功，但它在安全关键环境中的应用仍然受到缺乏正式验证的限制。然而，尽管神经网络通常被视为一种黑盒方法，但在验证简单网络的直接属性方面已经取得了一些进展。在我的研究中，我将专注于改进现有的分支和定界方法，这些方法利用神经网络的分段线性结构，目的是能够将它们应用于更大的网络。对分支定界算法的三个部分进行了改进：搜索策略（选择要进行分支的下一个域）、分支规则（将给定的域划分为不相交的子域）和边界方法（估计每个子域的下界和上界）。

This project mainly falls within EPSRC "theoretical computer science" research area. However, there are numerous other research areas which are also relevant to my project such as "artificial intelligence technologies", "image and vision computing", and to a lesser degree "natural language processing".Despite the recent success Deep Learning has had in a variety of scientific fields its use in safety-critical settings is still limited by the lack of formal verification. However, even though neural networks are generally being treated as a black-box method, some progress has been made on verifying straight-forward properties in simple networks. In my research I will focus on improving existing branch and bound methods that exploit the piecewise linear structure of neural networks with the aim of being able to apply them to larger networks. Improvements can be made to all three parts of the branch and bound algorithm: the search strategy, which picks the next domain to branch on, the branching rule, which given a domain divides it into non-intersecting subdomains, and finally the bounding methods, which estimate lower and upper bounds for each subdomain.