An Introduction to Neural Network Analysis via Semidefinite Programming
An Introduction to Neural Network Analysis via Semidefinite Programming
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DOI：
10.1109/cdc45484.2021.9683096
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发表时间：
2021-12
期刊：
影响因子：
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通讯作者：
Mahyar Fazlyab;M. Morari;George Pappas
中科院分区：
文献类型：
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作者：
Mahyar Fazlyab;M. Morari;George Pappas
神经网络在许多困难的机器学习任务中变得越来越有效。然而，神经网络的非线性和大规模性质使其难以分析，因此，它们大多被用作没有正式保证的黑箱模型。当神经网络用于学习闭环系统时，这个问题变得更加复杂，其中一个小的扰动可能会对被控制的系统产生重大影响。因此，它是至关重要的开发工具，可以提供有用的证书的稳定性，安全性和鲁棒性的神经网络驱动systems.In这篇综述中，我们提出了一个凸优化框架的神经网络的分析。其主要思想是抽象神经网络中难以分析的组件（例如，非线性激活函数）与二次约束的形式主义。这种抽象允许我们推理神经网络的各种属性（安全性，鲁棒性，泛化性，闭环设置的稳定性等）。通过半定规划。
Neural networks have become increasingly effective at many difficult machine learning tasks. However, the nonlinear and large-scale nature of neural networks makes them hard to analyze, and, therefore, they are mostly used as blackbox models without formal guarantees. This issue becomes even more complicated when neural networks are used in learning-enabled closed-loop systems, where a small perturbation can substantially impact the system being controlled. Therefore, it is of utmost importance to develop tools that can provide useful certificates of stability, safety, and robustness for neural network-driven systems.In this overview, we present a convex optimization framework for the analysis of neural networks. The main idea is to abstract hard-to-analyze components of a neural network (e.g., the nonlinear activation functions) with the formalism of quadratic constraints. This abstraction allows us to reason about various properties of neural networks (safety, robustness, generalization, stability in closed-loop settings, etc.) via semidefinite programming.