In this paper, we consider the problem of automatically designing a Rectified Linear Unit (ReLU) Neural Network (NN) architecture (number of layers and number of neurons per layer) with the assurance that it is sufficiently parametrized to control a nonlinear system; i.e. control the system to satisfy a given formal specification. This is unlike current techniques, which provide no assurances on the resultant architecture. Moreover, our approach requires only limited knowledge of the underlying nonlinear system and specification. We assume only that the specification can be satisfied by a Lipschitz-continuous controller with a known bound on its Lipschitz constant; the specific controller need not be known. From this assumption, we bound the number of affine functions needed to construct a Continuous Piecewise Affine (CPWA) function that can approximate any Lipschitz-continuous controller that satisfies the specification. Then we connect this CPWA to a NN architecture using the authors' recent results on the Two-Level Lattice (TLL) NN architecture; the TLL architecture was shown to be parameterized by the number of affine functions present in the CPWA function it realizes.

中文翻译：

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用于控制和识别非线性系统的可靠神经网络架构

在本文中，我们考虑了自动设计整流线性单元 (ReLU) 神经网络 (NN) 架构（层数和每层神经元数）的问题，并确保其充分参数化以控制非线性系统；即控制系统满足给定的正式规范。这与当前的技术不同，当前的技术不提供对最终架构的保证。此外，我们的方法只需要对底层非线性系统和规范的有限了解。我们只假设规范可以被一个 Lipschitz 连续控制器满足，它的 Lipschitz 常数有一个已知的界限；不需要知道特定的控制器。从这个假设，我们限制了构建连续分段仿射 (CPWA) 函数所需的仿射函数的数量，该函数可以逼近满足规范的任何 Lipschitz 连续控制器。然后我们使用作者在两层格 (TLL) NN 架构上的最新结果将此 CPWA 连接到 NN 架构；TLL 架构被证明是通过它实现的 CPWA 函数中存在的仿射函数的数量来参数化的。