We study deep neural networks with binary activation functions (BDNN), i.e. the activation function only has two states. We show that the BDNN can be reformulated as a mixed-integer linear program which can be solved to global optimality by classical integer programming solvers. Additionally, a heuristic solution algorithm is presented and we study the model under data uncertainty, applying a two-stage robust optimization approach. We implemented our methods on random and real datasets and show that the heuristic version of the BDNN outperforms classical deep neural networks on the Breast Cancer Wisconsin dataset while performing worse on random data.

中文翻译：

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具有二元激活函数的深度神经网络的整数规划方法

我们研究具有二元激活函数（BDNN）的深度神经网络，即激活函数只有两种状态。我们表明 BDNN 可以重新表述为混合整数线性程序，可以通过经典整数规划求解器求解到全局最优。此外，还提出了一种启发式求解算法，我们在数据不确定性下研究模型，应用两阶段稳健优化方法。我们在随机和真实数据集上实施了我们的方法，并表明 BDNN 的启发式版本在威斯康星乳腺癌数据集上的表现优于经典深度神经网络，同时在随机数据上表现更差。