Boolean Connectives and Deep Learning: Three Interpretations

In this paper, we motivate three approaches for integrating symbolic logic systems and deep learning methods. First, we consider whether the hidden layers of neural networks can be used to represent and reason about Boolean functions via so-called Tractable Circuits. Second, we discuss a method for encoding domain knowledge into the training and outputs of neural networks via so-called MultiplexNets. Finally, we show how we can instantiate deep learning architectures that perform exact function learning, via so-called Signal Perceptrons.