Symbolic Techniques for Deep Learning: Challenges and Opportunities

As the number of deep learning frameworks increase and certain ones gain popularity, it spurs the discussion of what methodologies are employed by these frameworks and the reasoning behind them. The goal of this survey is to study how symbolic techniques are utilized in deep learning. To do this, we look at some of the most popular deep learning frameworks being used today, including TensorFlow, Keras, PyTorch, and MXNet. While these frameworks greatly differ from one another, many of them use symbolic techniques, whether it be symbolic execution, graphs, or programming. We focus this paper on symbolic techniques because they influence not only how neural networks are built but also the way in which they are executed. Limitations of symbolic techniques have led to efforts in integrating symbolic and nonsymbolic aspects in deep learning, opening up new possibilities for symbolic techniques. For example, the Gluon API by Apache MXNet bridges the gap between imperative programming and symbolic execution through hybridization. Frameworks such as JANUS attempt to translate imperative programs into symbolic graphs, while approaches like DeepCheck attempt to use symbolic execution to analyze and validate imperative neural network programs. Symbolic analysis has also been paired with concrete execution in a technique called concolic testing in order to better test deep neural networks. Our study of these developments exemplifies just a few of the many ways the symbolic techniques employed by popular frameworks have the opportunity to be altered and utilized to achieve better performance.