Hierarchically Learning the Laws of Boolean Algebra and Applying them to Digital Circuits and the Stock Market

Abstract

While the use of machine learning has increased drastically over the past few years, most al gorithms are still data-hungry and do not generalize well. In addition, they are limited with regards to what tasks and domains they can be applied to. However, a new neuro-symbolic machine learning model called Dreamcoder, designed by a team of researchers from MIT, overcomes these limitations by developing a library of generalizable, interpretable knowledge through program induction and synthesis. In this paper, we propose applying the Dreamcoder algorithm to the domain of circuit design because the process of designing a circuit is very time-intensive and requires a significant amount of domain expertise. In order to do so, first we define the primitives of the domain-specific language Dreamcoder needs to learn. Then we generate a list of training and test tasks geared to teach the algorithm about the laws of Boolean algebra and various types of logic gates, combinational logic circuits, and sequential logic circuits. The end goal of this domain is for Dreamcoder to be able to design a register transfer level circuit given a state table, and this should be possible if our methodology is implemented. In the second part of the paper, we show how this learned knowledge of Boolean algebra can be combined with a different domain to facilitate technical analysis of publicly-listed stocks. Dreamcoder’s ability to generalize allows the model to use concepts from other domains to learn how to solve tasks much faster and with far less data than if the model was trained from scratch for each domain.