Quantifying The Limits of AI Reasoning: Systematic Neural Network Representations of Algorithms

A main open question in contemporary AI research is quantifying the forms of reasoning neural networks can perform when perfectly trained. This paper answers this by interpreting reasoning tasks as circuit emulation, where the gates define the type of reasoning; e.g. Boolean gates for predicate logic, tropical circuits for dynamic programming, arithmetic and analytic gates for symbolic mathematical representation, and hybrids thereof for deeper reasoning; e.g. higher-order logic.