Analogies are 4-ary relations of the form “A is to B as C is to D”. When A, B and C are fixed, we call analogical equation the problem of finding the correct D. Even though this task has been shown to be simple for the human cognition, it remains extremely challenging for artificial agents. In this presentation, we introduce our recent advances in solving morphological analogies on words based on a principle of minimum of complexity. The idea of our method is to find a transformation from A to B which also applies to C and is maximally simple to describe algorithmically. We will show which new perspectives this principle of minimum complexity can open for the field of analogical reasoning: For that purpose, we demonstrate the flexibility of our approach toward various related domains, such as interactive AI, case-based reasoning, AI assistance or transfer learning. As a complement, we will discuss the underlying assumptions of our framework as well as the algorithmic challenges of such an approach, and show what these limitations imply for the application of this method to other problems.
