Use-driven concept formation

Abstract

When faced with a complex task, humans often identify domain-specific concepts that make the task more tractable. In this thesis, I investigate the formation of domain-specific concepts of this sort. I propose a set of principles for formulating domain-specific concepts, including a new inductive bias that I call the equivalence class principle. I then use the domain of two-player, perfect-information games to test and refine those principles. I show how the principles can be applied in a semiautomated fashion to identify strategically-important visual concepts, discover highlevel structure in a game's state space, create human-interpretable descriptions of tactics, and uncover both offensive and defensive strategies within five deterministic, perfect-information games that have up to forty-two million states apiece. I introduce a visualization technique for networks that discovers a new strategy for exploiting an opponent's mistakes in lose tic-tac-toe; discovers the optimal defensive strategies in five and six men's morris; discovers the optimal offensive strategies in pong hau k'i, tic-tac-toe, and lose tic-tac-toe; simplifies state spaces by up to two orders of magnitude; and creates a hierarchical depiction of a game's state space that allows the user to explore the space at multiple levels of granularity. I also introduce the equivalence class principle, an inductive bias that identifies concepts by building connections between two representations in the same domain. I demonstrate how this principle can be used to rediscover visual concepts that would help a person learn to play a game, propose a procedure for using such concepts to create succinct, human-interpretable descriptions of offensive and defensive tactics, and show that these tactics can compress important information in the five men's morris state space by two orders of magnitude.