Reinforcement learning has seen a lot of progress in recent years. From DeepMind success with teaching machines how to play Atari games, then AlphaGo beating world champions in Go to recent OpenAI's progress on Dota 2, a multiplayer game where players divided into two teams compete with each other. The common thread is an artificial agent operating in a virtual world, where the prize is clear (e.g. On the other hand people are experimenting with AI agents operating in real-world. Each clip of Boston Dynamics gets a lot of press, showing robots performing amazing stunts, as you can see yourself here or here.
"They're this crazy contact between an imaginary, nonphysical world and biologically evolved creatures," said the cognitive scientist Simon DeDeo of Carnegie Mellon University, who studies mathematical certainty by analyzing the structure of proofs. "We did not evolve to do this." Computers are useful for big calculations, but proofs require something different. Conjectures arise from inductive reasoning -- a kind of intuition about an interesting problem -- and proofs generally follow deductive, step-by-step logic. They often require complicated creative thinking as well as the more laborious work of filling in the gaps, and machines can't achieve this combination. Computerized theorem provers can be broken down into two categories.
In the recent years, we have linked a large corpus of formal mathematics with automated theorem proving (ATP) tools, and started to develop combined AI/ATP systems working in this setting. In this paper we first relate this project to the earlier large-scale automated developments done by Quaife with McCune's Otter system, and to the discussions of the QED project about formalizing a significant part of mathematics. Then we summarize our adventure so far, argue that the QED dreams were right in anticipating the creation of a very interesting semantic AI field, and discuss its further research directions.
We present an environment, benchmark, and deep learning driven automated theorem prover for higher-order logic. Higher-order interactive theorem provers enable the formalization of arbitrary mathematical theories and thereby present an interesting, open-ended challenge for deep learning. We provide an open-source framework based on the HOL Light theorem prover that can be used as a reinforcement learning environment. HOL Light comes with a broad coverage of basic mathematical theorems on calculus and the formal proof of the Kepler conjecture, from which we derive a challenging benchmark for automated reasoning. We also present a deep reinforcement learning driven automated theorem prover, DeepHOL, with strong initial results on this benchmark.
On March 31, 1913, in the Great Hall of the Musikverein concert house in Vienna, a riot broke out in the middle of a performance of an orchestral song by Alban Berg. Police arrested the concert's organizer for punching Oscar Straus, a little-remembered composer of operettas. Later, at the trial, Straus quipped about the audience's frustration. The punch, he insisted, was the most harmonious sound of the entire evening. History has rendered a different verdict: the concert's conductor, Arnold Schoenberg, has gone down as perhaps the most creative and influential composer of the 20th century. You may not enjoy Schoenberg's dissonant music, which rejects conventional tonality to arrange the 12 notes of the scale according to rules that don't let any predominate. But he changed what humans understand music to be. This is what makes him a genuinely creative and innovative artist.