Wolfram Science

Alastair Hewitt: An Alternative Approach to Anticipative Reinforcement Learning

This was another decision-based talk using NKS, and I found this one just as interesting as the last. Hewitt studied a relatively simple but fascinating model of decision making based on choices between binary states with memory about which decisions led to which states. He had a very large number of of quantities he was using to describing the the behavior of the system, including predicatbility, desirability, and entropy.

The elementary system was a 2D CA with 2 choices, (turn left and no action), and 1 indicator with two states (right direction and wrong direction.) The agent must learn what to do when feedback indicates it is headed in the wrong direction based on past behavior, but with no indication of what moving toward the direction would be. Hewitt presented some state transition diagrams where the agent would determine the correct direction very quickly, but he quickly threw a wrench in the works by giving himself the ability to change the target point in real time.

He showed an interactive graphic of the agent seeking its target. The agent would head off in a direction more or less toward the target, but frequently get stuck in "orbits" once it had passed it on one side. I found it very amusing that the agent would get stuck in these orbits for some number of cycles and then finally get "frustrated" when it received enough negative feedback for each of its actions, and strike off in a random direction which would usually cause it to hit the target a few steps later.

Then he showed multiple agents where some of the agents were other agents targets. Their behaviors were reminiscent of bees milling around a hive, or as one of the audience members eloquently phrased it, "dating."

Hewitt ended with some graphics of distributions of various features of the agents' behavior.

Fritz Obermeyer: Mapping the Space of Programs, Searching the Space of Languages

Pure NKS lecture series

Fritz Obermeyer discusses mining the space of programming languages

Given a simple programming language family like lambda calculus, Fritz asks: what are the simplest few program behaviors? These behaviors form a basis that seems big but really isn't all that big. In an more abstract view, we can consider the behavior space of programs, and define a bigger map, and Fritz argues that this is the worthwhile space to map.

Since programs are elements of an algebra, like constants, binary operations, and equations and/or inequalities, a first starting place for this map is to try computational algebra methods. Fritz gave an example of making a map with the Todd-Coxeter algorithm. In theory, equivalence is undecidable, but in practice, given enough computation, equivalence is largely decidable (Fritz cites 96% in one particular case).

Then in the space of programs, Fritz can calculate the shape of an algebra of programs using Kolmogorov complexity. In order to visualize the space, Fritz posed the space as an eigenvector problem and is able to visually illustrate the difference in different programming styles in a program space. Through proper definition, the space of programs is a Reimannian manifold.

Potential applications of thes techniques include program simplification, using a database of simple rewritings, or software analysis, refactoring based on spatial proximity. It is also possible to program by searching.

Fritz's analysis shows that the average over all languages is simpler than any one.

Slides for Matthew Szudzik's Presentation

Here are the slides from my presentation, "An elegant pairing function" (in Mathematica format).  Download ElegantPairing.nb

Stephen Wolfram's Keynote Address: "The core of NKS is exploring the computational universe."

Posted by Kathryn Cramer.

Stephen Wolfram gave a wide-ranging Keynote Address that touched on many (or perhaps even all) of the subjects of the papers to be presented at the conference.

The central organizing metaphor of the talk was the field of NKS as an exploration of the computational universe: The core of NKS is exploring the computational universe.

My favorite line from the talk, from the portion in which he discussed NKS and aesthetics is: We are seeing the beauty of nature but not just from our world, but from all possible worlds.

As I was listening to his talk I explored the relationship between the various items on the program today. Here is my first draft version of this. As I listen to the talks I will modify and improve upon this.

Larger versions of the graphic are available here: 1024 x 642 and 3869 x 2424.

The talk will be available later. We will post the URL when we have it.