Speaker: Gerald Hoehn (K-State) and Philipp Hoehn (Bonn)

Abstract: Peg solitaire is a one-player board puzzle. A legal move jumps a peg orthogonally over an adjacent peg into a hole two positions away; the jumped peg is removed. The goal is to reach a board with a single peg in the center.

Supported by YouTube clips, we will introduce deep neural networks and reinforcement learning (especially Q-learning) in three lectures and apply these methods to Peg solitaire.

Lecture 1: AlexNet and the modern AI toolkit — entropy, cross-entropy, gradient descent, backpropagation.
Lecture 2: Reinforcement learning — Bellman equations, Q-learning, experience replay, and self-play on Peg solitaire.
Lecture 3: Large language models — from Transformers to reasoning models; vibe-coding a solver.

Prerequisites: Calculus, linear algebra; basic probability helpful.

Lecture 1 (by G.H.):

We open by introducing Peg Solitaire and, via vibe coding with GPT-5, quickly produce a working solution. The modern era of AI began in 2012 with AlexNet, created by Alex Krizhevsky, Ilya Sutskever, and Geoffrey Hinton. Sutskever, the former Chief Scientist of OpenAI, helped drive the development of GPT-3 and GPT-4. Hinton received the 2024 Nobel Prize in Physics for his work. We introduce the ideas of entropy and cross-entropy and explain how neural networks—continuous piecewise-affine function approximators—can be constructed and trained via gradient descent and backpropagation to minimize cross-entropy. To make these ideas accessible, we will use short YouTube clips that present them in a simplified, visually engaging way.