Georgia Institute of Technology College of Sciences

Spring 2025:

Math 8803-CHE: In this class, we will study review and study techniques harmonic analysis and spectral theory, and then apply them to study dynamics of nonlinear dispersive PDEs.

Math 8803-DUN: This will be a follow up for the course taught in Spring 2024. Potential topics include an introduction to sieve theory/advanced topics on primes or modular forms.

Math 8803-HOM: We will study knot concordance and homology cobordism, using both classical and modern tools.

Math 8803-MAT: 

Recently, transformers have achieved a major breakthrough and revolutionized society, especially since Chat-GPT became publicly accessible in the fall of 2022. Despite their impact, the inner workings of transformers remain poorly understood to this day. For further progress in AI, we believe that understanding logical thinking processes in terms of first-order logic will be crucial.

      In this course, we explore various aspects such as memorization, information compression, and logical reasoning. 

Traditional AI courses typically cover topics like first-order logic and ontologies, but GPT-based transformers—also known as large language models—were not built with these concepts in mind.

      We will explore the structure of modern transformers, such as GPT-3.5 and GPT-4, which power Chat-GPT, alongside traditional AI approaches like first-order logic and ontology building.

      We will cover several key topics, including:

      a) The basic structure of transformers, first-order logic, and Boolean logic.

      b) How the transformer architecture can effectively express certain forms of first-order logic.

      c) Numerical aspects of gradient descent training in transformers, focusing on how a simple, single-layer transformer trained to learn basic logic may encounter issues with unwanted zeros, which can be resolved using normalization techniques.

      d) How a neural network (e.g., ResNet-64) can mistakenly classify grass as a bear, illustrating a phenomenon known as shortcut learning. We will present a general approach to understanding this issue, which we believe also applies to transformers.

      e) Chatbots often need to understand the caller’s intent based on the first utterance, framing this as a text-classification problem. We will review several NLP methods that can be used alongside transformers, as well as how transformers themselves can be applied for this task.

      f) We introduce the Hugging Face ecosystem, which enables you to quickly run transformer models like GPT-J (6B) and experiment with them within minutes.

      g) Ethical and philosophical questions: Is current AI truly intelligent? Could it be trained to be impartial and unbiased?