My name is Benjamin Gerraty, and I am a PhD student at the University of Melbourne. I am interested in using singular learning theory (SLT) to study the structure of singularities in the population loss of neural networks, and using this structure to infer encoded computational structure in the network itself. My research involves modifying well established techniques from quantum field theory (QFT) and the renormalisation group (RG) to encode the bayesian learning of the network as a statistical field theory (SFT), and probe the geometry via correlation functions and RG transformations of natural observables.

Prior to my PhD, I completed my Masters degree at the Univeristy of Melbourne. My thesis investigated aspects of conformal field theory (CFT), which are conformally invariant quantum field theories, for describing statistical mechanical models at fixed points where exact solutions may be found. I focused on computing the structure constants of correlation functions at these fixed points for rational conformal field theories (RCFTs). My thesis can be found here.

I currently work as a Graduate Researcher Academic Associate (GRAA) at the University of Melbourne. I have taught undergraduate classes on linear algebra, calculus I and II, as well as real analysis. My role involves running tutorials, marking exams, assignments, and working as a course assistant designing assignment and exam questions.

Talks

Statistical Field Theory Seminar

Below is a series of seminars I gave on statistical field theory during my PhD.

  • 30/11/23 SFT1: Introduction and 1D Ising Model to Spin-1/2 Part 1 (notes)
  • 14/12/23 SFT1: Introduction and 1D Ising Model to Spin-1/2 Part 2 (notes)
  • 18/01/24 SFT2: 2D Classical Ising Model to 1D Quantum Ising Model (notes)
  • 08/02/24 SFT3: Path Integrals and Fermions Part 1 (notes)
  • 22/02/24 SFT3: Path Integrals and Fermions Part 2 (notes )
  • 07/03/24 SFT3: Path Integrals and Fermions Part 3 (notes )
  • 21/03/24 SFT4: Conformal Transformations and the Virasoro Algebra (notes )

References

  • R. Shankar (2017) Quantum Field Theory and Condensed Matter: An Introduction
  • G. Mussardo (2020) Statistical Field Theory: An Introduction to Exactly Solved Models in Statistical Physics
  • B. Hall (2013) Quantum Theory for Mathematicans
  • R. Volkas (2021) PHYC90007 Quantum Mechanics
  • D. Francesco + (1997) Conformal Field Theory
  • E. Olandini (2020) Lecture Notes of Statistical Mechanics
  • D. Ridout (2014) An Introduction to Conformal Field Theory: AMSI Summer School
  • B. Gerraty (2021) The Structure Constants of the Minimal Models