# Liam Carroll

## Who am I

My name is Liam Carroll and I am currently completing a Masters of Mathematics at The University of Melbourne, majoring in Applied Mathematics, but trying to become a jack of all trades and master of none by doing pure mathematics and statistics, too. I am completing the research component of my degree primarily under the supervision of Dr Daniel Murfet as part of the Melbourne Deep Learning Group. I also tutor first year mathematics such as Calculus 1 and Calculus 2 at Melbourne University. When I am not thinking about maths I am probably in a concert hall or on top of a mountain.

## Current work

The topic of my upcoming thesis is Phase Transitions in ReLU Neural Networks, in which I have demonstrated the existence of phase transitions in small ReLU networks using the theoretical grounding of Sumio Watanabe’s Singular Learning Theory.

You can read Draft 0.5 of this thesis, but be warned, this is quite incomplete. You probably shouldn’t read it. But I’ll be sure to upload the real version on October 8th 2021.

## Anything else?

Dan told me to make this website. So, *insert immortal words of Paul Roos here*.