Area: Inductive Bias in LLMs

Project: "Inductive bias of stochastic gradient descent".

Modern machine learning is all done by a variant of stochastic gradient descent on deep learning networks. This project is a pilot project for stress-testing mathematical models from prof. Strang's expertise ( Langevin stochastic dynamics, Fokker-Planck equations') for the inductive bias and behaviour of SGD. Understanding what the inductive bias of training processes is and whether it might be biased towards deceptive aligned AI has long been understood as important to AI alignment, see for example.

The current project is more preliminary; it does not purport to be able to settle this question directly but aims to make to stresstest mathematical models of that give precise quantitative predictions in toy models. The hope is that these may be eventually scaled to also give quantitative predictions at scale.

Alex Strang is an assistant professor in Statistics and Data Science at UC Berkeley. He served as a postdoctoral instructor in computational and applied mathematics at the University of Chicago from 2020 to 2023. He received his PhD in applied math from Case Western Reserve University in 2020.​

Alex studies the structures of networks that arise in a variety of disciplines including biophysics, ecology, neuroscience, and in competitive systems. In each field, he seeks to understand the interplay between structure and dynamics. He is particularly interested in random walks on networks associated with biophysical processes occurring at the molecular scale. He also works on networks that represent competing agents who evolve according to a training protocol. He draws on tools from discrete topology, non-equilibrium thermodynamics, and functional form game theory to study the interplay of structure and dynamics in these systems.

He also works on Bayesian inference and sparsity promotion via hierarchical hyperpriors. His work here has focused on coordinate ascent methods for MAP estimation, the sensitivity of estimators (and the effective regularizer) to changes in hyperparameters, and variational methods for estimating confidence intervals.

Alexander Gietelink Oldenziel: I am interested in mathematics and AI alignment. I work in Samson Abramsky's group at UCL. Outside of graduate school, I serve as Chief Bard at Timaeus. 

We’re looking for mentees with a strong mathematical background and familiarity with coding & neural networks.

You might be able to visit Berkeley for a period to work on this project.