Quantifying the Uncertainty of Large Language Models Using Spin Glass Theory, with Application to Evolutionary Biology

In recent years, Large Language Models (LLMs) have revolutionized Natural Language Processing with their ability to generate human-like texts. However, a fundamental challenge remains in understanding the underlying mechanisms driving their emergent behaviors, particularly the randomness in their outputs. This talk discusses the application of spin glass theory as a mathematical framework to quantify the uncertainty of LLMs. By making connections between LLMs and spin glass models, which are traditionally used in statistical physics and probability to describe disordered networks with random interactions and frustrations (conflicting constraints), we can gain insights into the high-dimensional optimization landscapes of LLMs, the uncertainty in their outputs, and the role of noise in their learning process.

In the first half of the talk, I will discuss joint work with Matthew Harper on using topology to study the shape of spin glass landscapes, which can help inform the design of optimization algorithms. In the second half, I will discuss joint work with my undergraduate students, Jackson George, Zach Yusaf, and Stephanie Zoltick on LLMs’ temperature-based phase transitions in the context of Flitzing, a unique tradition at Dartmouth College where students send rhymed emails to ask peers out. I will conclude by discussing how this framework can also be applied to studying evolutionary biology.