As large language models (LLMs) proliferate, understanding their emergent behaviors remains a central challenge. This talk proposes a framework for interpreting LLM behavior through the lens of geometry. We argue that the structure of an LLM’s internal semantic space—the high-dimensional arrangement of concepts—serves as a unique “geometric fingerprint.” We will explore how this fingerprint correlates with a model’s disposition along various behavioral axes, such as safety alignment, reasoning ability, and inherent biases. By analyzing the “shape” of a model’s latent knowledge, we can move beyond input-output evaluations toward a more fundamental characterization of its operational logic.

Bio:

Max Springer is an algorithms researcher and science communicator. His research focuses on algorithmic fairness, with an emphasis on theoretical guarantees for bias mitigation and equitable outcomes in machine learning and game-theoretic settings. Springer received his Ph.D. in applied mathematics from the University of Maryland, where he was advised by Mohammad Taghi Hajiaghayi. His thesis, titled “The Price of Fairness in Algorithmic Decision Making,” was supported by an NSF Graduate Research Fellowship. He earned a B.A. in mathematics from Cornell University. In addition to his research, Springer frequently writes science communication articles on mathematics and computer science. He was selected as a 2024 AAAS Mass Media Fellow at Scientific American and is a regular contributor to the magazine.

In-person attendance is open to Princeton University faculty, staff and students.

This talk will be livestreamed and recorded. The recording will be posted to the CITP website, the Princeton University Media Central channel and the CITP YouTube channel.

If you need an accommodation for a disability please contact Jean Butcher at butcher@princeton.edu.

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