[Colloquium] Symmetry in Brains and Machines: A Physics Perspective

Speaker: Nina Miolane, UCSB

Title: Symmetry in Brains and Machines: A Physics Perspective

Abstract: Symmetry—the invariance of a system's properties under certain transformations—is a central concept in physics, governing fundamental laws from particle interactions to fluid dynamics. In this talk, I will show how this same principle provides a powerful mathematical lens for understanding intelligence in both brains and machines.

I will begin with the simplest learning task that requires an understanding of symmetry: group composition. Both mathematically and empirically, I will demonstrate that brains and machines solve this task in a strikingly similar way. They converge on a spectral approach, relying on universal representations that transcend biological and artificial substrates.

Building on this observation, I will explore how we can leverage spectral theory to design novel, symmetry-aware AI systems. Drawing from experimental physics, I will introduce the selective group bispectrum to embed exact symmetry directly into neural networks, driving significant gains in both efficiency and robustness.

Ultimately, this talk will offer a unifying physics perspective on neuroscience and AI. In physics, symmetry radically transformed how we model the world with pen and paper; in neuroscience and AI, it is poised to transform how we model it with neurons and silicon.