Symmetry

NeurReps, Symmetry and Geometry in Neural Representations, is a NeurIPS workshop that brings together mathematicians, machine learning researchers and neuroscientists working to uncover the geometric principles shared by brains and machines. In neuroscience, mounting evidence suggests that neural circuits encode task and environmental structure through low-dimensional manifolds, conserved symmetries and structured transformations; in deep learning, sparsity, equivariance and compositionality are guiding the development of more generalisable and interpretable models. Following editions from 202

The conformal bootstrap studies strongly coupled quantum field theories through symmetry, unitarity and crossing symmetry without relying on perturbation theory. This talk reviews recent analytic functional approaches to the numerical bootstrap and introduces new results. It then considers how machine learning could navigate consistent conformal field theories. Neural networks can construct crossing-symmetric correlators from limited physical input; their tendency toward simple, smooth solutions may reveal additional organizing principles behind bootstrap constraints.

Jessica Fintzen discusses symmetry and representation theory, including how mathematical ideas can describe infinitely many related objects at once. The conversation introduces the work recognized by her European Mathematical Society Prize and offers a personal account of research and life in mathematics.

…and explains their relationship to symmetry. The discussion uses accessible examples to show the power of abstraction, then considers the challenges of explaining group theory to non-specialists. Chen also reflects on his experience communicating mathematics and his plans for further study.

Neuronal network computation and computation by avalanche supporting networks are of interest to the fields of physics, computer science (computation theory as well as statistical or machine learning) and neuroscience. Here we show that computation of complex Boolean functions arises spontaneously in threshold networks as a function of connectivity and antagonism (inhibition), computed by logic automata (motifs) in the form of computational cascades. We explain the emergent inverse relationship between the computational complexity of the motifs and their rank-ordering by function probabilities

Figure-ground organisation and perceptual grouping are classic topics in Gestalt and perceptual psychology. They often appear alongside one another in introductory textbook chapters on perception and have a long history of investigation. However, they are typically discussed as separate processes of perceptual organisation with their own distinct phenomena and mechanisms. Here, I will propose that perceptual grouping and figure-ground organisation are strongly linked. In particular, perceptual grouping can provide a basis for, and may share mechanisms with, a wide range of figure-ground princi