Symmetry and Geometry in Neural Representations

The fields of biological and artificial intelligence are increasingly converging on a shared principle: the geometry and topology of real-world structure play a central role in building efficient, robust, and interpretable representations. 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, principles such as sparsity, equivariance, and compositionality are guiding the development of more generalizable and interpretable models, including new approaches to foundation model distillation. The NeurReps workshop brings these threads together, fostering dialogue among machine learning researchers, neuroscientists, and mathematicians to uncover unifying geometric principles of neural representation. Just as geometry and symmetry once unified the models of 20th-century physics, we believe they may now illuminate the computational foundations of intelligence.