#manifolds — Public Fediverse posts

🧠 New paper by Pezon, Schmutz & Gerstner: Linking #NeuralManifolds to circuit structure in recurrent networks.

The study connects two common views of neural activity: low-dimensional #PopulationDynamics (“neural manifolds”) and single-neuron selectivity. Using recurrent network models, the authors show how circuit connectivity constrains both the geometry of neural #manifolds and the tuning of individual neurons.

📄 https://doi.org/10.1016/j.neuron.2025.12.047

#Neuroscience #NeuralDynamics #CompNeuro #RNN

"In the mid-19th century, Bernhard #Riemann conceived of a new way to think about #mathematical spaces, providing the foundation for modern #geometry and #physics."

Cool article on #manifolds on wired.com:

🌍 https://www.wired.com/story/behold-the-manifold-the-concept-that-changed-how-mathematicians-view-space/

#manifolds

📚 New Nat Rev Neurosci #JournalClub by @juangallego: Neural #manifolds: more than the sum of their neurons. He reflects on the shift from single-neuron mappings to population-level #ManifoldRepresentations and suggests that neural manifolds might capture fundamental principles of neural computation and do not just serve as interpretative tools 👍

🌍 https://doi.org/10.1038/s41583-025-00919-0

#Neuroscience #CompNeuro #NeuralManifolds

@axoaxonic Indeed! Here, for everyone else, is the link to the article I originally posted by mistake:

🌍 https://www.cell.com/trends/cognitive-sciences/fulltext/S1364-6613(24)00119-0
📝 Scott, Daniel N. et al. , Thalamocortical architectures for flexible cognition and efficient learning, 2024, Trends in Cognitive Sciences, Volume 28, Issue 8, 739 - 756

#CompNeuro #Neuroscience #NeuralManifolds #manifolds

I've worked out that the injectivity radius under the Euclidean metric for the #unitary group U(n) is π and for real and special subgroups O(n), SO(n), and SU(n) is π√2.

This seems like a pretty basic property, but I can't find a single reference that gives the injectivity radii for any of these groups. Anyone know of one?

#DifferentialGeometry #LieGroups #Manifolds