#manifolds — Public Fediverse posts

@LMPrida shares an inspiring perspective in @thetransmitter on how #neuron subtypes may control large-scale #NeuralPopulation activity, from #manifolds to #ripples:

🌍 https://www.thetransmitter.org/brain-inspired/liset-de-la-prida-explains-how-neuron-subtypes-may-control-the-activity-of-large-neural-populations-from-manifolds-to-ripples/

#CompNeuro #Neuroscience

🧠 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

🧠 New preprint by Guardamagna et al.: Using large-scale recordings in #rat pups, the authors show that toroidal #manifolds in #MEC emerge by P10, before eye and ear opening, upright gait, and active exploration. Ring-like manifolds appear even earlier, by P9. External spatial experience seems to align these preconfigured internal maps only later, as pups begin to navigate.

📄 https://doi.org/10.64898/2026.03.10.710908

#Neuroscience #GridCells #NeuralDynamics

🧠 New work by Codol et al. who show that #MotorCortex dynamics are remarkably conserved across #mice, #monkeys, and #humans. Despite very different #behaviors, #NeuralPopulation activity follows similar dynamical rules on low-dimensional #manifolds. Species differences arise mainly from the geometry of trajectories within this shared #DynamicalSystem.

📄 https://doi.org/10.64898/2026.03.06.709637

#Neuroscience #CompNeuro #NeuralDynamics

[ Lumo Kaŭstikaĵo ]

Matematika diferenciala geometrio priskribanta la ebenan koverton de kurboj spuritaj de radioj disvastiĝantaj tra manifoldo. 🤓 #nerd

~briletanta~

\eZ

#miksang #dailypic #aphotoaday
#Esperanto #photography #photo
#physics #optics #mathematics #maths
#caustics #differentialgeometry
#manifold #manifolds
#shimmering

🧠 New preprint by Behrad et al. introducing #fastDSA, a much faster way to compare neural systems at the level of their dynamics, not just geometry or task performance.

What’s cool here: similarity is defined by shared #VectorFields, i.e. by the computational mechanism itself. This provides the first tool for mechanistic comparison of neural computations (to my knowledge).

🌍 https://arxiv.org/abs/2511.22828
💻 https://github.com/CMC-lab/fastDSA

#Neuroscience #CompNeuro #NeuralDynamics #Manifolds #DynamicalSystems

"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

There is a new episode on the #TheoreticalNeurosciencePodcast on low-dimensional #manifolds in #MotorCortex with Sara Solla ✌️, one of the pioneers of the manifold modelling approach in #Neuroscience.

🌍 http://theoreticalneuroscience.no/thn36

#CompNeuro #ComputationalNeuroscience

🧠 New #preprint by Komi et al. (2025): Neural #manifolds that orchestrate walking and stopping. Using #Neuropixels recordings from the lumbar spinal cord of freely walking rats, they show that #locomotion arises from rotational #PopulationDynamics within a low-dimensional limit-cycle #manifold. When walking stops, the dynamics collapse into a postural manifold of stable fixed points, each encoding a distinct pose.

🌍 https://doi.org/10.1101/2025.11.08.687367

#CompNeuro #NeuralDynamics #Attractor #Neuroscience

@axoaxonic @adredish Fully agree 👍 Horner's framework really begs for a formal dynamical model: defining trajectories, #attractors, and #manifolds within that 3D space. Something that could turn his conceptual #StateSpace into a genuine #computational theory of #memory dynamics.

I didn’t know Redish's book ("Beyond the Cognitive Map") before your comment! Sounds highly relevant and I’ll definitely put it on my reading list 👌

🚀✨ Behold, a #groundbreaking revelation: #counting isn't just for toddlers anymore! This esteemed cabal of academics has boldly ventured into the complex realm of... counting #characters with #imaginary #shapes. 🤯 #Manifolds have never felt so, well, manipulated! 💁‍♂️🔍
https://transformer-circuits.pub/2025/linebreaks/index.html #revelation #academic #research #HackerNews #ngated

When models manipulate manifolds: The geometry of a counting task

https://transformer-circuits.pub/2025/linebreaks/index.html

#HackerNews #models #manifolds #geometry #counting #task #AI #research

📚 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

'Estimation of Local Geometric Structure on Manifolds from Noisy Data', by Yariv Aizenbud, Barak Sober.

http://jmlr.org/papers/v26/25-0183.html

#manifold #manifolds #submanifold

'Sliced-Wasserstein Distances and Flows on Cartan-Hadamard Manifolds', by Clément Bonet, Lucas Drumetz, Nicolas Courty.

http://jmlr.org/papers/v26/24-0359.html

#manifolds #manifold #wasserstein

'Manifold Learning by Mixture Models of VAEs for Inverse Problems', by Giovanni S. Alberti, Johannes Hertrich, Matteo Santacesaria, Silvia Sciutto.

http://jmlr.org/papers/v25/23-0396.html

#autoencoders #manifold #manifolds

By the way, you can see the poster I presented in 2017 here: https://aten.cool/documents/NCUWM_poster.pdf

This kind of idea appears in my work with Semin Yoo on constructing manifolds from quasigroups, so I'm still up to some of the same things seven years later.

Quasigroup manifolds paper: https://arxiv.org/abs/2110.05660

#algebra #topology #manifolds #UniversalAlgebra #combinatorics

Nonlinear #manifolds underlie #NeuralPopulation activity during #behaviour – new #preprint by Fortunato et al. (2023)

🌍 https://www.biorxiv.org/content/10.1101/2023.07.18.549575v2

#CompNeuro #Neuroscoence

I have a really weird #ICanHazPDF request. I remember a #MathOverflow question about the classification of #manifolds in which a paper (apparently unpublished) was linked from the author's website. I think it was by either Manolescu or Nicolaescu and it was a very nice, short survey of the current state of the classification. I thought I had a copy of this, but I can't find it or the original MathOverflow question. I've tried DuckDuckGo, Yandex, Google, and Bing to no avail. It's not this (https://pi.math.cornell.edu/~hatcher/Papers/3Msurvey.pdf) by Allen Hatcher. Did I hallucinate this survey article?

#topology #AlgebraicTopology #geometry

Looking forward to tomorrow’s 2nd workshop on #symmetry, invariance and #NeuralRepresentations at the #BernsteinConference: #GroupTheory, #manifolds, and #Euclidean vs #nonEuclidean #geometry #perception … I’m pretty excited 🤟😊
#CompNeuro #computationalneuroscience

🌏 https://bernstein-network.de/bernstein-conference/program/satellite-workshops/neural-representations/

Discussing slide 49/237 with #chatgpt

#Embedded vs #Immersed #Manifolds

https://chat.openai.com/share/6cbf3e83-a52d-469e-8ea8-c003c06a1073

and with #bard

https://g.co/bard/share/f9fd23a81646

Nonconvex-nonconcave min-max optimization on Riemannian manifolds

Andi Han, Bamdev Mishra, Pratik Jawanpuria, Junbin Gao

Action editor: Zhihui Zhu.

https://openreview.net/forum?id=EDVIHPZhFo

#manifolds #minimax #nonconcave

Tomorrow I will give a(n online) talk at the ICIAM within the minisymposium “Approximation and modeling with manifold-valued data” about the Riemannian DC algorithm
at 18:05 JST (11:05 CEST). The slides are already online at https://ronnybergmann.net/talks/2023-ICIAM-Difference-of-Convex.pdf #Manifolds #ICIAM #Optimization

ManifoldsBase.jl 0.14.10 introduces an interface to implement `Weigarten(M, p, X, V)` maps (https://juliamanifolds.github.io/ManifoldsBase.jl/dev/functions/#ManifoldsBase.Weingarten-Tuple{AbstractManifold,%20Any,%20Any,%20Any}).
Together with the new ManifoldDiff.jl 0.3.6 this allows for a generic implementation of a conversion from Euclidean to Riemannian Hessians for embedded submanifolds, see https://juliamanifolds.github.io/ManifoldDiff.jl/dev/library/#ManifoldDiff.riemannian_Hessian-Tuple{AbstractManifold,%20Any,%20Any,%20Any,%20Any}. #Manifolds #Julia

I will be at ICML for the workshops later this week. Thanks to @emtiyaz and Thomas (https://moellenh.github.io) for inviting me to the workshop on “Duality Principles for Modern Machine Learning” (https://dp4ml.github.io); hope to also attend the TAG-ML workshop https://www.tagds.com/events/conference-workshops/tag-ml23 Friday.

#ICML #Duality #Manifolds