Symmetry and Geometry in Neural Representations
A gathering of mathematicians, machine learning researchers, and neuroscientists working to uncover the geometric principles shared by brains and machines.
Exact day within this range to be confirmed by NeurIPS.
The fields of biological and artificial intelligence are 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, sparsity, equivariance, and compositionality are guiding the development of more generalizable and interpretable models.
NeurReps brings these threads together — fostering dialogue among machine learning researchers, neuroscientists, and mathematicians working to uncover unifying geometric principles of neural computation.
Just as geometry and symmetry once unified the models of twentieth-century physics, we believe they will now illuminate the computational foundations of intelligence.
Invited Speakers
Panelists
Joining the Session III discussion, "Topology, Geometry, and Neuroscience: Towards a Unified Framework."
Schedule
Organizers
Area Chairs
Call for Papers
Three tracks, one poster session — a subset of submissions will be selected for spotlight talks.
Proceedings Track
Self-contained, highly-developed research papers. Archivally published in a dedicated PMLR volume. Double-blind review via OpenReview.
Submit on OpenReview →Extended Abstract Track
Early-stage results, negative findings, opinion pieces, or novel datasets. Non-archival — may be posted to arXiv. Double-blind review via OpenReview.
Submit on OpenReview →Findings Track
New this year: high-impact collaborative work between experimentalists and theorists, in any standard preprint format. Single-blind, editorially reviewed by an advisory panel of experts in the field.
Submit on OpenReview →What We’re Looking For
We invite submissions of novel research at the intersection of applied mathematics, deep learning, and computational neuroscience — work that incorporates symmetry and geometry into neural network design, the mechanistic interpretability of neural systems (biological or artificial), or theories of neural computation. We welcome contributions spanning geometric and topological deep learning, computational and theoretical neuroscience, geometric statistics, and topological data analysis.
- Theory and methods for learning invariant and equivariant representations
- Statistical learning theory in the context of topology, geometry, and symmetry
- Representational geometry in neural data
- Learning and leveraging group structure in data
- Equivariant world models for robotics
- Dynamics of neural representations
- Topological deep learning and topological data analysis
- Geometric structure in language
- Geometric and topological analysis of generative models
- Symmetries, dynamical systems, and learning
We hope to see both theoretical contributions and applied results in domains including vision, motor control, navigation, and language, as well as the use of diverse mathematical objects such as quotient spaces, fiber bundles, Lie groups, Riemannian manifolds, graphs, topological domains, and group representations. We also welcome benchmark datasets and software. This list is guidance, not exhaustive — if you are unsure whether your work is in scope, please reach out to the organizers.
A Novel Findings Track
NeurReps has long been a primary home for broad computational and theoretical neuroscience work outside the scope of traditional machine learning venues. To honor and extend NeurIPS’s historic ties to systems neuroscience, we are introducing a Findings Track for high-impact collaborative work between experimentalists and theorists — early versions of work of the caliber published in venues such as Cell, Nature, or Science, with the goal of early community exposure and dialogue between ML researchers and experimental neuroscientists.
The track is designed with minimal barriers to entry: no page limits, and any standard preprint format is welcome. No complex machine learning or deep learning is required — just some form of geometry, topology, or algebra. For example, work such as Gardner et al.’s Toroidal topology of population activity in grid cells (Nature, 2022) would be a natural fit. Because lab and dataset identity are often inseparable from the work, submissions are single-blind. Contributors present as posters, with a subset selected for spotlight talks.
Dual Submission Policy
Papers in the Proceedings Track will be archivally published. Thus, submissions containing content that has been published or submitted elsewhere must include at least 30% new, unpublished/unsubmitted material. Likewise, to publish a NeurReps paper in another venue down the line, authors must add at least 30% new material. There are no restrictions on Extended Abstract submissions.
All submitting authors need an OpenReview profile for the Proceedings and Extended Abstract tracks — creating one can take a few days, so please don't wait until the deadline. For the Findings track, only the submitting author needs a profile; co-authors can be added by email.
Sponsors
Past Editions
A running history of NeurReps at NeurIPS — organizers, speakers, and proceedings from each year.