Symmetries and Continuous Attractors in Disordered Neural Circuits
Bibliographic record
Abstract
Abstract A major challenge in neuroscience is reconciling idealized theoretical models with complex, heterogeneous experimental data. We address this challenge through continuous-attractor networks, which model how neural circuits represent continuous variables such as head direction or spatial location through collective dynamics. Classical continuous-attractor models rely on continuous symmetry in the recurrent weights to generate a manifold of stable states, predicting tuning curves that are identical up to shifts. However, mouse head-direction cells exhibit substantial heterogeneity in their responses, seemingly incompatible with this classical picture. We demonstrate that mammalian circuits could nevertheless rely on the same dynamical mechanisms as classical continuous-attractor models. We construct recurrent neural networks directly from experimental head-direction tuning curves that exhibit quasi-continuous-attractor dynamics, then develop a statistical generative process quantitatively capturing the structure of tuning heterogeneity. This enables large- N analysis, where we show through dynamical mean-field theory that these networks become equivalent to classical ring-attractor models, with Mexican-hat interactions and continuous symmetry that is spontaneously broken, leading to bump states. In the seemingly disordered weights, the continuous symmetry essential to classical models is reflected through eigenvalue degeneracies, positioning spectral structure as a target for detecting continuous-attractor circuits in connectome data. We extend this framework to two-dimensional symmetries, constructing grid-cell models that similarly reduce to classical toroidal attractors. Our work demonstrates that the dynamical mechanisms of classical continuous-attractor models may operate not only in small brains or idealized systems but also in complex mammalian circuits.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".