# Decoding of neural data using cohomological feature extraction

arXiv: https://arxiv.org/abs/1711.07205 · HTML: https://mlsanity.com/paper/1711.07205/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Nov 2017.

## Built on by (most cited first, 6 of 6)

- [Generalized Shape Metrics on Neural Representations](https://mlsanity.com/paper/2110.14739/) (2021)
- [Toroidal Coordinates: Decorrelating Circular Coordinates With Lattice Reduction](https://mlsanity.com/paper/2212.07201/) (2022)
- [Understanding Neural Coding on Latent Manifolds by Sharing Features and Dividing Ensembles](https://mlsanity.com/paper/2210.03155/) (2022)
- [O(k)-Equivariant Dimensionality Reduction on Stiefel Manifolds](https://mlsanity.com/paper/2309.10775/) (2023)
- [Learning Coherent Representations: A Topological Approach to Interpretability](https://mlsanity.com/paper/2606.02841/) (2026)
- [Selecting Interpretable Circular Coordinates from Data](https://mlsanity.com/paper/2607.08230/) (2026)

## Abstract (arXiv)

We introduce a novel data-driven approach to discover and decode features in the neural code coming from large population neural recordings with minimal assumptions, using cohomological feature extraction. We apply our approach to neural recordings of mice moving freely in a box, where we find a circular feature. We then observe that the decoded value corresponds well to the head direction of the mouse. Thus we capture head direction cells and decode the head direction from the neural population activity without having to process the behaviour of the mouse. Interestingly, the decoded values convey more information about the neural activity than the tracked head direction does, with differences that have some spatial organization. Finally, we note that the residual population activity, after the head direction has been accounted for, retains some low-dimensional structure which is correlated with the speed of the mouse.