# Riemannian Geometry for the classification of brain states with intracortical brain-computer interfaces

arXiv: https://arxiv.org/abs/2504.05534 · HTML: https://mlsanity.com/paper/2504.05534/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 60 references that are in the map.
- First posted on arXiv 7 Apr 2025.

## Builds on (most cited first, 6 of 6)

- [How much data is needed to train a medical image deep learning system to achieve necessary high accuracy?](https://mlsanity.com/paper/1511.06348/) (2015)
- [A Survey of Geometric Optimization for Deep Learning: From Euclidean Space to Riemannian Manifold](https://mlsanity.com/paper/2302.08210/) (2023)
- [Deep Efficient Continuous Manifold Learning for Time Series Modeling](https://mlsanity.com/paper/2112.03379/) (2021)
- [Neural timescales from a computational perspective](https://mlsanity.com/paper/2409.02684/) (2024)
- [Multiscale Voxel Based Decoding For Enhanced Natural Image Reconstruction From Brain Activity](https://mlsanity.com/paper/2205.14177/) (2022)
- [Hopfield-Enhanced Deep Neural Networks for Artifact-Resilient Brain State Decoding](https://mlsanity.com/paper/2311.03421/) (2023)

## Abstract (arXiv)

This study investigates the application of Riemannian geometry-based methods for brain decoding using invasive electrophysiological recordings. Although previously employed in non-invasive, the utility of Riemannian geometry for invasive datasets, which are typically smaller and scarcer, remains less explored. Here, we propose a Minimum Distance to Mean (MDM) classifier using a Riemannian geometry approach based on covariance matrices extracted from intracortical Local Field Potential (LFP) recordings across various regions during different brain state dynamics. For benchmarking, we evaluated the performance of our approach against Convolutional Neural Networks (CNNs) and Euclidean MDM classifiers. Our results indicate that the Riemannian geometry-based classification not only achieves a superior mean F1 macro-averaged score across different channel configurations but also requires up to two orders of magnitude less computational training time. Additionally, the geometric framework reveals distinct spatial contributions of brain regions across varying brain states, suggesting a state-dependent organization that traditional time series-based methods often fail to capture. Our findings align with previous studies supporting the efficacy of geometry-based methods and extending their application to invasive brain recordings, highlighting their potential for broader clinical use, such as brain computer interface applications.