# Learning Cortico-Muscular Dependence through Orthonormal Decomposition of Density Ratios

arXiv: https://arxiv.org/abs/2410.14697 · HTML: https://mlsanity.com/paper/2410.14697/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 40 references that are in the map.
- First posted on arXiv 4 Oct 2024.

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

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [EEGNet: A Compact Convolutional Network for EEG-based Brain-Computer Interfaces](https://mlsanity.com/paper/1611.08024/) (2016)
- [On Universal Features for High-Dimensional Learning and Inference](https://mlsanity.com/paper/1911.09105/) (2019)
- [The Normalized Cross Density Functional: A Framework to Quantify Statistical Dependence for Random Processes](https://mlsanity.com/paper/2212.04631/) (2022)

## Built on by (most cited first, 3 of 3)

- [A Family of Kernelized Matrix Costs for Multiple-Output Mixture Neural Networks](https://mlsanity.com/paper/2509.24076/) (2025)
- [Adapting HFMCA to Graph Data: Self-Supervised Learning for Generalizable fMRI Representations](https://mlsanity.com/paper/2510.05177/) (2025)
- [A Stable Neural Statistical Dependence Estimator for Autoencoder Feature Analysis](https://mlsanity.com/paper/2603.11428/) (2026)

## Abstract (arXiv)

The cortico-spinal neural pathway is fundamental for motor control and movement execution, and in humans it is typically studied using concurrent electroencephalography (EEG) and electromyography (EMG) recordings. However, current approaches for capturing high-level and contextual connectivity between these recordings have important limitations. Here, we present a novel application of statistical dependence estimators based on orthonormal decomposition of density ratios to model the relationship between cortical and muscle oscillations. Our method extends from traditional scalar-valued measures by learning eigenvalues, eigenfunctions, and projection spaces of density ratios from realizations of the signal, addressing the interpretability, scalability, and local temporal dependence of cortico-muscular connectivity. We experimentally demonstrate that eigenfunctions learned from cortico-muscular connectivity can accurately classify movements and subjects. Moreover, they reveal channel and temporal dependencies that confirm the activation of specific EEG channels during movement. Our code is available at https://github.com/bohu615/corticomuscular-eigen-encoder.