Learning the dimension of BiMap layers in SPD networks

Abstract

Symmetric Positive Definite (SPD) networks, starting from the SPDNet, have demonstrated competitive performance for EEG-based Motor Imagery Brain-Computer Interfaces (BCIs) by exploiting the Riemannian geometry of covariance matrices. The critical hyperparameter of the BiMap layer, the core building block of all SPDNet-like networks, is its output dimension m, which controls both the geometry of the learned submanifold and the computational cost of subsequent layers. Yet, previous works either fix this dimension arbitrarily to half the number of available electrodes, with no theoretical grounding or data-driven justification, or perform a computationally intensive grid search. We propose an adaptive-dimension BiMap (ABiMap) layer that jointly learns the filter matrix and its output dimension via backpropagation, by continuously interpolating between two consecutive SPD manifold outputs along a Riemannian geodesic on the SPD manifold and dynamically expanding or shrinking the active set of spatial filters during training. Experiments on seven public Motor Imagery BCI benchmark datasets show that ABiMap matches or exceeds the classification accuracy of the standard BiMap layer with the arbitrary choice of the dimension while learning a significantly lower output dimension, largely independent of the electrode count. This yields a reduced carbon footprint while also improving performance, particularly on datasets with a large number of electrodes. ABiMap is an out-of-the-shell replacement for the standard BiMap layer. Python code is released as open-source.

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BibTeX RIS

BibTeX

@misc{meftah2026learning,
  title = {{Learning the dimension of BiMap layers in SPD networks}},
  author = {Yacine Meftah and Marco Congedo and Laurent Bougrain},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  url = {https://hal.science/hal-05753369v1},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Learning the dimension of BiMap layers in SPD networks
AU  - Yacine Meftah
AU  - Marco Congedo
AU  - Laurent Bougrain
PY  - 2026
DA  - 2026/09/17
PB  - HAL
UR  - https://hal.science/hal-05753369v1
AB  - Symmetric Positive Definite (SPD) networks, starting from the SPDNet, have demonstrated competitive performance for EEG-based Motor Imagery Brain-Computer Interfaces (BCIs) by exploiting the Riemannian geometry of covariance matrices. The critical hyperparameter of the BiMap layer, the core building block of all SPDNet-like networks, is its output dimension m, which controls both the geometry of the learned submanifold and the computational cost of subsequent layers. Yet, previous works either fix this dimension arbitrarily to half the number of available electrodes, with no theoretical grounding or data-driven justification, or perform a computationally intensive grid search. We propose an adaptive-dimension BiMap (ABiMap) layer that jointly learns the filter matrix and its output dimension via backpropagation, by continuously interpolating between two consecutive SPD manifold outputs along a Riemannian geodesic on the SPD manifold and dynamically expanding or shrinking the active set of spatial filters during training. Experiments on seven public Motor Imagery BCI benchmark datasets show that ABiMap matches or exceeds the classification accuracy of the standard BiMap layer with the arbitrary choice of the dimension while learning a significantly lower output dimension, largely independent of the electrode count. This yields a reduced carbon footprint while also improving performance, particularly on datasets with a large number of electrodes. ABiMap is an out-of-the-shell replacement for the standard BiMap layer. Python code is released as open-source.
ER  -

Abstract

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