In the context of EEG-based Brain-Computer Interfaces (BCIs), Deep Riemannian Neural Networks (DRNNs) have emerged as a state-ofthe-art framework, particularly in classifying motor imagery.A crucial component of these networks is the activation function, which must preserve the manifold's geometry.The ReEig function is the prevailing choice, providing a foundational but potentially limited nonlinear transformation.This work investigates whether alternative activation functions can improve the performance of DRNNs.We conduct a comparative analysis of the standard ReEig function against four alternatives -cosh, sinh, ReLU, and SiLU -within the SPDNet and EE(G)-SPDNet architectures.The experiments are performed on three public motor imagery datasets: BCI Competition IV2a, PhysioNetMI, and Cho.The results consistently indicate that alternative nonlinear functions perform better than the conventionally used ReEig, achieving superior classification accuracy.

Deep learning has shown impressive results, obtained at the cost of training huge neural networks.However, the larger the architecture, the higher the computational, financial, and environmental costs during training and inference.We aim at reducing both training and inference durations.We focus on Neural Architecture Growth, which can increase the size of a small model when needed, directly during training using information from the backpropagation.We expand existing work and freely grow neural networks in the form of any Directed Acyclic Graph.We design strategies that reduce excessive computations and steer network growth toward more parameter-efficient architectures.

Circular and non-flat data distribution are prevalent across diverse domains of data science, yet their specific geometric structures often remain underutilized in machine learning frameworks. A principled approach to accounting for the underlying geometry of such data is pivotal, particularly when extending statistical models, like the pervasive Gaussian distribution. In this work, we tackle those issue by focusing on the manifold of symmetric positive definite matrices, a key focus in information geometry. We introduced a non-isotropic wrapped Gaussian by leveraging the exponential map, we derive theoretical properties of this distribution and propose a maximum likelihood framework for parameter estimation. Furthermore, we reinterpret established classifiers on SPD through a probabilistic lens and introduce new classifiers based on the wrapped Gaussian model. Experiments on synthetic and real-world datasets demonstrate the robustness and flexibility of this geometry-aware distribution, underscoring its potential to advance manifold-based data analysis. This work lays the groundwork for extending classical machine learning and statistical methods to more complex and structured data.

Code modulated Visually Evoked Potentials (cVEP) is an emerging paradigm for Brain-Computer Interfaces (BCIs) that offers reduced calibration times.However, cVEP-based BCIs still encounter challenges related to cross-session/subject variabilities.As Riemannian approaches have demonstrated good robustness to these variabilities, we propose the first study of deep Riemannian neural architectures, namely SPDNets, on cVEP-based BCIs.To evaluate their performance with respect to subject variabilities, we conduct classification tasks in a domain adaptation framework using a burst cVEP open dataset.This study demonstrates that SPDNet yields the best accuracy with single-subject calibration and promising results in domain adaptation.

Electroencephalography (EEG) data is often collected from diverse contexts involving different populations and EEG devices. This variability can induce distribution shifts in the data $X$ and in the biomedical variables of interest $y$, thus limiting the application of supervised machine learning (ML) algorithms. While domain adaptation (DA) methods have been developed to mitigate the impact of these shifts, such methods struggle when distribution shifts occur simultaneously in $X$ and $y$. As state-of-the-art ML models for EEG represent the data by spatial covariance matrices, which lie on the Riemannian manifold of Symmetric Positive Definite (SPD) matrices, it is appealing to study DA techniques operating on the SPD manifold. This paper proposes a novel method termed Geodesic Optimization for Predictive Shift Adaptation (GOPSA) to address test-time multi-source DA for situations in which source domains have distinct $y$ distributions. GOPSA exploits the geodesic structure of the Riemannian manifold to jointly learn a domain-specific re-centering operator representing site-specific intercepts and the regression model. We performed empirical benchmarks on the cross-site generalization of age-prediction models with resting-state EEG data from a large multi-national dataset (HarMNqEEG), which included $14$ recording sites and more than $1500$ human participants. Compared to state-of-the-art methods, our results showed that GOPSA achieved significantly higher performance on three regression metrics ($R^2$, MAE, and Spearman's $\rho$) for several source-target site combinations, highlighting its effectiveness in tackling multi-source DA with predictive shifts in EEG data analysis. Our method has the potential to combine the advantages of mixed-effects modeling with machine learning for biomedical applications of EEG, such as multicenter clinical trials.

Riemannian BCI based on EEG covariance have won many data competitions and achieved very high classification results on BCI datasets. To increase the accuracy of BCI systems, we propose an approach grounded on Riemannian geometry that extends this framework to functional connectivity measures. This paper describes the approach submitted to the Clinical BCI Challenge-WCCI2020 and that ranked 1ston the task 1 of the competition.

Dimensionality reduction of high-dimensional electroencephalography (EEG) covariance matrices is crucial for effective utilization of Riemannian geometry in Brain-Computer Interfaces (BCI). In this paper, we propose a novel similarity-based classification method that relies on dimensionality reduction of EEG covariance matrices. Conventionally, the dimension of the original high-dimensional space is reduced by projecting into one low-dimensional space, and the similarity is learned only based on the single space. In contrast, our method, MUltiple SUbspace Mdm Estimation (MUSUME), obtains multiple low-dimensional spaces that enhance class separability by solving the proposed optimization problem, then the similarity is learned in each low-dimensional space. This multiple projection approach encourages finding the space that is more useful for similarity learning. Experimental evaluation with high-dimensionality EEG datasets (128 channels) confirmed that MUSUME proved significant improvement for classification (p < 0.001) and also it showed the potential to beat the existing method relying on only one subspace representation.

Symmetric positive definite (SPD) matrices permeates numerous scientific disciplines, including machine learning, optimization, and signal processing. Equipped with a Riemannian geometry, the space of SPD matrices benefits from compelling properties and its derived Riemannian mean is now the gold standard in some applications, e.g. brain-computer interfaces (BCI). This paper addresses the problem of averaging covariance matrices with missing variables. This situation often occurs with inexpensive or unreliable sensors, or when artifact-suppression techniques remove corrupted sensors leading to rank deficient matrices, hindering the use of the Riemannian geometry in covariance-based approaches. An alternate but questionable method consists in removing the matrices with missing variables, thus reducing the training set size. We address those limitations and propose a new formulation grounded in geodesic convexity. Our approach is evaluated on generated datasets with a controlled number of missing variables and a known baseline, demonstrating the robustness of the proposed estimator. The practical interest of this approach is assessed on real BCI datasets. Our results show that the proposed average is more robust and better suited for classification than classical data imputation methods.

Building upon advances on optimal transport and anomaly detection, we propose a generalization of an unsupervised and automatic method for detection of significant deviation from reference signals. Unlike most existing approaches for anomaly detection, our method is built on a non-parametric framework exploiting the optimal transportation to estimate deviation from an observed distribution. We described the theoretical background of our method and demonstrate its effectiveness on two datasets: an industrial predictive maintenance task based on audio recording and a detection of anomalous breathing relying on brain signals. In this type of problem, no negative or faulty samples are seen during training and the objective is to detect any abnormal sample without raising false alarm. The proposed approach outperforms all state-of-the-art methods for anomaly detection on the two considered datasets.

Overcomplete representations and dictionary learning algorithms are attracting a growing interest in the machine learning community. This paper addresses the emerging problem of comparing multivariate overcomplete dictionaries. Despite a recurrent need to rely on a distance for learning or assessing multivariate overcomplete dictionaries, no metrics in their underlying spaces have yet been proposed. Henceforth we propose to study overcomplete representations from the perspective of matrix manifolds. We consider distances between multivariate dictionaries as distances between their spans which reveal to be elements of a Grassmannian manifold. We introduce set-metrics defined on Grassmannian spaces and study their properties both theoretically and numerically. Thanks to the introduced metrics, experimental convergences of dictionary learning algorithms are assessed on synthetic datasets. Set-metrics are embedded in a clustering algorithm for a qualitative analysis of real EEG signals for Brain-Computer Interfaces (BCI). The obtained clusters of subjects are associated with subject performances. This is a major methodological advance to understand the BCI-inefficiency phenomenon and to predict the ability of a user to interact with a BCI.

Many complex systems, ranging from neural cell assemblies to insect societies, involve and rely on some division of labor. How to enforce such a division in a decentralized and distributed way, is tackled in this paper, using a spiking neuron network architecture. Specifically, a spatio-temporal model called SpikeAnts is shown to enforce the emergence of synchronized activities in an ant colony. Each ant is modelled from two spiking neurons; the ant colony is a sparsely connected spiking neuron network. Each ant makes its decision (among foraging, sleeping and self-grooming) from the competition between its two neurons, after the signals received from its neighbor ants. Interestingly, three types of temporal patterns emerge in the ant colony: asynchronous, synchronous, and synchronous periodic foraging activities - similar to the actual behavior of some living ant colonies. A phase diagram of the emergent activity patterns with respect to two control parameters, respectively accounting for ant sociability and receptivity, is presented and discussed.