Ce Ju

Ce Ju, Cuntai Guan

The motor imagery (MI) classification has been a prominent research topic in brain-computer interfaces based on electroencephalography (EEG). Over the past few decades, the performance of MI-EEG classifiers has seen gradual enhancement. In this study, we amplify the geometric deep learning-based MI-EEG classifiers from the perspective of time-frequency analysis, introducing a new architecture called Graph-CSPNet. We refer to this category of classifiers as Geometric Classifiers, highlighting their foundation in differential geometry stemming from EEG spatial covariance matrices. Graph-CSPNet utilizes novel manifold-valued graph convolutional techniques to capture the EEG features in the time-frequency domain, offering heightened flexibility in signal segmentation for capturing localized fluctuations. To evaluate the effectiveness of Graph-CSPNet, we employ five commonly-used publicly available MI-EEG datasets, achieving near-optimal classification accuracies in nine out of eleven scenarios. The Python repository can be found at https://github.com/GeometricBCI/Tensor-CSPNet-and-Graph-CSPNet.

Bruno Aristimunha, Ce Ju, Antoine Collas et al.

Implementations of symmetric positive definite (SPD) matrix-based neural networks for neural decoding remain fragmented across research codebases and Python packages. Existing implementations often employ ad hoc handling of manifold constraints and non-unified training setups, which hinders reproducibility and integration into modern deep-learning workflows. To address this gap, we introduce SPD Learn, a unified and modular Python package for geometric deep learning with SPD matrices. SPD Learn provides core SPD operators and neural-network layers, including numerically stable spectral operators, and enforces Stiefel/SPD constraints via trivialization-based parameterizations. This design enables standard backpropagation and optimization in unconstrained Euclidean spaces while producing manifold-constrained parameters by construction. The package also offers reference implementations of representative SPDNet-based models and interfaces with widely used brain computer interface/neuroimaging toolkits and modern machine-learning libraries (e.g., MOABB, Braindecode, Nilearn, and SKADA), facilitating reproducible benchmarking and practical deployment.

Yuhan Peng, Junwen Dong, Yuzhi Zeng et al.

Graph neural networks face two fundamental challenges rooted in the linear structure of Euclidean vector spaces: (1) Current architectures represent geometry through vectors (directions, gradients), yet many tasks require matrix-valued representations that capture relationships between directions-such as how atomic orientations covary in a molecule. These second-order representations are naturally captured by points on the symmetric positive definite matrices (SPD) manifold; (2) Standard message passing applies shared transformations across edges. Sheaf neural networks address this via edge-specific transformations, but existing formulations remain confined to vector spaces and therefore cannot propagate matrix-valued features. We address both challenges by developing the first sheaf neural network operates natively on the SPD manifold. Our key insight is that the SPD manifold admits a Lie group structure, enabling well-posed analogs of sheaf operators without projecting to Euclidean space. Theoretically, we prove that SPD-valued sheaves are strictly more expressive than Euclidean sheaves: they admit consistent configurations (global sections) that vector-valued sheaves cannot represent, directly translating to richer learned representations. Empirically, our sheaf convolution transforms effectively rank-1 directional inputs into full-rank matrices encoding local geometric structure. Our dual-stream architecture achieves SOTA on 6/7 MoleculeNet benchmarks, with the sheaf framework providing consistent depth robustness.

Antoine Collas, Ce Ju, Nicolas Salvy et al.

Generating realistic brain connectivity matrices is key to analyzing population heterogeneity in brain organization, understanding disease, and augmenting data in challenging classification problems. Functional connectivity matrices lie in constrained spaces, such as the set of symmetric positive definite or correlation matrices, that can be modeled as Riemannian manifolds. However, using Riemannian tools typically requires redefining core operations (geodesics, norms, integration), making generative modeling computationally inefficient. In this work, we propose DiffeoCFM, an approach that enables conditional flow matching (CFM) on matrix manifolds by exploiting pullback metrics induced by global diffeomorphisms on Euclidean spaces. We show that Riemannian CFM with such metrics is equivalent to applying standard CFM after data transformation. This equivalence allows efficient vector field learning, and fast sampling with standard ODE solvers. We instantiate DiffeoCFM with two different settings: the matrix logarithm for covariance matrices and the normalized Cholesky decomposition for correlation matrices. We evaluate DiffeoCFM on three large-scale fMRI datasets with more than 4600 scans from 2800 subjects (ADNI, ABIDE, OASIS-3) and two EEG motor imagery datasets with over 30000 trials from 26 subjects (BNCI2014-002 and BNCI2015-001). It enables fast training and achieves state-of-the-art performance, all while preserving manifold constraints. Code: https://github.com/antoinecollas/DiffeoCFM

Canyang Zhao, Bolin Peng, J. Patrick Mayo et al.

Cross-session nonstationarity in neural activity recorded by implanted electrodes is a major challenge for invasive Brain-computer interfaces (BCIs), as decoders trained on data from one session often fail to generalize to subsequent sessions. This issue is further exacerbated in practice, as retraining or adapting decoders becomes particularly challenging when only limited data are available from a new session. To address this challenge, we propose a Task-Conditioned Latent Alignment framework (TCLA) for cross-session neural decoding. Building upon an autoencoder architecture, TCLA first learns a low-dimensional representation of neural dynamics from a source session with sufficient data. For target sessions with limited data, TCLA then aligns target latent representations to the source in a task-conditioned manner, enabling effective transfer of learned neural dynamics. We evaluate TCLA on the macaque motor and oculomotor center-out dataset. Compared to baseline methods trained solely on target-session data, TCLA consistently improves decoding performance across datasets and decoding settings, with gains in the coefficient of determination of up to 0.386 for y coordinate velocity decoding in a motor dataset. These results suggest that TCLA provides an effective strategy for transferring knowledge from source to target sessions, enabling more robust neural decoding under conditions with limited data.

Ce Ju, Reinmar J. Kobler, Antoine Collas et al.

Neuroimaging provides a critical framework for characterizing brain activity by quantifying connectivity patterns and functional architecture across modalities. While modern machine learning has significantly advanced our understanding of neural processing mechanisms through these datasets, decoding task-specific signatures must contend with inherent neuroimaging constraints, for example, low signal-to-noise ratios in raw electrophysiological recordings, cross-session non-stationarity, and limited sample sizes. This review focuses on machine learning approaches for covariance-based neuroimaging data, where often symmetric positive definite (SPD) matrices under full-rank conditions encode inter-channel relationships. By equipping the space of SPD matrices with Riemannian metrics (e.g., affine-invariant or log-Euclidean), their space forms a Riemannian manifold enabling geometric analysis. We unify methodologies operating on this manifold under the SPD learning framework, which systematically leverages the SPD manifold's geometry to process covariance features, thereby advancing brain imaging analytics.

Ce Ju, Cuntai Guan

Deep learning (DL) has been widely investigated in a vast majority of applications in electroencephalography (EEG)-based brain-computer interfaces (BCIs), especially for motor imagery (MI) classification in the past five years. The mainstream DL methodology for the MI-EEG classification exploits the temporospatial patterns of EEG signals using convolutional neural networks (CNNs), which have remarkably succeeded in visual images. However, since the statistical characteristics of visual images depart radically from EEG signals, a natural question arises whether an alternative network architecture exists apart from CNNs. To address this question, we propose a novel geometric deep learning (GDL) framework called Tensor-CSPNet, which characterizes spatial covariance matrices derived from EEG signals on symmetric positive definite (SPD) manifolds and fully captures the temporospatiofrequency patterns using existing deep neural networks on SPD manifolds, integrating with experiences from many successful MI-EEG classifiers to optimize the framework. In the experiments, Tensor-CSPNet attains or slightly outperforms the current state-of-the-art performance on the cross-validation and holdout scenarios in two commonly-used MI-EEG datasets. Moreover, the visualization and interpretability analyses also exhibit the validity of Tensor-CSPNet for the MI-EEG classification. To conclude, in this study, we provide a feasible answer to the question by generalizing the DL methodologies on SPD manifolds, which indicates the start of a specific GDL methodology for the MI-EEG classification.

Ce Ju, Cuntai Guan

Recent progress in geometric deep learning has drawn increasing attention from the machine learning community toward domain adaptation on symmetric positive definite (SPD) manifolds, especially for neuroimaging data that often suffer from distribution shifts across sessions. These data, typically represented as covariance matrices of brain signals, inherently lie on SPD manifolds due to their symmetry and positive definiteness. However, conventional domain adaptation methods often overlook this geometric structure when applied directly to covariance matrices, which can result in suboptimal performance. To address this issue, we introduce a new geometric deep learning framework that combines optimal transport theory with the geometry of SPD manifolds. Our approach aligns data distributions while respecting the manifold structure, effectively reducing both marginal and conditional discrepancies. We validate our method on three cross-session brain computer interface datasets, KU, BNCI2014001, and BNCI2015001, where it consistently outperforms baseline approaches while maintaining the intrinsic geometry of the data. We also provide quantitative results and visualizations to better illustrate the behavior of the learned embeddings.

Chang Liu, Lixin Fan, Kam Woh Ng et al.

This paper proposes a novel ternary hash encoding for learning to hash methods, which provides a principled more efficient coding scheme with performances better than those of the state-of-the-art binary hashing counterparts. Two kinds of axiomatic ternary logic, Kleene logic and Łukasiewicz logic are adopted to calculate the Ternary Hamming Distance (THD) for both the learning/encoding and testing/querying phases. Our work demonstrates that, with an efficient implementation of ternary logic on standard binary machines, the proposed ternary hashing is compared favorably to the binary hashing methods with consistent improvements of retrieval mean average precision (mAP) ranging from 1\% to 5.9\% as shown in CIFAR10, NUS-WIDE and ImageNet100 datasets.

Yilun Jin, Lixin Fan, Kam Woh Ng et al.

Deep neural networks (DNNs) are known to be prone to adversarial attacks, for which many remedies are proposed. While adversarial training (AT) is regarded as the most robust defense, it suffers from poor performance both on clean examples and under other types of attacks, e.g. attacks with larger perturbations. Meanwhile, regularizers that encourage uncertain outputs, such as entropy maximization (EntM) and label smoothing (LS) can maintain accuracy on clean examples and improve performance under weak attacks, yet their ability to defend against strong attacks is still in doubt. In this paper, we revisit uncertainty promotion regularizers, including EntM and LS, in the field of adversarial learning. We show that EntM and LS alone provide robustness only under small perturbations. Contrarily, we show that uncertainty promotion regularizers complement AT in a principled manner, consistently improving performance on both clean examples and under various attacks, especially attacks with large perturbations. We further analyze how uncertainty promotion regularizers enhance the performance of AT from the perspective of Jacobian matrices $\nabla_X f(X;θ)$, and find out that EntM effectively shrinks the norm of Jacobian matrices and hence promotes robustness.

Ce Ju

This survey is written in summer, 2016. The purpose of this survey is to briefly introduce nonlinear dimensionality reduction (NLDR) in data reduction. The first two NLDR were respectively published in Science in 2000 in which they solve the similar reduction problem of high-dimensional data endowed with the intrinsic nonlinear structure. The intrinsic nonlinear structure is always interpreted as a concept in manifolds from geometry and topology in theoretical mathematics by computer scientists and theoretical physicists. In 2001, the concept of Manifold Learning first appears as an NLDR method called Laplacian Eigenmaps. In a typical manifold learning setup, the data set, also called the observation set, is distributed on or near a low dimensional manifold M embedded in RD, which yields that each observation has a D-dimensional representation. The goal of manifold learning is to reduce these observations as a compact lower-dimensional representation based on the geometric information. The reduction procedure is called the spectral manifold learning. In this paper, we derive each spectral manifold learning with the matrix and operator representation, and we then discuss the convergence behavior of each method in a geometric uniform language. Hence, the survey is named Geometric Foundations of Data Reduction.

Dashan Gao, Ben Tan, Ce Ju et al.

Matrix Factorization has been very successful in practical recommendation applications and e-commerce. Due to data shortage and stringent regulations, it can be hard to collect sufficient data to build performant recommender systems for a single company. Federated learning provides the possibility to bridge the data silos and build machine learning models without compromising privacy and security. Participants sharing common users or items collaboratively build a model over data from all the participants. There have been some works exploring the application of federated learning to recommender systems and the privacy issues in collaborative filtering systems. However, the privacy threats in federated matrix factorization are not studied. In this paper, we categorize federated matrix factorization into three types based on the partition of feature space and analyze privacy threats against each type of federated matrix factorization model. We also discuss privacy-preserving approaches. As far as we are aware, this is the first study of privacy threats of the matrix factorization method in the federated learning framework.

Lixin Fan, Kam Woh Ng, Ce Ju et al.

This paper investigates capabilities of Privacy-Preserving Deep Learning (PPDL) mechanisms against various forms of privacy attacks. First, we propose to quantitatively measure the trade-off between model accuracy and privacy losses incurred by reconstruction, tracing and membership attacks. Second, we formulate reconstruction attacks as solving a noisy system of linear equations, and prove that attacks are guaranteed to be defeated if condition (2) is unfulfilled. Third, based on theoretical analysis, a novel Secret Polarization Network (SPN) is proposed to thwart privacy attacks, which pose serious challenges to existing PPDL methods. Extensive experiments showed that model accuracies are improved on average by 5-20% compared with baseline mechanisms, in regimes where data privacy are satisfactorily protected.

Ce Ju, Ruihui Zhao, Jichao Sun et al.

Prevention of stroke with its associated risk factors has been one of the public health priorities worldwide. Emerging artificial intelligence technology is being increasingly adopted to predict stroke. Because of privacy concerns, patient data are stored in distributed electronic health record (EHR) databases, voluminous clinical datasets, which prevent patient data from being aggregated and restrains AI technology to boost the accuracy of stroke prediction with centralized training data. In this work, our scientists and engineers propose a privacy-preserving scheme to predict the risk of stroke and deploy our federated prediction model on cloud servers. Our system of federated prediction model asynchronously supports any number of client connections and arbitrary local gradient iterations in each communication round. It adopts federated averaging during the model training process, without patient data being taken out of the hospitals during the whole process of model training and forecasting. With the privacy-preserving mechanism, our federated prediction model trains over all the healthcare data from hospitals in a certain city without actual data sharing among them. Therefore, it is not only secure but also more accurate than any single prediction model that trains over the data only from one single hospital. Especially for small hospitals with few confirmed stroke cases, our federated model boosts model performance by 10%~20% in several machine learning metrics. To help stroke experts comprehend the advantage of our prediction system more intuitively, we developed a mobile app that collects the key information of patients' statistics and demonstrates performance comparisons between the federated prediction model and the single prediction model during the federated training process.

Ce Ju, Dashan Gao, Ravikiran Mane et al.

The success of deep learning (DL) methods in the Brain-Computer Interfaces (BCI) field for classification of electroencephalographic (EEG) recordings has been restricted by the lack of large datasets. Privacy concerns associated with EEG signals limit the possibility of constructing a large EEG-BCI dataset by the conglomeration of multiple small ones for jointly training machine learning models. Hence, in this paper, we propose a novel privacy-preserving DL architecture named federated transfer learning (FTL) for EEG classification that is based on the federated learning framework. Working with the single-trial covariance matrix, the proposed architecture extracts common discriminative information from multi-subject EEG data with the help of domain adaptation techniques. We evaluate the performance of the proposed architecture on the PhysioNet dataset for 2-class motor imagery classification. While avoiding the actual data sharing, our FTL approach achieves 2% higher classification accuracy in a subject-adaptive analysis. Also, in the absence of multi-subject data, our architecture provides 6% better accuracy compared to other state-of-the-art DL architectures.

Dashan Gao, Ce Ju, Xiguang Wei et al.

Electroencephalography (EEG) classification techniques have been widely studied for human behavior and emotion recognition tasks. But it is still a challenging issue since the data may vary from subject to subject, may change over time for the same subject, and maybe heterogeneous. Recent years, increasing privacy-preserving demands poses new challenges to this task. The data heterogeneity, as well as the privacy constraint of the EEG data, is not concerned in previous studies. To fill this gap, in this paper, we propose a heterogeneous federated learning approach to train machine learning models over heterogeneous EEG data, while preserving the data privacy of each party. To verify the effectiveness of our approach, we conduct experiments on a real-world EEG dataset, consisting of heterogeneous data collected from diverse devices. Our approach achieves consistent performance improvement on every task.

Ce Ju

The goal of the inverse reinforcement learning (IRL) problem is to recover the reward functions from expert demonstrations. However, the IRL problem like any ill-posed inverse problem suffers the congenital defect that the policy may be optimal for many reward functions, and expert demonstrations may be optimal for many policies. In this work, we generalize the IRL problem to a well-posed expectation optimization problem stochastic inverse reinforcement learning (SIRL) to recover the probability distribution over reward functions. We adopt the Monte Carlo expectation-maximization (MCEM) method to estimate the parameter of the probability distribution as the first solution to the SIRL problem. The solution is succinct, robust, and transferable for a learning task and can generate alternative solutions to the IRL problem. Through our formulation, it is possible to observe the intrinsic property of the IRL problem from a global viewpoint, and our approach achieves a considerable performance on the objectworld.

Ce Ju, Zheng Wang, Cheng Long et al.

Forecasting the motion of surrounding obstacles (vehicles, bicycles, pedestrians and etc.) benefits the on-road motion planning for intelligent and autonomous vehicles. Complex scenes always yield great challenges in modeling the patterns of surrounding traffic. For example, one main challenge comes from the intractable interaction effects in a complex traffic system. In this paper, we propose a multi-layer architecture Interaction-aware Kalman Neural Networks (IaKNN) which involves an interaction layer for resolving high-dimensional traffic environmental observations as interaction-aware accelerations, a motion layer for transforming the accelerations to interaction aware trajectories, and a filter layer for estimating future trajectories with a Kalman filter network. Attributed to the multiple traffic data sources, our end-to-end trainable approach technically fuses dynamic and interaction-aware trajectories boosting the prediction performance. Experiments on the NGSIM dataset demonstrate that IaKNN outperforms the state-of-the-art methods in terms of effectiveness for traffic trajectory prediction.

Zheng Wang, Ce Ju, Gao Cong et al.

Recently, the topic of graph representation learning has received plenty of attention. Existing approaches usually focus on structural properties only and thus they are not sufficient for those spatial graphs where the nodes are associated with some spatial information. In this paper, we present the first deep learning approach called s2vec for learning spatial graph representations, which is based on denoising autoencoders framework (DAF). We evaluate the learned representations on real datasets and the results verified the effectiveness of s2vec when used for spatial clustering.

Ce Ju, Zheng Wang, Xiaoyu Zhang

Trajectory prediction is a critical technique in the navigation of robots and autonomous vehicles. However, the complex traffic and dynamic uncertainties yield challenges in the effectiveness and robustness in modeling. We purpose a data-driven approach socially aware Kalman neural networks (SAKNN) where the interaction layer and the Kalman layer are embedded in the architecture, resulting in a class of architectures with huge potential to directly learn from high variance sensor input and robustly generate low variance outcomes. The evaluation of our approach on NGSIM dataset demonstrates that SAKNN performs state-of-the-art on prediction effectiveness in a relatively long-term horizon and significantly improves the signal-to-noise ratio of the predicted signal.