arXiv subjects

Ce Ju

Publications and source records attributed to Ce Ju.

At least 19 recordsLinked to original sources

arXiv2026

Benchmarking External Generalization of SPD Matrix Learning for Resting-State fMRI Connectome Prediction

Resting-state functional magnetic resonance imaging (rs-fMRI) functional connectivity (FC) matrices are widely used for individual-level prediction, but strong performance within one cohort may not generalize to a new cohort. We ask whether within-dataset performance remains when the test data come from an entirely held-out rs-fMRI dataset. Each scan is represented as a regularized symmetric positive definite (SPD) correlation connectome, which allows methods to use the geometry of the SPD manifold. We introduce a reproducible age-prediction benchmark across six rs-fMRI datasets: COBRE, ADNIDOD, Cam-CAN, ABIDE, OASIS-3, and ADNI. The benchmark compares a vectorized correlation baseline, Tangent-Space Ridge, SPDNet, and split-wise Riemannian harmonization under within-dataset GroupKFold, pooled GroupKFold, and leave-one-dataset-out (LODO) evaluation. Within-dataset and pooled GroupKFold results are substantially more favorable than LODO results. When an entire dataset is held out, prediction error increases, differences among methods narrow, and performance is strongly affected by age-range mismatch and cohort heterogeneity. The benchmark provides common inputs, model settings, data splits, and analysis scripts so that future SPD matrix learning methods can be evaluated under the same external-validation protocol.

eess.SP↗

arXiv2026

Bringing analytic rigor to agentic AI for science: The Brain Researcher platform for neuroimaging data analysis

AI agents can execute scientific analyses, but an analytic output becomes a defensible claim only after alternatives are weighed and the claim is limited to what the evidence supports. Agents may reproduce failures including selective analysis, premature declarations of success and optimization of imperfect criteria. We present Brain Researcher, an agentic research harness operating in a neuroimaging researcher's computational environment under rules for admissible analyses, required checks and claim scope. In benchmarks, Brain Researcher increased first-choice tool-selection accuracy across seven models by 70.2 percentage points (23.3% without it versus 93.6% with it) and verifiable grounding from 4.6% to 22.0%. In collaborator-led and self-evolving studies, multiverse analyses exposed analytic-choice sensitivity, and scientific review classified claims as accepted, qualified, revised, blocked, rejected or deferred. By linking decisions to evidence and provenance, Brain Researcher embeds methodological judgment within the workflow, not after it.

cs.AI↗

arXiv2026

Sheaf Neural Networks on SPD Manifolds: Second-Order Geometric Representation Learning

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.

cs.LG↗

arXiv2026

SPD Learn: A Geometric Deep Learning Python Library for Neural Decoding Through Trivialization

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.

q-bio.NC↗

arXiv2026

Cross-Session Decoding of Neural Spiking Data via Task-Conditioned Latent Alignment

Training a high-performing neural decoder can be difficult when only limited data are available from a recording session. To address this challenge, we propose a Task-Conditioned Latent Alignment framework (TCLA) for cross-session neural decoding with limited target-session data. Building upon an autoencoder architecture, TCLA first learns a low-dimensional neural representation from a source session with sufficient data. For target sessions with limited data, TCLA then aligns the target latent representations to the source session in a task-conditioned manner, enabling effective transfer of learned neural representations to support decoder training in the target session. We evaluate TCLA on the macaque motor and oculomotor center-out datasets. 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, improving neural decoding performance under conditions with limited target-session data.

cs.LG↗

arXiv2025

Riemannian Flow Matching for Brain Connectivity Matrices via Pullback Geometry

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

cs.LG↗

arXiv2025

SPD Matrix Learning for Neuroimaging Analysis: Perspectives, Methods, and Challenges

Neuroimaging provides essential tools for characterizing brain activity, structure, and connectivity through modalities that capture complementary aspects of brain organization. Across these diverse modalities, a unifying perspective arises when measurements are modeled as symmetric positive-definite (SPD)-valued representations through appropriate estimation or regularization procedures. Endowed with Riemannian geometry, the SPD manifold provides a non-Euclidean framework for principled statistical inference and machine learning on these representations. This review organizes these analytical and learning approaches within a framework for SPD matrix learning that connects classical geometric statistics with modern machine learning across neuroimaging and neurophysiological applications. We systematically survey the progression from modality-specific representations to geometric shallow and deep learning paradigms, highlighting how SPD matrix learning preserves underlying structural constraints while extending to modern AI applications in neuroimaging and brain-computer interfaces.

cs.LG↗

arXiv2023

Score-Based Data Generation for EEG Spatial Covariance Matrices: Towards Boosting BCI Performance

The efficacy of Electroencephalogram (EEG) classifiers can be augmented by increasing the quantity of available data. In the case of geometric deep learning classifiers, the input consists of spatial covariance matrices derived from EEGs. In order to synthesize these spatial covariance matrices and facilitate future improvements of geometric deep learning classifiers, we propose a generative modeling technique based on state-of-the-art score-based models. The quality of generated samples is evaluated through visual and quantitative assessments using a left/right-hand-movement motor imagery dataset. The exceptional pixel-level resolution of these generative samples highlights the formidable capacity of score-based generative modeling. Additionally, the center (Frechet mean) of the generated samples aligns with neurophysiological evidence that event-related desynchronization and synchronization occur on electrodes C3 and C4 within the Mu and Beta frequency bands during motor imagery processing. The quantitative evaluation revealed that 84.3% of the generated samples could be accurately predicted by a pre-trained classifier and an improvement of up to 8.7% in the average accuracy over ten runs for a specific test subject in a holdout experiment.

eess.SP↗

arXiv2022

Graph Neural Networks on SPD Manifolds for Motor Imagery Classification: A Perspective from the Time-Frequency Analysis

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.

eess.SP↗

arXiv2022

Tensor-CSPNet: A Novel Geometric Deep Learning Framework for Motor Imagery Classification

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.

eess.SP↗

arXiv2022

Deep Optimal Transport for Domain Adaptation on SPD Manifolds

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.

cs.LG↗

arXiv2021

Ternary Hashing

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 {\L}ukasiewicz 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.

cs.AI↗

arXiv2020

Rethinking Uncertainty in Deep Learning: Whether and How it Improves Robustness

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 $\nabla_X f(X;\theta)$, and find out that EntM effectively shrinks the norm of Jacobian matrices and hence promotes robustness.

cs.LG↗

arXiv2020

Survey: Geometric Foundations of Data Reduction

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.

cs.LG↗

arXiv2020

Privacy Threats Against Federated Matrix Factorization

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.

cs.CR↗

arXiv2020

Rethinking Privacy Preserving Deep Learning: How to Evaluate and Thwart Privacy Attacks

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.

cs.LG↗

arXiv2020

Privacy-Preserving Technology to Help Millions of People: Federated Prediction Model for Stroke Prevention

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.

cs.LG↗

arXiv2020

Federated Transfer Learning for EEG Signal Classification

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.

cs.LG↗