Research

My research lies at the intersection of artificial intelligence, applied and computational mathematics, brain–computer interfaces, and neuroimaging. I develop geometric AI methods for structured neural data, combining Riemannian geometry, optimization, and machine learning to model and analyze neural signals, neuroimaging data, and neural spiking activity.

A central focus of my research is geometric learning on symmetric positive-definite matrices arising from brain connectivity representations. By respecting the underlying non-Euclidean structure of these data, I develop methods in geometric representation learning, domain adaptation, and generative modeling to improve the accuracy, robustness, and generalizability of neural data analysis.

In brain–computer interfaces and neural decoding, I study variations across subjects, recording sessions, and data distributions. In neuroimaging, I investigate brain connectivity modeling and generation, as well as predicting age, neurological conditions, and cognitive states from brain imaging data. I also study multimodal learning and alignment across EEG, neural spiking, functional MRI, and other neural modalities.

More recently, I have been exploring how generative AI, foundation models, AI agents, and multimodal AI can support neuroimaging analysis and scientific discovery. I also develop open-source software and research infrastructure for reproducible workflows that integrate mathematical methods, AI algorithms, and neural data analysis pipelines.

My long-term goal is to connect mathematical foundations and AI algorithms to real-world neuroscience and medical applications, build open research platforms, and advance the next generation of brain–computer interfaces and NeuroAI.

我的研究位于人工智能、应用与计算数学、脑机接口和神经影像的交叉领域，主要发展面向结构化神经数据的几何人工智能方法。我结合黎曼几何、最优化和机器学习，对神经信号、神经影像数据以及神经脉冲活动进行建模与分析。

我的一个核心研究方向是基于脑连接表示的对称正定矩阵上的几何学习。针对这类数据内在的非欧几里得几何结构，我发展几何表示学习、跨域适应和生成式建模方法，以提升神经数据分析的准确性、鲁棒性和泛化能力。

在脑机接口和神经解码方面，我研究不同受试者、不同采集时段和不同数据分布之间的差异。在神经影像方面，我关注脑连接建模与生成，以及基于脑影像数据的年龄、神经疾病和认知状态预测。我也研究脑电、神经脉冲、功能磁共振成像及其他神经模态之间的多模态学习与对齐。

最近，我尝试探索生成式人工智能、基础模型、人工智能智能体和多模态人工智能如何支持神经影像分析与科学发现。同时，我也开发开放软件和科研基础设施，构建融合数学与统计方法、人工智能算法与神经数据分析流程的可复现研究体系。

我的长期目标是连接数学理论、人工智能算法与真实的神经科学和医学应用，建设开放的研究平台，并推动下一代脑机接口与神经人工智能的发展。

SPD Matrix Learning for Neuroimaging Analysis

SPD (Symmetric Positive-Definite) Matrix Learning has been the central theme of my research over the past five years, with a particular focus on neural data analysis, including EEG, fMRI, and multimodal neuroimaging. My work aims to establish a unified geometric framework for learning from covariance representations of neural signals using the latest artificial intelligence techniques by leveraging the intrinsic structure of symmetric positive-definite matrices. To provide a systematic overview of this growing field, our recent survey, SPD Matrix Learning, was accepted for publication in IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI).

This research direction has been developed through collaborations with researchers in Singapore, France, and Japan, and has led to a series of contributions spanning neural decoding, domain adaptation, multimodal representation learning, generative modeling, and geometric deep learning. Representative works include Tensor-CSPNet, Graph-CSPNet, Deep Optimal Transport, DeepGeoCCA, DiffeoCFM, Sheaf Neural Networks, and the SPDLearn software library. Although these studies address diverse scientific questions, they are unified by a common mathematical perspective: exploiting the geometry of SPD matrices to design principled and effective learning algorithms for neural data.

My research in this area has also been deeply influenced by the broader development of geometric machine learning and statistical neuroimaging. In particular, it builds upon two decades of pioneering work from the French statistical neuroimaging community, as well as advances from the international brain-computer interface research communities. Through my contributions, I hope to further bridge the fields of geometry, machine learning, and neuroscience, and to develop new methodological foundations for understanding complex neural data.

Selected Publications

My recent research contributions on SPD matrix learning have been recognized across leading venues in brain-computer interfaces and artificial intelligence. These works collectively establish a geometric learning framework for covariance-based representation learning and neural data analysis.

Ce Ju, Reinmar Kobler, Antoine Collas, Motoaki Kawanabe, Cuntai Guan, and Bertrand Thirion.
SPD Matrix Learning for Neuroimaging Analysis: Perspectives, Methods, and Challenges.
IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), 2026.
Ce Ju and Cuntai Guan.
Tensor-CSPNet: A Novel Geometric Deep Learning Framework for Motor Imagery Classification.
IEEE Transactions on Neural Networks and Learning Systems (TNNLS), 2023.
Ce Ju and Cuntai Guan.
Graph Neural Networks on SPD Manifolds for Motor Imagery Classification: A Perspective from Time-Frequency Analysis.
IEEE Transactions on Neural Networks and Learning Systems (TNNLS), 2024.
Ce Ju and Cuntai Guan.
Deep Optimal Transport for Domain Adaptation on SPD Manifolds.
Artificial Intelligence, 2025.
Ce Ju, Reinmar J. Kobler, Liyao Tang, Cuntai Guan, and Motoaki Kawanabe.
Deep Geodesic Canonical Correlation Analysis for Covariance-Based Neuroimaging Data.
International Conference on Learning Representations (ICLR), Spotlight, 2024.
Antoine Collas, Ce Ju, Nicolas Salvy, and Bertrand Thirion.
Riemannian Flow Matching for Brain Connectivity Matrices via Pullback Geometry.
Advances in Neural Information Processing Systems (NeurIPS), 2025.
Yuhan Peng, Junwen Dong, Yuzhi Zeng, Hao Li, Ce Ju, Huitao Feng, Diaaeldin Taha, Anna Wienhard, and Kelin Xia.
Sheaf Neural Networks on SPD Manifolds: Second-Order Geometric Representation Learning.
International Conference on Machine Learning (ICML), 2026.
Bruno Aristimunha, Ce Ju, Antoine Collas, Florent Bouchard, Ammar Mian, Bertrand Thirion, Sylvain Chevallier, and Reinmar Kobler.
SPD Learn: A Geometric Deep Learning Python Library for Neural Decoding Through Trivialization.
Open-source software contribution, 2026.

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

Ce Ju, Reinmar Kobler, Antoine Collas, Motoaki Kawanabe, Cuntai Guan, and Bertrand Thirion

Inria, CEA, and Université Paris-Saclay, France.
Advanced Telecommunications Research Institute International and RIKEN Artificial Intelligence Project, Japan.
College of Computing and Data Science and Centre of AI in Medicine, Nanyang Technological University, Singapore.

IEEE Transactions on Pattern Analysis and Machine Intelligence, 2026

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