发表机构
University of Strathclyde（斯特拉斯克莱德大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出GVD-CFM，一种基于图变量动态连接和流匹配的条件生成模型，用于高分辨率脑网络生成，在EEG数据集上实现最佳保真度与效率。
AI 中文摘要
高分辨率动态功能连接（DFC）能够揭示快速演变的脑网络交互，但短时间窗口会产生噪声较大且通常为低秩的协方差估计。图变量动态（GVD）连接通过用稳定的试验级支持调制快速的瞬时交互来解决这一问题。这抑制了虚假波动，并强调了持久且信息丰富的连接。我们证明，Hadamard构造将低秩瞬时连接从半正定锥提升到正定锥，无需岭正则化或事后投影即可在SPD流形上保持高分辨率轨迹。我们引入了GVD-CFM，一种用于高分辨率动态连接的条件生成模型。每个试验在乘积黎曼流形上表示为SPD GVD矩阵，然后通过全局对数欧几里得微分同胚和可逆时间DCT基进行映射。基于Transformer的条件流模型联合建模所有频谱模式，并在欧几里得坐标中非自回归地生成完整轨迹，同时保持与有效SPD序列的精确对应。保留完整的DCT基还使得无需重新训练即可在更密集的时间网格上进行解码。在多个EEG运动想象数据集上，GVD-CFM在保持分布保真度、时间动态保留和合成到真实分类方面取得了最强的整体结果。相对于强大的原始信号和直接GVD空间生成基线，它仍然保持计算效率。因此，GVD-CFM提供了一个实用框架，用于生成逼真、时间连贯、高分辨率的脑网络，同时保持流形结构和分辨率灵活的解码能力，且仅需单个训练模型。
英文摘要
High-resolution dynamic functional connectivity (DFC) can reveal rapidly evolving brain-network interactions, but short temporal windows yield noisy, often low-rank covariance estimates. Graph-Variate Dynamic (GVD) connectivity addresses this by modulating fast instantaneous interactions with stable trial-level support. This suppresses spurious fluctuations and emphasizes persistent, informative connections. We show that the Hadamard construction lifts low-rank instantaneous connectivity from the positive-semidefinite to the positive-definite cone, keeping high-resolution trajectories on the SPD manifold without ridge regularisation or post-hoc projection. We introduce GVD-CFM, a class-conditional generative model for high-resolution dynamic connectivity. Each trial is represented as SPD GVD matrices on a product Riemannian manifold, then mapped through a global log-Euclidean diffeomorphism and an invertible temporal DCT basis. A Transformer-based conditional flow models all spectral modes jointly and generates the full trajectory non-autoregressively in Euclidean coordinates while preserving exact correspondence with valid SPD sequences. Retaining the full DCT basis also enables decoding on denser temporal grids without retraining. Across multiple EEG motor-imagery datasets, GVD-CFM delivers the strongest overall results for held-out distributional fidelity, temporal-dynamics preservation, and synthetic-to-real classification. It also remains computationally efficient relative to strong raw-signal and direct GVD-space generative baselines. GVD-CFM therefore provides a practical framework for realistic, temporally coherent, high-resolution brain-network generation with preserved manifold structure and resolution-flexible decoding from a single trained model.
