Functional connectivities (FC) of brain network manifest remarkable geometric patterns, which is the gateway to understanding brain dynamics. In this work, we present a novel geometric-attention neural network to characterize the time-evolving brain state change from the functional neuroimages by tracking the trajectory of functional dynamics on high-dimension Riemannian manifold of symmetric positive definite (SPD) matrices. Specifically, we put the spotlight on learning the common state-specific manifold signatures that represent the underlying cognition. In this context, the driving force of our neural network is tied up with the learning of the evolution functionals on the Riemannian manifold of SPD matrix that underlies the known evolving brain states. To do so, we train a convolution neural network (CNN) on the Riemannian manifold of SPD matrices to seek for the putative low-dimension feature representations, followed by an end-to-end recurrent neural network (RNN) to yield the time-varying mapping function of SPD matrices which fits the evolutionary trajectories of the underlying states. Furthermore, we devise a geometric attention mechanism in CNN, allowing us to discover the latent geometric patterns in SPD matrices that are associated with the underlying states. Notably, our work has the potential to understand how brain function emerges behavior by investigating the geometrical patterns from functional brain networks, which is essentially a correlation matrix of neuronal activity signals. Our proposed manifold-based neural network achieves promising results in predicting brain state changes on both simulated data and task functional neuroimaging data from Human Connectome Project, which implies great applicability in neuroscience studies.

中文翻译：

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使用几何注意神经网络学习不断变化的功能 MRI 数据的大脑动力学

大脑网络的功能连接（FC）表现出显着的几何图案，这是理解大脑动力学的门户。在这项工作中，我们提出了一种新颖的几何注意神经网络，通过跟踪对称正定（SPD）矩阵的高维黎曼流形上的功能动力学轨迹来表征功能神经图像中随时间演化的大脑状态变化。具体来说，我们将重点放在学习代表潜在认知的常见特定于状态的流形签名上。在这种情况下，我们神经网络的驱动力与 SPD 矩阵黎曼流形上的进化泛函的学习密切相关，该矩阵是已知进化大脑状态的基础。为此，我们在 SPD 矩阵的黎曼流形上训练卷积神经网络 (CNN)，以寻找假定的低维特征表示，然后使用端到端循环神经网络 (RNN) 来产生时间-适合基础状态演化轨迹的 SPD 矩阵的变化映射函数。此外，我们在 CNN 中设计了一种几何注意力机制，使我们能够发现 SPD 矩阵中与底层状态相关的潜在几何模式。值得注意的是，我们的工作有可能通过研究功能性大脑网络的几何图案（本质上是神经元活动信号的相关矩阵）来了解大脑功能如何产生行为。我们提出的基于流形的神经网络在预测来自人类连接组项目的模拟数据和任务功能神经影像数据的大脑状态变化方面取得了有希望的结果，这意味着在神经科学研究中具有很大的适用性。