The neural dynamics underlying brain activity are critical to understanding cognitive processes and mental disorders. However, current voxel-based whole-brain dimensionality reduction techniques fall short of capturing these dynamics, producing latent timeseries that inadequately relate to behavioral tasks. To address this issue, we introduce a novel approach to learning low-dimensional approximations of neural dynamics by using a sequential variational autoencoder (SVAE) that represents the latent dynamical system via a neural ordinary differential equation (NODE). Importantly, our method finds smooth dynamics that can predict cognitive processes with accuracy higher than classical methods. Our method also shows improved spatial localization to task-relevant brain regions and identifies well-known structures such as the motor homunculus from fMRI motor task recordings. We also find that non-linear projections to the latent space enhance performance for specific tasks, offering a promising direction for future research. We evaluate our approach on various task-fMRI datasets, including motor, working memory, and relational processing tasks, and demonstrate that it outperforms widely used dimensionality reduction techniques in how well the latent timeseries relates to behavioral sub-tasks, such as left-hand or right-hand tapping. Additionally, we replace the NODE with a recurrent neural network (RNN) and compare the two approaches to understand the importance of explicitly learning a dynamical system. Lastly, we analyze the robustness of the learned dynamical systems themselves and find that their fixed points are robust across seeds, highlighting our method's potential for the analysis of cognitive processes as dynamical systems.

翻译：大脑活动背后的神经动力学对于理解认知过程和精神疾病至关重要。然而，当前基于体素的全脑降维技术在捕捉这些动力学方面存在不足，其产生的潜在时间序列与行为任务的相关性较弱。为解决这一问题，我们提出了一种新方法，通过使用顺序变分自编码器（SVAE）学习神经动力学的低维近似，该自编码器借助神经常微分方程（NODE）表示潜在动力学系统。重要的是，我们的方法能够发现平滑的动态过程，并以高于经典方法的精度预测认知过程。该方法还展现出对任务相关脑区更好的空间定位能力，能从功能磁共振成像（fMRI）运动任务记录中识别出运动侏儒等已知结构。我们还发现，对潜在空间进行非线性投影能够提升特定任务的性能，为未来研究指明了有前景的方向。我们在多种任务fMRI数据集上（包括运动、工作记忆和关系处理任务）评估了该方法，结果表明，在潜在时间序列与行为子任务（如左右手敲击）的相关性方面，它优于广泛使用的降维技术。此外，我们将NODE替换为循环神经网络（RNN），并比较了两种方法，以理解显式学习动力学系统的重要性。最后，我们分析了所学动力学系统本身的鲁棒性，发现其固定点在不同随机种子下保持稳定，这凸显了该方法将认知过程作为动力学系统进行分析的潜力。