The dynamics of neuron populations during diverse tasks often evolve on low-dimensional manifolds. However, it remains challenging to discern the contributions of geometry and dynamics for encoding relevant behavioural variables. Here, we introduce an unsupervised geometric deep learning framework for representing non-linear dynamical systems based on statistical distributions of local phase portrait features. Our method provides robust geometry-aware or geometry-agnostic representations for the unbiased comparison of dynamics based on measured trajectories. We demonstrate that our statistical representation can generalise across neural network instances to discriminate computational mechanisms, obtain interpretable embeddings of neural dynamics in a primate reaching task with geometric correspondence to hand kinematics, and develop a decoding algorithm with state-of-the-art accuracy. Our results highlight the importance of using the intrinsic manifold structure over temporal information to develop better decoding algorithms and assimilate data across experiments.

翻译：在不同任务中，神经元群体的动力学往往在低维流形上演化。然而，如何区分几何结构与动力学对编码相关行为变量的贡献仍具挑战性。本文提出一种无监督的几何深度学习框架，基于局部相平面特征的统计分布来表征非线性动力系统。该方法能够提供具有几何感知或几何无关性的鲁棒表征，从而基于实测轨迹实现动力学的无偏比较。我们证明，该统计表征可跨神经网络实例泛化，以区分计算机制；在灵长类动物伸手任务中，它能获得与手部运动学存在几何对应关系的可解释神经动力学嵌入；并开发出具有最先进精度的解码算法。研究结果凸显了利用内在流形结构（而非时序信息）对改进解码算法及跨实验数据整合的重要性。