Modelling the spatiotemporal dynamics in the activity of neural populations while also enabling their flexible inference is hindered by the complexity and noisiness of neural observations. Here we show that the lower-dimensional nonlinear latent factors and latent structures can be computationally modelled in a manner that allows for flexible inference causally, non-causally and in the presence of missing neural observations. To enable flexible inference, we developed a neural network that separates the model into jointly trained manifold and dynamic latent factors such that nonlinearity is captured through the manifold factors and the dynamics can be modelled in tractable linear form on this nonlinear manifold. We show that the model, which we named ‘DFINE’ (for ‘dynamical flexible inference for nonlinear embeddings’) achieves flexible inference in simulations of nonlinear dynamics and across neural datasets representing a diversity of brain regions and behaviours. Compared with earlier neural-network models, DFINE enables flexible inference, better predicts neural activity and behaviour, and better captures the latent neural manifold structure. DFINE may advance the development of neurotechnology and investigations in neuroscience.

对神经群体活动的时空动态进行建模，同时也使其能够进行灵活的推理，但神经观察的复杂性和噪声阻碍了它们的发展。在这里，我们表明，低维非线性潜在因子和潜在结构可以通过计算建模，从而允许灵活的因果推理、非因果推理以及在缺失神经观察的情况下进行推理。为了实现灵活的推理，我们开发了一个神经网络，将模型分为联合训练的流形和动态潜在因子，以便通过流形因子捕获非线性，并且可以在该非线性流形上以易于处理的线性形式对动力学进行建模。我们展示了该模型，我们将其命名为“DFINE”（“非线性嵌入的动态灵活推理”），可以在非线性动力学模拟中以及跨代表多种大脑区域和行为的神经数据集实现灵活推理。与早期的神经网络模型相比，DFINE 能够实现灵活的推理，更好地预测神经活动和行为，并更好地捕获潜在的神经流形结构。DFINE 可能会促进神经技术和神经科学研究的发展。