We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic dynamical system which implements computations through its state evolution. To model this dynamical system, we employ a system of coupled stochastic differential equations with differentiable drift and diffusion functions and use variational inference to infer its states and parameters. This formulation enables seamless integration of existing mathematical models in the literature, neural networks, or a hybrid of both to learn and compare different models. We demonstrate this in our framework by developing a generative model that combines coupled oscillators with neural networks to capture latent population dynamics from single-cell recordings. Evaluation across three neuroscience datasets spanning different species, brain regions, and behavioral tasks show that these hybrid models achieve competitive performance in predicting stimulus-evoked neural and behavioral responses compared to sophisticated black-box approaches while requiring an order of magnitude fewer parameters, providing uncertainty estimates, and offering a natural language for interpretation.

翻译：我们提出了一种用于开发生物神经系统计算模型的概率框架。在此框架中，生理记录被视为实现计算的状态演化之基础连续时间随机动力系统的离散时间部分观测。为建模该动力系统，我们采用具有可微漂移和扩散函数的耦合随机微分方程组，并利用变分推断来推断其状态与参数。此表述能够无缝整合文献中现有的数学模型、神经网络或两者的混合形式，以学习和比较不同模型。我们通过在框架中开发一个生成模型来演示这一点，该模型将耦合振荡器与神经网络相结合，以从单细胞记录中捕捉潜在群体动力学。在涵盖不同物种、脑区和行为任务的三个神经科学数据集上的评估表明，与复杂的黑箱方法相比，这些混合模型在预测刺激诱发的神经和行为响应方面取得了具有竞争力的性能，同时所需参数数量少一个数量级，并能提供不确定性估计及自然的解释性语言。