A major tenet in theoretical neuroscience is that cognitive and behavioral processes are ultimately implemented in terms of the neural system dynamics. Accordingly, a major aim for the analysis of neurophysiological measurements should lie in the identification of the computational dynamics underlying task processing. Here we advance a state space model (SSM) based on generative piecewise-linear recurrent neural networks (PLRNN) to assess dynamics from neuroimaging data. In contrast to many other nonlinear time series models which have been proposed for reconstructing latent dynamics, our model is easily interpretable in neural terms, amenable to systematic dynamical systems analysis of the resulting set of equations, and can straightforwardly be transformed into an equivalent continuous-time dynamical system. The major contributions of this paper are the introduction of a new observation model suitable for functional magnetic resonance imaging (fMRI) coupled to the latent PLRNN, an efficient stepwise training procedure that forces the latent model to capture the 'true' underlying dynamics rather than just fitting (or predicting) the observations, and of an empirical measure based on the Kullback-Leibler divergence to evaluate from empirical time series how well this goal of approximating the underlying dynamics has been achieved. We validate and illustrate the power of our approach on simulated 'ground-truth' dynamical (benchmark) systems as well as on actual experimental fMRI time series. Given that fMRI is one of the most common techniques for measuring brain activity non-invasively in human subjects, this approach may provide a novel step toward analyzing aberrant (nonlinear) dynamics for clinical assessment or neuroscientific research.
翻译:理论神经科学中的一项主要原则是,认知和行为过程最终在神经系统动态动态方面得到实施。 因此, 分析神经生理测量的主要目的应该在于识别计算动态基础任务处理。 在这里, 我们推出一个基于基因化的单线线性神经循环神经网络( PLNN) 的国家空间模型( SSM ), 以根据神经成像数据评估动态。 与为重建潜伏动态而提出的许多其他非线性时间序列模型相比, 我们的模型很容易以神经学术语解释, 能够对由此产生的方程式进行系统的动态系统分析, 并且可以直接地将神经生理生理测量转换成一个等效的连续动态动态系统。 本文的主要贡献是引入一个新的观测模型, 适合功能性磁共线性神经神经中反复神经中反复反应的成像像(fMRI), 一个高效的渐进式培训程序, 使潜伏模型能够捕捉到“ 真实的动态”, 而不是仅仅(或预测) 直径直径的直径直径, 以及基于 Kull- Learn- Lear 直径非直线的直径对等的直径直径对等的直径系统进行直径评估, 直径对等的直径测测测测测测测测测测测测测测测测测测测测测测测测测测测测测算。