Emergence of time persistence in an interpretable data-driven neural network model

Establishing accurate as well as interpretable models of neural networks activity is an open challenge in systems neuroscience. Here we infer an energy-based generative network model of the anterior rhombencephalic turning region (ARTR) of zebrafish larvae using calcium-imaging recordings of the spontaneous activity of hundreds of neurons. While our data-driven model is trained to solely reproduce the short-term statistics of the neural activity, its dynamics exhibits persistence on much longer time scales. The model's persistence time decreases with water temperature in agreement with neuronal and behavioral observations. Mathematical analysis of the model unveils a low-dimensional landscape-based representation of the population activity where the long-term dynamics reflects slow Arrhenius-like activated processes between metastable activity states. We show how this effective landscape is modified in the presence of light stimuli, which allows us to reinterpret previous experiments characterizing the visually-driven operation of the ARTR.