Neuronal dynamics are highly nonlinear and nonstationary. Traditional methods for extracting the underlying network structure from neuronal activity recordings mainly concentrate on modeling static connectivity, without accounting for key nonstationary aspects of biological neural systems, such as ongoing synaptic plasticity and neuronal modulation. To bridge this gap, we introduce the NetFormer model, an interpretable approach applicable to such systems. In NetFormer, the activity of each neuron across a series of historical time steps is defined as a token. These tokens are then linearly mapped through a query and key mechanism to generate a state- (and hence time-) dependent attention matrix that directly encodes nonstationary connectivity structures. We analyze our formulation from the perspective of nonstationary and nonlinear networked dynamical systems, and show both via an analytical expansion and targeted simulations how it can approximate the underlying ground truth. Next, we demonstrate NetFormer's ability to model a key feature of biological networks, spike-timing-dependent plasticity, whereby connection strengths continually change in response to local activity patterns. We further demonstrate that NetFormer can capture task-induced connectivity patterns on activity generated by task-trained recurrent neural networks. Thus informed, we apply NetFormer to a multi-modal dataset of real neural recordings, which contains neural activity, cell type, and behavioral state information. We show that the NetFormer effectively predicts neural dynamics and identifies cell-type specific, state-dependent dynamic connectivity that matches patterns measured in separate ground-truth physiology experiments, demonstrating its ability to help decode complex neural interactions based on population activity observations alone.