Opening the Black Box of Neural Computation from Neural Recordings with Gain-Modulated Linear Dynamical System

Inferring computational mechanisms from neural recordings is a central goal in systems neuro-science. Recent developments have identified low-rank recurrent neural networks (RNNs) as an effective tool for fitting observed neural activity and extracting neural dynamics. However, we show that accurate activity fitting alone does not guarantee mechanistic validity: even well-fitted low-rank RNNs can yield misleading circuit interpretations in the absence of ground-truth model settings on synthetic datasets. To address this limitation, we introduce a gain-modulated linear dynamical systems (gmLDS) method, which decomposes latent-variable interactions into a time-varying gain and static low-rank connectivity components. This decomposition captures linearized dynamics near neural trajectories and enables flexible adaptation to each neurons nonlinear responses without requiring a predefined activation function. Extensive validation across multiple synthetic datasets shows that gmLDS accurately reproduces neural activity, gain and connectivity, thereby capturing the fine structure of linearized dynamics and the underlying circuit mechanisms. When applying to neural recordings from a context-dependent decision-making task, gmLDS uncovers evidence for the coexistence of two prevalent selection mechanisms, offering new insights into a long-standing unresolved issue in the field. Together, our results establish gmLDS as a principled approach for opening the black box of neural computation from neural recordings.