Population trajectory analysis reveals divergent state-space geometries across three cortical excitatory cell types

Cortical population activity unfolds along structured trajectories in state space, reflecting underlying dynamics of the neural networks involved. However, how such geometry differs across neural cell types remains poorly understood. Using a large-scale two-photon calcium imaging dataset from the Allen Brain Observatory, we characterized the population trajectories of three cortical excitatory subtypes (Cux2, Emx1, and Slc17a7). These cells constitute most of the layer 2/3 excitatory populations, span distinct projection and functional hierarchies, and collectively orchestrate cortical integration and excitatory signaling. While viewing drifting gratings, Cux2 neurons exhibited compact and stable trajectories, whereas Emx1 and Slc17a7 showed broader and more distributed dynamics, implying their functional divergence in visual processes. Such geometric distinctions can be mechanistically accounted for within a low-dimensional control space where the dominant axes correspond to the effective integration timescale and recurrent gain. This geometric-mechanistic framework provides a generalizable route to bridging cortical dynamics with fundamental, cellular identity.