Encoding of interdependent features of head direction and angular head velocity in navigation

To navigate a dynamically changing environment, the brain must encode not only individual sensory or motor features but also their temporal interdependencies. A canonical example of this encoding challenge is the head direction (HD) system, where the current HD must be continuously updated based on its temporal derivative, angular head velocity (AHV). While previous studies have predominantly addressed the encoding of independent features, the neural representation of interdependent features remains inadequately characterized. Here, we investigated the population coding strategy for HD and AHV through a two-stage approach. First, a recurrent neural network was employed as a hypothesis-generating tool, trained to predict HD from AHV inputs, thus enabling analysis of the emergent neural responses. We observed two functionally distinct subpopulations: single-peaked (SP) units that precisely encode HD, and multipeaked (MP) units that preferentially represent AHV. Notably, both subpopulations exhibited mixed selectivity, yet diverged in their functional specialization. Then, empirical validation using neurophysiological recordings from the mouse HD system confirmed that SP and MP neurons indeed differentially encode HD and AHV. Neural geometric analysis further revealed that MP neurons expanded the dimensionality of the neural representation space, enabling a higher-resolution encoding of AHV. This configuration effectively balances the conflicting demands of specificity, achieved via sparsity, and interdependency, realized via mixed selectivity, forming a hybrid coding scheme previously uncharacterized for interdependent features. These findings together propose a hybrid coding scheme in the mouse HD system for representing dynamically coupled features and advocate future exploration of this scheme across sensorimotor and cognitive domains.