Behavior-derived social gain shapes multi-region subcortical dynamics in a low-rank recurrent model

Densely interconnected subcortical nuclei integrate diverse cues to orchestrate social behavior. These circuits operate under slowly varying internal state signals mediated by neuromodulation, but how such modulation interacts with neural dynamics across interconnected nuclei during natural social behavior remains unresolved. We introduce $\textbf{BiG}$ ($\underline{\textbf{B}}$ehav$\underline{\textbf{i}}$orally modulated $\underline{\textbf{G}}$ain), a low-rank, Dale's-law, multi-region RNN fit to multifiber calcium photometry data from hypothalamic and extended-amygdala nuclei during freely moving social behavior. A recurrent encoder subnetwork compresses pose and social features into a social gain variable that multiplicatively scales recurrent connectivity. Social gain improved held-out reconstruction of neural signals across all behavioral states and better recovered cross-signal correlation structure compared to models without gain. The inferred gain variable evolved on a slow timescale, was stable across initializations, and represented a continuous social engagement intensity. Clamping the gain at inference revealed a reconstruction cost that grew with social engagement and region specificity, with amygdalar activity mostly disrupted by social gain perturbations.