The hypothalamus plays a key role in regulating innate behaviors. It is widely believed to function as a system of ‘labeled lines’, containing behavior-specific neurons with characteristic transcriptomic and connectomic profiles. This view however fails to explain why, although activation of estrogen receptor-1 (Esr1) expressing neurons in the ventromedial hypothalamus (VMHvl) promotes aggression, few VMHvl neurons are tuned to attack. To address this paradox, we adopted an unsupervised dynamical systems framework to analyze population activity among VMHvlEsr1 neurons during aggression. We discovered that this activity contains an “integration” dimension exhibiting slow-ramping dynamics and persistent activity that correlates with escalating aggressiveness. These dynamics are implemented as an approximate line attractor in state space. Our analysis suggests a function for VMHvl to encode the intensity of behavior-relevant motive states using line attractors. This view reconciles observational and perturbational studies of VMHvl, and reveals a new mode of neural computation in the hypothalamus.