A framework for analyzing neural activity using multi-dimensional hyperbolic embedding.

Neurons represent changes in external and internal environments by altering their activity patterns. While coherent brain-wide patterns of neural activity have been observed in neuronal populations, very little is known about their dimensionality, geometry, and how they are correlated with sensory inputs. Here, we recorded the activity of most head neurons in experiencing changes in bacterial or control buffer stimuli around their nose. We first classified active neurons into six functional clusters: two sensory neuron clusters (ON and OFF responding to addition and removal of stimuli, respectively) and four motor/command neuron clusters (AVA, RME, SMDD and SMDV). Next, we estimated stimulus selectivity for each cluster and found that while sensory neurons exhibit their maximal responses within 15 seconds, changes in bacterial stimuli drive maximal responses in command and motor neuron clusters after tens of seconds. Furthermore, we show that bacterial stimuli induce neural dynamics that are best described by a hyperbolic, not Euclidean, space, of dimensionality eight. The hyperbolic space provided a better description of neural activity than the standard Euclidean space. This space can be separated into three components - one sensory, and two motor directions (forward-backward and dorsal-ventral). Collectively, we show that neural activity can be effectively represented in low-dimensional hyperbolic space to describe a sensorimotor transformation.