Self-supervised learning of scale-invariant neural representations of space and time.

Hippocampal representations of space and time seem to share a common coding scheme characterized by neurons with bell-shaped tuning curves called place and time cells. The properties of the tuning curves are consistent with Weber's law, such that, in the absence of visual inputs, width scales with the peak time for time cells and with distance for place cells. Building on earlier computational work, we examined how neurons with such properties can emerge through self-supervised learning. We found that a network based on autoencoders can, given a particular inputs and connectivity constraints, produce scale-invariant time cells. When the animal's velocity modulates the decay rate of the leaky integrators, the same network gives rise to scale-invariant place cells. Importantly, this is not the case when velocity is fed as a direct input to the leaky integrators, implying that weight modulation by velocity might be critical for developing scale-invariant spatial receptive fields. Finally, we demonstrated that after training, scale-invariant place cells emerge in environments larger than those used during training. Taken together, these findings bring us closer to understanding the emergence of neurons with bell-shaped tuning curves in the hippocampus and highlight the critical role of velocity modulation in the formation of scale-invariant place cells.