  Neurons can display highly variable dynamics. While such variability
presumably supports the wide range of behaviors generated by the organism,
their gene expressions are relatively stable in the adult brain. This suggests
that neuronal activity is a combination of its time-invariant identity and the
inputs the neuron receives from the rest of the circuit. Here, we propose a
self-supervised learning based method to assign time-invariant representations
to individual neurons based on permutation-, and population size-invariant
summary of population recordings. We fit dynamical models to neuronal activity
to learn a representation by considering the activity of both the individual
and the neighboring population. Our self-supervised approach and use of
implicit representations enable robust inference against imperfections such as
partial overlap of neurons across sessions, trial-to-trial variability, and
limited availability of molecular (transcriptomic) labels for downstream
supervised tasks. We demonstrate our method on a public multimodal dataset of
mouse cortical neuronal activity and transcriptomic labels. We report > 35%
improvement in predicting the transcriptomic subclass identity and > 20%
improvement in predicting class identity with respect to the state-of-the-art.
