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Complex time-varying systems are often studied by abstracting away from thedynamics of individual components to build a model of the population-leveldynamics from the start. However, when building a population-level description,it can be easy to lose sight of each individual and how they contribute to thelarger picture. In this paper, we present a novel transformer architecture forlearning from time-varying data that builds descriptions of both the individualas well as the collective population dynamics. Rather than combining all of ourdata into our model at the onset, we develop a separable architecture thatoperates on individual time-series first before passing them forward; thisinduces a permutation-invariance property and can be used to transfer acrosssystems of different size and order. After demonstrating that our model can beapplied to successfully recover complex interactions and dynamics in many-bodysystems, we apply our approach to populations of neurons in the nervous system.On neural activity datasets, we show that our model not only yields robustdecoding performance, but also provides impressive performance in transferacross recordings of different animals without any neuron-level correspondence.By enabling flexible pre-training that can be transferred to neural recordingsof different size and order, our work provides a first step towards creating afoundation model for neural decoding.

Seeing the forest and the tree: Building representations of both individual and collective dynamics with transformers