  The dynamics of neuron populations during many behavioural tasks evolve on
low-dimensional manifolds. However, it remains challenging to discover latent
representations from neural recordings that are interpretable and consistently
decodable across individuals and conditions without explicitly relying on
behavioural information. Here, we introduce MARBLE, a fully unsupervised
geometric deep learning framework for the data-driven representation of
non-linear dynamics based on statistical distributions of local dynamical
features. Using both in silico examples from non-linear dynamical systems and
recurrent neural networks and in vivo recordings from primates and rodents, we
demonstrate that MARBLE can infer latent representations that are highly
interpretable in terms of global system variables such as decision-thresholds,
kinematics or internal states. We also show that MARBLE representations are
consistent across neural networks and animals so that they can be used to
compare cognitive computations or train universal decoders. Through extensive
benchmarking, we show that unsupervised MARBLE provides best-in-class within-
and across-animal decoding accuracy, comparable to or significantly better than
current supervised approaches, yet without the need for behavioural labels. Our
results suggest that using the manifold structure in conjunction with the
temporal information of neural dynamics provides a common framework to develop
better decoding algorithms and assimilate data across experiments.
