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.
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