Latent variable models are ubiquitous in the exploratory analysis of neural population recordings, where they allow researchers to summarize the activity of large populations of neurons in lower dimensional ‘latent’ spaces. Existing methods can generally be categorized into (i) Bayesian methods that facilitate flexible incorporation of prior knowledge and uncertainty estimation, but which typically do not scale to large datasets; and (ii) highly parameterized methods without explicit priors that scale better but often struggle in the low-data regime. Here, we bridge this gap by developing a fully Bayesian yet scalable version of Gaussian process factor analysis (bGPFA), which models neural data as arising from a set of inferred latent processes with a prior that encourages smoothness over time. Additionally, bGPFA uses automatic relevance determination to infer the dimensionality of neural activity directly from the training data during optimization. To enable the analysis of continuous recordings without trial structure, we introduce a novel variational inference strategy that scales near-linearly in time and also allows for non-Gaussian noise models appropriate for electrophysiological recordings. We apply bGPFA to continuous recordings spanning 30 minutes with over 14 million data points from primate motor and somatosensory cortices during a self-paced reaching task. We show that neural activity progresses from an initial state at target onset to a reach- specific preparatory state well before movement onset. The distance between these initial and preparatory latent states is predictive of reaction times across reaches, suggesting that such preparatory dynamics have behavioral relevance despite the lack of externally imposed delay periods. Additionally, bGPFA discovers latent processes that evolve over slow timescales on the order of several seconds and contain complementary information about reaction time. These timescales are longer than those revealed by methods which focus on individual movement epochs and may reflect fluctuations in e.g. task engagement.

Biological agents are known to learn many different tasks over the course of their lives, and to be able to revisit previous tasks and behaviors with little to no loss in performance. In contrast, artificial agents are prone to ‘catastrophic forgetting’ whereby performance on previous tasks deteriorates rapidly as new ones are acquired. This shortcoming has recently been addressed using methods that encourage parameters to stay close to those used for previous tasks. This can be done by (i) using specific parameter regularizers that map out suitable destinations in parameter space, or (ii) guiding the optimization journey by projecting gradients into subspaces that do not interfere with previous tasks. However, these methods often exhibit subpar performance in both feedforward and recurrent neural networks, with recurrent networks being of interest to the study of neural dynamics supporting biological continual learning. In this work, we propose Natural Continual Learning (NCL), a new method that unifies weight regularization and projected gradient descent. NCL uses Bayesian weight regularization to encourage good performance on all tasks at convergence and combines this with gradient projection using the prior precision, which prevents catastrophic forgetting during optimization. Our method outperforms both standard weight regularization techniques and projection based approaches when applied to continual learning problems in feedforward and recurrent networks. Finally, the trained networks evolve task-specific dynamics that are strongly preserved as new tasks are learned, similar to experimental findings in biological circuits.

A common problem in neuroscience is to elucidate the collective neural representations of behaviorally important variables such as head direction, spatial location, upcoming movements, or mental spatial transformations. Often, these latent variables are internal constructs not directly accessible to the experimenter. Here, we propose a new probabilistic latent variable model to simultaneously identify the latent state and the way each neuron contributes to its representation in an unsupervised way. In contrast to previous models which assume Euclidean latent spaces, we embrace the fact that latent states often belong to symmetric manifolds such as spheres, tori, or rotation groups of various dimensions. We therefore propose the manifold Gaussian process latent variable model (mGPLVM), where neural responses arise from (i) a shared latent variable living on a specific manifold, and (ii) a set of non-parametric tuning curves determining how each neuron contributes to the representation. Cross-validated comparisons of models with different topologies can be used to distinguish between candidate manifolds, and variational inference enables quantification of uncertainty. We demonstrate the validity of the approach on several synthetic datasets, as well as on calcium recordings from the ellipsoid body of Drosophila melanogaster and extracellular recordings from the mouse anterodorsal thalamic nucleus. These circuits are both known to encode head direction, and mGPLVM correctly recovers the ring topology expected from neural populations representing a single angular variable.