The ability to continually learn new skills, retain, and flexibly deploy them to accomplish goals is a key feature of intelligent and efficient behavior. However, the neural mechanisms facilitating the continual learning and flexible (re-)composition of skills remain elusive. Here, we study continual learning and the compositional reuse of learned computations in recurrent neural network (RNN) models using a novel two-system approach: one system that infers 'what' computation to perform, and one that implements 'how' to perform it. We focus on a set of compositional cognitive tasks commonly studied in neuroscience. To construct the 'what' system, we first show that a large family of tasks can be systematically described by a probabilistic generative model, where compositionality stems from a shared underlying vocabulary of discrete task-epochs. The shared epoch structure makes these tasks inherently compositional. We first show that this compositionality can be systematically described by a probabilistic generative model. Furthermore, we develop an unsupervised online learning approach that can learn this model on a single-trial basis, building its vocabulary incrementally as it is exposed to new tasks, and inferring the latent epoch structure as a time-varying computational context within a trial. We implement the 'how' system as an RNN whose low-rank components are composed according to the context inferred by the 'what' system. The contextual inference facilitates the creation, learning, and reuse of the low-rank RNN components as new tasks are introduced sequentially, enabling continual learning without catastrophic forgetting. Using an example task set, we demonstrate the efficacy and competitive performance of this two-system learning framework, its potential for forward and backward transfer, as well as few-shot learning via re-composition.

Understanding how the collective activity of neural populations relates to computation and ultimately behavior is a key goal in neuroscience. To this end, statistical methods which describe high-dimensional neural time series in terms of low-dimensional latent dynamics have played a fundamental role in characterizing neural systems. Yet, what constitutes a successful method involves two opposing criteria: (1) methods should be expressive enough to capture complex nonlinear dynamics, and (2) they should maintain a notion of interpretability often only warranted by simpler linear models. In this paper, we develop an approach that balances these two objectives: the Gaussian Process Switching Linear Dynamical System (gpSLDS). Our method builds on previous work modeling the latent state evolution via a stochastic differential equation whose nonlinear dynamics are described by a Gaussian process (GP-SDEs). We propose a novel kernel function which enforces smoothly interpolated locally linear dynamics, and therefore expresses flexible -- yet interpretable -- dynamics akin to those of recurrent switching linear dynamical systems (rSLDS). Our approach resolves key limitations of the rSLDS such as artifactual oscillations in dynamics near discrete state boundaries, while also providing posterior uncertainty estimates of the dynamics. To fit our models, we leverage a modified learning objective which improves the estimation accuracy of kernel hyperparameters compared to previous GP-SDE fitting approaches. We apply our method to synthetic data and data recorded in two neuroscience experiments and demonstrate favorable performance in comparison to the rSLDS.

An important problem in systems neuroscience is to characterize how a neuron integrates sensory inputs across space and time. The linear receptive field provides a mathematical characterization of this weighting function and is commonly used to quantify neural response properties and classify cell types. However, estimating receptive fields is difficult in settings with limited data and correlated or high-dimensional stimuli. To overcome these difficulties, we propose a hierarchical model designed to flexibly parameterize low-rank receptive fields. The model includes gaussian process priors over spatial and temporal components of the receptive field, encouraging smoothness in space and time. We also propose a new temporal prior, temporal relevance determination, which imposes a variable degree of smoothness as a function of time lag. We derive a scalable algorithm for variational Bayesian inference for both spatial and temporal receptive field components and hyperparameters. The resulting estimator scales to high-dimensional settings in which full-rank maximum likelihood or a posteriori estimates are intractable. We evaluate our approach on neural data from rat retina and primate cortex and show that it substantially outperforms a variety of existing estimators. Our modeling approach will have useful extensions to a variety of other high-dimensional inference problems with smooth or low-rank structure.

A core goal in systems neuroscience and neuroethology is to understand how neural circuits generate naturalistic behavior. One foundational idea is that complex naturalistic behavior may be composed of sequences of stereotyped behavioral syllables, which combine to generate rich sequences of actions. To investigate this, a common approach is to use autoregressive hidden Markov models (ARHMMs) to segment video into discrete behavioral syllables. While these approaches have been successful in extracting syllables that are interpretable, they fail to account for other forms of behavioral variability, such as differences in speed, which may be better described as continuous in nature. To overcome these limitations, we introduce a class of warped ARHMMs (WARHMM). As is the case in the ARHMM, behavior is modeled as a mixture of autoregressive dynamics. However, the dynamics under each discrete latent state (i.e. each behavioral syllable) are additionally modulated by a continuous latent ``warping variable.'' We present two versions of warped ARHMM in which the warping variable affects the dynamics of each syllable either linearly or nonlinearly. Using depth-camera recordings of freely moving mice, we demonstrate that the failure of ARHMMs to account for continuous behavioral variability results in duplicate cluster assignments. WARHMM achieves similar performance to the standard ARHMM while using fewer behavioral syllables. Further analysis of behavioral measurements in mice demonstrates that WARHMM identifies structure relating to response vigor.

Biological systems face dynamic environments that require continual learning. It is not well understood how these systems balance the tension between flexibility for learning and robustness for memory of previous behaviors. Continual learning without catastrophic interference also remains a challenging problem in machine learning. Here, we develop a novel learning rule designed to minimize interference between sequentially learned tasks in recurrent networks. Our learning rule preserves network dynamics within activity-defined subspaces used for previously learned tasks. It encourages dynamics associated with new tasks that might otherwise interfere to instead explore orthogonal subspaces, and it allows for reuse of previously established dynamical motifs where possible. Employing a set of tasks used in neuroscience, we demonstrate that our approach successfully eliminates catastrophic interference and offers a substantial improvement over previous continual learning algorithms. Using dynamical systems analysis, we show that networks trained using our approach can reuse similar dynamical structures across similar tasks. This possibility for shared computation allows for faster learning during sequential training. Finally, we identify organizational differences that emerge when training tasks sequentially versus simultaneously.

We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear stochastic differential equation (SDE) driven by a Wiener process, with a drift evolution function drawn from a Gaussian process (GP) conditioned on a set of learnt fixed points and corresponding local Jacobian matrices. This form yields a flexible nonparametric model of the dynamics, with a representation corresponding directly to the interpretable portraits routinely employed in the study of nonlinear dynamical systems. The learning algorithm combines inference of continuous latent paths underlying observed data with a sparse variational description of the dynamical process. We demonstrate our approach on simulated data from different nonlinear dynamical systems.

We introduce a novel scalable approach to identifying common latent structure in neural population spike-trains, which allows for variability both in the trajectory and in the rate of progression of the underlying computation. Our approach is based on shared latent Gaussian processes (GPs) which are combined linearly, as in the Gaussian Process Factor Analysis (GPFA) algorithm. We extend GPFA to handle unbinned spike-train data by incorporating a continuous time point-process likelihood model, achieving scalability with a sparse variational approximation. Shared variability is separated into terms that express condition dependence, as well as trial-to-trial variation in trajectories. Finally, we introduce a nested GP formulation to capture variability in the rate of evolution along the trajectory. We show that the new method learns to recover latent trajectories in synthetic data, and can accurately identify the trial-to-trial timing of movement-related parameters from motor cortical data without any supervision.