Recent progress in the development of voltage indicators [1-8] has brought us closer to a longstanding goal incellular neuroscience: imaging the full spatiotemporal voltageonadendritic tree. These recordings have the potential (pun not intended) to resolve fundamental questions about the computations performed by dendrites -- questions that have remained open for more than a century[9,10].

Understanding how the collective activity of neural populations relates to computation and ultimately behavior is a key goal in neuroscience.

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).

Understanding how the collective activity of neural populations relates to computation and ultimately behavior is a key goal in neuroscience.

Switching dynamical systems can model complicated time series data while maintaining interpretability by inferring a finite set of dynamics primitives and explaining different portions of the observed time series with one of these primitives. However, due to the discrete nature of this set, such models struggle to capture smooth, variable-speed transitions, as well as stochastic mixtures of overlapping states, and the inferred dynamics often display spurious rapid switching on real-world datasets. Here, we propose the Gumbel Dynamical Model (GDM). First, by introducing a continuous relaxation of discrete states and a different noise model defined on the relaxed-discrete state space via the Gumbel distribution, GDM expands the set of available state dynamics, allowing the model to approximate smoother and non-stationary ground-truth dynamics more faithfully. Second, the relaxation makes the model fully differentiable, enabling fast and scalable training with standard gradient descent methods. We validate our approach on standard simulation datasets and highlight its ability to model soft, sticky states and transitions in a stochastic setting. Furthermore, we apply our model to two real-world datasets, demonstrating its ability to infer interpretable states in stochastic time series with multiple dynamics, a setting where traditional methods often fail.

Neural Information Processing Systems http://nips.cc/

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).

In this paper, we propose a novel model called Recurrent Explicit Duration Switching Linear Dynamical Systems (REDSLDS) that incorporates recurrent explicit duration variables into the rSLDS model. We also propose an inference and learning scheme that involves the use of P\'olya-gamma augmentation. We demonstrate the improved segmentation capabilities of our model on three benchmark datasets, including two quantitative datasets and one qualitative dataset.

An open problem in artificial intelligence is how systems can flexibly learn discrete abstractions that are useful for solving inherently continuous problems. Previous work in computational neuroscience has considered this functional integration of discrete and continuous variables during decision-making under the formalism of active inference (Parr, Friston & de Vries, 2017; Parr & Friston, 2018). However, their focus is on the expressive physical implementation of categorical decisions and the hierarchical mixed generative model is assumed to be known. As a consequence, it is unclear how this framework might be extended to learning. We therefore present a novel hierarchical hybrid active inference agent in which a high-level discrete active inference planner sits above a low-level continuous active inference controller. We make use of recent work in recurrent switching linear dynamical systems (rSLDS) which implement end-to-end learning of meaningful discrete representations via the piecewise linear decomposition of complex continuous dynamics (Linderman et al., 2016). The representations learned by the rSLDS inform the structure of the hybrid decision-making agent and allow us to (1) specify temporally-abstracted sub-goals in a method reminiscent of the options framework, (2) lift the exploration into discrete space allowing us to exploit information-theoretic exploration bonuses and (3) `cache' the approximate solutions to low-level problems in the discrete planner. We apply our model to the sparse Continuous Mountain Car task, demonstrating fast system identification via enhanced exploration and successful planning through the delineation of abstract sub-goals.

An open problem in artificial intelligence is how systems can flexibly learn discrete abstractions that are useful for solving inherently continuous problems. Previous work has demonstrated that a class of hybrid state-space model known as recurrent switching linear dynamical systems (rSLDS) discover meaningful behavioural units via the piecewise linear decomposition of complex continuous dynamics (Linderman et al., 2016). Furthermore, they model how the underlying continuous states drive these discrete mode switches. We propose that the rich representations formed by an rSLDS can provide useful abstractions for planning and control. We present a novel hierarchical model-based algorithm inspired by Active Inference in which a discrete MDP sits above a low-level linear-quadratic controller. The recurrent transition dynamics learned by the rSLDS allow us to (1) specify temporally-abstracted sub-goals in a method reminiscent of the options framework, (2) lift the exploration into discrete space allowing us to exploit information-theoretic exploration bonuses and (3) `cache' the approximate solutions to low-level problems in the discrete planner. We successfully apply our model to the sparse Continuous Mountain Car task, demonstrating fast system identification via enhanced exploration and non-trivial planning through the delineation of abstract sub-goals.