Traditional models of climate change use complex systems of coupled equations to simulate physical processes across the Earth system. These simulations are highly computationally expensive, limiting our predictions of climate change and analyses of its causes and effects. Machine learning has the potential to quickly emulate data from climate models, but current approaches are not able to incorporate physically-based causal relationships. Here, we develop an interpretable climate model emulator based on causal representation learning. We derive a novel approach including a Bayesian filter for stable long-term autoregressive emulation. We demonstrate that our emulator learns accurate climate dynamics, and we show the importance of each one of its components on a realistic synthetic dataset and data from two widely deployed climate models.

High-density electrophysiology probes have opened new possibilities for systems neuroscience in human and non-human animals, but probe motion poses a challenge for downstream analyses, particularly in human recordings. We improve on the state of the art for tracking this motion with four major contributions. First, we extend previous decentralized methods to use multiband information, leveraging the local field potential (LFP) in addition to spikes. Second, we show that the LFP-based approach enables registration at sub-second temporal resolution. Third, we introduce an efficient online motion tracking algorithm, enabling the method to scale up to longer and higher-resolution recordings, and possibly facilitating real-time applications. Finally, we improve the robustness of the approach by introducing a structure-aware objective and simple methods for adaptive parameter selection. Together, these advances enable fully automated scalable registration of challenging datasets from human and mouse.

Neural decoding and its applications to brain computer interfaces (BCI) are essential for understanding the association between neural activity and behavior. A prerequisite for many decoding approaches is spike sorting, the assignment of action potentials (spikes) to individual neurons. Current spike sorting algorithms, however, can be inaccurate and do not properly model uncertainty of spike assignments, therefore discarding information that could potentially improve decoding performance. Recent advances in high-density probes (e.g., Neuropixels) and computational methods now allow for extracting a rich set of spike features from unsorted data; these features can in turn be used to directly decode behavioral correlates. To this end, we propose a spike sorting-free decoding method that directly models the distribution of extracted spike features using a mixture of Gaussians (MoG) encoding the uncertainty of spike assignments, without aiming to solve the spike clustering problem explicitly. We allow the mixing proportion of the MoG to change over time in response to the behavior and develop variational inference methods to fit the resulting model and to perform decoding. We benchmark our method with an extensive suite of recordings from different animals and probe geometries, demonstrating that our proposed decoder can consistently outperform current methods based on thresholding (i.e. multi-unit activity) and spike sorting. Open source code is available at https://github.com/yzhang511/density_decoding.

Multi-electrode arrays such as "Neuropixels" probes enable the study of neuronal voltage signals at high temporal and single-cell spatial resolution. However, in vivo recordings from these devices often experience some shifting of the probe (due e.g. to animal movement), resulting in poorly localized voltage readings that in turn can corrupt estimates of neural activity. We introduce a new registration method to partially correct for this motion. In contrast to previous template-based registration methods, the proposed approach is decentralized, estimating shifts of the data recorded in multiple timebins with respect to one another, and then extracting a global registration estimate from the resulting estimated shift matrix. We find that the resulting decentralized registration is more robust and accurate than previous template-based approaches applied to both simulated and real data, but nonetheless some significant non-stationarity in the recovered neural activity remains that should be accounted for by downstream processing pipelines. Open source code is available at https://github.com/evarol/NeuropixelsRegistration.

Neuropixels (NP) probes are dense linear multi-electrode arrays that have rapidly become essential tools for studying the electrophysiology of large neural populations. Unfortunately, a number of challenges remain in analyzing the large datasets output by these probes. Here we introduce several new methods for extracting useful spiking information from NP probes. First, we use a simple point neuron model, together with a neural-network denoiser, to efficiently map spikes detected on the probe into three-dimensional localizations. Previous methods localized spikes in two dimensions only; we show that the new localization approach is significantly more robust and provides an improved feature set for clustering spikes according to neural identity (``spike sorting"). Next, we apply a Poisson denoising method to the resulting three-dimensional point-cloud representation of the data, and show that the resulting 3D images can be accurately registered over time, leading to improved tracking of time-varying neural activity over the probe, and in turn, crisper estimates of neural clusters over time. The code to reproduce our results and an example neuropixels dataset is provided in the supplementary material.

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.