Behavior is shaped by various factors operating across different timescales.

Neural radiance fields (NeRFs) have become a ubiquitous tool for modeling scene appearance and geometry from multiview imagery. Recent work has also begun to explore how to use additional supervision from lidar or depth sensor measurements in the NeRF framework. However, previous lidar-supervised NeRFs focus on rendering conventional camera imagery and use lidar-derived point cloud data as auxiliary supervision; thus, they fail to incorporate the underlying image formation model of the lidar. Here, we propose a novel method for rendering transient NeRFs that take as input the raw, time-resolved photon count histograms measured by a single-photon lidar system, and we seek to render such histograms from novel views. Different from conventional NeRFs, the approach relies on a time-resolved version of the volume rendering equation to render the lidar measurements and capture transient light transport phenomena at picosecond timescales. We evaluate our method on a first-of-its-kind dataset of simulated and captured transient multiview scans from a prototype single-photon lidar. Overall, our work brings NeRFs to a new dimension of imaging at transient timescales, newly enabling rendering of transient imagery from novel views. Additionally, we show that our approach recovers improved geometry and conventional appearance compared to point cloud-based supervision when training on few input viewpoints. Transient NeRFs may be especially useful for applications which seek to simulate raw lidar measurements for downstream tasks in autonomous driving, robotics, and remote sensing.

We quantify the efficiency of temporal difference (TD) learning over the direct, or Monte Carlo (MC), estimator for policy evaluation in reinforcement learning, with an emphasis on estimation of quantities related to rare events. Policy evaluation is complicated in the rare event setting by the long timescale of the event and by the need for \emph{relative accuracy} in estimates of very small values. Specifically, we focus on least-squares TD (LSTD) prediction for finite state Markov chains, and show that LSTD can achieve relative accuracy far more efficiently than MC. We prove a central limit theorem for the LSTD estimator and upper bound the \emph{relative asymptotic variance} by simple quantities characterizing the connectivity of states relative to the transition probabilities between them. Using this bound, we show that, even when both the timescale of the rare event and the relative accuracy of the MC estimator are exponentially large in the number of states, LSTD maintains a fixed level of relative accuracy with a total number of observed transitions of the Markov chain that is only \emph{polynomially} large in the number of states.

Accurate prediction of climate in the subseasonal-to-seasonal scale is crucial for disaster preparedness and robust decision making amidst climate change. Yet, forecasting beyond the weather timescale is challenging because it deals with problems other than initial condition, including boundary interaction, butterfly effect, and our inherent lack of physical understanding. At present, existing benchmarks tend to have shorter forecasting range of up-to 15 days, do not include a wide range of operational baselines, and lack physics-based constraints for explainability. Thus, we propose ChaosBench, a challenging benchmark to extend the predictability range of data-driven weather emulators to S2S timescale. First, ChaosBench is comprised of variables beyond the typical surface-atmospheric ERA5 to also include ocean, ice, and land reanalysis products that span over 45 years to allow for full Earth system emulation that respects boundary conditions. We also propose physics-based, in addition to deterministic and probabilistic metrics, to ensure a physically-consistent ensemble that accounts for butterfly effect. Furthermore, we evaluate on a diverse set of physics-based forecasts from four national weather agencies as baselines to our data-driven counterpart such as ViT/ClimaX, PanguWeather, GraphCast, and FourCastNetV2. Overall, we find methods originally developed for weather-scale applications fail on S2S task: their performance simply collapse to an unskilled climatology. Nonetheless, we outline and demonstrate several strategies that can extend the predictability range of existing weather emulators, including the use of ensembles, robust control of error propagation, and the use of physics-informed models.

Functional magnetic resonance imaging (fMRI) enables measuring human brain activity, in vivo. Yet, the fMRI hemodynamic response unfolds over very slow timescales (<0.1-1

Natural signals such as speech are hierarchically structured across many different timescales, spanning tens (e.g., phonemes) to hundreds (e.g., words) of milliseconds, each of which is highly variable and context-dependent. While deep neural networks (DNNs) excel at recognizing complex patterns from natural signals, relatively little is known about how DNNs flexibly integrate across multiple timescales. Here, we show how a recently developed method for studying temporal integration in biological neural systems - the temporal context invariance (TCI) paradigm - can be used to understand temporal integration in DNNs. The method is simple: we measure responses to a large number of stimulus segments presented in two different contexts and estimate the smallest segment duration needed to achieve a context invariant response. We applied our method to understand how the popular DeepSpeech2 model learns to integrate across time in speech.

Humans learn from visual inputs at multiple timescales, both rapidly and flexibly acquiring visual knowledge over short periods, and robustly accumulating online learning progress over longer periods. Modeling these powerful learning capabilities is an important problem for computational visual cognitive science, and models that could replicate them would be of substantial utility in real-world computer vision settings. In this work, we establish benchmarks for both real-time and life-long continual visual learning. Our real-time learning benchmark measures a model's ability to match the rapid visual behavior changes of real humans over the course of minutes and hours, given a stream of visual inputs. Our life-long learning benchmark evaluates the performance of models in a purely online learning curriculum obtained directly from child visual experience over the course of years of development.

Neurons in early sensory areas rapidly adapt to changing sensory statistics, both by normalizing the variance of their individual responses and by reducing correlations between their responses. Together, these transformations may be viewed as an adaptive form of statistical whitening. Existing mechanistic models of adaptive whitening exclusively use either synaptic plasticity or gain modulation as the biological substrate for adaptation; however, on their own, each of these models has significant limitations. In this work, we unify these approaches in a normative multi-timescale mechanistic model that adaptively whitens its responses with complementary computational roles for synaptic plasticity and gain modulation. Gains are modified on a fast timescale to adapt to the current statistical context, whereas synapses are modified on a slow timescale to match structural properties of the input statistics that are invariant across contexts. Our model is derived from a novel multi-timescale whitening objective that factorizes the inverse whitening matrix into basis vectors, which correspond to synaptic weights, and a diagonal matrix, which corresponds to neuronal gains. We test our model on synthetic and natural datasets and find that the synapses learn optimal configurations over long timescales that enable adaptive whitening on short timescales using gain modulation.

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.

Animals survive in dynamic environments changing at arbitrary timescales, but such data distribution shifts are a challenge to neural networks. To adapt to change, neural systems may change a large number of parameters, which is a slow process involving forgetting past information.