Accurate weather forecasting across time scales is critical for anticipating and mitigating the impacts of climate change. Recent data-driven methods based on deep learning have achieved significant success in the medium range, but struggle at longer subseasonal-to-seasonal (S2S) horizons due to error accumulation in their autoregressive approach. In this work, we propose OmniCast, a scalable and skillful probabilistic model that unifies weather forecasting across timescales. OmniCast consists of two components, a VAE model that encodes raw weather data into a continuous, lower-dimensional latent space, and a diffusion-based transformer model that generates a sequence of future latent tokens given the initial conditioning tokens. During training, we mask random future tokens and train the transformer to estimate their distribution given conditioning and visible tokens using a per-token diffusion head. During inference, the transformer generates the full sequence of future tokens by iteratively unmasking random subsets of tokens.

Efficient LLM pre-training requires well-tuned hyperparameters (HPs), including learning rate η and weight decay λ. We study scaling laws for HPs: formulas for how to scale HPs as we scale model size N, dataset size D, and batch size B. Recent work [1] suggests the AdamW timescale, τ = B/(ηλD), should remain constant across training settings, and we verify the implication that optimal λscales linearly with B, for a fixed N and D. However, as N and Dscale, we show optimal τ obeys a precise power law in the tokens-per-parameter ratio, D/N. This law thus provides a method to accurately predict λopt in advance of large-scale training. We also study scaling laws for optimal batch size Bopt (the B enabling lowest loss at a given N,D) and critical batch size Bcrit (the B beyond which further data parallelism becomes ineffective). In contrast to prior work, we find both Bopt and Bcrit scale as power laws in D, independent of model size, N. Finally, we analyze how these findings inform the real-world selection of Pareto-optimal N and D under dual training time and compute objectives.

The energy paradigm, exemplified by Hopfield networks, offers a principled framework for memory in neural systems by interpreting dynamics as descent on an energy surface. While powerful for static associative memories, it falls short in modeling sequential memory, where transitions between memories are essential. We introduce the Exponential Dynamic Energy Network (EDEN), a novel architecture that extends the energy paradigm to temporal domains by evolving the energy function over multiple timescales. EDEN combines a static high-capacity energy network with a slow, asymmetrically interacting modulatory population, enabling robust and controlled memory transitions. We formally derive short-timescale energy functions that govern local dynamics and use them to analytically compute memory escape times, revealing a phase transition between static and dynamic regimes. The analysis of capacity, defined as the number of memories that can be stored with minimal error rate as a function of the dimensions of the state space (number of feature neurons), for EDEN shows that it achieves exponential sequence memory capacity O(γN), outperforming the linear capacity O(N) of conventional models. Furthermore, EDEN's dynamics resemble the activity of time and ramping cells observed in the human brain during episodic memory tasks, grounding its biological relevance. By unifying static and sequential memory within a dynamic energy framework, EDEN offers a scalable and interpretable model for high-capacity temporal memory in both artificial and biological systems.

Real-time decoding of target variables from multiple simultaneously recorded neural time-series modalities, such as discrete spiking activity and continuous field potentials, is important across various neuroscience applications. However, a major challenge for doing so is that different neural modalities can have different timescales (i.e., sampling rates) and different probabilistic distributions, or can even be missing at some time-steps. Existing nonlinear models of multimodal neural activity do not address different timescales or missing samples across modalities. Further, some of these models do not allow for real-time decoding. Here, we develop a learning framework that can enable real-time recursive decoding while nonlinearly aggregating information across multiple modalities with different timescales and distributions and with missing samples. This framework consists of 1) a multiscale encoder that nonlinearly aggregates information after learning within-modality dynamics to handle different timescales and missing samples in real time, 2) a multiscale dynamical backbone that extracts multimodal temporal dynamics and enables real-time recursive decoding, and 3) modality-specific decoders to account for different probabilistic distributions across modalities. In both simulations and three distinct multiscale brain datasets, we show that our model can aggregate information across modalities with different timescales and distributions and missing samples to improve real-time target decoding. Further, our method outperforms various linear and nonlinear multimodal benchmarks in doing so.

Understanding the inductive bias and generalization properties of large overparametrized machine learning models requires to characterize the dynamics of the training algorithm. We study the learning dynamics of large two-layer neural networks via dynamical mean field theory, a well established technique of nonequilibrium statistical physics. We show that, for large network width m, and large number of samples per input dimension n/d, the training dynamics exhibits a separation of timescales which implies: (i) The emergence of a slow time scale associated with the growth in Gaussian/Rademacher complexity of the network; (ii) Inductive bias towards small complexity if the initialization has small enough complexity; (iii) A dynamical decoupling between feature learning and overfitting regimes; (iv)A non-monotone behavior of the test error, associated'feature unlearning' regime at large times.

The feedback that AI systems (e.g., recommender systems, chatbots) collect from user interactions is a crucial source of training data. While short-term feedback (e.g., clicks, engagement) is widely used for training, there is ample evidence that optimizing short-term feedback does not necessarily achieve the desired long-term objectives. Unfortunately, directly optimizing for long-term objectives is challenging, and we identify the disconnect in the timescales of short-term interventions (e.g., rankings) and the long-term feedback (e.g., user retention) as one of the key obstacles. To overcome this disconnect, we introduce the framework of MultiScale Policy Learning to contextually reconcile that AI systems need to act and optimize feedback at multiple interdependent timescales. Following a PAC-Bayes motivation, we show how the lower timescales with more plentiful data can provide a data-dependent hierarchical prior for faster learning at higher scales, where data is more scarce.

Accurate weather forecasting across time scales is critical for anticipating and mitigating the impacts of climate change. Recent data-driven methods based on deep learning have achieved significant success in the medium range, but struggle at longer subseasonal-to-seasonal (S2S) horizons due to error accumulation in their autoregressive approach. In this work, we propose OmniCast, a scalable and skillful probabilistic model that unifies weather forecasting across timescales. OmniCast consists of two components: a VAE model that encodes raw weather data into a continuous, lower-dimensional latent space, and a diffusion-based transformer model that generates a sequence of future latent tokens given the initial conditioning tokens. During training, we mask random future tokens and train the transformer to estimate their distribution given conditioning and visible tokens using a per-token diffusion head. During inference, the transformer generates the full sequence of future tokens by iteratively unmasking random subsets of tokens.

The feedback that AI systems (e.g., recommender systems, chatbots) collect from user interactions is a crucial source of training data. While short-term feedback (e.g., clicks, engagement) is widely used for training, there is ample evidence that optimizing short-term feedback does not necessarily achieve the desired long-term objectives. Unfortunately, directly optimizing for long-term objectives is challenging, and we identify the disconnect in the timescales of short-term interventions (e.g., rankings) and the long-term feedback (e.g., user retention) as one of the key obstacles. To overcome this disconnect, we introduce the framework of MultiScale Policy Learning to contextually reconcile that AI systems need to act and optimize feedback at multiple interdependent timescales. Following a PAC-Bayes motivation, we show how the lower timescales with more plentiful data can provide a data-dependent hierarchical prior for faster learning at higher scales, where data is more scarce.

Behavioral experiments on humans and animals suggest that the brain performs probabilistic inference to interpret its environment. Here we present a new generalpurpose, biologically-plausible neural implementation of approximate inference. The neural network represents uncertainty using Probabilistic Population Codes (PPCs), which are distributed neural representations that naturally encode probability distributions, and support marginalization and evidence integration in a biologically-plausible manner. By connecting multiple PPCs together as a probabilistic graphical model, we represent multivariate probability distributions. Approximate inference in graphical models can be accomplished by message-passing algorithms that disseminate local information throughout the graph. An attractive and often accurate example of such an algorithm is Loopy Belief Propagation (LBP), which uses local marginalization and evidence integration operations to perform approximate inference efficiently even for complex models.

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.