DySLIM: Dynamics Stable Learning by Invariant Measure for Chaotic Systems

Learning dynamics from dissipative chaotic systems is notoriously difficult due to their inherent instability, as formalized by their positive Lyapunov exponents, which exponentially amplify errors in the learned dynamics. However, many of these systems exhibit ergodicity and an attractor: a compact and highly complex manifold, to which trajectories converge in finite-time, that supports an invariant measure, i.e., a probability distribution that is invariant under the action of the dynamics, which dictates the long-term statistical behavior of the system. In this work, we leverage this structure to propose a new framework that targets learning the invariant measure as well as the dynamics, in contrast with typical methods that only target the misfit between trajectories, which often leads to divergence as the trajectories' length increases. We use our framework to propose a tractable and sample efficient objective that can be used with any existing learning objectives. Our Dynamics Stable Learning by Invariant Measures (DySLIM) objective enables model training that achieves better point-wise tracking and long-term statistical accuracy relative to other learning objectives. By targeting the distribution with a scalable regularization term, we hope that this approach can be extended to more complex systems exhibiting slowly-variant distributions, such as weather and climate models.

A Systematic Comparison of Syllogistic Reasoning in Humans and Language Models

A central component of rational behavior is logical inference: the process of determining which conclusions follow from a set of premises. Psychologists have documented several ways in which humans' inferences deviate from the rules of logic. Do language models, which are trained on text generated by humans, replicate these biases, or are they able to overcome them? Focusing on the case of syllogisms -- inferences from two simple premises, which have been studied extensively in psychology -- we show that larger models are more logical than smaller ones, and also more logical than humans. At the same time, even the largest models make systematic errors, some of which mirror human reasoning biases such as ordering effects and logical fallacies. Overall, we find that language models mimic the human biases included in their training data, but are able to overcome them in some cases.

The Impact of Depth and Width on Transformer Language Model Generalization

To process novel sentences, language models (LMs) must generalize compositionally -- combine familiar elements in new ways. What aspects of a model's structure promote compositional generalization? Focusing on transformers, we test the hypothesis, motivated by recent theoretical and empirical work, that transformers generalize more compositionally when they are deeper (have more layers). Because simply adding layers increases the total number of parameters, confounding depth and size, we construct three classes of models which trade off depth for width such that the total number of parameters is kept constant (41M, 134M and 374M parameters). We pretrain all models as LMs and fine-tune them on tasks that test for compositional generalization. We report three main conclusions: (1) after fine-tuning, deeper models generalize better out-of-distribution than shallower models do, but the relative benefit of additional layers diminishes rapidly; (2) within each family, deeper models show better language modeling performance, but returns are similarly diminishing; (3) the benefits of depth for compositional generalization cannot be attributed solely to better performance on language modeling or on in-distribution data.

WeatherBench 2: A benchmark for the next generation of data-driven global weather models

WeatherBench 2 is an update to the global, medium-range (1-14 day) weather forecasting benchmark proposed by Rasp et al. (2020), designed with the aim to accelerate progress in data-driven weather modeling. WeatherBench 2 consists of an open-source evaluation framework, publicly available training, ground truth and baseline data as well as a continuously updated website with the latest metrics and state-of-the-art models: https://sites.research.google/weatherbench. This paper describes the design principles of the evaluation framework and presents results for current state-of-the-art physical and data-driven weather models. The metrics are based on established practices for evaluating weather forecasts at leading operational weather centers. We define a set of headline scores to provide an overview of model performance. In addition, we also discuss caveats in the current evaluation setup and challenges for the future of data-driven weather forecasting.

SEEDS: Emulation of Weather Forecast Ensembles with Diffusion Models

Probabilistic forecasting is crucial to decision-making under uncertainty about future weather. The dominant approach is to use an ensemble of forecasts to represent and quantify uncertainty in operational numerical weather prediction. However, generating ensembles is computationally costly. In this paper, we propose to generate ensemble forecasts at scale by leveraging recent advances in generative artificial intelligence. Our approach learns a data-driven probabilistic diffusion model from the 5-member ensemble GEFS reforecast dataset. The model can then be sampled efficiently to produce realistic weather forecasts, conditioned on a few members of the operational GEFS forecasting system. The generated ensembles have similar predictive skill as the full GEFS 31-member ensemble, evaluated against ERA5 reanalysis, and emulate well the statistics of large physics-based ensembles. We also apply the same methodology to developing a diffusion model for generative post-processing: the model directly learns to correct biases present in the emulated forecasting system by leveraging reanalysis data as labels during training. Ensembles from this generative post-processing model show greater reliability and accuracy, particularly in extreme event classification. In general, they are more reliable and forecast the probability of extreme weather more accurately than the GEFS operational ensemble. Our models achieve these results at less than 1/10th of the computational cost incurred by the operational GEFS system.

Encyclopedic VQA: Visual questions about detailed properties of fine-grained categories

We propose Encyclopedic-VQA, a large scale visual question answering (VQA) dataset featuring visual questions about detailed properties of fine-grained categories and instances. It contains 221k unique question+answer pairs each matched with (up to) 5 images, resulting in a total of 1M VQA samples. Moreover, our dataset comes with a controlled knowledge base derived from Wikipedia, marking the evidence to support each answer. Empirically, we show that our dataset poses a hard challenge for large vision+language models as they perform poorly on our dataset: PaLI [14] is state-of-the-art on OK-VQA [37], yet it only achieves 13.0% accuracy on our dataset. Moreover, we experimentally show that progress on answering our encyclopedic questions can be achieved by augmenting large models with a mechanism that retrieves relevant information from the knowledge base. An oracle experiment with perfect retrieval achieves 87.0% accuracy on the single-hop portion of our dataset, and an automatic retrieval-augmented prototype yields 48.8%. We believe that our dataset enables future research on retrieval-augmented vision+language models.

User-defined Event Sampling and Uncertainty Quantification in Diffusion Models for Physical Dynamical Systems

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make predictions and provide uncertainty quantification for chaotic dynamical systems. In these applications, diffusion models can implicitly represent knowledge about outliers and extreme events; however, querying that knowledge through conditional sampling or measuring probabilities is surprisingly difficult. Existing methods for conditional sampling at inference time seek mainly to enforce the constraints, which is insufficient to match the statistics of the distribution or compute the probability of the chosen events. To achieve these ends, optimally one would use the conditional score function, but its computation is typically intractable. In this work, we develop a probabilistic approximation scheme for the conditional score function which provably converges to the true distribution as the noise level decreases. With this scheme we are able to sample conditionally on nonlinear userdefined events at inference time, and matches data statistics even when sampling from the tails of the distribution.

Neural Ideal Large Eddy Simulation: Modeling Turbulence with Neural Stochastic Differential Equations

We introduce a data-driven learning framework that assimilates two powerful ideas: ideal large eddy simulation (LES) from turbulence closure modeling and neural stochastic differential equations (SDE) for stochastic modeling. The ideal LES models the LES flow by treating each full-order trajectory as a random realization of the underlying dynamics, as such, the effect of small-scales is marginalized to obtain the deterministic evolution of the LES state. However, ideal LES is analytically intractable. In our work, we use a latent neural SDE to model the evolution of the stochastic process and an encoder-decoder pair for transforming between the latent space and the desired ideal flow field. This stands in sharp contrast to other types of neural parameterization of closure models where each trajectory is treated as a deterministic realization of the dynamics. We show the effectiveness of our approach (niLES - neural ideal LES) on a challenging chaotic dynamical system: Kolmogorov flow at a Reynolds number of 20,000. Compared to competing methods, our method can handle non-uniform geometries using unstructured meshes seamlessly. In particular, niLES leads to trajectories with more accurate statistics and enhances stability, particularly for long-horizon rollouts.

Debias Coarsely, Sample Conditionally: Statistical Downscaling through Optimal Transport and Probabilistic Diffusion Models

We introduce a two-stage probabilistic framework for statistical downscaling between unpaired data. Statistical downscaling seeks a probabilistic map to transform low-resolution data from a (possibly biased) coarse-grained numerical scheme to high-resolution data that is consistent with a high-fidelity scheme. Our framework tackles the problem by tandeming two transformations: a debiasing step that is performed by an optimal transport map, and an upsampling step that is achieved by a probabilistic diffusion model with \textit{a posteriori} conditional sampling. This approach characterizes a conditional distribution without the need for paired data, and faithfully recovers relevant physical statistics from biased samples. We demonstrate the utility of the proposed approach on one- and two-dimensional fluid flow problems, which are representative of the core difficulties present in numerical simulations of weather and climate. Our method produces realistic high-resolution outputs from low-resolution inputs, by upsampling resolutions of $8\times$ and $16\times$. Moreover, our procedure correctly matches the statistics of physical quantities, even when the low-frequency content of the inputs and outputs do not match, a crucial but difficult-to-satisfy assumption needed by current state-of-the-art alternatives.

V2Meow: Meowing to the Visual Beat via Music Generation

Generating high quality music that complements the visual content of a video is a challenging task. Most existing visual conditioned music generation systems generate symbolic music data, such as MIDI files, instead of raw audio waveform. Given the limited availability of symbolic music data, such methods can only generate music for a few instruments or for specific types of visual input. In this paper, we propose a novel approach called V2Meow that can generate high-quality music audio that aligns well with the visual semantics of a diverse range of video input types. Specifically, the proposed music generation system is a multi-stage autoregressive model which is trained with a number of O(100K) music audio clips paired with video frames, which are mined from in-the-wild music videos, and no parallel symbolic music data is involved. V2Meow is able to synthesize high-fidelity music audio waveform solely conditioned on pre-trained visual features extracted from an arbitrary silent video clip, and it also allows high-level control over the music style of generation examples via supporting text prompts in addition to the video frames conditioning. Through both qualitative and quantitative evaluations, we demonstrate that our model outperforms several existing music generation systems in terms of both visual-audio correspondence and audio quality.