Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning. A key reason for their success is their ability to accurately model long-range dependencies in spatio-temporal data by learning global convolutions in a computationally efficient manner. To this end, FNOs rely on the discrete Fourier transform (DFT), however, DFTs cause visual and spectral artifacts as well as pronounced dissipation when learning operators in spherical coordinates since they incorrectly assume a flat geometry. To overcome this limitation, we generalize FNOs on the sphere, introducing Spherical FNOs (SFNOs) for learning operators on spherical geometries. We apply SFNOs to forecasting atmospheric dynamics, and demonstrate stable auto\-regressive rollouts for a year of simulated time (1,460 steps), while retaining physically plausible dynamics. The SFNO has important implications for machine learning-based simulation of climate dynamics that could eventually help accelerate our response to climate change.

Carbon capture and storage (CCS) plays an essential role in global decarbonization. Scaling up CCS deployment requires accurate and high-resolution modeling of the storage reservoir pressure buildup and the gaseous plume migration. However, such modeling is very challenging at scale due to the high computational costs of existing numerical methods. This challenge leads to significant uncertainties in evaluating storage opportunities, which can delay the pace of large-scale CCS deployment. We introduce Nested Fourier Neural Operator (FNO), a machine-learning framework for high-resolution dynamic 3D CO2 storage modeling at a basin scale. Nested FNO produces forecasts at different refinement levels using a hierarchy of FNOs and speeds up flow prediction nearly 700,000 times compared to existing methods. By learning the solution operator for the family of governing partial differential equations, Nested FNO creates a general-purpose numerical simulator alternative for CO2 storage with diverse reservoir conditions, geological heterogeneity, and injection schemes. Our framework enables unprecedented real-time modeling and probabilistic simulations that can support the scale-up of global CCS deployment.

We present a scalable and effective exploration strategy based on Thompson sampling for reinforcement learning (RL). One of the key shortcomings of existing Thompson sampling algorithms is the need to perform a Gaussian approximation of the posterior distribution, which is not a good surrogate in most practical settings. We instead directly sample the Q function from its posterior distribution, by using Langevin Monte Carlo, an efficient type of Markov Chain Monte Carlo (MCMC) method. Our method only needs to perform noisy gradient descent updates to learn the exact posterior distribution of the Q function, which makes our approach easy to deploy in deep RL. We provide a rigorous theoretical analysis for the proposed method and demonstrate that, in the linear Markov decision process (linear MDP) setting, it has a regret bound of $\tilde{O}(d^{3/2}H^{5/2}\sqrt{T})$, where $d$ is the dimension of the feature mapping, $H$ is the planning horizon, and $T$ is the total number of steps. We apply this approach to deep RL, by using Adam optimizer to perform gradient updates. Our approach achieves better or similar results compared with state-of-the-art deep RL algorithms on several challenging exploration tasks from the Atari57 suite.

Prompt-based learning has emerged as a successful paradigm in natural language processing, where a single general-purpose language model can be instructed to perform any task specified by input prompts. Yet task specification in robotics comes in various forms, such as imitating one-shot demonstrations, following language instructions, and reaching visual goals. They are often considered different tasks and tackled by specialized models. We show that a wide spectrum of robot manipulation tasks can be expressed with multimodal prompts, interleaving textual and visual tokens. Accordingly, we develop a new simulation benchmark that consists of thousands of procedurally-generated tabletop tasks with multimodal prompts, 600K+ expert trajectories for imitation learning, and a four-level evaluation protocol for systematic generalization. We design a transformer-based robot agent, VIMA, that processes these prompts and outputs motor actions autoregressively. VIMA features a recipe that achieves strong model scalability and data efficiency. It outperforms alternative designs in the hardest zero-shot generalization setting by up to $2.9\times$ task success rate given the same training data. With $10\times$ less training data, VIMA still performs $2.7\times$ better than the best competing variant. Code and video demos are available at https://vimalabs.github.io/

We propose Image-to-Image Schr\"odinger Bridge (I$^2$SB), a new class of conditional diffusion models that directly learn the nonlinear diffusion processes between two given distributions. These diffusion bridges are particularly useful for image restoration, as the degraded images are structurally informative priors for reconstructing the clean images. I$^2$SB belongs to a tractable class of Schr\"odinger bridge, the nonlinear extension to score-based models, whose marginal distributions can be computed analytically given boundary pairs. This results in a simulation-free framework for nonlinear diffusions, where the I$^2$SB training becomes scalable by adopting practical techniques used in standard diffusion models. We validate I$^2$SB in solving various image restoration tasks, including inpainting, super-resolution, deblurring, and JPEG restoration on ImageNet 256x256 and show that I$^2$SB surpasses standard conditional diffusion models with more interpretable generative processes. Moreover, I$^2$SB matches the performance of inverse methods that additionally require the knowledge of the corruption operators. Our work opens up new algorithmic opportunities for developing efficient nonlinear diffusion models on a large scale. scale. Project page and codes: https://i2sb.github.io/

Closed-book question answering (QA) requires a model to directly answer an open-domain question without access to any external knowledge. Prior work on closed-book QA either directly finetunes or prompts a pretrained language model (LM) to leverage the stored knowledge. However, they do not fully exploit the parameterized knowledge. To address this issue, we propose a two-stage, closed-book QA framework which employs a coarse-to-fine approach to extract relevant knowledge and answer a question. Our approach first generates a related context for a given question by prompting a pretrained LM. We then prompt the same LM for answer prediction using the generated context and the question. Additionally, to eliminate failure caused by context uncertainty, we marginalize over generated contexts. Experimental results on three QA benchmarks show that our method significantly outperforms previous closed-book QA methods (e.g. exact matching 68.6% vs. 55.3%), and is on par with open-book methods that exploit external knowledge sources (e.g. 68.6% vs. 68.0%). Our method is able to better exploit the stored knowledge in pretrained LMs without adding extra learnable parameters or needing finetuning, and paves the way for hybrid models that integrate pretrained LMs with external knowledge.

Generating new molecules with specified chemical and biological properties via generative models has emerged as a promising direction for drug discovery. However, existing methods require extensive training/fine-tuning with a large dataset, often unavailable in real-world generation tasks. In this work, we propose a new retrieval-based framework for controllable molecule generation. We use a small set of exemplar molecules, i.e., those that (partially) satisfy the design criteria, to steer the pre-trained generative model towards synthesizing molecules that satisfy the given design criteria. We design a retrieval mechanism that retrieves and fuses the exemplar molecules with the input molecule, which is trained by a new self-supervised objective that predicts the nearest neighbor of the input molecule. We also propose an iterative refinement process to dynamically update the generated molecules and retrieval database for better generalization. Our approach is agnostic to the choice of generative models and requires no task-specific fine-tuning. On various tasks ranging from simple design criteria to a challenging real-world scenario for designing lead compounds that bind to the SARS-CoV-2 main protease, we demonstrate our approach extrapolates well beyond the retrieval database, and achieves better performance and wider applicability than previous methods. Code is available at https://github.com/NVlabs/RetMol.

The binding complexes formed by proteins and small molecule ligands are ubiquitous and critical to life. Despite recent advancements in protein structure prediction, existing algorithms are so far unable to systematically predict the binding ligand structures along with their regulatory effects on protein folding. To address this discrepancy, we present NeuralPLexer, a computational approach that can directly predict protein-ligand complex structures solely using protein sequence and ligand molecular graph inputs. NeuralPLexer adopts a deep generative model to sample the 3D structures of the binding complex and their conformational changes at an atomistic resolution. The model is based on a diffusion process that incorporates essential biophysical constraints and a multi-scale geometric deep learning system to iteratively sample residue-level contact maps and all heavy-atom coordinates in a hierarchical manner. NeuralPLexer achieves state-of-the-art performance compared to all existing methods on benchmarks for both protein-ligand blind docking and flexible binding site structure recovery. Moreover, owing to its specificity in sampling both ligand-free-state and ligand-bound-state ensembles, NeuralPLexer consistently outperforms AlphaFold2 in terms of global protein structure accuracy on both representative structure pairs with large conformational changes (average TM-score=0.93) and recently determined ligand-binding proteins (average TM-score=0.89). Case studies reveal that the predicted conformational variations are consistent with structure determination experiments for important targets, including human KRAS$^\textrm{G12C}$, ketol-acid reductoisomerase, and purine GPCRs. Our study suggests that a data-driven approach can capture the structural cooperativity between proteins and small molecules, showing promise in accelerating the design of enzymes, drug molecules, and beyond.

A significant gap remains between today's visual pattern recognition models and human-level visual cognition especially when it comes to few-shot learning and compositional reasoning of novel concepts. We introduce Bongard-HOI, a new visual reasoning benchmark that focuses on compositional learning of human-object interactions (HOIs) from natural images. It is inspired by two desirable characteristics from the classical Bongard problems (BPs): 1) few-shot concept learning, and 2) context-dependent reasoning. We carefully curate the few-shot instances with hard negatives, where positive and negative images only disagree on action labels, making mere recognition of object categories insufficient to complete our benchmarks. We also design multiple test sets to systematically study the generalization of visual learning models, where we vary the overlap of the HOI concepts between the training and test sets of few-shot instances, from partial to no overlaps. Bongard-HOI presents a substantial challenge to today's visual recognition models. The state-of-the-art HOI detection model achieves only 62% accuracy on few-shot binary prediction while even amateur human testers on MTurk have 91% accuracy. With the Bongard-HOI benchmark, we hope to further advance research efforts in visual reasoning, especially in holistic perception-reasoning systems and better representation learning.

The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets. We propose a generalization of neural networks to learn operators, termed neural operators, that map between infinite dimensional function spaces. We formulate the neural operator as a composition of linear integral operators and nonlinear activation functions. We prove a universal approximation theorem for our proposed neural operator, showing that it can approximate any given nonlinear continuous operator. The proposed neural operators are also discretization-invariant, i.e., they share the same model parameters among different discretization of the underlying function spaces. Furthermore, we introduce four classes of efficient parameterization, viz., graph neural operators, multi-pole graph neural operators, low-rank neural operators, and Fourier neural operators. An important application for neural operators is learning surrogate maps for the solution operators of partial differential equations (PDEs). We consider standard PDEs such as the Burgers, Darcy subsurface flow, and the Navier-Stokes equations, and show that the proposed neural operators have superior performance compared to existing machine learning based methodologies, while being several orders of magnitude faster than conventional PDE solvers.