Diffusion models have demonstrated competitive performance in missing data imputation (MDI) task. However, directly applying diffusion models to MDI produces suboptimal performance due to two primary defects. First, the sample diversity promoted by diffusion models hinders the accurate inference of missing values. Second, data masking reduces observable indices for model training, obstructing imputation performance. To address these challenges, we introduce Negative Entropy-regularized Wasserstein gradient flow for Imputation (NewImp), enhancing diffusion models for MDI from a gradient flow perspective. To handle the first defect, we incorporate a negative entropy regularization term into the cost functional to suppress diversity and improve accuracy. To handle the second defect, we demonstrate that the imputation procedure of NewImp, induced by the conditional distribution-related cost functional, can equivalently be replaced by that induced by the joint distribution, thereby naturally eliminating the need for data masking.

Natural images captured by mobile devices often suffer from multiple types of degradation, such as noise, blur, and low light. Traditional image restoration methods require manual selection of specific tasks, algorithms, and execution sequences, which is time-consuming and may yield suboptimal results. All-in-one models, though capable of handling multiple tasks, typically support only a limited range and often produce overly smooth, low-fidelity outcomes due to their broad data distribution fitting. To address these challenges, we first define a new pipeline for restoring images with multiple degradations, and then introduce RestoreAgent, an intelligent image restoration system leveraging multimodal large language models. RestoreAgent autonomously assesses the type and extent of degradation in input images and performs restoration through (1) determining the appropriate restoration tasks, (2) optimizing the task sequence, (3) selecting the most suitable models, and (4) executing the restoration. Experimental results demonstrate the superior performance of RestoreAgent in handling complex degradation, surpassing human experts.

Despite existing 3D cloth simulators producing realistic results, they predominantly operate on discrete surface representations (e.g., points and meshes) with a fixed spatial resolution, which often leads to large memory consumption and resolutiondependent simulations. Moreover, back-propagating gradients through the existing solvers is difficult, and they hence cannot be easily integrated into modern neural architectures. In response, this paper re-thinks physically accurate cloth simulation: We propose NeuralClothSim, i.e., a new quasistatic cloth simulator using thin shells, in which surface deformation is encoded in neural network weights in the form of a neural field. Our memory-efficient solver operates on a new continuous coordinatebased surface representation called neural deformation fields (NDFs); it supervises NDF equilibria with the laws of the non-linear Kirchhoff-Love shell theory with a non-linear anisotropic material model. NDFs are adaptive: They 1) allocate their capacity to the deformation details and 2) allow surface state queries at arbitrary spatial resolutions without re-training. We show how to train NeuralClothSim while imposing hard boundary conditions and demonstrate multiple applications, such as material interpolation and simulation editing. The experimental results highlight the effectiveness of our continuous neural formulation.

We present a new random walk for uniformly sampling high-dimensional convex bodies.

The slow rate is due to the Brownian Motion without a drift term.

Spatio-temporal (ST) prediction has garnered a De facto attention in earth sciences, such as meteorological prediction, human mobility perception. However, the scarcity of data coupled with the high expenses involved in sensor deployment results in notable data imbalances. Furthermore, models that are excessively customized and devoid of causal connections further undermine the generalizability and interpretability. To this end, we establish a framework for ST predictions from a causal perspective, termed CaPaint, which targets to identify causal regions in data and endow model with causal reasoning ability in a two-stage process. Going beyond this process, we build on the front door adjustment as the theoretical foundation to specifically address the sub-regions identified as non-causal in the upstream phase.

In this paper we consider the problem of how a reinforcement learning agent that is tasked with solving a sequence of reinforcement learning problems (a sequence of Markov decision processes) can use knowledge acquired early in its lifetime to improve its ability to solve new problems. We argue that previous experience with similar problems can provide an agent with information about how it should explore when facing a new but related problem. We show that the search for an optimal exploration strategy can be formulated as a reinforcement learning problem itself and demonstrate that such strategy can leverage patterns found in the structure of related problems. We conclude with experiments that show the benefits of optimizing an exploration strategy using our proposed framework.

Inspired by the success of foundation models in applications such as ChatGPT, as graph data has been ubiquitous, one can envision the far-reaching impacts that can be brought by Graph Foundation Models (GFMs) with broader applications in the areas such as scientific research, social network analysis, drug discovery, and e-commerce. Despite the significant progress of pre-trained graph neural networks, there haven't been GFMs that can achieve desired performance on various graph-learning-related tasks. Building GFMs may rely on a vocabulary that encodes transferable patterns shared among different tasks and domains. Unlike image and text, defining such transferable patterns for graphs remains an open question. In this paper, we aim to bridge this gap by rethinking the transferable patterns on graphs as computation trees - i.e., tree structures derived from the message-passing process. Based on this insight, we propose a cross-task, crossdomain graph foundation model named GFT, short for Graph Foundation model with transferable Tree vocabulary. By treating computation trees as tokens within the transferable vocabulary, GFT improves model generalization and reduces the risk of negative transfer. The theoretical analyses and extensive experimental studies have demonstrated the transferability of computation trees and shown the effectiveness of GFT across diverse tasks and domains in graph learning.

This paper considers the problem of efficient exploration of unseen environments, a key challenge in AI. We propose a'learning to explore' framework where we learn a policy from a distribution of environments. At test time, presented with an unseen environment from the same distribution, the policy aims to generalize the exploration strategy to visit the maximum number of unique states in a limited number of steps. We particularly focus on environments with graph-structured state-spaces that are encountered in many important real-world applications like software testing and map building. We formulate this task as a reinforcement learning problem where the'exploration' agent is rewarded for transitioning to previously unseen environment states and employ a graph-structured memory to encode the agent's past trajectory. Experimental results demonstrate that our approach is extremely effective for exploration of spatial maps; and when applied on the challenging problems of coverage-guided software-testing of domain-specific programs and real-world mobile applications, it outperforms methods that have been hand-engineered by human experts.

Existing neural operator architectures face challenges when solving multiphysics problems with coupled partial differential equations (PDEs) due to complex geometries, interactions between physical variables, and the limited amounts of high-resolution training data. To address these issues, we propose Codomain Attention Neural Operator (CoDA-NO), which tokenizes functions along the codomain or channel space, enabling self-supervised learning or pretraining of multiple PDE systems. Specifically, we extend positional encoding, self-attention, and normalization layers to function spaces. CoDA-NO can learn representations of different PDE systems with a single model. We evaluate CoDA-NO's potential as a backbone for learning multiphysics PDEs over multiple systems by considering few-shot learning settings. On complex downstream tasks with limited data, such as fluid flow simulations, fluid-structure interactions, and Rayleigh-Bénard convection, we found CoDA-NO to outperform existing methods by over 36%.