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We consider optimal experimental design (OED) for nonlinear Bayesian inverse problems governed by large-scale partial differential equations (PDEs). For the optimality criteria of Bayesian OED, we consider both expected information gain and summary statistics including the trace and determinant of the information matrix that involves the evaluation of the parameter-to-observable (PtO) map and its derivatives. However, it is prohibitive to compute and optimize these criteria when the PDEs are very expensive to solve, the parameters to estimate are high-dimensional, and the optimization problem is combinatorial, high-dimensional, and non-convex. To address these challenges, we develop an accurate, scalable, and efficient computational framework to accelerate the solution of Bayesian OED. In particular, the framework is developed based on derivative-informed neural operator (DINO) surrogates with proper dimension reduction techniques and a modified swapping greedy algorithm. We demonstrate the high accuracy of the DINO surrogates in the computation of the PtO map and the optimality criteria compared to high-fidelity finite element approximations. We also show that the proposed method is scalable with increasing parameter dimensions. Moreover, we demonstrate that it achieves high efficiency with over 1000X speedup compared to a high-fidelity Bayesian OED solution for a three-dimensional PDE example with tens of thousands of parameters, including both online evaluation and offline construction costs of the surrogates.

This work considers the asymptotic behavior of the distance between two sample covariance matrices (SCM). A general result is provided for a class of functionals that can be expressed as sums of traces of functions that are separately applied to each covariance matrix. In particular, this class includes very conventional metrics, such as the Euclidean distance or Jeffrery's divergence, as well as a number of other more sophisticated distances recently derived from Riemannian geometry considerations, such as the log-Euclidean metric. In particular, we analyze the asymptotic behavior of this class of functionals by establishing a central limit theorem that allows us to describe their asymptotic statistical law. In order to account for the fact that the sample sizes of two SCMs are of the same order of magnitude as their observation dimension, results are provided by assuming that these parameters grow to infinity while their quotients converge to fixed quantities. Numerical results illustrate how this type of result can be used in order to predict the performance of these metrics in practical machine learning algorithms, such as clustering of SCMs.

We propose a novel end-to-end method for cross-view pose estimation. Given a ground-level query image and an aerial image that covers the query's local neighborhood, the 3 Degrees-of-Freedom camera pose of the query is estimated by matching its image descriptor to descriptors of local regions within the aerial image. The orientation-aware descriptors are obtained by using a translationally equivariant convolutional ground image encoder and contrastive learning. The Localization Decoder produces a dense probability distribution in a coarse-to-fine manner with a novel Localization Matching Upsampling module. A smaller Orientation Decoder produces a vector field to condition the orientation estimate on the localization. Our method is validated on the VIGOR and KITTI datasets, where it surpasses the state-of-the-art baseline by 72% and 36% in median localization error for comparable orientation estimation accuracy. The predicted probability distribution can represent localization ambiguity, and enables rejecting possible erroneous predictions. Without re-training, the model can infer on ground images with different field of views and utilize orientation priors if available. On the Oxford RobotCar dataset, our method can reliably estimate the ego-vehicle's pose over time, achieving a median localization error under 1 meter and a median orientation error of around 1 degree at 14 FPS.

Physics-Informed Neural Networks (PINNs) have proven effective in solving partial differential equations (PDEs), especially when some data are available by blending seamlessly data and physics. However, extending PINNs to high-dimensional and even high-order PDEs encounters significant challenges due to the computational cost associated with automatic differentiation in the residual loss. Herein, we address the limitations of PINNs in handling high-dimensional and high-order PDEs by introducing Hutchinson Trace Estimation (HTE). Starting with the second-order high-dimensional PDEs ubiquitous in scientific computing, HTE transforms the calculation of the entire Hessian matrix into a Hessian vector product (HVP). This approach alleviates the computational bottleneck via Taylor-mode automatic differentiation and significantly reduces memory consumption from the Hessian matrix to HVP. We further showcase HTE's convergence to the original PINN loss and its unbiased behavior under specific conditions. Comparisons with Stochastic Dimension Gradient Descent (SDGD) highlight the distinct advantages of HTE, particularly in scenarios with significant variance among dimensions. We further extend HTE to higher-order and higher-dimensional PDEs, specifically addressing the biharmonic equation. By employing tensor-vector products (TVP), HTE efficiently computes the colossal tensor associated with the fourth-order high-dimensional biharmonic equation, saving memory and enabling rapid computation. The effectiveness of HTE is illustrated through experimental setups, demonstrating comparable convergence rates with SDGD under memory and speed constraints. Additionally, HTE proves valuable in accelerating the Gradient-Enhanced PINN (gPINN) version as well as the Biharmonic equation. Overall, HTE opens up a new capability in scientific machine learning for tackling high-order and high-dimensional PDEs.

Gait recognition is a biometric technology that has received extensive attention. Most existing gait recognition algorithms are unimodal, and a few multimodal gait recognition algorithms perform multimodal fusion only once. None of these algorithms may fully exploit the complementary advantages of the multiple modalities. In this paper, by considering the temporal and spatial characteristics of gait data, we propose a multi-stage feature fusion strategy (MSFFS), which performs multimodal fusions at different stages in the feature extraction process. Also, we propose an adaptive feature fusion module (AFFM) that considers the semantic association between silhouettes and skeletons. The fusion process fuses different silhouette areas with their more related skeleton joints. Since visual appearance changes and time passage co-occur in a gait period, we propose a multiscale spatial-temporal feature extractor (MSSTFE) to learn the spatial-temporal linkage features thoroughly. Specifically, MSSTFE extracts and aggregates spatial-temporal linkages information at different spatial scales. Combining the strategy and modules mentioned above, we propose a multi-stage adaptive feature fusion (MSAFF) neural network, which shows state-of-the-art performance in many experiments on three datasets. Besides, MSAFF is equipped with feature dimensional pooling (FD Pooling), which can significantly reduce the dimension of the gait representations without hindering the accuracy. //github.com/ShinanZou/MSAFF

Recent artificial intelligence (AI) systems have reached milestones in "grand challenges" ranging from Go to protein-folding. The capability to retrieve medical knowledge, reason over it, and answer medical questions comparably to physicians has long been viewed as one such grand challenge. Large language models (LLMs) have catalyzed significant progress in medical question answering; Med-PaLM was the first model to exceed a "passing" score in US Medical Licensing Examination (USMLE) style questions with a score of 67.2% on the MedQA dataset. However, this and other prior work suggested significant room for improvement, especially when models' answers were compared to clinicians' answers. Here we present Med-PaLM 2, which bridges these gaps by leveraging a combination of base LLM improvements (PaLM 2), medical domain finetuning, and prompting strategies including a novel ensemble refinement approach. Med-PaLM 2 scored up to 86.5% on the MedQA dataset, improving upon Med-PaLM by over 19% and setting a new state-of-the-art. We also observed performance approaching or exceeding state-of-the-art across MedMCQA, PubMedQA, and MMLU clinical topics datasets. We performed detailed human evaluations on long-form questions along multiple axes relevant to clinical applications. In pairwise comparative ranking of 1066 consumer medical questions, physicians preferred Med-PaLM 2 answers to those produced by physicians on eight of nine axes pertaining to clinical utility (p < 0.001). We also observed significant improvements compared to Med-PaLM on every evaluation axis (p < 0.001) on newly introduced datasets of 240 long-form "adversarial" questions to probe LLM limitations. While further studies are necessary to validate the efficacy of these models in real-world settings, these results highlight rapid progress towards physician-level performance in medical question answering.

Advances in artificial intelligence often stem from the development of new environments that abstract real-world situations into a form where research can be done conveniently. This paper contributes such an environment based on ideas inspired by elementary Microeconomics. Agents learn to produce resources in a spatially complex world, trade them with one another, and consume those that they prefer. We show that the emergent production, consumption, and pricing behaviors respond to environmental conditions in the directions predicted by supply and demand shifts in Microeconomics. We also demonstrate settings where the agents' emergent prices for goods vary over space, reflecting the local abundance of goods. After the price disparities emerge, some agents then discover a niche of transporting goods between regions with different prevailing prices -- a profitable strategy because they can buy goods where they are cheap and sell them where they are expensive. Finally, in a series of ablation experiments, we investigate how choices in the environmental rewards, bartering actions, agent architecture, and ability to consume tradable goods can either aid or inhibit the emergence of this economic behavior. This work is part of the environment development branch of a research program that aims to build human-like artificial general intelligence through multi-agent interactions in simulated societies. By exploring which environment features are needed for the basic phenomena of elementary microeconomics to emerge automatically from learning, we arrive at an environment that differs from those studied in prior multi-agent reinforcement learning work along several dimensions. For example, the model incorporates heterogeneous tastes and physical abilities, and agents negotiate with one another as a grounded form of communication.

We consider the problem of explaining the predictions of graph neural networks (GNNs), which otherwise are considered as black boxes. Existing methods invariably focus on explaining the importance of graph nodes or edges but ignore the substructures of graphs, which are more intuitive and human-intelligible. In this work, we propose a novel method, known as SubgraphX, to explain GNNs by identifying important subgraphs. Given a trained GNN model and an input graph, our SubgraphX explains its predictions by efficiently exploring different subgraphs with Monte Carlo tree search. To make the tree search more effective, we propose to use Shapley values as a measure of subgraph importance, which can also capture the interactions among different subgraphs. To expedite computations, we propose efficient approximation schemes to compute Shapley values for graph data. Our work represents the first attempt to explain GNNs via identifying subgraphs explicitly and directly. Experimental results show that our SubgraphX achieves significantly improved explanations, while keeping computations at a reasonable level.

Recently, a considerable literature has grown up around the theme of Graph Convolutional Network (GCN). How to effectively leverage the rich structural information in complex graphs, such as knowledge graphs with heterogeneous types of entities and relations, is a primary open challenge in the field. Most GCN methods are either restricted to graphs with a homogeneous type of edges (e.g., citation links only), or focusing on representation learning for nodes only instead of jointly propagating and updating the embeddings of both nodes and edges for target-driven objectives. This paper addresses these limitations by proposing a novel framework, namely the Knowledge Embedding based Graph Convolutional Network (KE-GCN), which combines the power of GCNs in graph-based belief propagation and the strengths of advanced knowledge embedding (a.k.a. knowledge graph embedding) methods, and goes beyond. Our theoretical analysis shows that KE-GCN offers an elegant unification of several well-known GCN methods as specific cases, with a new perspective of graph convolution. Experimental results on benchmark datasets show the advantageous performance of KE-GCN over strong baseline methods in the tasks of knowledge graph alignment and entity classification.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis.