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Probabilistic couplings are the foundation for many probabilistic relational program logics and arise when relating random sampling statements across two programs. In relational program logics, this manifests as dedicated coupling rules that, e.g., say we may reason as if two sampling statements return the same value. However, this approach fundamentally requires aligning or "synchronizing" the sampling statements of the two programs which is not always possible. In this paper, we develop Clutch, a higher-order probabilistic relational separation logic that addresses this issue by supporting asynchronous probabilistic couplings. We use Clutch to develop a logical step-indexed logical relational to reason about contextual refinement and equivalence of higher-order programs written in a rich language with higher-order local state and impredicative polymorphism. Finally, we demonstrate the usefulness of our approach on a number of case studies. All the results that appear in the paper have been formalized in the Coq proof assistant using the Coquelicot library and the Iris separation logic framework.

In this paper, we improve the kernel alignment regret bound for online kernel learning in the regime of the Hinge loss function. Previous algorithm achieves a regret of $O((\mathcal{A}_TT\ln{T})^{\frac{1}{4}})$ at a computational complexity (space and per-round time) of $O(\sqrt{\mathcal{A}_TT\ln{T}})$, where $\mathcal{A}_T$ is called \textit{kernel alignment}. We propose an algorithm whose regret bound and computational complexity are better than previous results. Our results depend on the decay rate of eigenvalues of the kernel matrix. If the eigenvalues of the kernel matrix decay exponentially, then our algorithm enjoys a regret of $O(\sqrt{\mathcal{A}_T})$ at a computational complexity of $O(\ln^2{T})$. Otherwise, our algorithm enjoys a regret of $O((\mathcal{A}_TT)^{\frac{1}{4}})$ at a computational complexity of $O(\sqrt{\mathcal{A}_TT})$. We extend our algorithm to batch learning and obtain a $O(\frac{1}{T}\sqrt{\mathbb{E}[\mathcal{A}_T]})$ excess risk bound which improves the previous $O(1/\sqrt{T})$ bound.

Data-based surrogate modeling has surged in capability in recent years with the emergence of graph neural networks (GNNs), which can operate directly on mesh-based representations of data. The goal of this work is to introduce an interpretable fine-tuning strategy for GNNs, with application to unstructured mesh-based fluid dynamics modeling. The end result is a fine-tuned GNN that adds interpretability to a pre-trained baseline GNN through an adaptive sub-graph sampling strategy that isolates regions in physical space intrinsically linked to the forecasting task, while retaining the predictive capability of the baseline. The structures identified by the fine-tuned GNNs, which are adaptively produced in the forward pass as explicit functions of the input, serve as an accessible link between the baseline model architecture, the optimization goal, and known problem-specific physics. Additionally, through a regularization procedure, the fine-tuned GNNs can also be used to identify, during inference, graph nodes that correspond to a majority of the anticipated forecasting error, adding a novel interpretable error-tagging capability to baseline models. Demonstrations are performed using unstructured flow data sourced from flow over a backward-facing step at high Reynolds numbers.

Magnetic resonance imaging (MRI) using hyperpolarized noble gases provides a way to visualize the structure and function of human lung, but the long imaging time limits its broad research and clinical applications. Deep learning has demonstrated great potential for accelerating MRI by reconstructing images from undersampled data. However, most existing deep conventional neural networks (CNN) directly apply square convolution to k-space data without considering the inherent properties of k-space sampling, limiting k-space learning efficiency and image reconstruction quality. In this work, we propose an encoding enhanced (EN2) complex CNN for highly undersampled pulmonary MRI reconstruction. EN2 employs convolution along either the frequency or phase-encoding direction, resembling the mechanisms of k-space sampling, to maximize the utilization of the encoding correlation and integrity within a row or column of k-space. We also employ complex convolution to learn rich representations from the complex k-space data. In addition, we develop a feature-strengthened modularized unit to further boost the reconstruction performance. Experiments demonstrate that our approach can accurately reconstruct hyperpolarized 129Xe and 1H lung MRI from 6-fold undersampled k-space data and provide lung function measurements with minimal biases compared with fully-sampled image. These results demonstrate the effectiveness of the proposed algorithmic components and indicate that the proposed approach could be used for accelerated pulmonary MRI in research and clinical lung disease patient care.

Nonresponse after probability sampling is a universal challenge in survey sampling, often necessitating adjustments to mitigate sampling and selection bias simultaneously. This study explored the removal of bias and effective utilization of available information, not just in nonresponse but also in the scenario of data integration, where summary statistics from other data sources are accessible. We reformulate these settings within a two-step monotone missing data framework, where the first step of missingness arises from sampling and the second originates from nonresponse. Subsequently, we derive the semiparametric efficiency bound for the target parameter. We also propose adaptive estimators utilizing methods of moments and empirical likelihood approaches to attain the lower bound. The proposed estimator exhibits both efficiency and double robustness. However, attaining efficiency with an adaptive estimator requires the correct specification of certain working models. To reinforce robustness against the misspecification of working models, we extend the property of double robustness to multiple robustness by proposing a two-step empirical likelihood method that effectively leverages empirical weights. A numerical study is undertaken to investigate the finite-sample performance of the proposed methods. We further applied our methods to a dataset from the National Health and Nutrition Examination Survey data by efficiently incorporating summary statistics from the National Health Interview Survey data.

We consider problems related to initial meshing and adaptive mesh refinement for the electromagnetic simulation of various structures. The quality of the initial mesh and the performance of the adaptive refinement are of great importance for the finite element solution of the Maxwell equations, since they directly affect the accuracy and the computational time. In this paper, we describe the complete meshing workflow, which allows the simulation of arbitrary structures. Test simulations confirm that the presented approach allows to reach the quality of the industrial simulation software.

We design an additive approximation scheme for estimating the cost of the min-weight bipartite matching problem: given a bipartite graph with non-negative edge costs and $\varepsilon > 0$, our algorithm estimates the cost of matching all but $O(\varepsilon)$-fraction of the vertices in truly subquadratic time $O(n^{2-\delta(\varepsilon)})$. Our algorithm has a natural interpretation for computing the Earth Mover's Distance (EMD), up to a $\varepsilon$-additive approximation. Notably, we make no assumptions about the underlying metric (more generally, the costs do not have to satisfy triangle inequality). Note that compared to the size of the instance (an arbitrary $n \times n$ cost matrix), our algorithm runs in {\em sublinear} time. Our algorithm can approximate a slightly more general problem: max-cardinality bipartite matching with a knapsack constraint, where the goal is to maximize the number of vertices that can be matched up to a total cost $B$.

Graph-based kNN algorithms have garnered widespread popularity for machine learning tasks due to their simplicity and effectiveness. However, as factual data often inherit complex distributions, the conventional kNN graph's reliance on a unified k-value can hinder its performance. A crucial factor behind this challenge is the presence of ambiguous samples along decision boundaries that are inevitably more prone to incorrect classifications. To address the situation, we propose the Distribution-Informed adaptive kNN Graph (DaNNG), which combines adaptive kNN with distribution-aware graph construction. By incorporating an approximation of the distribution with customized k-adaption criteria, DaNNG can significantly improve performance on ambiguous samples, and hence enhance overall accuracy and generalization capability. Through rigorous evaluations on diverse benchmark datasets, DaNNG outperforms state-of-the-art algorithms, showcasing its adaptability and efficacy across various real-world scenarios.

Humans perceive the world by concurrently processing and fusing high-dimensional inputs from multiple modalities such as vision and audio. Machine perception models, in stark contrast, are typically modality-specific and optimised for unimodal benchmarks, and hence late-stage fusion of final representations or predictions from each modality (`late-fusion') is still a dominant paradigm for multimodal video classification. Instead, we introduce a novel transformer based architecture that uses `fusion bottlenecks' for modality fusion at multiple layers. Compared to traditional pairwise self-attention, our model forces information between different modalities to pass through a small number of bottleneck latents, requiring the model to collate and condense the most relevant information in each modality and only share what is necessary. We find that such a strategy improves fusion performance, at the same time reducing computational cost. We conduct thorough ablation studies, and achieve state-of-the-art results on multiple audio-visual classification benchmarks including Audioset, Epic-Kitchens and VGGSound. All code and models will be released.

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.