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Data-driven machine learning approaches are being increasingly used to solve partial differential equations (PDEs). They have shown particularly striking successes when training an operator, which takes as input a PDE in some family, and outputs its solution. However, the architectural design space, especially given structural knowledge of the PDE family of interest, is still poorly understood. We seek to remedy this gap by studying the benefits of weight-tied neural network architectures for steady-state PDEs. To achieve this, we first demonstrate that the solution of most steady-state PDEs can be expressed as a fixed point of a non-linear operator. Motivated by this observation, we propose FNO-DEQ, a deep equilibrium variant of the FNO architecture that directly solves for the solution of a steady-state PDE as the infinite-depth fixed point of an implicit operator layer using a black-box root solver and differentiates analytically through this fixed point resulting in $\mathcal{O}(1)$ training memory. Our experiments indicate that FNO-DEQ-based architectures outperform FNO-based baselines with $4\times$ the number of parameters in predicting the solution to steady-state PDEs such as Darcy Flow and steady-state incompressible Navier-Stokes. Finally, we show FNO-DEQ is more robust when trained with datasets with more noisy observations than the FNO-based baselines, demonstrating the benefits of using appropriate inductive biases in architectural design for different neural network based PDE solvers. Further, we show a universal approximation result that demonstrates that FNO-DEQ can approximate the solution to any steady-state PDE that can be written as a fixed point equation.

Contents generated by recent advanced Text-to-Image (T2I) diffusion models are sometimes too imaginative for existing off-the-shelf property semantic predictors to estimate due to the immitigable domain gap. We introduce DMP, a pipeline utilizing pre-trained T2I models as a prior for pixel-level semantic prediction tasks. To address the misalignment between deterministic prediction tasks and stochastic T2I models, we reformulate the diffusion process through a sequence of interpolations, establishing a deterministic mapping between input RGB images and output prediction distributions. To preserve generalizability, we use low-rank adaptation to fine-tune pre-trained models. Extensive experiments across five tasks, including 3D property estimation, semantic segmentation, and intrinsic image decomposition, showcase the efficacy of the proposed method. Despite limited-domain training data, the approach yields faithful estimations for arbitrary images, surpassing existing state-of-the-art algorithms.

Mediation analysis is an important statistical tool in many research fields. Its aim is to investigate the mechanism along the causal pathway between an exposure and an outcome. The joint significance test is widely utilized as a prominent statistical approach for examining mediation effects in practical applications. Nevertheless, the limitation of this mediation testing method stems from its conservative Type I error, which reduces its statistical power and imposes certain constraints on its popularity and utility. The proposed solution to address this gap is the adaptive joint significance test for one mediator, a novel data-adaptive test for mediation effect that exhibits significant advancements compared to traditional joint significance test. The proposed method is designed to be user-friendly, eliminating the need for complicated procedures. We have derived explicit expressions for size and power, ensuring the theoretical validity of our approach. Furthermore, we extend the proposed adaptive joint significance tests for small-scale mediation hypotheses with family-wise error rate (FWER) control. Additionally, a novel adaptive Sobel-type approach is proposed for the estimation of confidence intervals for the mediation effects, demonstrating significant advancements over conventional Sobel's confidence intervals in terms of achieving desirable coverage probabilities. Our mediation testing and confidence intervals procedure is evaluated through comprehensive simulations, and compared with numerous existing approaches. Finally, we illustrate the usefulness of our method by analysing three real-world datasets with continuous, binary and time-to-event outcomes, respectively.

We demonstrate a user-focused verification approach for evaluating probability forecasts of binary outcomes (also known as probabilistic classifiers) that is (i) based on proper scoring rules, (ii) focuses on user decision thresholds, and (iii) provides actionable insights. We argue that the widespread use of categorical performance diagrams and the critical success index to evaluate probabilistic forecasts may produce misleading results and instead illustrate how Murphy diagrams are better for understanding performance across user decision thresholds. The use of proper scoring rules that account for the relative importance of different user decision thresholds is shown to impact scores of overall performance, as well as supporting measures of discrimination and calibration. These methods are demonstrated by evaluating several probabilistic thunderstorm forecast systems. Furthermore, we illustrate an approach that allows a fair comparison between continuous probabilistic forecasts and categorical outlooks using the FIxed Risk Multicategorical (FIRM) score and establish the relationship between the FIRM score and Murphy diagrams. The results highlight how the performance of thunderstorm forecasts produced for tropical Australian waters varies between operational meteorologists and an automated system depending on what decision thresholds a user is acting on. A hindcast of a new automated system is shown to generally perform better than both meteorologists and the old automated system across tropical Australian waters. While the methods are illustrated using thunderstorm forecasts, they are applicable for evaluating probabilistic forecasts for any situation with binary outcomes.

Deep neural networks, while powerful for image classification, often operate as "black boxes," complicating the understanding of their decision-making processes. Various explanation methods, particularly those generating saliency maps, aim to address this challenge. However, the inconsistency issues of faithfulness metrics hinder reliable benchmarking of explanation methods. This paper employs an approach inspired by psychometrics, utilizing Krippendorf's alpha to quantify the benchmark reliability of post-hoc methods in image classification. The study proposes model training modifications, including feeding perturbed samples and employing focal loss, to enhance robustness and calibration. Empirical evaluations demonstrate significant improvements in benchmark reliability across metrics, datasets, and post-hoc methods. This pioneering work establishes a foundation for more reliable evaluation practices in the realm of post-hoc explanation methods, emphasizing the importance of model robustness in the assessment process.

The Detection Transformer (DETR) has emerged as a pivotal role in object detection tasks, setting new performance benchmarks due to its end-to-end design and scalability. Despite its advancements, the application of DETR in detecting rotated objects has demonstrated suboptimal performance relative to established oriented object detectors. Our analysis identifies a key limitation: the L1 cost used in Hungarian Matching leads to duplicate predictions due to the square-like problem in oriented object detection, thereby obstructing the training process of the detector. We introduce a Hausdorff distance-based cost for Hungarian matching, which more accurately quantifies the discrepancy between predictions and ground truths. Moreover, we note that a static denoising approach hampers the training of rotated DETR, particularly when the detector's predictions surpass the quality of noised ground truths. We propose an adaptive query denoising technique, employing Hungarian matching to selectively filter out superfluous noised queries that no longer contribute to model improvement. Our proposed modifications to DETR have resulted in superior performance, surpassing previous rotated DETR models and other alternatives. This is evidenced by our model's state-of-the-art achievements in benchmarks such as DOTA-v1.0/v1.5/v2.0, and DIOR-R.

Social relations are often used to improve recommendation quality when user-item interaction data is sparse in recommender systems. Most existing social recommendation models exploit pairwise relations to mine potential user preferences. However, real-life interactions among users are very complicated and user relations can be high-order. Hypergraph provides a natural way to model complex high-order relations, while its potentials for improving social recommendation are under-explored. In this paper, we fill this gap and propose a multi-channel hypergraph convolutional network to enhance social recommendation by leveraging high-order user relations. Technically, each channel in the network encodes a hypergraph that depicts a common high-order user relation pattern via hypergraph convolution. By aggregating the embeddings learned through multiple channels, we obtain comprehensive user representations to generate recommendation results. However, the aggregation operation might also obscure the inherent characteristics of different types of high-order connectivity information. To compensate for the aggregating loss, we innovatively integrate self-supervised learning into the training of the hypergraph convolutional network to regain the connectivity information with hierarchical mutual information maximization. The experimental results on multiple real-world datasets show that the proposed model outperforms the SOTA methods, and the ablation study verifies the effectiveness of the multi-channel setting and the self-supervised task. The implementation of our model is available via //github.com/Coder-Yu/RecQ.

Collaborative filtering often suffers from sparsity and cold start problems in real recommendation scenarios, therefore, researchers and engineers usually use side information to address the issues and improve the performance of recommender systems. In this paper, we consider knowledge graphs as the source of side information. We propose MKR, a Multi-task feature learning approach for Knowledge graph enhanced Recommendation. MKR is a deep end-to-end framework that utilizes knowledge graph embedding task to assist recommendation task. The two tasks are associated by cross&compress units, which automatically share latent features and learn high-order interactions between items in recommender systems and entities in the knowledge graph. We prove that cross&compress units have sufficient capability of polynomial approximation, and show that MKR is a generalized framework over several representative methods of recommender systems and multi-task learning. Through extensive experiments on real-world datasets, we demonstrate that MKR achieves substantial gains in movie, book, music, and news recommendation, over state-of-the-art baselines. MKR is also shown to be able to maintain a decent performance even if user-item interactions are sparse.

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, thereby allowing manual manipulation in predicting the final answer.

While existing machine learning models have achieved great success for sentiment classification, they typically do not explicitly capture sentiment-oriented word interaction, which can lead to poor results for fine-grained analysis at the snippet level (a phrase or sentence). Factorization Machine provides a possible approach to learning element-wise interaction for recommender systems, but they are not directly applicable to our task due to the inability to model contexts and word sequences. In this work, we develop two Position-aware Factorization Machines which consider word interaction, context and position information. Such information is jointly encoded in a set of sentiment-oriented word interaction vectors. Compared to traditional word embeddings, SWI vectors explicitly capture sentiment-oriented word interaction and simplify the parameter learning. Experimental results show that while they have comparable performance with state-of-the-art methods for document-level classification, they benefit the snippet/sentence-level sentiment analysis.