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Effective modeling of group interactions and dynamic semantic intentions is crucial for forecasting behaviors like trajectories or movements. In complex scenarios like sports, agents' trajectories are influenced by group interactions and intentions, including team strategies and opponent actions. To this end, we propose a novel diffusion-based trajectory prediction framework that integrates group-level interactions into a conditional diffusion model, enabling the generation of diverse trajectories aligned with specific group activity. To capture dynamic semantic intentions, we frame group interaction prediction as a cooperative game, using Banzhaf interaction to model cooperation trends. We then fuse semantic intentions with enhanced agent embeddings, which are refined through both global and local aggregation. Furthermore, we expand the NBA SportVU dataset by adding human annotations of team-level tactics for trajectory and tactic prediction tasks. Extensive experiments on three widely-adopted datasets demonstrate that our model outperforms state-of-the-art methods. Our source code and data are available at //github.com/aurora-xin/Group2Int-trajectory.

Neural operators effectively solve PDE problems from data without knowing the explicit equations, which learn the map from the input sequences of observed samples to the predicted values. Most existing works build the model in the original geometric space, leading to high computational costs when the number of sample points is large. We present the Latent Neural Operator (LNO) solving PDEs in the latent space. In particular, we first propose Physics-Cross-Attention (PhCA) transforming representation from the geometric space to the latent space, then learn the operator in the latent space, and finally recover the real-world geometric space via the inverse PhCA map. Our model retains flexibility that can decode values in any position not limited to locations defined in the training set, and therefore can naturally perform interpolation and extrapolation tasks particularly useful for inverse problems. Moreover, the proposed LNO improves both prediction accuracy and computational efficiency. Experiments show that LNO reduces the GPU memory by 50%, speeds up training 1.8 times, and reaches state-of-the-art accuracy on four out of six benchmarks for forward problems and a benchmark for inverse problem. Code is available at //github.com/L-I-M-I-T/LatentNeuralOperator.

We consider the variable selection problem for two-sample tests, aiming to select the most informative variables to determine whether two collections of samples follow the same distribution. To address this, we propose a novel framework based on the kernel maximum mean discrepancy (MMD). Our approach seeks a subset of variables with a pre-specified size that maximizes the variance-regularized kernel MMD statistic. We focus on three commonly used types of kernels: linear, quadratic, and Gaussian. From a computational perspective, we derive mixed-integer programming formulations and propose exact and approximation algorithms with performance guarantees to solve these formulations. From a statistical viewpoint, we derive the rate of testing power of our framework under appropriate conditions. These results show that the sample size requirements for the three kernels depend crucially on the number of selected variables, rather than the data dimension. Experimental results on synthetic and real datasets demonstrate the superior performance of our method, compared to other variable selection frameworks, particularly in high-dimensional settings.

Recent theoretical results in quantum machine learning have demonstrated a general trade-off between the expressive power of quantum neural networks (QNNs) and their trainability; as a corollary of these results, practical exponential separations in expressive power over classical machine learning models are believed to be infeasible as such QNNs take a time to train that is exponential in the model size. We here circumvent these negative results by constructing a hierarchy of efficiently trainable QNNs that exhibit unconditionally provable, polynomial memory separations of arbitrary constant degree over classical neural networks -- including state-of-the-art models, such as Transformers -- in performing a classical sequence modeling task. This construction is also computationally efficient, as each unit cell of the introduced class of QNNs only has constant gate complexity. We show that contextuality -- informally, a quantitative notion of semantic ambiguity -- is the source of the expressivity separation, suggesting that other learning tasks with this property may be a natural setting for the use of quantum learning algorithms.

We introduce a method for performing cross-validation without sample splitting. The method is well-suited for problems where traditional sample splitting is infeasible, such as when data are not assumed to be independently and identically distributed. Even in scenarios where sample splitting is possible, our method offers a computationally efficient alternative for estimating prediction error, achieving comparable or even lower error than standard cross-validation at a significantly reduced computational cost. Our approach constructs train-test data pairs using externally generated Gaussian randomization variables, drawing inspiration from recent randomization techniques such as data-fission and data-thinning. The key innovation lies in a carefully designed correlation structure among these randomization variables, referred to as antithetic Gaussian randomization. This correlation is crucial in maintaining a bounded variance while allowing the bias to vanish, offering an additional advantage over standard cross-validation, whose performance depends heavily on the bias-variance tradeoff dictated by the number of folds. We provide a theoretical analysis of the mean squared error of the proposed estimator, proving that as the level of randomization decreases to zero, the bias converges to zero, while the variance remains bounded and decays linearly with the number of repetitions. This analysis highlights the benefits of the antithetic Gaussian randomization over independent randomization. Simulation studies corroborate our theoretical findings, illustrating the robust performance of our cross-validated estimator across various data types and loss functions.

We introduce a class of neural controlled differential equation inspired by quantum mechanics. Neural quantum controlled differential equations (NQDEs) model the dynamics by analogue of the Schr\"{o}dinger equation. Specifically, the hidden state represents the wave function, and its collapse leads to an interpretation of the classification probability. We implement and compare the results of four variants of NQDEs on a toy spiral classification problem.

Photoacoustic imaging (PAI) suffers from inherent limitations that can degrade the quality of reconstructed results, such as noise, artifacts and incomplete data acquisition caused by sparse sampling or partial array detection. In this study, we proposed a new optimization method for both two-dimensional (2D) and three-dimensional (3D) PAI reconstruction results, called the regularized iteration method with shape prior. The shape prior is a probability matrix derived from the reconstruction results of multiple sets of random partial array signals in a computational imaging system using any reconstruction algorithm, such as Delay-and-Sum (DAS) and Back-Projection (BP). In the probability matrix, high-probability locations indicate high consistency among multiple reconstruction results at those positions, suggesting a high likelihood of representing the true imaging results. In contrast, low-probability locations indicate higher randomness, leaning more towards noise or artifacts. As a shape prior, this probability matrix guides the iteration and regularization of the entire array signal reconstruction results using the original reconstruction algorithm (the same algorithm for processing random partial array signals). The method takes advantage of the property that the similarity of the object to be imitated is higher than that of noise or artifact in the results reconstructed by multiple sets of random partial array signals of the entire imaging system. The probability matrix is taken as a prerequisite for improving the original reconstruction results, and the optimizer is used to further iterate the imaging results to remove noise and artifacts and improve the imaging fidelity. Especially in the case involving sparse view which brings more artifacts, the effect is remarkable. Simulation and real experiments have both demonstrated the superiority of this method.

Deep neural networks (DNNs) are vulnerable to adversarial examples (AEs) that mislead the model while appearing benign to human observers. A critical concern is the transferability of AEs, which enables black-box attacks without direct access to the target model. However, many previous attacks have failed to explain the intrinsic mechanism of adversarial transferability. In this paper, we rethink the property of transferable AEs and reformalize the formulation of transferability. Building on insights from this mechanism, we analyze the generalization of AEs across models with different architectures and prove that we can find a local perturbation to mitigate the gap between surrogate and target models. We further establish the inner connections between model smoothness and flat local maxima, both of which contribute to the transferability of AEs. Further, we propose a new adversarial attack algorithm, \textbf{A}dversarial \textbf{W}eight \textbf{T}uning (AWT), which adaptively adjusts the parameters of the surrogate model using generated AEs to optimize the flat local maxima and model smoothness simultaneously, without the need for extra data. AWT is a data-free tuning method that combines gradient-based and model-based attack methods to enhance the transferability of AEs. Extensive experiments on a variety of models with different architectures on ImageNet demonstrate that AWT yields superior performance over other attacks, with an average increase of nearly 5\% and 10\% attack success rates on CNN-based and Transformer-based models, respectively, compared to state-of-the-art attacks.

Incompleteness is a common problem for existing knowledge graphs (KGs), and the completion of KG which aims to predict links between entities is challenging. Most existing KG completion methods only consider the direct relation between nodes and ignore the relation paths which contain useful information for link prediction. Recently, a few methods take relation paths into consideration but pay less attention to the order of relations in paths which is important for reasoning. In addition, these path-based models always ignore nonlinear contributions of path features for link prediction. To solve these problems, we propose a novel KG completion method named OPTransE. Instead of embedding both entities of a relation into the same latent space as in previous methods, we project the head entity and the tail entity of each relation into different spaces to guarantee the order of relations in the path. Meanwhile, we adopt a pooling strategy to extract nonlinear and complex features of different paths to further improve the performance of link prediction. Experimental results on two benchmark datasets show that the proposed model OPTransE performs better than state-of-the-art methods.

It is important to detect anomalous inputs when deploying machine learning systems. The use of larger and more complex inputs in deep learning magnifies the difficulty of distinguishing between anomalous and in-distribution examples. At the same time, diverse image and text data are available in enormous quantities. We propose leveraging these data to improve deep anomaly detection by training anomaly detectors against an auxiliary dataset of outliers, an approach we call Outlier Exposure (OE). This enables anomaly detectors to generalize and detect unseen anomalies. In extensive experiments on natural language processing and small- and large-scale vision tasks, we find that Outlier Exposure significantly improves detection performance. We also observe that cutting-edge generative models trained on CIFAR-10 may assign higher likelihoods to SVHN images than to CIFAR-10 images; we use OE to mitigate this issue. We also analyze the flexibility and robustness of Outlier Exposure, and identify characteristics of the auxiliary dataset that improve performance.