Recently, flow-based generative models have shown superior efficiency compared to diffusion models. In this paper, we study rectified flow models, which constrain transport trajectories to be linear from the base distribution to the data distribution. This structural restriction greatly accelerates sampling, often enabling high-quality generation with a single Euler step. Under standard assumptions on the neural network classes used to parameterize the velocity field and data distribution, we prove that rectified flows achieve sample complexity $\tilde{O}(\varepsilon^{-2})$. This improves on the best known $O(\varepsilon^{-4})$ bounds for flow matching model and matches the optimal rate for mean estimation. Our analysis exploits the particular structure of rectified flows: because the model is trained with a squared loss along linear paths, the associated hypothesis class admits a sharply controlled localized Rademacher complexity. This yields the improved, order-optimal sample complexity and provides a theoretical explanation for the strong empirical performance of rectified flow models.

In this paper, we introduce the A2 Copula Spatial Bayesian Neural Network (A2-SBNN), a predictive spatial model designed to map coordinates to continuous fields while capturing both typical spatial patterns and extreme dependencies. By embedding the dual-tail novel Archimedean copula viz. A2 directly into the network's weight initialization, A2-SBNN naturally models complex spatial relationships, including rare co-movements in the data. The model is trained through a calibration-driven process combining Wasserstein loss, moment matching, and correlation penalties to refine predictions and manage uncertainty. Simulation results show that A2-SBNN consistently delivers high accuracy across a wide range of dependency strengths, offering a new, effective solution for spatial data modeling beyond traditional Gaussian-based approaches.

We propose a novel framework for representing neural fields on triangle meshes that is multi-resolution across both spatial and frequency domains. Inspired by the Neural Fourier Filter Bank (NFFB), our architecture decomposes the spatial and frequency domains by associating finer spatial resolution levels with higher frequency bands, while coarser resolutions are mapped to lower frequencies. To achieve geometry-aware spatial decomposition we leverage multiple DiffusionNet components, each associated with a different spatial resolution level. Subsequently, we apply a Fourier feature mapping to encourage finer resolution levels to be associated with higher frequencies. The final signal is composed in a wavelet-inspired manner using a sine-activated MLP, aggregating higher-frequency signals on top of lower-frequency ones. Our architecture attains high accuracy in learning complex neural fields and is robust to discontinuities, exponential scale variations of the target field, and mesh modification. We demonstrate the effectiveness of our approach through its application to diverse neural fields, such as synthetic RGB functions, UV texture coordinates, and vertex normals, illustrating different challenges. To validate our method, we compare its performance against two alternatives, showcasing the advantages of our multi-resolution architecture.

The magnetic inversion method is one of the non-destructive geophysical methods, which aims to estimate the subsurface susceptibility distribution from surface magnetic anomaly data. Recently, supervised deep learning methods have been widely utilized in lots of geophysical fields including magnetic inversion. However, these methods rely heavily on synthetic training data, whose performance is limited since the synthetic data is not independently and identically distributed with the field data. Thus, we proposed to realize magnetic inversion by self-supervised deep learning. The proposed self-supervised knowledge-driven 3D magnetic inversion method (SSKMI) learns on the target field data by a closed loop of the inversion and forward models. Given that the parameters of the forward model are preset, SSKMI can optimize the inversion model by minimizing the mean absolute error between observed and re-estimated surface magnetic anomalies. Besides, there is a knowledge-driven module in the proposed inversion model, which makes the deep learning method more explicable. Meanwhile, comparative experiments demonstrate that the knowledge-driven module can accelerate the training of the proposed method and achieve better results. Since magnetic inversion is an ill-pose task, SSKMI proposed to constrain the inversion model by a guideline in the auxiliary loop. The experimental results demonstrate that the proposed method is a reliable magnetic inversion method with outstanding performance.

Click-Through Rate (CTR) prediction is one of the main tasks of the recommendation system, which is conducted by a user for different items to give the recommendation results. Cross-domain CTR prediction models have been proposed to overcome problems of data sparsity, long tail distribution of user-item interactions, and cold start of items or users. In order to make knowledge transfer from source domain to target domain more smoothly, an innovative deep learning cross-domain CTR prediction model, Domain Adversarial Deep Interest Network (DADIN) is proposed to convert the cross-domain recommendation task into a domain adaptation problem. The joint distribution alignment of two domains is innovatively realized by introducing domain agnostic layers and specially designed loss, and optimized together with CTR prediction loss in a way of adversarial training. It is found that the Area Under Curve (AUC) of DADIN is 0.08% higher than the most competitive baseline on Huawei dataset and is 0.71% higher than its competitors on Amazon dataset, achieving the state-of-the-art results on the basis of the evaluation of this model performance on two real datasets. The ablation study shows that by introducing adversarial method, this model has respectively led to the AUC improvements of 2.34% on Huawei dataset and 16.67% on Amazon dataset.

Diffusion models generate samples by reversing a fixed forward diffusion process. Despite already providing impressive empirical results, these diffusion models algorithms can be further improved by reducing the variance of the training targets in their denoising score-matching objective. We argue that the source of such variance lies in the handling of intermediate noise-variance scales, where multiple modes in the data affect the direction of reverse paths. We propose to remedy the problem by incorporating a reference batch which we use to calculate weighted conditional scores as more stable training targets. We show that the procedure indeed helps in the challenging intermediate regime by reducing (the trace of) the covariance of training targets. The new stable targets can be seen as trading bias for reduced variance, where the bias vanishes with increasing reference batch size. Empirically, we show that the new objective improves the image quality, stability, and training speed of various popular diffusion models across datasets with both general ODE and SDE solvers. When used in combination with EDM, our method yields a current SOTA FID of 1.90 with 35 network evaluations on the unconditional CIFAR-10 generation task. The code is available at https://github.com/Newbeeer/stf

Diffusion models generate samples by reversing a fixed forward diffusion process. Despite already providing impressive empirical results, these diffusion models algorithms can be further improved by reducing the variance of the training targets in their denoising score-matching objective. We argue that the source of such variance lies in the handling of intermediate noise-variance scales, where multiple modes in the data affect the direction of reverse paths. We propose to remedy the problem by incorporating a reference batch which we use to calculate weighted conditional scores as more stable training targets. We show that the procedure indeed helps in the challenging intermediate regime by reducing (the trace of) the covariance of training targets. The new stable targets can be seen as trading bias for reduced variance, where the bias vanishes with increasing reference batch size. Empirically, we show that the new objective improves the image quality, stability, and training speed of various popular diffusion models across datasets with both general ODE and SDE solvers. When used in combination with EDM, our method yields a current SOTA FID of 1.90 with 35 network evaluations on the unconditional CIFAR-10 generation task. The code is available at https://github.com/Newbeeer/stf

Many business workflows require extracting important fields from form-like documents (e.g. bank statements, bills of lading, purchase orders, etc.). Recent techniques for automating this task work well only when trained with large datasets. In this work we propose a novel data augmentation technique to improve performance when training data is scarce, e.g. 10-250 documents. Our technique, which we call FieldSwap, works by swapping out the key phrases of a source field with the key phrases of a target field to generate new synthetic examples of the target field for use in training. We demonstrate that this approach can yield 1-7 F1 point improvements in extraction performance.

In this study, we address the challenges in developing a deep learning-based automatic patent citation recommendation system. Although deep learning-based recommendation systems have exhibited outstanding performance in various domains (such as movies, products, and paper citations), their validity in patent citations has not been investigated, owing to the lack of a freely available high-quality dataset and relevant benchmark model. To solve these problems, we present a novel dataset called PatentNet that includes textual information and metadata for approximately 110,000 patents from the Google Big Query service. Further, we propose strong benchmark models considering the similarity of textual information and metadata (such as cooperative patent classification code). Compared with existing recommendation methods, the proposed benchmark method achieved a mean reciprocal rank of 0.2377 on the test set, whereas the existing state-of-the-art recommendation method achieved 0.2073.

How can teams protect players and staff? A drone flew over Target Field prior to the start of a Minnesota Twins and Pittsburgh Pirates game on Tuesday, which forced a delay. According to The Athletic, players were trying to throw baseballs at the drone, but they were unable to hit it. Eventually, it flew out of the stadium, and around one of the parking lots. The umpires made the players get off the field because the drone presents a safety issue.