This study explores the dynamics of a gated memory car-following system, with a focus on the challenges encountered when training models using fine-grained spatiotemporal data. To address the issues of redundant gradient updates and limited generalization inherent in traditional sequential training methods, a novel Spatiotemporal-Decoupled Training (SDT) method is proposed. This method enhances gradient variance by decoupling temporal dependencies and mixing trajectory segments from different vehicles, thereby improving model generalization performance and achieving a zero collision rate on test dataset. Experimental validation is carried out using three datasets (HighD, NGSIM-I80 and Lyft) and two basic models (GRU and LSTM) to assess the effectiveness of the proposed method. The results demonstrate significant improvements in model performance, including an 80% reduction in generalization error on the HighD dataset, a 14% reduction on the NGSIM-I80 dataset a 57% reduction on Lyft dataset, and the achievement of a Zero-collision rate on all test datasets, showcasing the potential of the SDT method for intelligent driving systems. Our code and experimental configurations are publicly available on GitHub to facilitate reproducibility and comparison:https://github.com/LiangzgJlu/Spatiotemporal-Decoupled-Training

In recent years, neural operators have emerged as a prominent approach for learning mappings between function spaces, such as the solution operators of parametric PDEs. A notable example is the Fourier Neural Operator (FNO), which models the integral kernel as a convolution operator and uses the Convolution Theorem to learn the kernel directly in the frequency domain. The parameters are decoupled from the resolution of the data, allowing the FNO to take inputs of different resolutions. However, training at a lower resolution and inferring at a finer resolution does not guarantee consistent performance, nor can fine details, present only in fine-scale data, be learned solely from coarse data. In this work, we address this misconception by defining and examining the discretization mismatch error: the discrepancy between the outputs of the neural operator when using different discretizations of the input data. We demonstrate that neural operators may suffer from discretization mismatch errors that hinder their effectiveness when inferred on data with resolutions different from that of the training data or when trained on data with varying resolutions. As neural operators underpin many critical cross-resolution scientific tasks, such as climate modeling and fluid dynamics, understanding discretization mismatch errors is essential. Based on our findings, we propose a Cross-Resolution Operator-learning Pipeline that is free of aliasing and discretization mismatch errors, enabling efficient cross-resolution and multi-spatial-scale learning, and resulting in superior performance.

Recent theoretical studies (Kou et al., 2023; Cao et al., 2022) revealed a sharp phase transition from benign to harmful overfitting when the noise-to-feature ratio exceeds a threshold—a situation common in long-tailed data distributions where atypical data is prevalent. However, such harmful overfitting rarely happens in overparameterized neural networks. Further experimental results suggested that memorization is necessary for achieving near-optimal generalization error in long-tailed data distributions (Feldman & Zhang, 2020). We argue that this discrepancy between theoretical predictions and empirical observations arises because previous feature-noise data models overlook the heterogeneous nature of noise across different data classes. In this paper, we refine the feature-noise data model by incorporating class-dependent heterogeneous noise and re-examine the overfitting phenomenon in neural networks. Through a comprehensive analysis of the training dynamics, we establish test loss bounds for the refined model. Our findings reveal that neural networks can leverage "data noise" to learn implicit features that improve the classification accuracy for long-tailed data. Our analysis also provides a training-free metric for evaluating data influence on test performance. Experimental validation on both synthetic and real-world datasets supports our theoretical results.

We propose a Kolmogorov–Arnold Representation-based Hamiltonian Neural Network (KAR-HNN) that replaces the Multilayer Perceptrons (MLPs) with univariate transformations. While Hamiltonian Neural Networks (HNNs) ensure energy conservation by learning Hamiltonian functions directly from data, existing implementations, often relying on MLPs, cause hypersensitivity to the hyperparameters while exploring complex energy landscapes. Our approach exploits the localized function approximations to better capture high-frequency and multi-scale dynamics, reducing energy drift and improving long-term predictive stability. The networks preserve the symplectic form of Hamiltonian systems, and, thus, maintain interpretability and physical consistency. After assessing KAR-HNN on four benchmark problems including spin-mass, simple pendulum, two-and three-body problem, we foresee its effectiveness for accurate and stable modeling of realistic physical processes often at high dimensions and with few known parameters.

Differentially private federated learning enables clients with privacy concerns to collaboratively train a model while preserving their privacy. Clients' locally available data and maximum tolerable privacy budgets will affect their contributions to the training performance. To date, existing studies focus on homogeneous privacy budgets and thus there lack systematic studies regarding the impact of clients' diverse privacy budgets (privacy heterogeneity). This paper represents the first step toward filling this gap. Through rigorous convergence analysis, we illustrate that the influence of privacy protection on training loss is affected by client selection probabilities. In addition, client selection and privacy protection together induce a non-vanishing training error in federated learning. Our analysis then shows that the non-vanishing training error is a convex function of client selection probabilities and thus allows us to formulate privacy-aware client selection as a convex optimization problem. Numerical results demonstrate that the privacy-aware client selection strategy can significantly improve learning performance. For example, compared with unbiased selection, the privacy-aware client selection strategy decreases the test loss by up to 63% on MNIST convolutional neural network classifier.

High performance of Cell-ID localization depends on the effective system to process Cell-ID information where an efficient Cell-ID information exchanging way is crucial. However, in some applications, classical Cell-ID positioning algorithm (yellow pages) cannot meet the accuracy requirements and support some specific functions, i.e. cell residual dwell time estimation. To solve these two problems, a novel Cell-ID localization algorithm based on hidden semi-Markov model (HSMM) is proposed here. First, instead of building localization decision only on the serving station, all the Cell-IDs detected by mobile nodes are utilized. Second, it gets the positioning results by maximum a posteriori estimation criterion via HSMM This algorithm, as supported by simulation results, shows two main features: (a) a superior positioning accuracy of 455 m compared with the classical Cell-ID approach on average; (b) a new function of estimating the cell residual dwell time.