Time series foundation models have demonstrated strong performance in zero-shot learning, making them well-suited for predicting rapidly evolving patterns in real-world applications where relevant training data are scarce. However, most of these models rely on the Transformer architecture, which incurs quadratic complexity as input length increases. To address this, we introduce TSMamba, a linear-complexity foundation model for time series forecasting built on the Mamba architecture. The model captures temporal dependencies through both forward and backward Mamba encoders, achieving high prediction accuracy. To reduce reliance on large datasets and lower training costs, TSMamba employs a two-stage transfer learning process that leverages pretrained Mamba LLMs, allowing effective time series modeling with a moderate training set. In the first stage, the forward and backward backbones are optimized via patch-wise autoregressive prediction; in the second stage, the model trains a prediction head and refines other components for long-term forecasting. While the backbone assumes channel independence to manage varying channel numbers across datasets, a channel-wise compressed attention module is introduced to capture cross-channel dependencies during fine-tuning on specific multivariate datasets. Experiments show that TSMamba's zero-shot performance is comparable to state-of-the-art time series foundation models, despite using significantly less training data. It also achieves competitive or superior full-shot performance compared to task-specific prediction models. The code will be made publicly available.

Perception sensors, particularly camera and Lidar, are key elements of Autonomous Driving Systems (ADS) that enable them to comprehend their surroundings for informed driving and control decisions. Therefore, developing realistic camera and Lidar simulation methods, also known as camera and Lidar models, is of paramount importance to effectively conduct simulation-based testing for ADS. Moreover, the rise of deep learning-based perception models has propelled the prevalence of perception sensor models as valuable tools for synthesising diverse training datasets. The traditional sensor simulation methods rely on computationally expensive physics-based algorithms, specifically in complex systems such as ADS. Hence, the current potential resides in learning-based models, driven by the success of deep generative models in synthesising high-dimensional data. This paper reviews the current state-of-the-art in learning-based sensor simulation methods and validation approaches, focusing on two main types of perception sensors: cameras and Lidars. This review covers two categories of learning-based approaches, namely raw-data-based and object-based models. Raw-data-based methods are explained concerning the employed learning strategy, while object-based models are categorised based on the type of error considered. Finally, the paper illustrates commonly used validation techniques for evaluating perception sensor models and highlights the existing research gaps in the area.

It has broad applications including but not limited to climatology, energy, finance, trading, and logistics (Petropoulos et al., 2022). Following the great success of Transformers (Vaswani et al., 2017) in NLP (Kalyan et al., 2021), CV (Khan et al., 2021), and speech (Karita et al., 2019), Transformers have been introduced in time series forecasting and achieves promising results (Wen et al., 2022). One of the primary drawbacks of Transformers is their quadratic complexity in both computation and memory, making them less suitable for long-term forecasting. To address this limitation, a plethora of Transformer-based models, e.g., LogTrans, Informer, AutoFormer, Performer, and PyraFormer (Li et al., 2019; Zhou et al., 2021; Wu et al., 2021; Choromanski et al., 2021; Liu et al., 2022a), have been proposed to enhance predictive performance while maintaining low complexity. Notably, Zhou et al. (2022b) observed that most time series which are dense in the time domain (TD) tend to have a sparse representation in the frequency domain (FD).

We introduce NAMSG, an adaptive first-order algorithm for training neural networks. The method is efficient in computation and memory, and is straightforward to implement. It computes the gradients at configurable remote observation points, in order to expedite the convergence by adjusting the step size for directions with different curvatures in the stochastic setting. It also scales the updating vector elementwise by a nonincreasing preconditioner to take the advantages of AMSGRAD. We analyze the convergence properties for both convex and nonconvex problems by modeling the training process as a dynamic system, and provide a guideline to select the observation distance without grid search. A data-dependent regret bound is proposed to guarantee the convergence in the convex setting. Experiments demonstrate that NAMSG works well in practical problems and compares favorably to popular adaptive methods, such as ADAM, NADAM, and AMSGRAD.