Time series forecasting (TSF) has long been a crucial task in both industry and daily life. Most classical statistical models may have certain limitations when applied to practical scenarios in fields such as energy, healthcare, traffic, meteorology, and economics, especially when high accuracy is required. With the continuous development of deep learning, numerous new models have emerged in the field of time series forecasting in recent years. However, existing surveys have not provided a unified summary of the wide range of model architectures in this field, nor have they given detailed summaries of works in feature extraction and datasets. To address this gap, in this review, we comprehensively study the previous works and summarize the general paradigms of Deep Time Series Forecasting (DTSF) in terms of model architectures. Besides, we take an innovative approach by focusing on the composition of time series and systematically explain important feature extraction methods. Additionally, we provide an overall compilation of datasets from various domains in existing works. Finally, we systematically emphasize the significant challenges faced and future research directions in this field.

State space models, such as Mamba, have recently garnered attention in time series forecasting due to their ability to capture sequence patterns. However, in electricity consumption benchmarks, Mamba forecasts exhibit a mean error of approximately 8\%. Similarly, in traffic occupancy benchmarks, the mean error reaches 18\%. This discrepancy leaves us to wonder whether the prediction is simply inaccurate or falls within error given spread in historical data. To address this limitation, we propose a method to quantify the predictive uncertainty of Mamba forecasts. Here, we propose a dual-network framework based on the Mamba architecture for probabilistic forecasting, where one network generates point forecasts while the other estimates predictive uncertainty by modeling variance. We abbreviate our tool, Mamba with probabilistic time series forecasting, as Mamba-ProbTSF and the code for its implementation is available on GitHub (https://github.com/PessoaP/Mamba-ProbTSF). Evaluating this approach on synthetic and real-world benchmark datasets, we find Kullback-Leibler divergence between the learned distributions and the data--which, in the limit of infinite data, should converge to zero if the model correctly captures the underlying probability distribution--reduced to the order of $10^{-3}$ for synthetic data and $10^{-1}$ for real-world benchmark, demonstrating its effectiveness. We find that in both the electricity consumption and traffic occupancy benchmark, the true trajectory stays within the predicted uncertainty interval at the two-sigma level about 95\% of the time. We end with a consideration of potential limitations, adjustments to improve performance, and considerations for applying this framework to processes for purely or largely stochastic dynamics where the stochastic changes accumulate, as observed for example in pure Brownian motion or molecular dynamics trajectories.

Waymo is expanding to new (but actually old) territory. The Waymo One service will soon be available in more of the San Francisco Bay Area, specifically Mountain View, Los Altos, Palo Alto and parts of Sunnyvale. The company spent several years testing its self-driving cars in Mountain View, the city where its headquarters is located. According to TechCrunch, Waymo One will be available across 27 square miles of Silicon Valley, in addition to the 55 square miles it covers elsewhere in the Bay Area, including San Francisco. This is the latest in a string of expansions for the company. Waymo has been up and running in Los Angeles and Phoenix for a while.

Recent research has shown an increasing interest in utilizing pre-trained large language models (LLMs) for a variety of time series applications. However, there are three main challenges when using LLMs as foundational models for time series forecasting: (1) Cross-domain generalization. (2) Cross-modality alignment. (3) Error accumulation in autoregressive frameworks. To address these challenges, we proposed LangTime, a language-guided unified model for time series forecasting that incorporates cross-domain pre-training with reinforcement learning-based fine-tuning. Specifically, LangTime constructs Temporal Comprehension Prompts (TCPs), which include dataset-wise and channel-wise instructions, to facilitate domain adaptation and condense time series into a single token, enabling LLMs to understand better and align temporal data. To improve autoregressive forecasting, we introduce TimePPO, a reinforcement learning-based fine-tuning algorithm. TimePPO mitigates error accumulation by leveraging a multidimensional rewards function tailored for time series and a repeat-based value estimation strategy. Extensive experiments demonstrate that LangTime achieves state-of-the-art cross-domain forecasting performance, while TimePPO fine-tuning effectively enhances the stability and accuracy of autoregressive forecasting.

Extreme weather events are increasing in frequency and intensity due to climate change. This, in turn, is exacting a significant toll in communities worldwide. While prediction skills are increasing with advances in numerical weather prediction and artificial intelligence tools, extreme weather still present challenges. More specifically, identifying the precursors of such extreme weather events and how these precursors may evolve under climate change remain unclear. In this paper, we propose to use post-hoc interpretability methods to construct relevance weather maps that show the key extreme-weather precursors identified by deep learning models. We then compare this machine view with existing domain knowledge to understand whether deep learning models identified patterns in data that may enrich our understanding of extreme-weather precursors. We finally bin these relevant maps into different multi-year time periods to understand the role that climate change is having on these precursors. The experiments are carried out on Indochina heatwaves, but the methodology can be readily extended to other extreme weather events worldwide.

With the recent development and advancement of Transformer and MLP architectures, significant strides have been made in time series analysis. Conversely, the performance of Convolutional Neural Networks (CNNs) in time series analysis has fallen short of expectations, diminishing their potential for future applications. Our research aims to enhance the representational capacity of Convolutional Neural Networks (CNNs) in time series analysis by introducing novel perspectives and design innovations. To be specific, We introduce a novel time series reshaping technique that considers the inter-patch, intra-patch, and cross-variable dimensions. Consequently, we propose TVNet, a dynamic convolutional network leveraging a 3D perspective to employ time series analysis. TVNet retains the computational efficiency of CNNs and achieves state-of-the-art results in five key time series analysis tasks, offering a superior balance of efficiency and performance over the state-of-the-art Transformer-based and MLP-based models. Additionally, our findings suggest that TVNet exhibits enhanced transferability and robustness. Therefore, it provides a new perspective for applying CNN in advanced time series analysis tasks.

Time series forecasting (TSF) plays a crucial role in many applications. Transformer-based methods are one of the mainstream techniques for TSF. Existing methods treat all token dependencies equally. However, we find that the effectiveness of token dependencies varies across different forecasting scenarios, and existing methods ignore these differences, which affects their performance. This raises two issues: (1) What are effective token dependencies? (2) How can we learn effective dependencies? From a logical perspective, we align Transformer-based TSF methods with the logical framework and define effective token dependencies as those that ensure the tokens as atomic formulas (Issue 1). We then align the learning process of Transformer methods with the process of obtaining atomic formulas in logic, which inspires us to design a method for learning these effective dependencies (Issue 2). Specifically, we propose Attention Logic Regularization (Attn-L-Reg), a plug-and-play method that guides the model to use fewer but more effective dependencies by making the attention map sparse, thereby ensuring the tokens as atomic formulas and improving prediction performance. Extensive experiments and theoretical analysis confirm the effectiveness of Attn-L-Reg.

This work suggests faster and space-efficient index construction algorithms for LSH for Euclidean distance (\textit{a.k.a.}~\ELSH) and cosine similarity (\textit{a.k.a.}~\SRP). The index construction step of these LSHs relies on grouping data points into several bins of hash tables based on their hashcode. To generate an $m$-dimensional hashcode of the $d$-dimensional data point, these LSHs first project the data point onto a $d$-dimensional random Gaussian vector and then discretise the resulting inner product. The time and space complexity of both \ELSH~and \SRP~for computing an $m$-sized hashcode of a $d$-dimensional vector is $O(md)$, which becomes impractical for large values of $m$ and $d$. To overcome this problem, we propose two alternative LSH hashcode generation algorithms both for Euclidean distance and cosine similarity, namely, \CSELSH, \HCSELSH~and \CSSRP, \HCSSRP, respectively. \CSELSH~and \CSSRP~are based on count sketch \cite{count_sketch} and \HCSELSH~and \HCSSRP~utilize higher-order count sketch \cite{shi2019higher}. These proposals significantly reduce the hashcode computation time from $O(md)$ to $O(d)$. Additionally, both \CSELSH~and \CSSRP~reduce the space complexity from $O(md)$ to $O(d)$; ~and \HCSELSH, \HCSSRP~ reduce the space complexity from $O(md)$ to $O(N \sqrt[N]{d})$ respectively, where $N\geq 1$ denotes the size of the input/reshaped tensor. Our proposals are backed by strong mathematical guarantees, and we validate their performance through simulations on various real-world datasets.

Years before she became the peculiar central thread linking a double homicide in Pennsylvania, the fatal shooting of a federal agent in Vermont and the murder of an elderly landlord in California, a computer programmer bought a sailboat. The programmer was known to friends, foes and followers as Ziz. She had come to the San Francisco Bay Area in 2016 as part of an influx of young people arriving to study the dangers that artificial intelligence could pose to humanity. In one of the most expensive regions of the United States, however, it is difficult to save the world when you can't make rent. So she bought a boat for 600 and moored it next to a friend's vessel in a marina. For five years, she used it as an occasional, cramped bunk. In her waking hours, she worked on a blog of provocative and increasingly extreme ideas about confrontation and retaliation. At night, she fell asleep as the boat rocked back and forth, drifting with the flotsam of greater Silicon Valley. Then, on the night of 19 August 2022, her sister and a friend reported that they saw her fall overboard. The Coast Guard and local authorities scrambled boats and aircraft. After a nearly 30-hour search, neither Ziz nor her body could be found. A newspaper in Alaska, where she was born, published a short obituary referring to her by her birth name: "Jack Amadeus LaSota left our lives but not our hearts on Aug 19 after a boating accident. Loving adventure, friends and family, music, blueberries, biking, computer games and animals, you are missed." Ziz's ideas did not die in the waters of the California coast. She had faked her drowning and gone underground, before being arrested last month in western Maryland and charged with trespassing and illegal transportation of a firearm. The targets of Ziz's ire, who include some of Silicon Valley's most prominent intellectuals, have taken security precautions. "Ziz is not stupid," someone familiar with her, who asked to remain anonymous, told me. "This is a very smart person – both smart and crazy." Ziz's writing had polarized members of a niche but influential movement of AI theorists and tech bloggers who call themselves the "rationalists". The movement is less about specific ideas than it is about an ethos – applying rigorous, mathematically informed thinking to AI, philosophy, psychology and the big questions of our time. Rationalists are odd, though often charming, people. They tend to be fantasy and sci-fi geeks, use lots of jargon and think intensely about things other people barely think about at all.

For example, realistic Time-series Generation (TSG) is a prominent synthetic medical electrocardiogram (ECG) patterns research area with broad applications in simulations, can be used to train medical residents (Hong & Chun, 2023), data augmentation, and counterfactual while simulating regional electricity usage can be used to analysis. While existing methods have shown stress test the power grid (Westgaard et al., 2021). Although promise in unconditional single-domain TSG, some remarkable works (Huang & Deng, 2023; Bao et al., real-world applications demand for cross-domain 2024) have been done for TSG, showing promising results approaches capable of controlled generation tailored in generating realistic and coherent time series (TS), most to domain-specific constraints and instancelevel of them focus on the basic setting--unconditional single requirements. In this paper, we argue that domain generation. However, in real application scenarios, text can provide semantic insights, domain information there are specific constraints or requirements for the generated and instance-specific temporal patterns, TS to be met, such as specifying domain-specific characteristics, to guide and improve TSG. We introduce "Text-incorporating prior knowledge (Yuan & Qiao, Controlled TSG", a task focused on generating realistic 2024), or satisfying operational constraints (Coletta et al., time series by incorporating textual descriptions.