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Deep Learning · Sequential Models, Time series

Annan Yu, Michael W Mahoney, N. Benjamin Erichson

State-space models (SSMs) that utilize linear, time-invariant (LTI) systems are known for their effectiveness in learning long sequences. To achieve state-of-the-art performance, an SSM often needs a specifically designed initialization, and the training of state matrices is on a logarithmic scale with a very small learning rate. To understand these choices from a unified perspective, we view SSMs through the lens of Hankel operator theory. Building upon it, we develop a new parameterization scheme, called HOPE, for LTI systems that utilizes Markov parameters within Hankel operators. Our approach helps improve the initialization and training stability, leading to a more robust parameterization. We efficiently implement these innovations by nonuniformly sampling the transfer functions of LTI systems, and they require fewer parameters compared to canonical SSMs. When benchmarked against HiPPO-initialized models such as S4 and S4D, an SSM parameterized by Hankel operators demonstrates improved performance on Long-Range Arena (LRA) tasks. Moreover, our new parameterization endows the SSM with non-decaying memory within a fixed time window, which is empirically corroborated by a sequential CIFAR-10 task with padded noise.

Deep Learning · Sequential Models, Time series

Qinshuo Liu, Weiqin Zhao, Wei Huang, Yanwen Fang, Lequan Yu, Guodong Li

The depth of neural networks is a critical factor for their capability, with deeper models often demonstrating superior performance. Motivated by this, significant efforts have been made to enhance layer aggregation - reusing information from previous layers to better extract features at the current layer, to improve the representational power of deep neural networks. However, previous works have primarily addressed this problem from a discrete-state perspective which is not suitable as the number of network layers grows. This paper novelly treats the outputs from layers as states of a continuous process and considers leveraging the state space model (SSM) to design the aggregation of layers in very deep neural networks. Moreover, inspired by its advancements in modeling long sequences, the Selective State Space Models (S6) is employed to design a new module called Selective State Space Model Layer Aggregation (S6LA). This module aims to combine traditional CNN or transformer architectures within a sequential framework, enhancing the representational capabilities of state-of-the-art vision networks. Extensive experiments show that S6LA delivers substantial improvements in both image classification and detection tasks, highlighting the potential of integrating SSMs with contemporary deep learning techniques.

Deep Learning · Sequential Models, Time series

Woojin Cho, Minju Jo, Kookjin Lee, Noseong Park

As function approximators, deep neural networks have served as an effective tool to represent various signal types. Recent approaches utilize multi-layer perceptrons (MLPs) to learn a nonlinear mapping from a coordinate to its corresponding signal, facilitating the learning of continuous neural representations from discrete data points. Despite notable successes in learning diverse signal types, coordinate-based MLPs often face issues of overfitting and limited generalizability beyond the training region, resulting in subpar extrapolation performance. This study addresses scenarios where the underlying true signals exhibit periodic properties, either spatially or temporally. We propose a novel network architecture, which extracts periodic patterns from measurements and leverages this information to represent the signal, thereby enhancing generalization and improving extrapolation performance. We demonstrate the efficacy of the proposed method through comprehensive experiments, including the learning of the periodic solutions for differential equations, and time series imputation (interpolation) and forecasting (extrapolation) on real-world datasets.

Miscellaneous Aspects of Machine Learning · Sequential, Network, and Time Series Modeling

Junxi Wu, Dongjian Hu, Yajie Bao, Shu-Tao Xia, Changliang Zou

Uncertainty quantification in time series prediction is challenging due to the temporal dependence and distribution shift on sequential data. Conformal prediction provides a pivotal and flexible instrument for assessing the uncertainty of machine learning models through prediction sets. Recently, a series of online conformal inference methods updated thresholds of prediction sets by performing online gradient descent on a sequence of quantile loss functions. A drawback of such methods is that they only use the information of revealed non-conformity scores via miscoverage indicators but ignore error quantification, namely the distance between the non-conformity score and the current threshold. To accurately leverage the dynamic of miscoverage error, we propose Error-quantified Conformal Inference (ECI) by smoothing the quantile loss function. ECI introduces a continuous and adaptive feedback scale with the miscoverage error, rather than simple binary feedback in existing methods. We establish a long-term coverage guarantee for ECI under arbitrary dependence and distribution shift. The extensive experimental results show that ECI can achieve valid miscoverage control and output tighter prediction sets than other baselines.

Deep Learning · Sequential Models, Time series

Jerry Liu, Jessica Grogan, Owen Dugan, Ashish Rao, Simran Arora, Atri Rudra, Christopher Re

This paper investigates whether sequence models can learn to perform numerical algorithms, e.g. gradient descent, on the fundamental problem of least squares. Our goal is to inherit two properties of standard algorithms from numerical analysis: (1) machine precision, i.e. we want to obtain solutions that are accurate to near floating point error, and (2) numerical generality, i.e. we want them to apply broadly across problem instances. We find that prior approaches using Transformers fail to meet these criteria, and identify limitations present in existing architectures and training procedures. First, we show that softmax Transformers struggle to perform high-precision multiplications, which prevents them from precisely learning numerical algorithms. Second, we identify an alternate class of architectures, comprised entirely of polynomials, that can efficiently represent high-precision gradient descent iterates. Finally, we investigate precision bottlenecks during training and address them via a high-precision training recipe that reduces stochastic gradient noise. Our recipe enables us to train two polynomial architectures, gated convolutions and linear attention, to perform gradient descent iterates on least squares problems. For the first time, we demonstrate the ability to train to near machine precision. Applied iteratively, our models obtain $100,000\times$ lower MSE than standard Transformers trained end-to-end and they incur a $10,000\times$ smaller generalization gap on out-of-distribution problems. We make progress towards end-to-end learning of numerical algorithms for least squares.

Yujie Lin, Chen Zhao, Minglai Shao, Baoluo Meng, Xujiang Zhao, Haifeng Chen

Recognizing domain generalization as a commonplace challenge in machine learning, data distribution might progressively evolve across a continuum of sequential domains in practical scenarios. While current methodologies primarily concentrate on bolstering model effectiveness within these new domains, they tend to neglect issues of fairness throughout the learning process. In response, we propose an innovative framework known as Disentanglement for Counterfactual Fairness-aware Domain Generalization (DCFDG). This approach adeptly removes domain-specific information and sensitive information from the embedded representation of classification features. To scrutinize the intricate interplay between semantic information, domain-specific information, and sensitive attributes, we systematically partition the exogenous factors into four latent variables. By incorporating fairness regularization, we utilize semantic information exclusively for classification purposes. Empirical validation on synthetic and authentic datasets substantiates the efficacy of our approach, demonstrating elevated accuracy levels while ensuring the preservation of fairness amidst the evolving landscape of continuous domains.

Qihe Huang, Zhengyang Zhou, Kuo Yang, Gengyu Lin, Zhongchao Yi, Yang Wang

Time series forecasting (TSF) plays a pivotal role in many real-world applications. Recently, the utilization of Large Language Models (LLM) in TSF has demonstrated exceptional predictive performance, surpassing most task-specific forecasting models. The success of LLM-based forecasting methods underscores the importance of causal dependence modeling and pre-trained knowledge transfer. However, challenges persist in directly applying LLM to TSF, i.e., the unacceptable parameter scales for resource-intensive model optimization, and the significant gap of feature space between structural numerical time series and natural language. To this end, we propose LeRet, a Language-empowered Retentive network for TSF. Technically, inspired by the causal extraction in LLM, we propose a causal dependence learner, enhanced by a patch-level pre-training task, to capture sequential causal evolution. To minimize the gap between numeric and language, we initialize a language description protocol for time series and design a TS-related language knowledge extractor to learn from language description, avoiding training with large-scale parameters. Finally, we dedicatedly achieve a Language-TS Modality Integrator for the fusion of two types data, and enable language-empowered sequence forecasting. Extensive evaluations demonstrate the effectiveness of our LeRet, especially reveal superiority on few-shot, and zero-shot forecasting tasks. Code is available at https://github.com/hqh0728/LeRet.

Yimeng Fan, Pedram Agand, Mo Chen, Edward J. Park, Allison Kennedy, Chanwoo Bae

The maritime industry's continuous commitment to sustainability has led to a dedicated exploration of methods to reduce vessel fuel consumption. This paper undertakes this challenge through a machine learning approach, leveraging a real-world dataset spanning two years of a passenger vessel in west coast Canada. Our focus centers on the creation of a time series forecasting model given the dynamic and static states, actions, and disturbances. This model is designed to predict dynamic states based on the actions provided, subsequently serving as an evaluative tool to assess the proficiency of the vessel's operation under the captain's guidance. Additionally, it lays the foundation for future optimization algorithms, providing valuable feedback on decision-making processes. To facilitate future studies, our code is available at https://github.com/pagand/model_optimze_vessel/tree/AAAI.

Mingrui Liu

The current analysis of federated optimization algorithms for training deep neural networks assumes that the data is non-sequential (e.g., images), which incurs a smooth loss objective. In contrast, edge devices generate lots of sequential data every day, where these sequences exhibit significant sequential correlation at different time stamps (e.g., text messages). In order to learn from such sequential data, people typically use a class of neural networks that is inherently nonsmooth, with a potentially unbounded smoothness parameter. Examples include recurrent neural networks, long-short-term memory networks, and transformers. It remains unclear how to design provably efficient algorithms for training these neural networks to learn from sequential data. My goal is to lay the algorithmic foundation of federated learning with sequential data, which contributes novel algorithms for learning from a range of real-world sequential data (e.g., natural language, electronic health record, transportation, time series, etc.) using state-of-the-art deep neural networks. In this talk, I will first motivate the problem by showing that the transformer, which is widely used for sequential data learning, has an unbounded smooth landscape. Then, I will introduce provably efficient federated deep learning algorithms in the presence of unbounded smoothness. In particular, I will introduce a few efficient algorithms for various settings of federated learning, including homogeneous data, heterogeneous data, and partial client participation. The main result is twofold. First, we show that the designed algorithms provably small computational and communication complexities. Second, we establish fundamental hardness results in the unbounded smoothness setting. Ultimately, I will discuss the future challenges of extending our research framework from small-scale neural networks to large language models.

Jingge Xiao, Leonie Basso, Wolfgang Nejdl, Niloy Ganguly, Sandipan Sikdar

Continuous-time models such as Neural ODEs and Neural Flows have shown promising results in analyzing irregularly sampled time series frequently encountered in electronic health records. Based on these models, time series are typically processed with a hybrid of an initial value problem (IVP) solver and a recurrent neural network within the variational autoencoder architecture. Sequentially solving IVPs makes such models computationally less efficient. In this paper, we propose to model time series purely with continuous processes whose state evolution can be approximated directly by IVPs. This eliminates the need for recurrent computation and enables multiple states to evolve in parallel. We further fuse the encoder and decoder with one IVP solver utilizing its invertibility, which leads to fewer parameters and faster convergence. Experiments on three real-world datasets show that the proposed method can systematically outperform its predecessors, achieve state-of-the-art results, and have significant advantages in terms of data efficiency.

Yucheng Wang, Yuecong Xu, Jianfei Yang, Min Wu, Xiaoli Li, Lihua Xie, Zhenghua Chen

Multivariate Time-Series (MTS) data is crucial in various application fields. With its sequential and multi-source (multiple sensors) properties, MTS data inherently exhibits Spatial-Temporal (ST) dependencies, involving temporal correlations between timestamps and spatial correlations between sensors in each timestamp. To effectively leverage this information, Graph Neural Network-based methods (GNNs) have been widely adopted. However, existing approaches separately capture spatial dependency and temporal dependency and fail to capture the correlations between Different sEnsors at Different Timestamps (DEDT). Overlooking such correlations hinders the comprehensive modelling of ST dependencies within MTS data, thus restricting existing GNNs from learning effective representations. To address this limitation, we propose a novel method called Fully-Connected Spatial-Temporal Graph Neural Network (FC-STGNN), including two key components namely FC graph construction and FC graph convolution. For graph construction, we design a decay graph to connect sensors across all timestamps based on their temporal distances, enabling us to fully model the ST dependencies by considering the correlations between DEDT. Further, we devise FC graph convolution with a moving-pooling GNN layer to effectively capture the ST dependencies for learning effective representations. Extensive experiments show the effectiveness of FC-STGNN on multiple MTS datasets compared to SOTA methods. The code is available at https://github.com/Frank-Wang-oss/FCSTGNN.

Jihyeon Seong, Jungmin Kim, Jaesik Choi

In Time Series Classification (TSC), temporal pooling methods that consider sequential information have been proposed. However, we found that each temporal pooling has a distinct mechanism, and can perform better or worse depending on time series data. We term this fixed pooling mechanism a single perspective of temporal poolings. In this paper, we propose a novel temporal pooling method with diverse perspective learning: Selection over Multiple Temporal Poolings (SoM-TP). SoM-TP dynamically selects the optimal temporal pooling among multiple methods for each data by attention. The dynamic pooling selection is motivated by the ensemble concept of Multiple Choice Learning (MCL), which selects the best among multiple outputs. The pooling selection by SoM-TP's attention enables a non-iterative pooling ensemble within a single classifier. Additionally, we define a perspective loss and Diverse Perspective Learning Network (DPLN). The loss works as a regularizer to reflect all the pooling perspectives from DPLN. Our perspective analysis using Layer-wise Relevance Propagation (LRP) reveals the limitation of a single perspective and ultimately demonstrates diverse perspective learning of SoM-TP. We also show that SoM-TP outperforms CNN models based on other temporal poolings and state-of-the-art models in TSC with extensive UCR/UEA repositories.

Xinyu Sun, Zhikun Zhao, Lili Wei, Congyan Lang, Mingxuan Cai, Longfei Han, Juan Wang, Bing Li, Yuxuan Guo

Hardware image signal processing (ISP), aiming at converting RAW inputs to RGB images, consists of a series of processing blocks, each with multiple parameters. Traditionally, ISP parameters are manually tuned in isolation by imaging experts according to application-specific quality and performance metrics, which is time-consuming and biased towards human perception due to complex interaction with the output image. Since the relationship between any single parameter’s variation and the output performance metric is a complex, non-linear function, optimizing such a large number of ISP parameters is challenging. To address this challenge, we propose a novel Sequential ISP parameter optimization model, called the RL-SeqISP model, which utilizes deep reinforcement learning to jointly optimize all ISP parameters for a variety of imaging applications. Concretely, inspired by the sequential tuning process of human experts, the proposed model can progressively enhance image quality by seamlessly integrating information from both the image feature space and the parameter space. Furthermore, a dynamic parameter optimization module is introduced to avoid ISP parameters getting stuck into local optima, which is able to more effectively guarantee the optimal parameters resulting from the sequential learning strategy. These merits of the RL-SeqISP model as well as its high efficiency are substantiated by comprehensive experiments on a wide range of downstream tasks, including two visual analysis tasks (instance segmentation and object detection), and image quality assessment (IQA), as compared with representative methods both quantitatively and qualitatively. In particular, even using only 10% of the training data, our model outperforms other SOTA methods by an average of 7% mAP on two visual analysis tasks.

Tong Li, Zhaoyang Liu, Yanyan Shen, Xue Wang, Haokun Chen, Sen Huang

Stock price forecasting has remained an extremely challenging problem for many decades due to the high volatility of the stock market. Recent efforts have been devoted to modeling complex stock correlations toward joint stock price forecasting. Existing works share a common neural architecture that learns temporal patterns from individual stock series and then mixes up temporal representations to establish stock correlations. However, they only consider time-aligned stock correlations stemming from all the input stock features, which suffer from two limitations. First, stock correlations often occur momentarily and in a cross-time manner. Second, the feature effectiveness is dynamic with market variation, which affects both the stock sequential patterns and their correlations. To address the limitations, this paper introduces MASTER, a MArkert-guided Stock TransformER, which models the momentary and cross-time stock correlation and leverages market information for automatic feature selection. MASTER elegantly tackles the complex stock correlation by alternatively engaging in intra-stock and inter-stock information aggregation. Experiments show the superiority of MASTER compared with previous works and visualize the captured realistic stock correlation to provide valuable insights.

Raja Kumar, Kishan Maharaj, Ashita Saxena, Pushpak Bhattacharyya

Mental disorders pose a global challenge, aggravated by the shortage of qualified mental health professionals. Mental disorder prediction from social media posts by current LLMs is challenging due to the complexities of sequential text data and the limited context length of language models. Current language model-based approaches split a single data instance into multiple chunks to compensate for limited context size. The predictive model is then applied to each chunk individually, and the most voted output is selected as the final prediction. This results in the loss of inter-post dependencies and important time variant information, leading to poor performance. We propose a novel framework which first compresses the large sequence of chronologically ordered social media posts into a series of numbers. We then use this time variant representation for mental disorder classification. We demonstrate the generalization capabilities of our framework by outperforming the current SOTA in three different mental conditions: depression, self-harm, and anorexia, by an absolute improvement of 5% in the F1 score. We also investigate the situation when current data instances fall within the context length of language models and present empirical results highlighting the importance of temporal properties of textual data. Furthermore, we utilize the proposed framework for a cross-domain study, exploring commonalities across disorders and the possibility of inter-domain data usage.

Deep Learning · Algorithms

QIUHAO Zeng, Long-Kai Huang, Qi CHEN, Charles Ling, Boyu Wang

In many machine learning tasks, data is inherently sequential. Most existing algorithms learn from sequential data in an auto-regressive manner, which predicts the next unseen data point based on the observed sequence, implicitly assuming the presence of an \emph{evolving pattern} embedded in the data that can be leveraged. However, identifying and assessing evolving patterns in learning tasks often relies on subjective judgments rooted in the prior knowledge of human experts, lacking a standardized quantitative measure. Furthermore, such measures enable us to determine the suitability of employing sequential models effectively and make informed decisions on the temporal order of time series data, and feature/data selection processes. To address this issue, we introduce the Evolving Rate (EvoRate), which quantitatively approximates the intensity of evolving patterns in the data with Mutual Information. Furthermore, in some temporal data with neural mutual information estimations, we only have snapshots at different timestamps, lacking correspondence, which hinders EvoRate estimation. To tackle this challenge, we propose EvoRate$_\mathcal{W}$, aiming to establish correspondence with optimal transport for estimating the first-order EvoRate. Experiments on synthetic and real-world datasets including images and tabular data validate the efficacy of our EvoRate.

Time Series

Yong Liu, Guo Qin, Xiangdong Huang, Jianmin Wang, Mingsheng Long

Foundation models of time series have not been fully developed due to the limited availability of time series corpora and the underexploration of scalable pre-training. Based on the similar sequential formulation of time series and natural language, increasing research demonstrates the feasibility of leveraging large language models (LLM) for time series. Nevertheless, the inherent autoregressive property and decoder-only architecture of LLMs have not been fully considered, resulting in insufficient utilization of LLM abilities. To fully revitalize the general-purpose token transition and multi-step generation capability of large language models, we propose AutoTimes to repurpose LLMs as autoregressive time series forecasters, which projects time series into the embedding space of language tokens and autoregressively generates future predictions with arbitrary lengths. Compatible with any decoder-only LLMs, the consequent forecaster exhibits the flexibility of the lookback length and scalability with larger LLMs. Further, we formulate time series as prompts, extending the context for prediction beyond the lookback window, termed in-context forecasting. By introducing LLM-embedded textual timestamps, AutoTimes can utilize chronological information to align multivariate time series. Empirically, AutoTimes achieves state-of-the-art with 0.1% trainable parameters and over $5\times$ training/inference speedup compared to advanced LLM-based forecasters. Code is available at this repository: https://github.com/thuml/AutoTimes.

Time Series

Yuxin Jia, Youfang Lin, Jing Yu, Shuo Wang, Tianhao Liu, Huaiyu Wan

Due to the recurrent structure of RNN, the long information propagation path poses limitations in capturing long-term dependencies, gradient explosion/vanishing issues, and inefficient sequential execution. Based on this, we propose a novel paradigm called Parallel Gated Network (PGN) as the new successor to RNN. PGN directly captures information from previous time steps through the designed Historical Information Extraction (HIE) layer and leverages gated mechanisms to select and fuse it with the current time step information. This reduces the information propagation path to $\mathcal{O}(1)$, effectively addressing the limitations of RNN. To enhance PGN's performance in long-range time series forecasting tasks, we propose a novel temporal modeling framework called Temporal PGN (TPGN). TPGN incorporates two branches to comprehensively capture the semantic information of time series. One branch utilizes PGN to capture long-term periodic patterns while preserving their local characteristics. The other branch employs patches to capture short-term information and aggregate the global representation of the series. TPGN achieves a theoretical complexity of $\mathcal{O}(\sqrt{L})$, ensuring efficiency in its operations. Experimental results on five benchmark datasets demonstrate the state-of-the-art (SOTA) performance and high efficiency of TPGN, further confirming the effectiveness of PGN as the new successor to RNN in long-range time series forecasting. The code is available in this repository: https://github.com/Water2sea/TPGN.

Neuroscience, Cognitive Science

Changze Lv, Dongqi Han, Yansen Wang, Xiaoqing Zheng, Xuanjing Huang, Dongsheng Li

Spiking neural networks (SNNs) represent a promising approach to developing artificial neural networks that are both energy-efficient and biologically plausible.However, applying SNNs to sequential tasks, such as text classification and time-series forecasting, has been hindered by the challenge of creating an effective and hardware-friendly spike-form positional encoding (PE) strategy.Drawing inspiration from the central pattern generators (CPGs) in the human brain, which produce rhythmic patterned outputs without requiring rhythmic inputs, we propose a novel PE technique for SNNs, termed CPG-PE.We demonstrate that the commonly used sinusoidal PE is mathematically a specific solution to the membrane potential dynamics of a particular CPG.Moreover, extensive experiments across various domains, including time-series forecasting, natural language processing, and image classification, show that SNNs with CPG-PE outperform their conventional counterparts.Additionally, we perform analysis experiments to elucidate the mechanism through which SNNs encode positional information and to explore the function of CPGs in the human brain.This investigation may offer valuable insights into the fundamental principles of neural computation.

Time Series

Mingtian Tan, Mike Merrill, Vinayak Gupta, Tim Althoff, Tom Hartvigsen

Large language models (LLMs) are being applied to time series forecasting. But are language models actually useful for time series? In a series of ablation studies on three recent and popular LLM-based time series forecasting methods, we find that removing the LLM component or replacing it with a basic attention layer does not degrade forecasting performance---in most cases, the results even improve! We also find that despite their significant computational cost, pretrained LLMs do no better than models trained from scratch, do not represent the sequential dependencies in time series, and do not assist in few-shot settings. Additionally, we explore time series encoders and find that patching and attention structures perform similarly to LLM-based forecasters. All resources needed to reproduce our work are available: https://github.com/BennyTMT/LLMsForTimeSeries.