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Applications · Time Series

Linus Bleistein, Van NGUYEN, Adeline Fermanian, Agathe Guilloux

We consider the task of learning individual-specific intensities of counting processes from a set of static variables and irregularly sampled time series. We introduce a novel modelization approach in which the intensity is the solution to a controlled differential equation. We first design a neural estimator by building on neural controlled differential equations. In a second time, we show that our model can be linearized in the signature space under sufficient regularity conditions, yielding a signature-based estimator which we call CoxSig. We provide theoretical learning guarantees for both estimators, before showcasing the performance of our models on a vast array of simulated and real-world datasets from finance, predictive maintenance and food supply chain management.

Applications · Time Series

Yuxuan Bian, Xuan Ju, Jiangtong Li, Zhijian Xu, Dawei Cheng, Qiang Xu

In this study, we present $\text{aL\small{LM}4T\small{S}}$, an innovative framework that adapts Large Language Models (LLMs) for time-series representation learning. Central to our approach is that we reconceive time-series forecasting as a self-supervised, multi-patch prediction task, which, compared to traditional mask-and-reconstruction methods, captures temporal dynamics in patch representations more effectively. Our strategy encompasses two-stage training: (i). a causal continual pre-training phase on various time-series datasets, anchored on next patch prediction, effectively syncing LLM capabilities with the intricacies of time-series data; (ii). fine-tuning for multi-patch prediction in the targeted time-series context. A distinctive element of our framework is the patch-wise decoding layer, which departs from previous methods reliant on sequence-level decoding. Such a design directly transposes individual patches into temporal sequences, thereby significantly bolstering the model's proficiency in mastering temporal patch-based representations. $\text{aL\small{LM}4T\small{S}}$ demonstrates superior performance in several downstream tasks, proving its effectiveness in deriving temporal representations with enhanced transferability and marking a pivotal advancement in the adaptation of LLMs for time-series analysis.

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

Yongqiang Cai

In recent years, deep learning-based sequence modelings, such as language models, have received much attention and success, which pushes researchers to explore the possibility of transforming non-sequential problems into a sequential form. Following this thought, deep neural networks can be represented as composite functions of a sequence of mappings, linear or nonlinear, where each composition can be viewed as a word. However, the weights of linear mappings are undetermined and hence require an infinite number of words. In this article, we investigate the finite case and constructively prove the existence of a finite vocabulary $V$=$\phi_i: \mathbb{R}^d \to \mathbb{R}^d | i=1,...,n$ with $n=O(d^2)$ for the universal approximation. That is, for any continuous mapping $f: \mathbb{R}^d \to \mathbb{R}^d$, compact domain $\Omega$ and $\varepsilon>0$, there is a sequence of mappings $\phi_{i_1}, ..., \phi_{i_m} \in V, m \in \mathbb{Z}^+$, such that the composition $\phi_{i_m} \circ ... \circ \phi_{i_1} $ approximates $f$ on $\Omega$ with an error less than $\varepsilon$. Our results demonstrate an unusual approximation power of mapping compositions and motivate a novel compositional model for regular languages.

Deep Learning · Sequential Models, Time series

Carles Balsells-Rodas, Yixin Wang, Yingzhen Li

The identifiability of latent variable models has received increasing attention due to its relevance in interpretability and out-of-distribution generalisation. In this work, we study the identifiability of Switching Dynamical Systems, taking an initial step toward extending identifiability analysis to sequential latent variable models. We first prove the identifiability of Markov Switching Models, which commonly serve as the prior distribution for the continuous latent variables in Switching Dynamical Systems. We present identification conditions for first-order Markov dependency structures, whose transition distribution is parametrised via non-linear Gaussians. We then establish the identifiability of the latent variables and non-linear mappings in Switching Dynamical Systems up to affine transformations, by leveraging identifiability analysis techniques from identifiable deep latent variable models. We finally develop estimation algorithms for identifiable Switching Dynamical Systems. Throughout empirical studies, we demonstrate the practicality of identifiable Switching Dynamical Systems for segmenting high-dimensional time series such as videos, and showcase the use of identifiable Markov Switching Models for regime-dependent causal discovery in climate data.

Applications · Time Series

Romain Ilbert, Ambroise Odonnat, Vasilii Feofanov, Aladin Virmaux, Giuseppe Paolo, Themis Palpanas, Ievgen Redko

Transformer-based architectures achieved breakthrough performance in natural language processing and computer vision, yet they remain inferior to simpler linear baselines in multivariate long-term forecasting. To better understand this phenomenon, we start by studying a toy linear forecasting problem for which we show that transformers are incapable of converging to their true solution despite their high expressive power. We further identify the attention of transformers as being responsible for this low generalization capacity. Building upon this insight, we propose a shallow lightweight transformer model that successfully escapes bad local minima when optimized with sharpness-aware optimization. We empirically demonstrate that this result extends to all commonly used real-world multivariate time series datasets. In particular, SAMformer surpasses current state-of-the-art methods and is on par with the biggest foundation model MOIRAI while having significantly fewer parameters. The code is available at https://github.com/romilbert/samformer.

Applications · Time Series

Weijia Zhang, Chenlong Yin, Hao Liu, Xiaofang Zhou, Hui Xiong

Forecasting of Irregular Multivariate Time Series (IMTS) is critical for numerous areas, such as healthcare, biomechanics, climate science, and astronomy. Despite existing research addressing irregularities in time series through ordinary differential equations, the challenge of modeling correlations between asynchronous IMTS remains underexplored. To bridge this gap, this study proposes Transformable Patching Graph Neural Networks (t-PatchGNN), which transforms each univariate irregular time series into a series of transformable patches encompassing a varying number of observations with uniform temporal resolution. It seamlessly facilitates local semantics capture and inter-time series correlation modeling while avoiding sequence length explosion in aligned IMTS. Building on the aligned patching outcomes, we then present time-adaptive graph neural networks to model dynamic intertime series correlation based on a series of learned time-varying adaptive graphs. We demonstrate the remarkable superiority of t-PatchGNN on a comprehensive IMTS forecasting benchmark we build, which contains four real-world scientific datasets covering healthcare, biomechanics and climate science, and seventeen competitive baselines adapted from relevant research fields.

Applications · Time Series

Rahul Thapa, Bryan He, Magnus Ruud Kjaer, Hyatt Moore, Gauri Ganjoo, Emmanuel Mignot, James Zou

Sleep is a complex physiological process evaluated through various modalities recording electrical brain, cardiac, and respiratory activities. We curate a large polysomnography dataset from over 14,000 participants comprising over 100,000 hours of multi-modal sleep recordings. Leveraging this extensive dataset, we developed SleepFM, the first multi-modal foundation model for sleep analysis. We show that a novel leave-one-out approach for contrastive learning significantly improves downstream task performance compared to representations from standard pairwise contrastive learning. A logistic regression model trained on SleepFM's learned embeddings outperforms an end-to-end trained convolutional neural network (CNN) on sleep stage classification (macro AUROC 0.88 vs 0.72 and macro AUPRC 0.72 vs 0.48) and sleep disordered breathing detection (AUROC 0.85 vs 0.69 and AUPRC 0.77 vs 0.61). Notably, the learned embeddings achieve 48% top-1 average accuracy in retrieving modality clip pairs from 90,000 candidates. This work demonstrates the value of holistic multi-modal sleep modeling to fully capture the richness of sleep recordings. SleepFM is open source and available at https://anonymous.4open.science/r/sleepfm.

Applications · Time Series

Haoxin Liu, Harshavardhan Kamarthi, Lingkai Kong, Zhiyuan Zhao, Chao Zhang, B. Aditya Prakash

Time-series forecasting (TSF) finds broad applications in real-world scenarios. Due to the dynamic nature of time-series data, it is crucial for TSF models to preserve out-of-distribution (OOD) generalization abilities, as training and test sets represent historical and future data respectively. In this paper, we aim to alleviate the inherent OOD problem in TSF via invariant learning. We identify fundamental challenges of invariant learning for TSF. First, the target variables in TSF may not be sufficiently determined by the input due to unobserved core variables in TSF, breaking the fundamental assumption of invariant learning. Second, time-series datasets lack adequate environment labels, while existing environmental inference methods are not suitable for TSF. To address these challenges, we propose FOIL, a model-agnostic framework that endows time-series forecasting for out-of-distribution generalization via invariant learning. Specifically, FOIL employs a novel surrogate loss to mitigate the impact of unobserved variables. Further, FOIL implements joint optimization by alternately inferring environments effectively with a multi-head network while preserving the temporal adjacency structure and learning invariant representations across inferred environments for OOD generalized TSF. Extensive experiments demonstrate that the proposed FOIL significantly and consistently improves the performance of various TSF models, achieving gains of up to 85%.

Haokun Gui, Xiucheng Li, Xinyang Chen

In this paper, we propose a BERT-style self-supervised learning model, VQ-MTM (Vector Quantization Masked Time-Series Modeling), for the EEG time series data analysis. At its core, VQ-MTM comprises a theoretically grounded random-projection quantization module and a phase-aligning module guided by the Time-Phase-Shift Equivariance of Fourier Transform, the two modules can generate well-defined semantic units (akin to words in natural language) for the corrupted and periodic time series, thus offering robust and consistent learning signals for the EEG self-supervised learning. VQ-MTM also owns low model complexity and can easily adapt to large-scale datasets. We conduct experiments on five real-world datasets including two large-scale datasets to verify the efficacy of our proposed model, the experiment results show that VQ-MTM is able to consistently surpass the existing methods by large margins on both seizure detection and classification tasks. Our code is available at https://github.com/HaokunGUI/VQ_MTM.

Miscellaneous Aspects of Machine Learning · Representation Learning

Nimrod Berman, Ilan Naiman, Idan Arbiv, Gal Fadlon, Omri Azencot

One of the fundamental representation learning tasks is unsupervised sequential disentanglement, where latent codes of inputs are decomposed to a single static factor and a sequence of dynamic factors. To extract this latent information, existing methods condition the static and dynamic codes on the entire input sequence. Unfortunately, these models often suffer from information leakage, i.e., the dynamic vectors encode both static and dynamic information, or vice versa, leading to a non-disentangled representation. Attempts to alleviate this problem via reducing the dynamic dimension and auxiliary loss terms gain only partial success. Instead, we propose a novel and simple architecture that mitigates information leakage by offering a simple and effective subtraction inductive bias while conditioning on a single sample. Remarkably, the resulting variational framework is simpler in terms of required loss terms, hyper-parameters, and data augmentation. We evaluate our method on multiple data-modality benchmarks including general time series, video, and audio, and we show beyond state-of-the-art results on generation and prediction tasks in comparison to several strong baselines.

Deep Learning · Robustness

Yunjuan Wang, Kaibo Zhang, Raman Arora

Benign overfitting is the phenomenon wherein none of the predictors in the hypothesis class can achieve perfect accuracy (i.e., non-realizable or noisy setting), but a model that interpolates the training data still achieves good generalization. A series of recent works aim to understand this phenomenon for regression and classification tasks using linear predictors as well as two-layer neural networks. In this paper, we study such a benign overfitting phenomenon in an adversarial setting. We show that under a distributional assumption, interpolating neural networks found using adversarial training generalize well despite inference-time attacks. Specifically, we provide convergence and generalization guarantees for adversarial training of two-layer networks (with smooth as well as non-smooth activation functions) showing that under moderate $\ell_2$ norm perturbation budget, the trained model has near-zero robust training loss and near-optimal robust generalization error. We support our theoretical findings with an empirical study on synthetic and real-world data.

Applications · Time Series

Shengsheng Lin, Weiwei Lin, Wentai Wu, Haojun Chen, Junjie Yang

This paper introduces SparseTSF, a novel, extremely lightweight model for Long-term Time Series Forecasting (LTSF), designed to address the challenges of modeling complex temporal dependencies over extended horizons with minimal computational resources. At the heart of SparseTSF lies the Cross-Period Sparse Forecasting technique, which simplifies the forecasting task by decoupling the periodicity and trend in time series data. This technique involves downsampling the original sequences to focus on cross-period trend prediction, effectively extracting periodic features while minimizing the model's complexity and parameter count. Based on this technique, the SparseTSF model uses fewer than *1k* parameters to achieve competitive or superior performance compared to state-of-the-art models. Furthermore, SparseTSF showcases remarkable generalization capabilities, making it well-suited for scenarios with limited computational resources, small samples, or low-quality data. The code is publicly available at this repository: https://github.com/lss-1138/SparseTSF.

Deep Learning · Sequential Models, Time series

Gerald Woo, Chenghao Liu, Akshat Kumar, Caiming Xiong, Silvio Savarese, Doyen Sahoo

Deep learning for time series forecasting has traditionally operated within a one-model-per-dataset framework, limiting its potential to leverage the game-changing impact of large pre-trained models. The concept of *universal forecasting*, emerging from pre-training on a vast collection of time series datasets, envisions a single Large Time Series Model capable of addressing diverse downstream forecasting tasks. However, constructing such a model poses unique challenges specific to time series data: (i) cross-frequency learning, (ii) accommodating an arbitrary number of variates for multivariate time series, and (iii) addressing the varying distributional properties inherent in large-scale data. To address these challenges, we present novel enhancements to the conventional time series Transformer architecture, resulting in our proposed **M**asked Enc**o**der-based Un**i**ve**r**s**a**l T**i**me Series Forecasting Transformer (**Moirai**). Trained on our newly introduced Large-scale Open Time Series Archive (LOTSA) featuring over 27B observations across nine domains, Moirai achieves competitive or superior performance as a zero-shot forecaster when compared to full-shot models. Code, data, and model weights can be found at https://github.com/SalesforceAIResearch/uni2ts.

Applications · Neuroscience, Cognitive Science

Noga Mudrik, Yenho Chen, Eva Yezerets, Christopher Rozell, Adam Charles

Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how observed neural activity relates to perception and behavior. Models of neural dynamics often focus on either low-dimensional projections of neural activity or on learning dynamical systems that explicitly relate to the neural state over time. We discuss how these two approaches are interrelated by considering dynamical systems as representative of flows on a low-dimensional manifold. Building on this concept, we propose a new decomposed dynamical system model that represents complex non-stationary and nonlinear dynamics of time series data as a sparse combination of simpler, more interpretable components. Our model is trained through a dictionary learning procedure, where we leverage recent results in tracking sparse vectors over time. The decomposed nature of the dynamics is more expressive than previous switched approaches for a given number of parameters and enables modeling of overlapping and non-stationary dynamics. In both continuous-time and discrete-time instructional examples, we demonstrate that our model effectively approximates the original system, learns efficient representations, and captures smooth transitions between dynamical modes. Furthermore, we highlight our model’s ability to efficiently capture and demix population dynamics generated from multiple independent subnetworks, a task that is computationally impractical for switched models. Finally, we apply our model to neural ``full brain'' recordings of C. elegans data, illustrating a diversity of dynamics that is obscured when classified into discrete states.

Deep Learning · Sequential Models, Time series

Xinyao Fan, Yueying Wu, Chang XU, Yu-Hao Huang, Weiqing Liu, Jiang Bian

Recently, diffusion probabilistic models have attracted attention in generative time series forecasting due to their remarkable capacity to generate high-fidelity samples. However, the effective utilization of their strong modeling ability in the probabilistic time series forecasting task remains an open question, partially due to the challenge of instability arising from their stochastic nature. To address this challenge, we introduce a novel Multi-Granularity Time Series Diffusion (MG-TSD) model, which achieves state-of-the-art predictive performance by leveraging the inherent granularity levels within the data as given targets at intermediate diffusion steps to guide the learning process of diffusion models. The way to construct the targets is motivated by the observation that forward process of the diffusion model, which sequentially corrupts the data distribution to a standard normal distribution, intuitively aligns with the process of smoothing fine-grained data into a coarse-grained representation, both of which result in a gradual loss of fine distribution features. In the study, we derive a novel multi-granularity guidance diffusion loss function and propose a concise implementation method to effectively utilize coarse-grained data across various granularity levels.More importantly, our approach does not rely on additional external data, making it versatile and applicable across various domains. Extensive experiments conducted on real-world datasets demonstrate that our MG-TSD model outperforms existing time series prediction methods.

Applications · Time Series

Hongbin Huang, Minghua Chen, Xiao Qiao

Limited data availability poses a major obstacle in training deep learning models for financial applications. Synthesizing financial time series to augment real-world data is challenging due to the irregular and scale-invariant patterns uniquely associated with financial time series - temporal dynamics that repeat with varying duration and magnitude. Such dynamics cannot be captured by existing approaches, which often assume regularity and uniformity in the underlying data. We develop a novel generative framework called FTS-Diffusion to model irregular and scale-invariant patterns that consists of three modules. First, we develop a scale-invariant pattern recognition algorithm to extract recurring patterns that vary in duration and magnitude. Second, we construct a diffusion-based generative network to synthesize segments of patterns. Third, we model the temporal transition of patterns in order to aggregate the generated segments. Extensive experiments show that FTS-Diffusion generates synthetic financial time series highly resembling observed data, outperforming state-of-the-art alternatives. Two downstream experiments demonstrate that augmenting real-world data with synthetic data generated by FTS-Diffusion reduces the error of stock market prediction by up to 17.9%. To the best of our knowledge, this is the first work on generating intricate time series with irregular and scale-invariant patterns, addressing data limitation issues in finance.

Deep Learning · Sequential Models, Time series

Arnab Mondal, Siba Smarak Panigrahi, Sai Rajeswar, Kaleem Siddiqi, Siamak Ravanbakhsh

The accurate modeling of dynamics in interactive environments is critical for successful long-range prediction. Such a capability could advance Reinforcement Learning (RL) and Planning algorithms, but achieving it is challenging. Inaccuracies in model estimates can compound, resulting in increased errors over long horizons.We approach this problem from the lens of Koopman theory, where the nonlinear dynamics of the environment can be linearized in a high-dimensional latent space. This allows us to efficiently parallelize the sequential problem of long-range prediction using convolution while accounting for the agent's action at every time step.Our approach also enables stability analysis and better control over gradients through time. Taken together, these advantages result in significant improvement over the existing approaches, both in the efficiency and the accuracy of modeling dynamics over extended horizons. We also show that this model can be easily incorporated into dynamics modeling for model-based planning and model-free RL and report promising experimental results.

Deep Learning · Generative Models and Autoencoders

Yiyang Ma, Huan Yang, Wenhan Yang, Jianlong Fu, Jiaying Liu

Diffusion models, as a kind of powerful generative model, have given impressive results on image super-resolution (SR) tasks. However, due to the randomness introduced in the reverse process of diffusion models, the performances of diffusion-based SR models are fluctuating at every time of sampling, especially for samplers with few resampled steps. This inherent randomness of diffusion models results in ineffectiveness and instability, making it challenging for users to guarantee the quality of SR results. However, our work takes this randomness as an opportunity: fully analyzing and leveraging it leads to the construction of an effective plug-and-play sampling method that owns the potential to benefit a series of diffusion-based SR methods. More in detail, we propose to steadily sample high-quality SR images from pre-trained diffusion-based SR models by solving diffusion ordinary differential equations (diffusion ODEs) with optimal boundary conditions (BCs) and analyze the characteristics between the choices of BCs and their corresponding SR results. Our analysis shows the route to obtain an approximately optimal BC via an efficient exploration in the whole space. The quality of SR results sampled by the proposed method with fewer steps outperforms the quality of results sampled by current methods with randomness from the same pre-trained diffusion-based SR model, which means that our sampling method ''boosts'' current diffusion-based SR models without any additional training.

Applications · Time Series

DongHao Luo, Xue Wang

Recently, Transformer-based and MLP-based models have emerged rapidly andwon dominance in time series analysis. In contrast, convolution is losing steamin time series tasks nowadays for inferior performance. This paper studies theopen question of how to better use convolution in time series analysis and makesefforts to bring convolution back to the arena of time series analysis. To this end,we modernize the traditional TCN and conduct time series related modificationsto make it more suitable for time series tasks. As the outcome, we proposeModernTCN and successfully solve this open question through a seldom-exploredway in time series community. As a pure convolution structure, ModernTCN stillachieves the consistent state-of-the-art performance on five mainstream time seriesanalysis tasks while maintaining the efficiency advantage of convolution-basedmodels, therefore providing a better balance of efficiency and performance thanstate-of-the-art Transformer-based and MLP-based models. Our study furtherreveals that, compared with previous convolution-based models, our ModernTCNhas much larger effective receptive fields (ERFs), therefore can better unleash thepotential of convolution in time series analysis. Code is available at this repository:https://github.com/luodhhh/ModernTCN.

Miscellaneous Aspects of Machine Learning · Unsupervised and Semi-supervised Learning

Biswadeep Chakraborty, Beomseok Kang, Harshit Kumar, Saibal Mukhopadhyay

Recurrent Spiking Neural Networks (RSNNs) have emerged as a computationally efficient and brain-inspired machine learning model. The design of sparse RSNNs with fewer neurons and synapses helps reduce the computational complexity of RSNNs. Traditionally, sparse SNNs are obtained by first training a dense and complex SNN for a target task and, next, eliminating neurons with low activity (activity-based pruning) while maintaining task performance. In contrast, this paper presents a task-agnostic methodology for designing sparse RSNNs by pruning an untrained (arbitrarily initialized) large model. We introduce a novel Lyapunov Noise Pruning (LNP) algorithm that uses graph sparsification methods and utilizes Lyapunov exponents to design a stable sparse RSNN from an untrained RSNN. We show that the LNP can leverage diversity in neuronal timescales to design a sparse Heterogeneous RSNN (HRSNN). Further, we show that the same sparse HRSNN model can be trained for different tasks, such as image classification and time-series prediction. The experimental results show that, in spite of being task-agnostic, LNP increases computational efficiency (fewer neurons and synapses) and prediction performance of RSNNs compared to traditional activity-based pruning of trained dense models.