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Deep Learning · Sequential Models, Time series

Manuel Brenner, Elias Weber, Georgia Koppe, Daniel Durstewitz

In science, we are often interested in obtaining a generative model of the underlying system dynamics from observed time series. While powerful methods for dynamical systems reconstruction (DSR) exist when data come from a single domain, how to best integrate data from multiple dynamical regimes and leverage it for generalization is still an open question. This becomes particularly important when individual time series are short, and group-level information may help to fill in for gaps in single-domain data. Here we introduce a hierarchical framework that enables to harvest group-level (multi-domain) information while retaining all single-domain characteristics, and showcase it on popular DSR benchmarks, as well as on neuroscience and medical data. In addition to faithful reconstruction of all individual dynamical regimes, our unsupervised methodology discovers common low-dimensional feature spaces in which datasets with similar dynamics cluster. The features spanning these spaces were further dynamically highly interpretable, surprisingly in often linear relation to control parameters that govern the dynamics of the underlying system. Finally, we illustrate transfer learning and generalization to new parameter regimes, paving the way toward DSR foundation models.

Deep Learning · Sequential Models, Time series

Julius Aka, Johannes Brunnemann, Jörg Eiden, Arne Speerforck, Lars Mikelsons

Variational Autoencoders (VAEs) are a powerful framework for learning latent representations of reduced dimensionality, while Neural ODEs excel in learning transient system dynamics. This work combines the strengths of both to generate fast surrogate models with adjustable complexity reacting on time-varying inputs signals. By leveraging the VAE’s dimensionality reduction using a non-hierarchical prior, our method adaptively assigns stochastic noise, naturally complementing known NeuralODE training enhancements and enabling probabilistictime series modeling. We show that standard Latent ODEs struggle with dimensionality reduction in systems with time-varying inputs. Our approach mitigates this by continuously propagating variational parameters through time, establishing fixed information channels in latent space. This results in a flexible and robust method that can learn different system complexities, e.g. deep neural networks orlinear matrices. Hereby, it enables efficient approximation of the Koopman operator without the need for predefining its dimensionality. As our method balances dimensionality reduction and reconstruction accuracy, we call it Balanced Neural ODE (B-NODE). We demonstrate the effectiveness of this methods on several academic and real-world test cases, e.g. a power plant or MuJoCo data.

Deep Learning · Robustness

Berken Utku Demirel, Christian Holz

Deep learning models lack shift invariance, making them sensitive to input shifts that cause changes in output. While recent techniques seek to address this for images, our findings show that these approaches fail to provide shift-invariance in time series, where the data generation mechanism is more challenging due to the interaction of low and high frequencies. Worse, they also decrease performance across several tasks. In this paper, we propose a novel differentiable bijective function that maps samples from their high-dimensional data manifold to another manifold of the same dimension, without any dimensional reduction. Our approach guarantees that samples---when subjected to random shifts---are mapped to a unique point in the manifold while preserving all task-relevant information without loss. We theoretically and empirically demonstrate that the proposed transformation guarantees shift-invariance in deep learning models without imposing any limits to the shift. Our experiments on six time series tasks with state-of-the-art methods show that our approach consistently improves the performance while enabling models to achieve complete shift-invariance without modifying or imposing restrictions on the model's topology. The source code is available on GitHub.

Deep Learning · Generative Models and Autoencoders

Nate Gillman, Daksh Aggarwal, Michael Freeman, Chen Sun

As the quality of large language models has improved, there has been increased interest in using them to model non-linguistic tokens. For example, the Decision Transformer recasts agentic decision making as a sequence modeling problem, using a decoder-only LLM to model the distribution over the discrete action space for an Atari agent. However, when adapting LLMs to non-linguistic domains, it remains unclear if softmax over discrete bins captures the continuous structure of the tokens and the potentially complex distributions needed for high quality token generation. We introduce a neural network layer, constructed using Fourier series, which we can easily substitute for any linear layer if we want the outputs to have a more continuous structure. We perform extensive analysis on synthetic datasets, as well as on large-scale decision making and time series forecasting tasks. We also provide theoretical evidence that this layer can better learn signal from data while ignoring high-frequency noise. All of our results support the effectiveness of our proposed Fourier head in scenarios where the underlying data distribution has a natural continuous structure. For example, the Fourier head improves a Decision Transformer agent's returns across four benchmark Atari games by as much as 377\%, and increases a state-of-the-art times series foundation model's forecasting performance by 3.5\% across 20 benchmarks unseen during training.We release our implementation at https://nategillman.com/fourier-head

Probabilistic Methods · Bayesian Models and Methods

Manuel Gloeckler, Shoji Toyota, Kenji Fukumizu, Jakob Macke

Amortized simulation-based inference (SBI) methods train neural networks on simulated data to perform Bayesian inference. While this strategy avoids the need for tractable likelihoods, it often requires a large number of simulations and has been challenging to scale to time series data. Scientific simulators frequently emulate real-world dynamics through thousands of single-state transitions over time. We propose an SBI approach that can exploit such Markovian simulators by locally identifying parameters consistent with individual state transitions. We then compose these local results to obtain a posterior over parameters that align with the entire time series observation. We focus on applying this approach to neural posterior score estimation but also show how it can be applied, e.g., to neural likelihood (ratio) estimation. We demonstrate that our approach is more simulation-efficient than directly estimating the global posterior on several synthetic benchmark tasks and simulators used in ecology and epidemiology. Finally, we validate scalability and simulation efficiency of our approach by applying it to a high-dimensional Kolmogorov flow simulator with around one million data dimensions.

Deep Learning · Sequential Models, Time series

Ryan Missel, Linwei Wang

An increasing interest in learning to forecast for time-series of high-dimensional observations is the ability to adapt to systems with diverse underlying dynamics. Access to observations that define a stationary distribution of these systems is often unattainable, as the underlying dynamics may change over time. Naively training or retraining models at each shift may lead to catastrophic forgetting about previously-seen systems. We present a new continual meta-learning (CML) framework to realize continual slow-and fast adaptation of latent dynamics (CoSFan). We leverage a feed-forward meta-model to infer *what* the current system is and *how* to adapt a latent dynamics function to it, enabling *fast adaptation* to specific dynamics. We then develop novel strategies to automatically detect *when* a shift of data distribution occurs, with which to identify its underlying dynamics and its relation with previously-seen dynamics. In combination with fixed-memory experience replay mechanisms, this enables continual *slow update* of the *what-how* meta-model. Empirical studies demonstrated that both the meta- and continual-learning component was critical for learning to forecast across non-stationary distributions of diverse dynamics systems, and the feed-forward meta-model combined with task-aware/-relational continual learning strategies significantly outperformed existing CML alternatives.

Applications · Time Series

Francesco Carzaniga, Gary Hoppeler, Michael Hersche, Kaspar Schindler, Abbas Rahimi

All data modalities are not created equal, even when the signal they measure comes from the same source. In the case of the brain, two of the most important data modalities are the scalp electroencephalogram (EEG), and the intracranial electroencephalogram (iEEG). iEEG benefits from a higher signal-to-noise ratio (SNR), as it measures the electrical activity directly in the brain, while EEG is noisier and has lower spatial and temporal resolutions. Nonetheless, both EEG and iEEG are important sources of data for human neurology, from healthcare to brain–machine interfaces. They are used by human experts, supported by deep learning (DL) models, to accomplish a variety of tasks, such as seizure detection and motor imagery classification. Although the differences between EEG and iEEG are well understood by human experts, the performance of DL models across these two modalities remains under-explored. To help characterize the importance of clean data on the performance of DL models, we propose BrainCodec, a high-fidelity EEG and iEEG neural compressor. We find that training BrainCodec on iEEG and then transferring to EEG yields higher reconstruction quality than training on EEG directly. In addition, we also find that training BrainCodec on both EEG and iEEG improves fidelity when reconstructing EEG. Our work indicates that data sources with higher SNR, such as iEEG, provide better performance across the board also in the medical time-series domain. This finding is consistent with reports coming from natural language processing, where clean data sources appear to have an outsized effect on the performance of the DL model overall. BrainCodec also achieves up to a 64x compression on iEEG and EEG without a notable decrease in quality. BrainCodec markedly surpasses current state-of-the-art compression models both in final compression ratio and in reconstruction fidelity. We also evaluate the fidelity of the compressed signals objectively on a seizure detection and a motor imagery task performed by standard DL models. Here, we find that BrainCodec achieves a reconstruction fidelity high enough to ensure no performance degradation on the downstream tasks. Finally, we collect the subjective assessment of an expert neurologist, that confirms the high reconstruction quality of BrainCodec in a realistic scenario. The code is available at https://github.com/IBM/eeg-ieeg-brain-compressor.

Jing Peng, Meiqi Yang, Qiong Zhang, Xiaoxiao Li

Multivariate time series data play a pivotal role in a wide range of real-world applications, such as finance, healthcare, and meteorology, where accurate forecasting is critical for informed decision-making and proactive interventions. However, the presence of block missing data introduces significant challenges, often compromising the performance of predictive models. Traditional two-step approaches, which first impute missing values and then perform forecasting, are prone to error accumulation, particularly in complex multivariate settings characterized by high missing ratios and intricate dependency structures. In this work, we introduce S4M, an end-to-end time series forecasting framework that seamlessly integrates missing data handling into the Structured State Space Sequence (S4) model architecture. Unlike conventional methods that treat imputation as a separate preprocessing step, S4M leverages the latent space of S4 models to directly recognize and represent missing data patterns, thereby more effectively capturing the underlying temporal and multivariate dependencies. Our framework comprises two key components: the Adaptive Temporal Prototype Mapper (ATPM) and the Missing-Aware Dual Stream S4 (MDS-S4). The ATPM employs a prototype bank to derive robust and informative representations from historical data patterns, while the MDS-S4 processes these representations alongside missingness masks as dual input streams to enable accurate forecasting. Through extensive empirical evaluations on diverse real-world datasets, we demonstrate that S4M consistently achieves state-of-the-art performance. These results underscore the efficacy of our integrated approach in handling missing data, showcasing its robustness and superiority over traditional imputation-based methods. Our findings highlight the potential of S4M to advance reliable time series forecasting in practical applications, offering a promising direction for future research and deployment. Code is available at https://github.com/WINTERWEEL/S4M.git.

Deep Learning · Sequential Models, Time series

T. Konstantin Rusch, Daniela Rus

We propose Linear Oscillatory State-Space models (LinOSS) for efficiently learning on long sequences. Inspired by cortical dynamics of biological neural networks, we base our proposed LinOSS model on a system of forced harmonic oscillators. A stable discretization, integrated over time using fast associative parallel scans, yields the proposed state-space model. We prove that LinOSS produces stable dynamics only requiring nonnegative diagonal state matrix. This is in stark contrast to many previous state-space models relying heavily on restrictive parameterizations. Moreover, we rigorously show that LinOSS is universal, i.e., it can approximate any continuous and causal operator mapping between time-varying functions, to desired accuracy. In addition, we show that an implicit-explicit discretization of LinOSS perfectly conserves the symmetry of time reversibility of the underlying dynamics. Together, these properties enable efficient modeling of long-range interactions, while ensuring stable and accurate long-horizon forecasting. Finally, our empirical results, spanning a wide range of time-series tasks from mid-range to very long-range classification and regression, as well as long-horizon forecasting, demonstrate that our proposed LinOSS model consistently outperforms state-of-the-art sequence models. Notably, LinOSS outperforms Mamba and LRU by nearly 2x on a sequence modeling task with sequences of length 50k.

Applications · Time Series

Hao Wang, Lichen Pan, Yuan Shen, Zhichao Chen, Degui Yang, Yifei Yang, Sen Zhang, Xinggao Liu, Haoxuan Li, Dacheng Tao

Time series modeling presents unique challenges due to autocorrelation in both historical data and future sequences. While current research predominantly addresses autocorrelation within historical data, the correlations among future labels are often overlooked. Specifically, modern forecasting models primarily adhere to the Direct Forecast (DF) paradigm, generating multi-step forecasts independently and disregarding label correlations over time. In this work, we demonstrate that the learning objective of DF is biased in the presence of label correlation. To address this issue, we propose the Frequency-enhanced Direct Forecast (FreDF), which mitigates label correlation by learning to forecast in the frequency domain, thereby reducing estimation bias. Our experiments show that FreDF significantly outperforms existing state-of-the-art methods and is compatible with a variety of forecast models. Code is available at https://github.com/Master-PLC/FreDF.

Deep Learning · Generative Models and Autoencoders

Yangming Li, Max Ruiz Luyten, Mihaela van der Schaar

Diffusion models are mainly studied on image data. However, non-image data (e.g., tabular data) are also prevalent in real applications and tend to be noisy due to some inevitable factors in the stage of data collection, degrading the generation quality of diffusion models. In this paper, we consider a novel problem setting where every collected sample is paired with a vector indicating the data quality: risk vector. This setting applies to many scenarios involving noisy data and we propose risk-sensitive SDE, a type of stochastic differential equation (SDE) parameterized by the risk vector, to address it. With some proper coefficients, risk-sensitive SDE can minimize the negative effect of noisy samples on the optimization of diffusion models. We conduct systematic studies for both Gaussian and non-Gaussian noise distributions, providing analytical forms of risk-sensitive SDE. To verify the effectiveness of our method, we have conducted extensive experiments on multiple tabular and time-series datasets, showing that risk-sensitive SDE permits a robust optimization of diffusion models with noisy samples and significantly outperforms previous baselines.

Applications · Time Series

Xiao Han, Saima Absar, Lu Zhang, Shuhan Yuan

Identifying the root causes of anomalies in multivariate time series is challenging due to the complex dependencies among the series. In this paper, we propose a comprehensive approach called AERCA that inherently integrates Granger causal discovery with root cause analysis. By defining anomalies as interventions on the exogenous variables of time series, AERCA not only learns the Granger causality among time series but also explicitly models the distributions of exogenous variables under normal conditions. AERCA then identifies the root causes of anomalies by highlighting exogenous variables that significantly deviate from their normal states. Experiments on multiple synthetic and real-world datasets demonstrate that AERCA can accurately capture the causal relationships among time series and effectively identify the root causes of anomalies.

Applications · Time Series

Xiao Han, Saima Absar, Lu Zhang, Shuhan Yuan

Identifying the root causes of anomalies in multivariate time series is challenging due to the complex dependencies among the series. In this paper, we propose a comprehensive approach called AERCA that inherently integrates Granger causal discovery with root cause analysis. By defining anomalies as interventions on the exogenous variables of time series, AERCA not only learns the Granger causality among time series but also explicitly models the distributions of exogenous variables under normal conditions. AERCA then identifies the root causes of anomalies by highlighting exogenous variables that significantly deviate from their normal states. Experiments on multiple synthetic and real-world datasets demonstrate that AERCA can accurately capture the causal relationships among time series and effectively identify the root causes of anomalies.

Applications · Time Series

Chenghan Li, Mingchen LI, Ruisheng Diao

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.

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

Jindou Jia, Zihan Yang, Meng Wang, Kexin Guo, Jianfei Yang, Xiang Yu, Lei Guo

The well-known generalization problem hinders the application of artificial neural networks in continuous-time prediction tasks with varying latent dynamics. In sharp contrast, biological systems can neatly adapt to evolving environments benefiting from real-time feedback mechanisms. Inspired by the feedback philosophy, we present feedback neural networks, showing that a feedback loop can flexibly correct the learned latent dynamics of neural ordinary differential equations (neural ODEs), leading to a prominent generalization improvement. The feedback neural network is a novel two-DOF neural network, which possesses robust performance in unseen scenarios with no loss of accuracy performance on previous tasks. A linear feedback form is presented to correct the learned latent dynamics firstly, with a convergence guarantee. Then, domain randomization is utilized to learn a nonlinear neural feedback form. Finally, extensive tests including trajectory prediction of a real irregular object and model predictive control of a quadrotor with various uncertainties, are implemented, indicating significant improvements over state-of-the-art model-based and learning-based methods.

Deep Learning · Sequential Models, Time series

Jiecheng Lu, Yan Sun, Shihao Yang

Recent Transformer-based large language models (LLMs) demonstrate in-context learning ability to perform various functions based solely on the provided context, without updating model parameters. To fully utilize the in-context capabilities in time series forecasting (TSF) problems, unlike previous Transformer-based or LLM-based time series forecasting methods, we reformulate "time series forecasting tasks" as input tokens by constructing a series of (lookback, future) pairs within the tokens. This method aligns more closely with the inherent in-context mechanisms and is more parameter-efficient without the need of using pre-trained LLM parameters. Furthermore, it addresses issues such as overfitting in existing Transformer-based TSF models, consistently achieving better performance across full-data, few-shot, and zero-shot settings compared to previous architectures.

Deep Learning · Large Language Models

Qizhou Wang, Jin Zhou, (Andrew) Zhanke Zhou, Saebyeol Shin, Bo Han, Kilian Weinberger

Large language models (LLMs) should undergo rigorous audits to identify potential risks, such as copyright and privacy infringements. Once these risks emerge, timely updates are crucial to remove undesirable responses, ensuring legal and safe model usage. It has spurred recent research into LLM unlearning, focusing on erasing targeted undesirable knowledge without compromising the integrity of other, non-targeted responses. Existing studies have introduced various unlearning objectives to pursue LLM unlearning without necessitating complete retraining. However, each of these objectives has unique properties, and no unified framework is currently available to comprehend them thoroughly. To fill the gap, we propose the metric of the G-effect, quantifying the impacts of unlearning objectives on model performance from a gradient lens. A significant advantage of our metric is its broad ability to detail the unlearning impacts from various aspects across instances, updating steps, and LLM layers. Accordingly, the G-effect offers new insights into identifying drawbacks of existing unlearning objectives, further motivating us to explore a series of candidate solutions for their mitigation and improvements. Finally, we outline promising directions that merit further studies, aiming at contributing to the community to advance this critical field.

Applications · Health

Nguyen Thach, Patrick Habecker, Anika Eisenbraun, W. Alex Mason, Kimberly Tyler, Bilal Khan, Hau Chan

Longitudinal human behavior modeling has received increasing attention over the years due to its widespread applications to patient monitoring, dietary and lifestyle recommendations, and just-in-time intervention for at-risk individuals (e.g., problematic drug users and struggling students), to name a few. Using in-the-moment health data collected via ubiquitous devices (e.g., smartphones and smartwatches), this multidisciplinary field focuses on developing predictive models for certain health or well-being outcomes (e.g., depression and stress) in the short future given the time series of individual behaviors (e.g., resting heart rate, sleep quality, and current feelings). Yet, most existing models on these data, which we refer to as ubiquitous health data, do not achieve adequate accuracy. The latest works that yielded promising results have yet to consider realistic aspects of ubiquitous health data (e.g., containing features of different types and high rate of missing values) and the consumption of various resources (e.g., computing power, time, and cost). Given these two shortcomings, it is dubious whether these studies could translate to realistic settings. In this paper, we propose MuHBoost, a multi-label boosting method for addressing these shortcomings, by leveraging advanced methods in large language model (LLM) prompting and multi-label classification (MLC) to jointly predict multiple health or well-being outcomes. Because LLMs can hallucinate when tasked with answering multiple questions simultaneously, we also develop two variants of MuHBoost that alleviate this issue and thereby enhance its predictive performance. We conduct extensive experiments to evaluate MuHBoost and its variants on 13 health and well-being prediction tasks defined from four realistic ubiquitous health datasets. Our results show that our three developed methods outperform all considered baselines across three standard MLC metrics, demonstrating their effectiveness while ensuring resource efficiency.

Deep Learning · Sequential Models, Time series

Arkaprava Majumdar, M Anand Krishna, P. K. Srijith

Sequence labeling problems arise in several real-world applications such as healthcare and robotics. In many such applications, sequence data are irregularly sampled and are of varying complexities. Recently, efforts have been made to develop neural ODE-based architectures to model the evolution of hidden states continuously in time, to address irregularly sampled sequence data. However, they assume a fixed architectural depth and limit their flexibility to adapt to data sets with varying complexities. We propose the neural wave equation, a novel deep learning method inspired by the wave equation, to address this through continuous modeling of depth. Neural Wave Equation models the evolution of hidden states continuously across time as well as depth by using a non-homogeneous wave equation parameterized by a neural network. Through d'Alembert's analytical solution of the wave equation, we also show that the neural wave equation provides denser connections across the hidden states, allowing for better modeling capability. We conduct experiments on several sequence labeling problems involving irregularly sampled sequence data and demonstrate the superior performance of the proposed neural wave equation model.

Deep Learning · Large Language Models

Mutian He, Philip N. Garner

Architectures such as Linformer and Mamba have recently emerged as competitive linear time replacements for transformers. However, corresponding large pretrained models are often unavailable, especially in non-text domains. To remedy this, we present a Cross-Architecture Layerwise Distillation (CALD) approach that jointly converts a transformer model to a linear time substitute and fine-tunes it to a target task. We also compare several means to guide the fine-tuning to optimally retain the desired inference capability from the original model. The methods differ in their use of the target model and the trajectory of the parameters. In a series of empirical studies on language processing, language modeling, and speech processing, we show that CALD can effectively recover the result of the original model, and that the guiding strategy contributes to the result. Some reasons for the variation are suggested.