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Social Aspects · Everything Else

Jacob Morrison, Clara Na, Jared Fernandez, Tim Dettmers, Emma Strubell, Jesse Dodge

As the performance of artificial intelligence systems has dramatically increased, so too has the environmental impact of creating these systems. While many model developers release estimates of the power consumption and carbon emissions from the final training runs for their latest models, there is comparatively little transparency into the impact of model development, hardware manufacturing, and total water usage throughout. In this work, we estimate the real-world environmental impact of developing a series of language models, ranging from 20 million to 13 billion active parameters, trained on up to 5.6 trillion tokens each. When accounting for hardware manufacturing, model development, and our final training runs, we find that our series of models released **493 metric tons** of carbon emissions, equivalent to powering about 98 homes in the United States for one year, and consumed **2.769 million liters of water**, equivalent to about 24.5 years of water usage by a person in the United States, even though our data center is extremely water-efficient. We measure and report the environmental impact of our model development; to the best of our knowledge we are the first to do so for LLMs, and we find that model development, the impact of which is generally not disclosed by most model developers, amounted to **~50%** of that of training. By looking at detailed time series data for power consumption, we also find that power usage throughout training is not consistent, fluctuating between ~15% and ~85% of our hardware's maximum power draw, with negative implications for grid-scale planning as demand continues to grow. We close with a discussion on the continued difficulty of estimating the environmental impact of AI systems, and key takeaways for model developers and the public at large.

Applications · Time Series

Daning Huang, Hanyang He, John Harlim, Yan Li

We address the problem of learning ordinary differential equations (ODEs) on manifolds. Existing machine learning methods, particularly those using neural networks, often struggle with high computational demands. To overcome this issue, we introduce a geometrically constrained operator-valued kernel that allows us to represent vector fields on tangent bundles of smooth manifolds. The construction of the kernel imposes the geometric constraints that are estimated from the data and ensures the computational feasibility for learning high dimensional systems of ODEs. Once the vector fields are estimated, e.g., by the kernel ridge regression, we need an ODE solver that guarantees the solution to stay on (or close to) the manifold. To overcome this issue, we propose a geometry-preserving ODE solver that approximates the exponential maps corresponding to the ODE solutions. We deduce a theoretical error bound for the proposed solver that guarantees the approximate solutions to lie on the manifold in the limit of large data. We verify the effectiveness of the proposed approach on high-dimensional dynamical systems, including the cavity flow problem, the beating and travelling waves in Kuramoto-Sivashinsky equations, and the reaction-diffusion dynamics.

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

BO HU, Tat-Jen Cham

To predict future trajectories of pedestrians, scene is as important as the history trajectory since i) scene reflects the position of possible goals of the pedestrian ii) trajectories are affected by the semantic information of the scene. It requires the model to capture scene information and learn the relation between scenes and trajectories. However, existing methods either apply Convolutional Neural Networks (CNNs) to summarize the scene to a feature vector, which raises the feature misalignment issue, or convert trajectory to heatmaps to align with the scene map, which ignores the interactions among different pedestrians. In this work, we introduce the trajectory-scene-cell feature to represent both trajectories and scenes in one feature space. By decoupling the trajectory in temporal domain and the scene in spatial domain, trajectory feature and scene feature are re-organized in different types of cell feature, which well aligns trajectory and scene, and allows the framework to model both human-human and human-scene interactions. Moreover, the Trajectory-Scene-Cell Network (TSC-Net) with new trajectory prediction manner is proposed, where both goal and intermediate positions of the trajectory are predict by cell classification and offset regression. Comparative experiments show that TSC-Net achieves the SOTA performance on several datasets with most of the metrics. Especially for the goal estimation, TSC-Net is demonstrated better on predicting goals for trajectories with irregular speed.

Miscellaneous Aspects of Machine Learning · Causality

Konstantin Hess, Stefan Feuerriegel

Patient trajectories from electronic health records are widely used to estimate conditional average potential outcomes (CAPOs) of treatments over time, which then allows to personalize care. Yet, existing neural methods for this purpose have a key limitation: while some adjust for time-varying confounding, these methods assume that the time series are recorded in discrete time. In other words, they are constrained to settings where measurements and treatments are conducted at fixed time steps, even though this is unrealistic in medical practice. In this work, we aim to estimate CAPOs in continuous time. The latter is of direct practical relevance because it allows for modeling patient trajectories where measurements and treatments take place at arbitrary, irregular timestamps. We thus propose a new method called stabilized continuous time inverse propensity network (SCIP-Net). For this, we further derive stabilized inverse propensity weights for robust estimation of the CAPOs. To the best of our knowledge, our SCIP-Net is the first neural method that performs proper adjustments for time-varying confounding in continuous time.

Deep Learning · Sequential Models, Time series

Filip Matzner, František Mráz

Echo State Networks (ESNs) are a class of recurrent neural networks in which only a small readout regression layer is trained, while the weights of the recurrent network, termed the reservoir, are randomly assigned and remain fixed. Our work introduces the Locally Connected ESN (LCESN), a novel ESN variant with a locally connected reservoir, forced memory, and a weight adaptation strategy. LCESN significantly reduces the asymptotic time and space complexities compared to the conventional ESN, enabling substantially larger networks. LCESN also improves the memory properties of ESNs without affecting network stability. We evaluate LCESN's performance on the NARMA10 benchmark task and compare it to state-of-the-art models on nine real-world datasets. Despite the simplicity of our model and its one-shot training approach, LCESN achieves competitive results, even surpassing several state-of-the-art models. LCESN introduces a fresh approach to real-world time series forecasting and demonstrates that large, well-tuned random recurrent networks can rival complex gradient-trained feedforward models. We provide our GPU-based implementation of LCESN as an open-source library.

Deep Learning · Sequential Models, Time series

Annan Yu, Dongwei Lyu, Soon Hoe Lim, Michael W Mahoney, N. Benjamin Erichson

State space models (SSMs) leverage linear, time-invariant (LTI) systems to effectively learn sequences with long-range dependencies. By analyzing the transfer functions of LTI systems, we find that SSMs exhibit an implicit bias toward capturing low-frequency components more effectively than high-frequency ones. This behavior aligns with the broader notion of frequency bias in deep learning model training. We show that the initialization of an SSM assigns it an innate frequency bias and that training the model in a conventional way does not alter this bias. Based on our theory, we propose two mechanisms to tune frequency bias: either by scaling the initialization to tune the inborn frequency bias; or by applying a Sobolev-norm-based filter to adjust the sensitivity of the gradients to high-frequency inputs, which allows us to change the frequency bias via training. Using an image-denoising task, we empirically show that we can strengthen, weaken, or even reverse the frequency bias using both mechanisms. By tuning the frequency bias, we can also improve SSMs' performance on learning long-range sequences, averaging an $88.26\\%$ accuracy on the Long-Range Arena (LRA) benchmark tasks.

Applications · Health

Arvind Pillai, Dimitris Spathis, Fahim Kawsar, Mohammad Malekzadeh

Photoplethysmography (PPG) is the leading non-invasive technique for monitoring biosignals and cardiovascular health, with widespread adoption in both clinical settings and consumer wearable devices. While machine learning models trained on PPG signals have shown promise, they tend to be task-specific and struggle with generalization. Current research is limited by the use of single-device datasets, insufficient exploration of out-of-domain generalization, and a lack of publicly available models, which hampers reproducibility. To address these limitations, we present PaPaGei, the first open foundation model for PPG signals. The model is pre-trained on over 57,000 hours of data, comprising 20 million unlabeled PPG segments from publicly available datasets. We introduce a novel representation learning approach that leverages domain knowledge of PPG signal morphology across individuals, enabling the capture of richer representations compared to traditional contrastive learning methods. We evaluate PaPaGei against state-of-the-art time-series foundation models and self-supervised learning benchmarks across 20 tasks from 10 diverse datasets, spanning cardiovascular health, sleep disorders, pregnancy monitoring, and wellbeing assessment. Our model demonstrates superior performance, improving classification and regression metrics by 6.3% and 2.9% respectively in at least 14 tasks. Notably, PaPaGei achieves these results while being more data- and parameter-efficient, outperforming models that are 70x larger. Beyond accuracy, we examine model robustness across different skin tones, establishing a benchmark for bias evaluation in future models. PaPaGei can serve as both a feature extractor and an encoder for multimodal models, opening up new opportunities for multimodal health monitoring. Models, data, and code are available at: https://github.com/nokia-bell-labs/papagei-foundation-model

Applications · Neuroscience, Cognitive Science

Ziyu Lu, Wuwei Zhang, Trung Le, Hao Wang, Uygar Sümbül, Eric SheaBrown, Lu Mi

Neuronal dynamics are highly nonlinear and nonstationary. Traditional methods for extracting the underlying network structure from neuronal activity recordings mainly concentrate on modeling static connectivity, without accounting for key nonstationary aspects of biological neural systems, such as ongoing synaptic plasticity and neuronal modulation. To bridge this gap, we introduce the NetFormer model, an interpretable approach applicable to such systems. In NetFormer, the activity of each neuron across a series of historical time steps is defined as a token. These tokens are then linearly mapped through a query and key mechanism to generate a state- (and hence time-) dependent attention matrix that directly encodes nonstationary connectivity structures. We analyze our formulation from the perspective of nonstationary and nonlinear networked dynamical systems, and show both via an analytical expansion and targeted simulations how it can approximate the underlying ground truth. Next, we demonstrate NetFormer's ability to model a key feature of biological networks, spike-timing-dependent plasticity, whereby connection strengths continually change in response to local activity patterns. We further demonstrate that NetFormer can capture task-induced connectivity patterns on activity generated by task-trained recurrent neural networks. Thus informed, we apply NetFormer to a multi-modal dataset of real neural recordings, which contains neural activity, cell type, and behavioral state information. We show that the NetFormer effectively predicts neural dynamics and identifies cell-type specific, state-dependent dynamic connectivity that matches patterns measured in separate ground-truth physiology experiments, demonstrating its ability to help decode complex neural interactions based on population activity observations alone.

Deep Learning · Sequential Models, Time series

Armand Foucault, Francois Malgouyres, Franck Mamalet

Binary and sparse ternary weights in neural networks enable faster computations and lighter representations, facilitating their use on edge devices with limited computational power. Meanwhile, vanilla RNNs are highly sensitive to changes in their recurrent weights, making the binarization and ternarization of these weights inherently challenging. To date, no method has successfully achieved binarizationor ternarization of vanilla RNN weights. We present a new approach leveraging the properties of Hadamard matrices to parameterize a subset of binary and sparse ternary orthogonal matrices. This method enables the training of orthogonal RNNs (ORNNs) with binary and sparse ternary recurrent weights, effectively creating a specific class of binary and sparse ternary vanilla RNNs. The resulting ORNNs, called HadamRNN and Block-HadamRNN, are evaluated on benchmarks such as the copy task, permuted and sequential MNIST tasks, and IMDB dataset. Despite binarization or sparse ternarization, these RNNs maintain performance levels comparable to state-of-the-art full-precision models, highlighting the effectiveness of our approach. Notably, our approach is the first solution with binary recurrent weights capable of tackling the copy task over 1000 timesteps.

Probabilistic Methods · Gaussian Processes

Ameer Qaqish, Didong Li

Gaussian processes (GPs) are widely recognized for their robustness and flexibility across various domains, including machine learning, time series, spatial statistics, and biomedicine. In addition to their common usage in regression tasks, GP kernel parameters are frequently interpreted in various applications. For example, in spatial transcriptomics, estimated kernel parameters are used to identify spatial variable genes, which exhibit significant expression patterns across different tissue locations. However, before these parameters can be meaningfully interpreted, it is essential to establish their identifiability. Existing studies of GP parameter identifiability have focused primarily on Mat\'ern-type kernels, as their spectral densities allow for more established mathematical tools. In many real-world applications, particuarly in time series analysis, other kernels such as the squared exponential, periodic, and rational quadratic kernels, as well as their combinations, are also widely used. These kernels share the property of being holomorphic around zero, and their parameter identifiability remains underexplored.In this paper, we bridge this gap by developing a novel theoretical framework for determining kernel parameter identifiability for kernels holomorphic near zero. Our findings enable practitioners to determine which parameters are identifiable in both existing and newly constructed kernels, supporting application-specific interpretation of the identifiable parameters, and highlighting non-identifiable parameters that require careful interpretation.

Deep Learning · Sequential Models, Time series

Jiale Chen, Dingling Yao, Adeel Pervez, Dan Alistarh, Francesco Locatello

We propose Scalable Mechanistic Neural Network (S-MNN), an enhanced neural network framework designed for scientific machine learning applications involving long temporal sequences. By reformulating the original Mechanistic Neural Network (MNN) (Pervez et al., 2024), we reduce the computational time and space complexities from cubic and quadratic with respect to the sequence length, respectively, to linear. This significant improvement enables efficient modeling of long-term dynamics without sacrificing accuracy or interpretability. Extensive experiments demonstrate that S-MNN matches the original MNN in precision while substantially reducing computational resources. Consequently, S-MNN can drop-in replace the original MNN in applications, providing a practical and efficient tool for integrating mechanistic bottlenecks into neural network models of complex dynamical systems. Source code is available at https://github.com/IST-DASLab/ScalableMNN.

Applications · Time Series

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

We present Timer-XL, a causal Transformer for unified time series forecasting. To uniformly predict multidimensional time series, we generalize next token prediction, predominantly adopted for 1D token sequences, to multivariate next token prediction. The paradigm formulates various forecasting tasks as a long-context prediction problem. We opt for decoder-only Transformers that capture causal dependencies from varying-length contexts for unified forecasting, making predictions on non-stationary univariate time series, multivariate series with complicated dynamics and correlations, as well as covariate-informed contexts that include exogenous variables. Technically, we propose a universal TimeAttention to capture fine-grained intra- and inter-series dependencies of flattened time series tokens (patches), which is further enhanced by deft position embedding for temporal causality and variable equivalence. Timer-XL achieves state-of-the-art performance across task-specific forecasting benchmarks through a unified approach. Based on large-scale pre-training, Timer-XL achieves state-of-the-art zero-shot performance, making it a promising architecture for pre-trained time series models. Code is available at this repository: https://github.com/thuml/Timer-XL.

Deep Learning · Sequential Models, Time series

Zihao Zhou, Rose Yu

Large Language Models (LLMs) have gained popularity in time series forecasting, but their potential for anomaly detection remains largely unexplored. Our study investigates whether LLMs can understand and detect anomalies in time series data, focusing on zero-shot and few-shot scenarios. Inspired by conjectures about LLMs' behavior from time series forecasting research, we formulate key hypotheses about LLMs' capabilities in time series anomaly detection. We design and conduct principled experiments to test each of these hypotheses. Our investigation reveals several surprising findings about LLMs for time series: (1) LLMs understand time series better as *images* rather than as text, (2) LLMs do not demonstrate enhanced performance when prompted to engage in *explicit reasoning* about time series analysis. (3) Contrary to common beliefs, LLMs' understanding of time series *do not* stem from their repetition biases or arithmetic abilities. (4) LLMs' behaviors and performance in time series analysis *vary significantly* across different models. This study provides the first comprehensive analysis of contemporary LLM capabilities in time series anomaly detection. Our results suggest that while LLMs can understand trivial time series anomalies (we have no evidence that they can understand more subtle real-world anomalies), many common conjectures based on their reasoning capabilities do not hold. All synthetic dataset generators, final prompts, and evaluation scripts have been made available in https://github.com/rose-stl-lab/anomllm.

Applications · Time Series

Marcel Kollovieh, Marten Lienen, David Lüdke, Leo Schwinn, Stephan Günnemann

Recent advancements in generative modeling, particularly diffusion models, have opened new directions for time series modeling, achieving state-of-the-art performance in forecasting and synthesis. However, the reliance of diffusion-based models on a simple, fixed prior complicates the generative process since the data and prior distributions differ significantly. We introduce TSFlow, a conditional flow matching (CFM) model for time series combining Gaussian processes, optimal transport paths, and data-dependent prior distributions. By incorporating (conditional) Gaussian processes, TSFlow aligns the prior distribution more closely with the temporal structure of the data, enhancing both unconditional and conditional generation. Furthermore, we propose conditional prior sampling to enable probabilistic forecasting with an unconditionally trained model. In our experimental evaluation on eight real-world datasets, we demonstrate the generative capabilities of TSFlow, producing high-quality unconditional samples. Finally, we show that both conditionally and unconditionally trained models achieve competitive results across multiple forecasting benchmarks.

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.

Applications · Time Series

Yue Cheng, Bochen Lyu, Weiwei Xing, Zhanxing Zhu

Understanding the dynamics of causal structures is crucial for uncovering the underlying processes in time series data. Previous approaches rely on static assumptions, where contemporaneous and time-lagged dependencies are assumed to have invariant topological structures. However, these models fail to capture the evolving causal relationship between variables when the underlying process exhibits such dynamics. To address this limitation, we propose DyCAST, a novel framework designed to learn dynamic causal structures in time series using Neural Ordinary Differential Equations (Neural ODEs). The key innovation lies in modeling the temporal dynamics of the contemporaneous structure, drawing inspiration from recent advances in Neural ODEs on constrained manifolds. We reformulate the task of learning causal structures at each time step as solving the solution trajectory of a Neural ODE on the directed acyclic graph (DAG) manifold. To accommodate high-dimensional causal structures, we extend DyCAST by learning the temporal dynamics of the hidden state for contemporaneous causal structure. Experiments on both synthetic and real-world datasets demonstrate that DyCAST achieves superior or comparable performance compared to existing causal discovery models.

Applications · Time Series

Xingwei Qu, yuelin bai, Yinghao MA, Ziya Zhou, Ka Man Lo, JIAHENG LIU, Ruibin Yuan, Lejun Min, Xueling Liu, Tianyu Zhang 等

In this paper, we explore the application of Large Language Models (LLMs) to the pre-training of music. While the prevalent use of MIDI in music modeling is well-established, our findings suggest that LLMs are inherently more compatible with ABC Notation, which aligns more closely with their design and strengths, thereby enhancing the model's performance in musical composition.To address the challenges associated with misaligned measures from different tracks during generation, we propose the development of a $\underline{S}$ynchronized $\underline{M}$ulti-$\underline{T}$rack ABC Notation ($\textbf{SMT-ABC Notation}$), which aims to preserve coherence across multiple musical tracks. Our contributions include a series of models capable of handling up to 8192 tokens, covering 90\% of the symbolic music data in our training set. Furthermore, we explore the implications of the $\underline{S}$ymbolic $\underline{M}$usic $\underline{S}$caling Law ($\textbf{SMS Law}$) on model performance. The results indicate a promising research direction in music generation, offering extensive resources for further research through our open-source contributions.

Applications · Time Series

Akinori F. Ebihara, Taiki Miyagawa, Kazuyuki Sakurai, Hitoshi Imaoka

Time-sensitive machine learning benefits from Sequential Probability Ratio Test (SPRT), which provides an optimal stopping time for early classification of time series. However, in *finite horizon* scenarios, where input lengths are finite, determining the optimal stopping rule becomes computationally intensive due to the need for *backward induction*, limiting practical applicability. We thus introduce FIRMBOUND, an SPRT-based framework that efficiently estimates the solution to backward induction from training data, bridging the gap between optimal stopping theory and real-world deployment. It employs *density ratio estimation* and *convex function learning* to provide statistically consistent estimators for sufficient statistic and conditional expectation, both essential for solving backward induction; consequently, FIRMBOUND minimizes Bayes risk to reach optimality. Additionally, we present a faster alternative using Gaussian process regression, which significantly reduces training time while retaining low deployment overhead, albeit with potential compromise in statistical consistency. Experiments across independent and identically distributed (i.i.d.), non-i.i.d., binary, multiclass, synthetic, and real-world datasets show that FIRMBOUND achieves optimalities in the sense of Bayes risk and speed-accuracy tradeoff. Furthermore, it advances the tradeoff boundary toward optimality when possible and reduces decision-time variance, ensuring reliable decision-making. Code is included in the supplementary materials.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Gaurav Patel, Christopher M. Sandino, Behrooz Mahasseni, Ellen Zippi, Erdrin Azemi, Ali Moin, Juri Minxha

In this paper, we propose a framework for efficient Source-Free Domain Adaptation (SFDA) in the context of time-series, focusing on enhancing both parameter efficiency and data-sample utilization. Our approach introduces an improved paradigm for source-model preparation and target-side adaptation, aiming to enhance training efficiency during target adaptation. Specifically, we reparameterize the source model's weights in a Tucker-style decomposed manner, factorizing the model into a compact form during the source model preparation phase. During target-side adaptation, only a subset of these decomposed factors is fine-tuned, leading to significant improvements in training efficiency. We demonstrate using PAC Bayesian analysis that this selective fine-tuning strategy implicitly regularizes the adaptation process by constraining the model's learning capacity. Furthermore, this re-parameterization reduces the overall model size and enhances inference efficiency, making the approach particularly well suited for resource-constrained devices. Additionally, we demonstrate that our framework is compatible with various SFDA methods and achieves significant computational efficiency, reducing the number of fine-tuned parameters and inference overhead in terms of MACs by over 90\% while maintaining model performance.

Applications · Time Series

Ayush Mohanty, Nazal Mohamed, Paritosh Ramanan, Nagi Gebraeel

Advanced sensors and IoT devices have improved the monitoring and control of complex industrial enterprises. They have also created an interdependent fabric of geographically distributed process operations (clients) across these enterprises. Granger causality is an effective approach to detect and quantify interdependencies by examining how the state of one client affects the states of others over time. Understanding these interdependencies helps capture how localized events, such as faults and disruptions, can propagate throughout the system, potentially leading to widespread operational impacts. However, the large volume and complexity of industrial data present significant challenges in effectively modeling these interdependencies. This paper develops a federated approach to learning Granger causality. We utilize a linear state space system framework that leverages low-dimensional state estimates to analyze interdependencies. This helps address bandwidth limitations and the computational burden commonly associated with centralized data processing. We propose augmenting the client models with the Granger causality information learned by the server through a MachineLearning (ML) function. We examine the co-dependence between the augmented client and server models and reformulate the framework as a standalone ML algorithm providing conditions for its sublinear and linear convergence rates. We also study the convergence of the framework to a centralized oracle model. Moreover, we include a differential privacy analysis to ensure data security while preserving causal insights. Using synthetic data, we conduct comprehensive experiments to demonstrate the robustness of our approach to perturbations in causality, the scalability to the size of communication, number of clients, and the dimensions of raw data. We also evaluate the performance on two real-world industrial control system datasets by reporting the volume of data saved by decentralization.