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Applications · Time Series

Nassim Oufattole, Matthew McDermott, Collin Stultz

Autoregressive generative models for irregularly sampled clinical time-series data are increasingly used for zero-shot risk forecasting. Prior work typically adopts a single fine-grained discretization of time, where tokens are generated at one fixed, pre-determined, temporal resolution. We demonstrate that zero-shot accuracy for a given task varies depending on the temporal dynamics of the task in question, where performance will be low when the temporal dynamics is not well-matched to temporal resolution of the generative model. We then propose MoRGen (Mixture-of-Resolutions Generation), which fuses zero-shot generative experts trained at multiple resolutions, to improve zero-shot performance across tasks with very different temporal dynamics. Across multiple horizons and outcomes on three independent clinical datasets, MoRGen achieves lower binary-cross entropy (BCE) and statistically significant AUROC gains over autoregressive generative models that forecast tokens at a fixed temporal resolution.

Applications · Time Series

Fan Zhang, Shiming Fan, Hua Wang

Multivariate time series forecasting is critical in many real-world systems, and thus modeling cross-channel dependencies is essential. Although existing methods improve overall accuracy by enhancing representations and cross-channel interactions, it remains challenging to reliably capture inter-variable dependencies under specific conditions. We observe that dependencies in real data are often state-dependent and noisy; in such cases, dense interactions can amplify spurious correlations and lead to representation over-smoothing, which may yield unreliable predictions in certain scenarios. Motivated by this, we propose MS-FLOW, a sparse-bottleneck framework that explicitly models inter-variable interaction as capacity-limited information flow. Specifically, MS-FLOW replaces fully connected communication with selective sparse routing, retaining only a few critical dependency paths and injecting cross-variable signals under a strict communication budget, thereby suppressing redundant connections and spurious-correlation propagation. Extensive experiments demonstrate that MS-FLOW learns more reliable multivariate correlations, achieving state-of-the-art forecasting accuracy on 12 real-world benchmarks while producing fewer yet more reliable dependencies, shifting multivariate forecasting from “more interaction” to “more effective interaction”.

Social Aspects · Safety

Qizhuo Han, Xiangrui Cai, Sihan Xu, Ying Zhang, Zheli Liu

While deep neural network-based long-term time series forecasting (LTSF) has become indispensable for critical infrastructures such as smart grids and IoT platforms, the deployment of these models as black-box APIs introduces severe security vulnerabilities that remain largely underexplored. In this paper, we propose TSFAdv, a query-efficient adversarial framework for LTSF models. The framework systematically analyzes model sensitivity to spectral perturbations in both magnitude and phase of the frequency domain. By embedding frequency-domain priors into Natural Evolution Strategies, we achieve sensitivity-guided gradient estimation that improves perturbation efficacy without violating practical query constraints. To overcome ambiguities inherent to point-wise regression metrics, we adopt a trajectory-level evaluation protocol based on Dynamic Time Warping (DTW) and Slope Misalignment Error (SME), enabling the capture of complex geometric and directional deviations. Extensive experiments across seven state-of-the-art architectures demonstrate that TSFAdv achieves substantial performance gains, with average DTW improvements of 21.91–85.00% and SME improvements of 15.04–61.97% under a restrictive 200-query budget. These findings reveal that existing defense mechanisms are ineffective against frequency-domain manipulation, underscoring an urgent necessity for robust LTSF models; the code and artifacts are available at https:// anonymous.4open.science/r/TSFAdv.

Applications · Time Series

Jiayu Fang, Xuande Liu, Sangsha Fang, Zhen Tian, Hongwei Ma, Zhiqi Shao, Junbin Gao

Time series forecasting fundamentally involves learning probability distributions over future observations. However, existing loss functions rely on point-wise Euclidean metrics, neglecting the intrinsic geometric structure of probability distributions. This leads to suboptimal alignment between predicted and true distributions, particularly for uncertainty quantification. We propose InfoGeo Loss, a principled loss function grounded in information geometry that measures distributional discrepancies on statistical manifolds. Our approach comprises three key components: (1) a distribution parameterization module that models predictions with learnable sufficient statistics, (2) a Fisher information metric that quantifies intrinsic distributional distance, and (3) a Bregman divergence component that captures asymmetric prediction errors. We further introduce a natural gradient weighting strategy for efficient optimization on statistical manifolds. Theoretically, we prove statistical consistency and establish convergence guarantees. Extensive experiments on seven datasets with five architectures show that InfoGeo Loss consistently outperforms existing losses, achieving average improvements of 6.8% in MSE and 5.3% in MAE.

Social Aspects · Accountability, Transparency, and Interpretability

Giovanni De Felice, Riccardo D`Elia, Alberto Termine, Pietro Barbiero, Giuseppe Marra, Silvia Santini

Deep time series models continue to improve predictive performance, yet their deployment remains limited by their black-box nature. In response, existing interpretability approaches in the field keep focusing on explaining the internal model computations, without addressing whether they align or not with how a human would reason about the studied phenomenon. Instead, we state interpretability in deep time series models should pursue semantic alignment: predictions should be expressed in terms of variables that are meaningful to the end user, mediated by spatial and temporal mechanisms that admit user-dependent constraints. In this paper, we formalize this requirement and require that, once established, semantic alignment must be preserved under temporal evolution: a constraint with no analog in static settings. Provided with this definition, we outline a blueprint for semantically aligned deep time series models, identify properties that support trust, and discuss implications for model design.

General Machine Learning · Methodology

Hanyang Jiang, Yao Xie

Reliable uncertainty quantification at unobserved spatial locations is a key challenge in spatial statistics, particularly for complex and heterogeneous datasets. While traditional methods such as Kriging rely on strong distributional assumptions, conformal prediction (CP) offers a distribution-free alternative. However, although non-i.i.d. CP theory is well established for time-series data, a significant gap remains for spatial data, where the lack of a natural ordering and discrete index complicates theoretical guarantees. Existing CP theory for spatial data often relies on exchangeability. We propose Localized Spatial Conformal Prediction (LSCP), a model-agnostic framework that bridges this gap by coupling local quantile regression with conformal calibration. LSCP conditions on spatial neighborhoods to capture local heterogeneity. We show that LSCP retains finite-sample marginal coverage under spatial exchangeability and attains asymptotic conditional coverage under stationarity and spatial mixing. Across synthetic and real datasets, LSCP consistently achieves near-nominal coverage with tighter and more stable prediction intervals than existing methods that fail to capture these spatial dependencies.

Pierre-Louis Cauvin, Panayotis Mertikopoulos

We study the robustness of stochastic mirror descent (SMD) under heavy-tailed noise, focusing on whether the method retains its convergence guarantees when run with infinite-variance stochastic gradient input. To address this question in a principled manner, we begin by introducing a continuous-time model of SMD as a stochastic differential equation (SDE) driven by a centered Lévy noise process with finite $p$-th order moments, $1 < p \leq 2$. This scheme---which we call the Lévy mirror flow (LMF)---arises naturally as the scaling limit of SMD in the presence of heavy-tailed noise. In particular, when $p < 2$---the heavy noise regime---the trajectories of LMF generically exhibit jump discontinuities of arbitrary magnitude which, if frequent enough, lead to infinite variance. Nonetheless, despite this highly singular behavior, we show that LMF attains $\epsilon$-optimality within $\mathcal{O}(\epsilon^{-p/(p-1)})$ time in the convex case, and within $\tilde{\mathcal{O}}(\epsilon^{-1/(p-1)})$ time for (relatively) strongly convex objectives. These guarantees provide a transparent characterization of the impact of frequent long jumps on the convergence of the process, and percolate to a series of matching discrete-time guarantees for several variants of SMD under heavy-tailed noise.

Deep Learning · Sequential Models, Time series

Junghoon Lim

Irregular Multivariate Time Series (IMTS) arise naturally in many real-world domains, yet their irregular sampling patterns pose significant challenges for effective modeling. Existing approaches for IMTS fall into two categories: architecture-based and data-based methods. Architecture-based methods require specialized modeling for IMTS, limiting reuse of established Multivariate Time Series (MTS) models, data-based methods convert IMTS into regular time series through imputation or interpolation, often introducing artificial values that distort temporal dynamics. In this work, we propose a novel input-embedding-based approach for modeling the IMTS. Our method preserves the original MTS backbone and operates directly on IMTS. We introduce QuITE (Query-based Irregular Time-series Embedding), a simple yet effective, backbone-agnostic embedding module that enables MTS models to directly process IMTS. QuITE leverages a set of learnable query tokens to aggregate irregular observations via a single self-attention layer, producing fixed-dimensional latent representations. Extensive experiments on real-world benchmarks demonstrate that QuITE consistently improves the performance of existing MTS models, achieving average relative performance gains up to 45.9% across diverse datasets and backbone architectures.

Applications · Neuroscience, Cognitive Science

Ganchao Wei, Daniela de Albuquerque, Miles Martinez, Shiyang Pan, John Pearson

While neuroscience experiments have repeatedly demonstrated the involvement of large populations of neurons in even simple behaviors, these studies have just as often reported that the collective dynamics of neural activity are approximately low-dimensional. As a result, methods for identifying low-dimensional latent representations of time series data have become increasingly prominent in neuroscience. However, most existing methods either ignore temporal structure or model time evolution using latent dynamical systems approaches. In the first case, dynamics may be distorted or even scrambled in the latent space, while in the second, many possible latent dynamics may give rise to the same data. Here, we address these challenges using a novel flow-matching approach in which data are generated by a pair of flow fields, one governing time evolution, the other a mapping between data and a low-dimensional latent space. Importantly, the dimension-reducing flow is trained to minimize distortions of the temporal dynamics, learning an identifiable low-dimensional representation that preserves temporal relations in the original data. Additionally, we constrain our latent spaces to have low-dimensional support in a soft, parameterized manner, taking inspiration from ideas on nested dropout. Across both neural and behavioral data, we show that this dual flow approach produces both more interpretable dynamics and higher-quality reconstructions than competing models, including in noise-dominated data sets where conventional approaches fail.

Applications · Social Sciences

Haofei Yu, Yining Zhao, Guanyu Lin, Jiaxuan You

Understanding and predicting how social beliefs evolve in response to events—from policy changes to scientific breakthroughs—remains a fundamental challenge in social science. Given LLMs’ commonsense knowledge and social intelligence, we ask: *Can LLMs model the dynamics of social beliefs following social events?* In this work, we introduce the concept of the Social World Model (SWM), a general framework designed to capture how social beliefs evolve in response to major events. SWM learns state-transition functions for social beliefs by mining temporal patterns in social data and optimizing evidence lower bound, without the need for explicit human annotations that link events to belief shifts or expensive census data. To evaluate SWM, we introduce a benchmark, SWM-Bench, derived from real-world prediction market data from both Kalshi and Polymarket. SWM-Bench includes over 10k datapoints for social belief prediction tasks spanning diverse domains such as politics, sports, cryptocurrency, and elections. Our experimental results show that SWM significantly outperforms time-series foundation models, achieving RMSE reductions of 8.4% and 11.2% on Polymarket and Kalshi respectively, while offering interpretable insights into the underlying mechanisms of social belief dynamics.

Applications · Time Series

Binqing Wu, Jian Zhou, Zongjiang Shang, Ling Chen

Spatial–temporal time series forecasting is challenging due to complex lead–lag dependencies, which are often ignored or inadequately modeled by existing methods. Thus, we propose LagLLM, the first LLM-empowered framework that explicitly models lead–lag dependencies by unifying data-driven dynamics modeling and knowledge-driven semantic reasoning. Specifically, LagLLM constructs a lead–lag graph by integrating learnable embeddings, spatial proximity, and prompt-guided reasoning from a frozen LLM, which can capture lead-lag dependencies informed by underlying data structure and semantic knowledge. In addition, LagLLM introduces structural token sorting based on the graph, which can make a fine-turned LLM explicitly perceive directional and delayed interactions. Experiments on eight real-world datasets show that LagLLM achieves the state-of-the-art performance with improved accuracy, robustness, and interpretability. The code is available at https://anonymous.4open.science/r/LagLLM.

General Machine Learning · Causality

Oana-Iuliana Popescu, Wiebke Günther, Martin Rabel, Jakob Runge

Many real-world systems exhibit both context- and time-dependent causal dynamics, where the dynamical system state also influences its context. For instance, soil moisture is driven by precipitation, yet also provides the context for heat-flux realization. We capture such dynamics in Structural Causal Models (SCMs) by introducing endogenous and time-dependent discrete context variables, also allowing for possibly lagged dependencies with the system variables. While context variables are discrete, they may also be proxies of continuous variables. The enabling assumptions for causal discovery of our model are either persistence of the context or sparsity of the context–system dependencies. We design two new PCMCI-based algorithms for causal discovery with endogenous context variables for time series and prove their soundness. A systematic evaluation on synthetic benchmarks and an application to a real-world land-atmosphere feedback problem demonstrate their effectiveness and applicability.

Deep Learning · Sequential Models, Time series

Homanga Bharadhwaj

The AI community is rapidly converging on generalist foundation models trained on web-scale data. While this paradigm has yielded impressive gains, in this paper we argue that this objective needs to shift for enabling AI that reliably helps people in their daily activities. The most valuable systems will not be those that attempt do everything for everyone, but those that do the right things for a specific individual over a long period of time. We take the position that \emph{specialist models}---defined not by narrow task taxonomies, but by a tight coupling to an individual user and their local environment---represent the endgame for high-impact assistive AI. We substantiate this argument through three case studies: (i) AI agents that need to help humans automate daily web activities; (ii) wearable assistants that must predict actions in-context from continuous egocentric streams; and (iii) home robots that require helping humans in daily tasks with safety and compliance guarantees. In these settings, standard scaling assumptions are inverted: the most critical data is generated \emph{after deployment} as a streaming, on-policy interaction trace. We outline research directions for building specialists that learn from organic observational data, avoid self-reinforcing errors, and improve safely over long horizons.

Theory · Everything Else

Victor Charpenay, Steven Schockaert

Embedding methods are among the most efficient approaches for learning to reason about relational knowledge. In this paper, we focus on the framework of region-based embeddings, where relations are encoded as geometric regions. The spatial arrangement of these regions allows such models to capture symbolic rules, enabling them to simulate some forms of symbolic reasoning. A crucial consideration is how the regions are parameterized, as this affects which rule bases can be captured. Most methods use convex regions which are defined in terms of coordinate-wise comparisons. This makes them highly efficient, but the implications of this choice have thus far remained unclear. We present a series of results that shed light on this issue, showing that convex coordinate-wise models indeed have important limitations, while at the same time showing that there is still room for pushing the expressivity of existing coordinate-wise models.

Applications · Time Series

Yihang Lu, Xianwei Meng, Enhong Chen

Neural Forecasters (NFs) have become a cornerstone of Long-term Time Series Forecasting (LTSF). However, recent progress has been hampered by an overemphasis on architectural complexity at the expense of fundamental forecasting principles. In this work, we revisit the principles of LTSF. We begin by formulating a Variance Reduction Hypothesis (VRH), positing that generating and combining multiple forecasts is essential to reducing the inherent uncertainty of NFs. Guided by this, we propose Boosted Direct Output (BDO), a streamlined paradigm that synergistically hybridizes the causal structure of Auto-Regressive (AR) with the stability of Direct Output (DO), while implicitly realizing the principle of forecast combination within a single network. Furthermore, we address the critical validation-test generalization gap by employing parameter smoothing to stabilize optimization. Extensive experiments demonstrate that these trivial yet principled improvements enable a direct temporal MLP to outperform recent, complex state-of-the-art models in nearly all benchmarks, without relying on intricate inductive biases. Finally, we empirically verify our hypothesis, establishing a dynamic performance bound that highlights promising directions for future research. The code for review is available at: \url{https://anonymous.4open.science/r/ReNF-A151}.

Applications · Time Series

Mengzhou Gao, Kaiwei Wang, Pengfei Jiao

Neural Flows efficiently model irregular multivariate time series by directly learning ODE solution trajectories with neural networks, bypassing step-by-step numerical solvers. Despite their efficiency, many existing approaches treat variables independently, leaving inter-variable interactions underexplored. Moreover, their one-step mapping makes interaction modeling inherently challenging, as it removes the iterative refinement of interactions during learning. To address this challenge, we propose one-step Graph-Structured Neural Flows (GSNF), which introduce two auxiliary-trajectory self-supervision strategies to strengthen interaction learning: (i) interaction-aware trajectory generation via re-initialization, which induces trajectory divergence to expose graph-induced interactions, with a theoretically derived lower bound on divergence; and (ii) reverse-time trajectory generation, which enforces forward–backward consistency to regularize graph learning, enabled by flow invertibility. Experiments on five real-world datasets show that GSNF achieves state-of-the-art classification performance with highly competitive training time and memory usage.

Applications · Time Series

Zehao Liu, Pengfei Jiao, Yuhan Wu, Jianqi Yang, Yuyu Yin

Although causal discovery from multivariate time series is widely used, it remains challenging under noise. Convergent cross mapping (CCM) infers causality by reconstructing shadow manifolds via time-delay embedding (TDE) and evaluating cross-map skill between manifolds. Despite Takens’ theorem guarantees in ideal settings, TDE effectively attempts to recover system state from a single noisy view, often yielding geometrically degraded manifolds and unreliable distance-based neighborhoods, which in turn weakens causal identification. We propose TopoDistill, a topology-informed knowledge distillation framework that improves univariate shadow-manifold reconstruction by aligning local neighborhood structure to a multivariate system representation. A global embedder trained on multivariate observations captures a global attractor representation, while a delay embedder is distilled to produce embeddings whose neighborhood distributions match the global topology. This cross-view alignment yields smoother and more reliable neighborhoods, improving cross mapping under noise while maintaining specificity against spurious correlations. Theoretical analysis and experimental results demonstrate that our method enables effective causal discovery.

Applications · Time Series

Daniel Durstewitz, Christoph Jürgen Hemmer, Florian Hess, Charlotte Ricarda Doll, Lukas Eisenmann

Time series (TS) modeling has come a long way from early statistical, mainly linear, approaches to the current trend in TS foundation models. With a lot of hype and industrial demand in this field, it is not always clear how much progress there really is. To advance TS forecasting and analysis to the next level, here we argue that the field needs a *dynamical systems (DS)* perspective. TS of observations from natural or engineered systems almost always originate from some underlying DS, and arguably access to its governing equations would yield theoretically optimal forecasts. This is the promise of *DS reconstruction (DSR)*, a class of ML/AI approaches that aim to infer *surrogate models* of the underlying DS from data. But models based on DS principles offer other profound advantages: Beyond short-term forecasts, they enable to predict the *long-term statistics* of an observed system, which in many practical scenarios may be the more relevant quantities. DS theory furthermore provides domain-independent *theoretical insight into mechanisms* underlying TS generation, and thereby will inform us, e.g., about upper bounds on performance of *any* TS model, generalization into unseen regimes as in tipping points, or potential control strategies. After reviewing some of the central concepts, methods, measures, and models in DS theory and DSR, we will discuss how insights from this field can advance TS modeling in crucial ways, enabling better forecasting with much lower computational and memory footprints. We conclude with a number of specific suggestions for translating insights from DSR into TS modeling.

Deep Learning · Sequential Models, Time series

Alena Brändle, Lukas Eisenmann, Florian Götz, Daniel Durstewitz

In dynamical systems reconstruction (DSR) we aim to recover the dynamical system (DS) underlying observed time series. Specifically, we aim to learn a generative surrogate model which approximates the underlying, data-generating DS, and recreates its long-term properties (`climate statistics'). In scientific and medical areas, in particular, these models need to be mechanistically tractable -- through their mathematical analysis we would like to obtain insight into the recovered system's workings. Piecewise-linear (PL), ReLU-based RNNs (PLRNNs) have a strong track-record in this regard, representing SOTA DSR models while allowing mathematical insight by virtue of their PL design. However, all current PLRNN variants are *discrete-time maps*. This is in disaccord with the assumed continuous-time nature of most physical and biological processes, and makes it hard to accommodate data arriving at *irregular* temporal intervals. Neural ODEs are one solution, but they do not reach the DSR performance of PLRNNs and often lack their tractability. Here we develop theory for *continuous-time* PLRNNs (cPLRNNs): We present a novel algorithm for training and simulating such models, bypassing numerical integration by efficiently exploiting their PL structure. We further demonstrate how important topological objects like equilibria or limit cycles can be determined semi-analytically in trained models. We compare cPLRNNs to both their discrete-time cousins as well as Neural ODEs on DSR benchmarks, including systems with discontinuities which come with hard thresholds.

Applications · Time Series

Difei Hou, Jiaqi Yue, Chunhui Zhao

Explainability is essential for applying time series analysis in high-stakes domains. While Time Series Captioning (TSC) offers a pathway to enhance temporal explainability, achieving reliable caption generation usually necessitates high-quality textual annotations. However, as interpreting abstract temporal dynamics requires specialized domain knowledge, acquiring such caption annotations is challenging, thereby impeding the advancement of TSC. To address this challenge, we introduce a novel Caption Label-Free Learning (CLFL) paradigm. Departing from the supervised learning tradition of imitating human annotations, CLFL formulates captioning as an agentic exploration task optimized by feedback from a proxy reward. Specifically, we propose a Dual Loop Agentic Captioning (DLAC) framework to achieve such an exploration-feedback mechanism. In the inner loop, a Time Series Captioning LLM Agent (TSCAgent) reflectively explores potential semantic captions. In turn, the outer loop evaluates these captions via downstream reasoning to derive a proxy reward, which feeds back to optimize the TSCAgent. Empirical results validate the effectiveness of the CLFL, proving that the exploration-feedback mechanism is sufficient for learning complex temporal semantics and autonomously generating captions, without any caption label supervision. Furthermore, we release TFTSC, an industrial expert-level time series caption dataset, which is available at: \url{https://anonymous.4open.science/r/TFTSC-05ED/}.