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Applications · Time Series

Shuqi Gu, Yongxiang Zhao, Baoyu Jing, Kan Ren

Time series forecasting has become increasingly critical in real-world scenarios, where future sequences are influenced not only by historical patterns but also by forthcoming events. In this context, forecasting must dynamically adapt to complex and stochastic future conditions, which introduces fundamental challenges in both forecasting and evaluation. Traditional methods typically rely on historical data or factual future conditions, while overlooking counterfactual scenarios. Furthermore, many existing approaches are restricted to simple structured conditions, limiting their ability to generalize to the real-world complexities. To address these gaps, we introduce the task of counterfactual time series forecasting with textual conditions, enabling more flexible and condition-aware forecasting. We propose a comprehensive evaluation framework that encompasses both factual and counterfactual settings, even in the absence of ground truth time series. Additionally, we present a novel text-attribution mechanism that distinguishes mutable from immutable factors, thereby improving forecast accuracy under sophisticated and stochastic textual conditions.

Applications · Time Series

Shaocheng Lan, Shuqi Gu, Zhangzhi Xiong, Kan Ren

Conditional time series generation plays a critical role in addressing data scarcity and enabling causal analysis in real-world applications. Despite its increasing importance, the field lacks a standardized and systematic benchmarking framework for evaluating generative models across diverse conditions. To address this gap, we introduce the **Con**ditional **T**ime **S**eries **G**eneration **Bench**mark (ConTSG-Bench). ConTSG-Bench comprises a large-scale, well-aligned dataset spanning diverse conditioning modalities and levels of semantic abstraction, first enabling systematic evaluation of representative generation methods across these dimensions with a comprehensive suite of metrics for generation fidelity and condition adherence. Both the quantitative benchmarking and in-depth analyses of conditional generation behaviors have revealed the traits and limitations of the current approaches, highlighting critical challenges and promising research directions, particularly with respect to precise structural controllability and downstream task utility under complex conditions.

Applications · Time Series

Haiqi Jiang, Hui Xiong

Conventional time-series discriminative forecasting relies on point-wise regression, which inherently induces over-smoothing and fails to capture stochastic volatility in complex systems. While first-order generative flow matching methods mitigate this issue, they ignore system inertia, resulting in phase-space ambiguities and high sensitivity to noise. We introduce KineFlow, a generative time-series forecasting framework that augments flow matching with a phase-space Neural Acceleration Field, treating exogenous inputs as driving forces that produce gradual momentum shifts rather than abrupt state perturbations. This second-order formulation serves as a structural filter via double integration, suppressing high-frequency noise and producing robust, physically consistent predictions. Extensive experiments on six real-world benchmarks demonstrate that KineFlow achieves an average 15% MSE improvement over discriminative baselines and an 8% gain in CRPS compared to state-of-the-art generative methods.

Applications · Time Series

Valentina Moretti, Andrea Cini, Ivan Marisca, Cesare Alippi

Deep learning models have grown popular in time series applications. However, the large quantity of newly proposed architectures and the often contradictory empirical results make it difficult to assess which design choice and model component drives performance. In this position paper, we argue that current benchmarking practices fail to identify the factors responsible for performance differences, thus slowing down progress in the field. In particular, differences in crucial design dimensions are overlooked when comparing architectures, ultimately leading to inconsistent outcomes. To support our position, we show that such differences—often treated as mere implementation details—can have a greater impact than adopting specific sequence modeling layers. We discuss how overlooked aspects (such as globality and locality) can (1) fundamentally change the class of the forecasting method and (2) drastically affect empirical results. Our findings suggest rethinking our benchmarking practices and focusing on the foundational aspects of the forecasting problem when designing and comparing architectures. As a concrete step, we propose an *auxiliary forecasting model card*, i.e., a template with a set of fields to characterize existing and new forecasting architectures based on key design choices.

Deep Learning · Sequential Models, Time series

Qilin Wang

We argue that long-term forecasting requires learning local Jacobians with explicit spectral structure, going beyond simple conditional mean matching. Our method, \textsc{Fern}, invokes Brenier's theorem to directly parameterize the Jacobian as a symmetric positive semi-definite (SPD) factorization, treating forecasting as the optimal transport of probability mass from a fixed Gaussian source to data-dependent ellipsoids. This formulation reduces the computational cost of eigen-decomposition from cubic to linear time while providing interpretable, geometry-aware projections. To rigorously evaluate robustness, we introduce a synthetic benchmark with controlled non-stationary shocks alongside new metrics like Effective Prediction Time (EPT). \textsc{Fern} demonstrates exceptional stability, outperforming baselines like DLinear and Koopa by over two orders of magnitude (up to $790\times$) on nonstationary settings where standard benchmarks fail to expose model brittleness.

Applications · Neuroscience, Cognitive Science

Binghao Ye, Wenjuan Li, Dengfeng Xue, Bing Li, Weiming Hu, Dong Liang, Kun Shang

Spiking Neural Networks (SNNs) have garnered increasing attention for their biological plausibility, energy efficiency, and temporal modeling capability. Due to the non-differentiability of spike generation, a widely used supervised training method for SNNs is backpropagation through time with surrogate gradients, which achieves competitive performance with a small number of timesteps. Intuitively, scaling timesteps should further improve performance by enriching temporal dynamics. However, we observe timestep scaling paradox (TSP), a counter-intuitive degradation in accuracy when scaling timesteps. We investigate TSP and link it to long-term temporal gradient vanishing and weakened cross-timestep dependencies. To address this, we propose the Timestep-Scalable (TS) neuron model. It introduces long-term memory reconsolidation to enhance cross-timestep information flow and enable effective learning with more timesteps. In parallel, a temporal forgetting mechanism periodically truncates the accumulation path, suppressing excessive temporal information buildup and improving training stability. Supported by theoretical analysis and extensive experiments, TS consistently improves performance when scaling timesteps. Beyond gains from timestep scaling, it attains state-of-the-art results on EEG signals, event-based recognition, and time-series forecasting, while remaining strong on conventional image classification and object detection datasets.

Applications · Health / Medicine

Nikita Makarov, Maria Bordukova, Lena von Voithenberg, Estrella Pivel-Villanueva, Sabrina Mielke, Jonathan Wickes, Hanchen Wang, Mingyu Ma, Keunwoo Choi, Kyunghyun Cho 等

Precision oncology requires forecasting clinical events and trajectories, yet modeling sparse, multi-modal clinical time series remains a critical challenge. We introduce TwinWeaver, an open-source framework that serializes longitudinal patient histories into text, enabling unified event prediction as well as forecasting with large language models, and use it to build Genie Digital Twin (GDT) on 93,054 patients across 20 cancer types. In benchmarks, GDT significantly reduces forecasting errors, achieving a median Mean Absolute Scaled Error (MASE) of 0.87 compared to 0.97 for the strongest time-series baseline ($p<0.001$). Furthermore, GDT improves risk stratification, achieving an average concordance index (C-index) of 0.703 across survival, progression, and therapy switching tasks, surpassing the best baseline of 0.662. GDT also generalizes to out-of-distribution clinical trials, matching trained baselines at zero-shot and surpassing them with fine-tuning, achieving a median MASE of 0.75–0.88 and outperforming the strongest baseline in event prediction with an average C-index of 0.672 versus 0.648. Finally, TwinWeaver enables an interpretable clinical reasoning extension, providing a scalable and transparent foundation for longitudinal clinical modeling.

Applications · Health / Medicine

Yuhan Wang, Yuanyuan Zou, Jie Cheng, Bin Dai, Jinhong Guo

Accurately capturing local variations in long series has always been one of the most challenging problems in time-series forecasting especially in medical signals, where local variations often indicate pathological events. Our study reveals a previously overlooked key bottleneck in this field: traditional global and local branches learn similar representations, leading to strong feature coupling and reduced sensitivity to local variations. To address this challenge, we propose the novel Dual-Stream Enhancement Mechanism, which structurally enlarges the difference between global and local patterns, enabling weak interactions between the two. Based on this idea, we introduce a new baseline model for blood glucose prediction: Dual-Stream Enhancement Network (DSENet), which fundamentally alleviates the problem of excessively strong coupling between global and local features. Experimental results show that our model achieves SOTA performance on multiple public datasets. Moreover, benefiting from extremely low computational cost, our model demonstrates strong application potential and can serve as a baseline model in multiple domains in the future.

General Machine Learning · Sequential, Network, and Time Series Modeling

Wenlong Shang, Shihao Tian, Xutong Wan, Peng Chang

Reconstruction-based methods are a dominant paradigm in time series anomaly detection (TSAD), however, their near-universal reliance on Mean Squared Error (MSE) loss results in statistically flawed reconstruction residuals. This fundamental weakness leads to noisy, unstable anomaly scores, hindering reliable detection. To address this, we propose Constrained Gaussian-Noise Optimization and Smoothing (COGNOS), a universal, model-agnostic enhancement framework that tackles this issue at its source. COGNOS introduces a novel Gaussian-White Noise Regularization strategy during training, which directly constrains the model's output residuals to conform to a Gaussian white noise distribution. This engineered statistical property creates the ideal precondition for our second contribution: Adaptive Residual Kalman Smoother that provably operates as a statistically robust estimator to denoise the raw anomaly scores. Extensive experiments on multiple benchmarks demonstrate that COGNOS consistently enhances the performance of state-of-the-art backbones significantly, validating the efficacy of coupling statistical regularization with adaptive filtering.

General Machine Learning · Sequential, Network, and Time Series Modeling

Cheonwoo Lee, Dooho Lee, Doyun Choi, Jaemin Yoo

Multi-scale modeling has emerged as an effective design principle for time-series forecasting by capturing temporal dynamics at multiple resolutions. As no principled foundation has been established in the literature, we unify existing scaling methods into a scaling operator family, revealing a fundamental limitation of existing approaches: reliance on fixed and discrete scaling. To address this limitation, we propose SiGMA (Single Generalized Multi-scale Architecture), which enables position-wise scaling via the learnable discrete Gaussian (LDG) kernel grounded in scale-space theory. We evaluate SiGMA comprehensively on long- and short-term forecasting benchmarks against state-of-the-art multi-scale baselines. SiGMA outperforms all competitors on both tasks, especially achieving the best performance in 13 out of 16 long-term evaluation settings. Beyond accuracy, SiGMA significantly improves training speed by up to 5.3 times and reduces memory consumption by up to 3.8 times over the strongest competitors.

Deep Learning · Sequential Models, Time series

Wei Chen, Xingyu Guo, Shuang Li, Fuwei Zhang, Meng Yuan, Jing Fan, Zhao Zhang, deqing wang, Fuzhen Zhuang

Generative Recommendation (GR) has emerged as a promising paradigm by formulating item recommendation as a sequence-to-sequence generation task over item identifiers. Recent studies have incorporated multimodal signals to provide richer token-level evidence for generation. However, existing approaches largely rely on alignment- centric fusion and underexplore synergistic information across modalities. In practice, synergistic information plays a critical role in capturing emergent item properties that cannot be inferred from any single modality alone. Such properties encode intrinsic item semantics and guide user preferences, enabling models to move beyond surface-level feature matching. To address this limitation, we propose SynGR, a synergistic generative recommendation framework that explicitly encourages the exploitation of cross-modal dependencies during generation. By constraining overreliance on dominant modalities, SynGR enables the model to capture emergent item semantics beyond shared or modality-specific signals. Extensive experiments across three benchmark datasets demonstrate that SynGR achieves superior recommendation performance, with an average improvement of 9.01%.

Lehui Li, Yuyao Wang, Jisheng Yan, Wei Zhang, Jinliang Deng, Haoliang Sun, Zhongyi Han, Yongshun Gong

Incorporating textual information into time-series forecasting holds promise for addressing event-driven non-stationarity; however, a fundamental modality gap hinders effective fusion: textual descriptions express temporal impacts implicitly and qualitatively, whereas forecasting models rely on explicit and quantitative signals. Through controlled semi-synthetic experiments, we show that existing methods over-attend to redundant tokens and struggle to reliably translate textual semantics into usable numerical cues. To bridge this gap, we propose \method{}, which introduces a Temporal Evolution Semantic Space as an intermediate bottleneck between modalities. This space consists of interpretable, numerically grounded temporal primitives—mean shift, volatility, shape, and lag—extracted from text by an LLM via structured prompting and filtered through confidence-aware gating. Experiments on four real-world datasets demonstrate up to a 29\% reduction in forecasting error compared to state-of-the-art uni-modal and multimodal baselines. The code is available at https://anonymous.4open.science/r/MMTSF.

Applications · Time Series

Wanjin Feng, Yuan Yuan, Jingtao Ding, Yong Li

In the era of increasingly complex AI models for time series forecasting, progress is often measured by marginal improvements on benchmark leaderboards. However, standard evaluations rely on aggregate metrics (e.g., MSE) that conflate model capability with the intrinsic difficulty of the evaluated instances. To address this, we propose a diagnostic framework anchored in **Spectral Coherence Predictability (SCP)**, which provides an efficient $\mathcal{O}(N\log N)$ per-instance difficulty reference and yields a corresponding linear MSE lower bound. Complementing this, we introduce the **Linear Utilization Ratio (LUR)** to quantify how effectively models exploit linearly predictable structures across frequencies. Experiments on synthetic and real-world benchmarks show that SCP aligns strongly with realized forecasting errors across diverse state-of-the-art forecasters. Using this lens, we uncover ``predictability drift,'' revealing that task difficulty is not static but fluctuates significantly over time and variables. Furthermore, stratified evaluation exposes complementary architectural strengths across distinct frequency bands and difficulty regimes. Overall, we advocate moving beyond leaderboard-style ranking toward a more insightful, predictability-aware evaluation that fosters fairer model comparisons and a deeper understanding of model behavior. Code and data are available at https://anonymous.4open.science/r/TS_Predictability-C8B7.

General Machine Learning · Sequential, Network, and Time Series Modeling

SATOSHI NOGUCHI, Yoshinobu Kawahara

We present Mesh Field Theory (MeshFT) and its neural realization, MeshFT-Net: a structure-preserving framework for mesh-based continuum physics that cleanly separates the physics’ topological structure from its metric structure. Imposing minimal physical principles (locality, permutation equivariance, orientation covariance, and energy balance/dissipation inequality), we prove a reduction theorem for mesh-based physics. Under these conditions, the physical dynamics admit a local factorization into a port–Hamiltonian form: the conservative interconnection is fixed uniquely by mesh topology, whereas metric effects enter only through constitutive relations and dissipation. This reduction clarifies what must be fixed and what should be learned, directly informing MeshFT-Net’s design. Across evaluations on analytic and realistic datasets, physics-consistency tests, and out-of-distribution validation, MeshFT-Net achieves near-zero energy drift and strong physical fidelity (correct dispersion and momentum conservation) along with robust extrapolation and high data efficiency. By eliminating non-physical degrees of freedom and learning only metric-dependent structure, MeshFT provides a principled inductive bias for stable, faithful, and data-efficient learning-based physical simulation.

Applications · Time Series

Jiawen Zhu, Shuhan Liu, Di Weng, Yingcai Wu

Non-stationary time series forecasting is challenged by evolving distribution shifts that static models struggle to capture. While Mixture-of-Experts (MoE) architectures offer a promising paradigm for decoupling complex drift patterns, existing approaches are limited by fixed expert pools and memoryless routing, hampering their ability to adapt to abrupt regime shifts. To address this, we propose **Dynamic TMoE**, a framework that unifies architectural evolution with temporal continuity during learning phase. By detecting distribution shifts via Maximum Mean Discrepancy (MMD), we dynamically instantiate heterogeneous experts and prune redundant ones to optimize capacity. Additionally, a temporal memory router leverages recurrent states and an anomaly repository to ensure stable, context-aware expert selection without requiring test-time updates. Experiments on nine benchmarks demonstrate state-of-the-art performance, reducing MSE by 10.4\% and MAE by 7.8\%. Code is available at https://anonymous.4open.science/r/Dynamic-TMoE.

Deep Learning · Sequential Models, Time series

Chris Cameron, Wangzheng Wang, Nikita Ivanov, Ashmita Bhattacharyya, Didier Chételat, Yingxue Zhang

Looped transformers scale computational depth independent of parameter count by repeatedly applying the same layer. However, training these models over long horizons creates significant optimization challenges. Specifically, it is difficult for looped transformers that start from noise to steer towards a potentially complex output without additional supervision. Diffusion models tackle this issue by corrupting data with varying magnitudes of noise and training the model to reverse it in a single step. However, this process misaligns training and testing behaviour. We introduce Denoising Recursion Models, a method that similarly corrupts data with noise but trains the model to reverse the corruption over multiple recursive steps. This strategy provides a tractable curriculum of intermediate states, while better aligning training with testing and incentivizing non-greedy, forward-looking generation. Through extensive experiments, we showed this approach outperformed the Tiny Recursion Model (TRM) on ARC-AGI, where it recently achieved breakthrough performance.

Applications · Time Series

Chao Yang, Wendi Ren, Shuang Li

Event sequences from complex systems, such as clinical workflows, are often sparse and incomplete. As a result, downstream models are trained on data that only partially captures the underlying dynamics. Synthetic sequence generation can augment real data by filling in missing structure and improving coverage of rare patterns, but generated trajectories must remain realistic, satisfy domain constraints, and allow control. We propose the Forward-Chaining Temporal Point Process (FC-TPP), a framework for constraint-aware and controllable sequence generation in continuous time. FC-TPP maintains an explicit latent symbolic state encoding high-level predicates, which evolves through a differentiable multi-hop forward-chaining operator. Logical rules update the latent state based on recent events, while a temporal point process decoder generates future event times and types conditioned on this evolving state. By tying the generative dynamics to multi-hop reasoning in latent space, FC-TPP incorporates symbolic structure throughout generation rather than relying directly on raw event histories. Experiments on synthetic data and four semi-synthetic/real-world benchmarks—LogiCity, MIMIC-IV, EPIC-100, and IKEA ASM—show that FC-TPP achieves higher generation quality under limited and incomplete data, with stronger constraint adherence and greater controllability than purely neural and prior neuro-symbolic baselines.

Deep Learning · Generative Models and Autoencoders

RuiKang OuYang, Louis Grenioux, Jose Miguel Hernandez-Lobato

Score-based generative models have recently achieved remarkable success. While they are usually parameterized by the score, an alternative way is to use a series of time-dependent energy-based models (EBMs), where the score is obtained from the negative input-gradient of the energy. Crucially, EBMs can be leveraged not only for generation, but also for tasks such as compositional sampling or building Boltzmann Generators via Monte Carlo methods. However, training EBMs remains challenging. Direct maximum likelihood is computationally prohibitive due to the need for nested sampling, while score matching, though efficient, suffers from mode blindness. To address these issues, we introduce the Diffusive Classification (DiffCLF) objective, a simple method that avoids blindness while remaining computationally efficient. DiffCLF reframes EBM learning as a supervised classification problem across noise levels, and can be seamlessly combined with standard score-based objectives. We validate the effectiveness of DiffCLF by comparing the estimated energies against ground truth in analytical Gaussian mixture cases, and by applying the trained models to tasks such as model composition and Boltzmann Generator sampling. Our results show that DiffCLF enables EBMs with higher fidelity and broader applicability than existing approaches.

Applications · Time Series

Liu Chong, Yingjie Zhou, Hao Li, Pengyang Wang, Qingsong Wen, Ce Zhu

Time-series forecasting is critical in various scenarios, such as energy, transportation, and public health. However, most existing forecasters rely primarily on one-way inference, \textit{i.e.}, mapping \textbf{history} to \textbf{target}, and overlook the structural information provided by a revised natural chain (``\textbf{history} (model input) -- \textbf{target} (ground-truth output) -- \textbf{post-target continuation}''). The post-target continuation records how trajectories evolve after the target, which can help stabilize forecasting, but it is not observable at inference time. In this work, we aim to obtain an approximate proxy of the post-target continuation for the current input, providing structural knowledge for bidirectional forecasting. This idea is instantiated as KUP-BI (Knowledge Utilization Paradigm with Bidirectional Inspiration), a new time-series modeling paradigm that distills continuation-style knowledge (as an approximate post-target continuation proxy) from a \emph{train-only} historical library and integrates it into standard forecasting backbones. The input stream and the continuation-proxy stream are fused via a lightweight feature-level gating module. This design does not introduce information beyond what is already contained in the training trajectories; instead, it provides a structured inductive bias that helps backbones exploit typical continuation patterns rather than relying solely on parametric extrapolation. Experimental results on six public datasets show that KUP-BI consistently improves the forecasting performance of state-of-the-art models, with small additional overhead.

General Machine Learning · Sequential, Network, and Time Series Modeling

Shiqi Zhang, Pan Mu, HantingYan, Yuchao Zhu, jinglin zhang, Cong Bai

Multi-modal spatio-temporal forecasting underpins many real-world applications but remains challenging due to the complex and evolving interactions across modalities and time steps. Moreover, the lack of interpretability in existing models limits their reliability in safety-critical scenarios. In this paper, we present CausalX, a unified and causally interpretable plug-and-play model for multi-modal spatio-temporal forecasting. CausalX achieves interpretability by learning a dynamic causal graph across modalities and time, whose edge weights quantify causal attribution strength, and are further refined by a diffusion-based generative process guided by structural priors. To overcome the absence of ground-truth causal structures, CausalX aggregates multi-source constraints from causal analysis techniques and a variational autoencoder, spanning predictive, temporal, interventional, and generative aspects to jointly learn a more comprehensive causal graph. Extensive experiments on real-world forecasting tasks, including pedestrian trajectory prediction and tropical cyclone forecasting, demonstrate that CausalX achieves superior accuracy while producing interpretable causal graphs. CausalX is modular, architecture-agnostic, and generalizable, offering a new perspective on bridging causal inference and spatio-temporal forecasting.