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Deep Learning · Sequential Models, Time series

Zinuo You, Jin Zheng, John Cartlidge

Irregular multivariate time series pose a fundamental trade-off for long-horizon forecasting: discrete methods can distort temporal structure via re-gridding, while continuous-time models often rely on sequential numerical solvers that are prone to drift. To bridge this gap, we present the Latent Laplace Diffusion (LLapDiff), a generative framework that models the target as a low-dimensional latent trajectory, enabling horizon-wide generation without step-by-step integration over physical time. We guide the reverse process using a stable modal parameterization motivated by stochastic port-Hamiltonian dynamics, and parameterize its mean evolution in the Laplace domain via learnable complex-conjugate poles, allowing for direct evaluation over irregular timestamps. Moreover, we link continuous dynamics to irregular observations through renewal-averaging analysis, which maps sampling gaps to effective event-domain poles and theoretically motivates a gap-aware history summarizer for conditioning. Extensive experiments demonstrate that LLapDiff consistently outperforms baselines in long-horizon forecasting, and its continuous-time generative nature also supports missing-value imputation by querying the same model at historical timestamps.

Deep Learning · Sequential Models, Time series

Thai Khanh Nguyen, Ngoc Bich Uyen Vo, Thieu Vo, Tan Nguyen, Cuong Pham

State-space models (SSMs) have emerged as efficient linear-time alternatives to attention for long-sequence modeling. However, existing SSMs often suffer from instability and memory degradation over extended horizons due to poorly conditioned first-order updates and uncontrolled spectral geometry. We introduce MuonSSM, a general framework that stabilizes SSM training by explicitly conditioning the geometry of memory updates rather than the recurrent transition matrix. MuonSSM augments standard SSMs with a momentum-based pathway and lightweight Newton–Schulz iterations on low-rank input injections, yielding approximately norm-preserving and spectrally balanced updates while preserving parallel scan complexity. Theoretical analysis demonstrates substantial improvements in gradient propagation and mitigation of vanishing gradients over long horizons. Extensive experiments across language, vision, and time-series benchmarks show consistent gains in accuracy, robustness, and long-context performance when integrated into diverse SSM backbones. These results establish geometric conditioning of updates as a principled pathway to stable, scalable sequence modeling.

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

Wencheng Zhang, Long Li, Huayi Qin, Zongjuan Wu, Jing Li, Wanghu Chen

Effective time series representation is critical for revealing temporal dynamics in many fields. However, existing approaches encounter fundamental limitations. Discrete-time representations struggle with irregular sampling and the tradeoff of fidelity and efficiency, while traditional implicit neural representations suffer from spectral bias and frequency entanglement. To address these challenges, we conceptualize time series as the superposition of continuous trends and discrete events from a continuous-time perspective and propose DualTimesField, a framework that utilizes dual implicit neural fields. Its Continuous Time Field captures smooth trends through bandwidth-limited parameterization, while a Discrete Geometric Field models transient events using learnable Gabor atoms, gated sparsity, and coarse-to-fine scale annealing. This explicit field separation effectively overcomes both limitations. Experiments on nine real-world benchmarks demonstrate substantial improvements in representation fidelity, achieving 51.2% average MSE reduction over discrete-time baselines and competitive interpolation on irregular data. Code is available at https://anonymous.4open.science/r/DualTimesField-AF32.

Deep Learning · Large Language Models

Shvat Messica, Jiawen Zhang, Kevin Li, Theodoros Tsiligkaridis, Marinka Zitnik

Time series reasoning tasks increasingly start from a natural language question and require targeted analysis of time series. Relevant evidence may be global or confined to a few short segments, so the model must decide what to inspect. Most existing methods compress the full series into a fixed representation before inference, preventing question-adaptive analysis. We introduce ARTIST, an approach that formulates time-series reasoning as a sequential decision problem and trains models to interleave reasoning with adaptive temporal segment selection. ARTIST uses a controller-reasoner architecture and reinforcement learning to optimize segment selection based on answer correctness, allowing the model to actively acquire task-relevant information during inference. We evaluate ARTIST on six time-series reasoning benchmarks against large language models, vision-language models, and prior time series reasoning systems. ARTIST improves average accuracy by 6.46 percentage points over the strongest model, with the largest gains on rare event localization and multi-segment evidence accumulation. Supervised fine-tuning improves performance, and reinforcement learning yields further gains by optimizing question-adaptive segment selection. Across datasets, ARTIST achieves higher accuracy while using a smaller fraction of the input time series, highlighting the importance of learned, selective data utilization for time series reasoning.

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

Haruka Ezoe, Hiroki Matsumoto, Ryohei Hisano

Dynamic relational data arise in many machine learning applications, yet their evolving structure poses challenges for learning representations that remain consistent and interpretable over time. A common approach is to learn time varying node embeddings, whose usefulness depends on well defined stability properties across nodes and across time. We introduce Unfolded Laplacian Spectral Embedding (ULSE), a principled extension of unfolded adjacency spectral embedding to normalized Laplacian operators, a setting where stability guarantees have remained out of reach. We prove that ULSE satisfies both cross-sectional and longitudinal stability under a dynamic stochastic block model. Moreover, the Laplacian formulation yields a dynamic Cheeger-type inequality linking the spectrum of the unfolded normalized Laplacian to worst case conductance over time, providing structural insight into the embeddings. Empirical results on synthetic and real world dynamic networks validate the theory.

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

Jingtian Ma, Jingyuan Wang, Leong Hou U

Learning unified road representations across diverse cities is a pivotal challenge in urban computing. However, existing approaches predominantly focus on single-city modeling, failing to handle the distribution shifts caused by heterogeneous urban layouts. We identify *spectral misalignment*, manifested as the significant divergence of spectral distributions across different cities, as the primary barrier preventing standard Graph Neural Networks from capturing universal patterns. To bridge this gap, we propose **CoSpec**, a framework that disentangles road networks into shareable low-frequency commonalities and city-specific high-frequency specificities. CoSpec employs a hierarchical dual-path architecture where the low-frequency path aligns global functional semantics via adaptive prototypes, while the high-frequency path modulates local geometric residuals to fit specific urban textures. Theoretical analysis shows CoSpec bounds the Wasserstein distance between city distributions, and extensive experiments demonstrate its superior generalization over state-of-the-art baselines.

Deep Learning · Sequential Models, Time series

Quan Cheng, Hao Yu, Da-Wei Zhou, Lijun Zhang

Recently, vision-language models (e.g., CLIP) are increasingly adopted for continual learning to mitigate catastrophic forgetting. However, existing CLIP-based methods typically freeze the backbone to preserve pre-trained knowledge, which limits the model's ability to learn discriminative features for downstream tasks. In this paper, we introduce HypCL, a parameter-efficient framework that continually adapts CLIP in hyperbolic space for continual learning. Our key insight is that the exponentially expanding capacity of hyperbolic geometry naturally accommodates the growing class space and promotes stronger inter-class separation. Specifically, HypCL learns task-specific hyperbolic transformations and employs a lightweight task-weighting mechanism to aggregate transformations across tasks. To fully exploit the enhanced feature separability afforded by hyperbolic geometry, HypCL maintains class prototypes computed from the adapted features, which serve as stable anchors for calibrating predictions during inference. Extensive experiments on standard class-incremental benchmarks demonstrate that HypCL consistently outperforms existing CLIP-based continual learning methods.

Deep Learning · Sequential Models, Time series

Shohaib Shaffiey, Massimiliano Pierobon

The fields of AI-based disease fingerprinting, drug discovery and repurposing are currently among the emerging frontiers of machine learning applied to medicine. One major challenge is to obtain robust $\textit{in-silico}$ modeling of disease progression while accounting for the vastly different time scales of biochemical interactions, from gene expression to protein abundance and metabolic flux. Discrete sequence models inadequately represent such multi-scale interactions, and standard Neural Ordinary Differential Equations (NODEs) often fail to train stably under stiffness (different time scales). To address this, in this paper a Tri-Scale Stiff NODE is introduced, defined by hierarchically coupled latent differential equations that model the causal flow from genes to proteins and metabolites, and optimized using reconstruction error and information-theoretic mutual information. This enables continuous-time modeling of cellular responses to identify not only disease dynamics, but also drug perturbations that act within narrow time windows, often invisible to discrete-time approaches. Lyapunov analysis provides a theoretical guarantee that the modeled trajectories remain stable and well-behaved even under extreme stiffness. The developed modeling methodology is tested upon a public dataset (STATegra B-cell differentiation) and utilized for a proof-of-concept drug repurposing pipeline.

Deep Learning · Sequential Models, Time series

Yisong Fu, Zezhi Shao, Chengqing Yu, Yujie Li, Yongjun Xu, Xueqi Cheng, Fei Wang

We present Zeus, a unified tuning-free Time Series Foundation Model (TSFM) that delivers superior performance across diverse analysis tasks without any task-specific fine-tuning. Unlike prior studies that primarily focus on zero-shot forecasting but require task-specific tuning for other tasks, Zeus bridges this gap by addressing two fundamental challenges in multi-task generalization. First, to reconcile point-level granularity with long-sequence scalability, Zeus incorporates a multi-scale Transformer featuring point-wise tokenization and a U-shaped hierarchy, effectively balancing fine-grained fidelity with computational efficiency. Second, to accommodate varying inductive biases across different tasks, Zeus introduces Multi-Objective Temporal Masking (MOTM), a unified strategy that supports heterogeneous tasks (e.g., extrapolation, interpolation, and global abstraction) within a single framework. Extensive experiments across five representative tasks demonstrate that Zeus consistently achieves competitive results in tuning-free settings, underscoring its potential as a general-purpose TSFM.

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

Lele Cao

Game world modeling (GWM) and reinforcement learning (RL) are often confounded because research papers rarely quantify how difficult the underlying transition prediction problem is at the declared interface (pixels/tokens/latents with finite history). We propose the Transition Complexity Profile (TCP): a small, reproducible set of metrics that characterizes an environment's (or gameplay dataset's) induced transition kernel by (i) intrinsic one-step branching, (ii) interaction-induced uncertainty and opponent influence when observable, and (iii) temporal/spatial dependency span via standardized probe curves. TCP is reported with an explicit reference distribution, protocol stochasticity, and a versioned measurement budget (sampling/resampling and fixed probe compute), enabling comparable numbers across benchmarks. We outline how common game families and modern "neural game engine" domains populate this landscape and call for TCP to become standard benchmark metadata and a required statistic in GWM and RL papers.

Deep Learning · Sequential Models, Time series

Ruben Solozabal, Velibor Bojkovic, Hilal AlQuabeh, Klea Ziu, Kentaro Inui, Martin Takac

State-space models (SSMs) have emerged as a powerful foundation for long-range sequence modeling, with the HiPPO framework showing that continuous-time projection operators can be used to derive stable, memory-efficient dynamical systems that encode the past history of the input signal. However, existing projection-based SSMs often rely on polynomial bases with global temporal support, whose inductive biases are poorly matched to signals exhibiting localized or transient structure. In this work, we introduce \emph{WaveSSM}, a collection of SSMs constructed over wavelet frames. Our key observation is that wavelet frames yield a localized support on the temporal dimension, useful for tasks requiring precise localization. Empirically, we show that on equal conditions, \textit{WaveSSM} outperforms orthogonal counterparts as S4 on real-world datasets with transient dynamics, including physiological signals on the PTB-XL dataset and raw audio on Speech Commands.

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.

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%.

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.

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.

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.

Deep Learning · Sequential Models, Time series

Shenglei Fang, Xianfang Sun, You Zhou

Sequence models typically operate at a fixed temporal or spatial scale and struggle to generalize to substantially longer horizons or higher resolutions without retraining. Existing hierarchical architectures expand receptive fields but rely on scale-specific parameters and lack mechanisms to enforce consistent dynamics across scales. We propose \textbf{Dynamic Fractal Mamba (DF-Mamba)}, a recursive state-space model that applies a single shared operator across multiple scales. By sharing parameters across recursion depths and exponentially scaling the effective time step, DF-Mamba achieves an exponentially expanding receptive field while preserving linear computational complexity. A learned content-aware coarse-graining module aggregates representations across scales. Auxiliary reconstruction and cross-scale consistency objectives stabilize recursive training. We evaluate DF-Mamba on long-range time-series forecasting, spatial transcriptomics, and computational pathology. Across all tasks, DF-Mamba consistently outperforms Transformers and flat Mamba baselines while using fewer parameters and maintaining linear-time scalability. Importantly, models trained on short sequences or low-resolution inputs generalize in a zero-shot manner to substantially larger temporal and spatial scales unseen during training. These results demonstrate that recursive parameter sharing provides an effective inductive bias for learning scale-consistent and efficient sequence representations.

Applications · Time Series

Hwijin Kim, Jaeho Kim, Changhee Lee

Explaining predictions of black-box time-series models remains a challenging problem due to the dynamically evolving patterns within individual sequences and their complex temporal dependencies. Unfortunately, existing explanation methods largely focus on point-wise explanations, which fail to capture broader temporal context, while methods that attempt to highlight interpretable temporal patterns (e.g., achieved by incorporating a regularizer or fixed-length patches) often lack principled definitions of meaningful segments. This limitation frequently leads to fragmented and confusing explanations for end users. As such, the notion of segment-wise explanations has remained underexplored, with little consensus on what constitutes an *interpretable* segment or how such segments should be identified. To bridge this gap, we define segment-wise explanation for black-box time-series models as the task of selecting contiguous subsequences that maximize their joint mutual information with the target prediction. Building on this formulation, we propose TimeSeg, a novel information-theoretic framework that employs reinforcement learning to sequentially identify predictive temporal segments at a per-instance level. By doing so, TimeSeg produces segment-wise explanations that capture holistic temporal patterns rather than fragmented points, providing class-predictive patterns in a human-interpretable manner. Extensive experiments on both synthetic and real‑world datasets demonstrate that TimeSeg produces more coherent and human-understandable explanations, while achieving performance that matches or surpasses existing methods on downstream tasks using the identified segments.