Time Series

Recent advances in multimodal learning have motivated the integration of auxiliary modalities such as text or vision into time series (TS) forecasting. However, most existing methods provide limited gains, often improving performance only in specific datasets or relying on architecture-specific designs that limit generalization. In this paper, we show that multimodal models with naive fusion strategies (e.g., simple addition or concatenation) often underperform unimodal TS models, which we attribute to the uncontrolled integration of auxiliary modalities which may introduce irrelevant information. Motivated by this observation, we explore various constrained fusion methods designed to control such integration and find that they consistently outperform naive fusion methods. Furthermore, we propose Controlled Fusion Adapter (CFA), a simple plug-in method that enables controlled cross-modal interactions without modifying the TS backbone, integrating only relevant textual information aligned with TS dynamics. CFA employs low rank adapters to filter irrelevant textual information before fusing it into temporal representations. We conduct over 20K experiments across various datasets and TS/text models, demonstrating the effectiveness of the constrained fusion methods. Code is available at: https://github.com/seunghan96/cfa.

Retrieval-augmented generation (RAG) enhances zero-shot time series (TS) forecasting by leveraging external knowledge bases, yet existing approaches overlook input-level relevance when fusing retrieved samples with the query. We argue that not all retrievals are equally useful, and irrelevant ones can degrade performance. To this end, we propose Cross-RAG, a zero-shot RAG-based forecasting framework that selectively attends to query-relevant retrieved samples via query--retrieval cross-attention. By modeling input-level relevance between the query and retrieved samples, Cross-RAG jointly incorporates three sources of information: 1) the query itself, 2) the retrieved samples, and 3) their relational interactions. In particular, this input-aware design enables Cross-RAG to remain stable as the number of retrieved samples $k$ grows, whereas prior methods without cross-attention require careful $k$ tuning to avoid degradation from irrelevant retrievals. Extensive experiments demonstrate that Cross-RAG consistently improves zero-shot forecasting performance across multiple TSFM backbones and various RAG methods, with additional analyses confirming its effectiveness across various retrieval scenarios. Code is available at https://github.com/seunghan96/cross-rag/.

Context-aided forecasting (CAF) holds promise for integrating domain knowledge and forward-looking information, enabling AI systems to surpass traditional statistical methods. However, recent empirical studies reveal a puzzling gap: multimodal models often fail to outperform their unimodal counterparts. We hypothesize that this underperformance stems from poor context quality in existing datasets, as verification is challenging. To address these limitations, we introduce a semi-synthetic data augmentation method that generates contexts both descriptive of temporal dynamics and verifiably complementary to numerical histories. This approach enables massive-scale dataset creation, resulting in CAF-7M, a corpus of 7 million context-augmented time series windows, including a rigorously verified test set. We demonstrate that semi-synthetic pre-training transfers effectively to real-world evaluation, and show clear evidence of context utilization. Our results suggest that dataset quality, rather than architectural limitations, has been the primary bottleneck in context-aided forecasting.

Deep generative models for anomaly detection in multivariate time-series are typically trained by maximizing observed data likelihood. However, likelihood in observation space measures marginal density rather than conformity to structured temporal dynamics, and therefore can assign high probability to anomalous or out-of-distribution samples. We address this structural limitation by relocating the notion of anomaly to a prescribed latent space. We introduce explicit inductive biases in conditional normalizing flows, modeling time-series observations within a discrete-time state-space framework that constrains latent representations to evolve according to prescribed temporal dynamics. Under this formulation, expected behavior corresponds to compliance with a specified distribution over latent trajectories, while anomalies are defined as violations of these dynamics. Anomaly detection is consequently reformulated as a statistically grounded compliance test, such that observations are mapped to latent space and evaluated via goodness-of-fit tests against the prescribed latent evolution. This yields a principled decision rule that remains effective even in regions of high observation likelihood. Experiments on synthetic and real-world time-series demonstrate reliable detection of anomalies in frequency, amplitude, and observation noise, while providing interpretable diagnostics of model compliance.

Accurate prediction of multivariate time series is essential for emerging network intelligent control, observability, and management functions. Existing statistical-based and shallow machine learning models have shown limited prediction capabilities on multivariate time series. They prioritize improvements in average prediction accuracy, while overlooking heterogeneous dependency structures and performance variability across individual time series. Recent advances in large language models have introduced new directions for multivariate time series forecasting; however, their application in conjunction with explicit structural dependency modeling remains relatively underexplored, especially in networked environments. In this paper, we present a topology-aware learning framework for large-scale network traffic prediction that explicitly models both temporal dynamics and structural dependencies in multivariate network time series. We first investigate a graph attention model designed to capture topology-induced correlations among network traffic time series. We then evaluate a fine-tuned large language model-based representations for improved generalization across heterogeneous traffic patterns. To further address the diversity of cross-correlations in high-dimensional traffic data, we introduce a clustering-based preprocessing stage that groups traffic flows with similar dependency characteristics prior to model training, reducing input complexity and improving learning stability. Experiments on real backbone traffic data show consistent improvements over statistical and recurrent neural network baselines. In addition to average accuracy, we evaluate performance across individual time series and observe reduced variability in prediction quality.

Multivariate time series forecasting is fundamental to numerous domains such as energy, finance, and environmental monitoring, where complex temporal dependencies and cross-variable interactions pose enduring challenges. Existing Transformer-based methods capture temporal correlations through attention mechanisms but suffer from quadratic computational cost, while state-space models like Mamba achieve efficient long-context modeling yet lack explicit temporal pattern recognition. Therefore we introduce UniMamba, a unified spatial-temporal forecasting framework that integrates efficient state-space dynamics with attention-based dependency learning. UniMamba employs a Mamba Variate-Channel Encoding Layer enhanced with FFT-Laplace Transform and TCN to capture global temporal dependencies, and a Spatial Temporal Attention Layer to jointly model inter-variate correlations and temporal evolution. A Feedforward Temporal Dynamics Layer further fuses continuous and discrete contexts for accurate forecasting. Comprehensive experiments on eight public benchmark datasets demonstrate that UniMamba consistently outperforms state-of-the-art forecasting models in both forecasting accuracy and computational efficiency, establishing a scalable and robust solution for long-sequence multivariate time-series prediction.

Proper scoring rules are essential for evaluating probabilistic forecasts. We propose a simple algebraic rearrangement of the Yates covariance decomposition of the Brier score into three independently non-negative terms: a variance mismatch term, a correlation deficit term, and a calibration-in-the-large term. This rearrangement makes the optimality conditions for perfect forecasting transparent: the optimal forecast must simultaneously match the variance of outcomes, achieve perfect positive correlation with outcomes, and match the mean of outcomes. Any deviation from these conditions results in a positive contribution to the Brier score.

Personal AI assistants are changing how individuals use advice. We study how an advisor should design its recommendation in anticipation of stochastic consultation with personal AI whose recommendation is predictable. Personal AI enters through two dimensions: consultation probability and relative trust, which captures the relative influence personal AI receives when consulted. In the baseline model, the advisor optimally counteracts the personal AI signal. Counteraction increases with consultation probability but is hump-shaped in relative trust. The advisor's minimized loss is hump-shaped in consultation probability, vanishing when personal AI is never or always consulted. Greater relative trust in personal AI increases the irreducible loss arising from stochastic consultation. We extend the analysis to partial predictability and costly recommendation adjustment, characterizing their effects on optimal recommendations and minimized loss. The framework also accommodates richer information structures, including settings in which personal AI is perceived as having access to private information relevant to the task. We introduce an online forecasting experiment that examines how participants obtain personal AI advice and combine it with an advisor's recommendation and their initial judgments. Participants place weight on all three inputs. When access requires an additional action, some participants do not seek personal AI advice, while some others attempt to obtain it without success. Together, these findings highlight two distinct aspects of personal AI use: whether advice is obtained and how much weight it receives when available.

The Nash-Sutcliffe efficiency ($\text{NSE}$) is a widely used, positively oriented relative measure for evaluating forecasts across multiple time series. However, it lacks a decision-theoretic foundation for this purpose. To address this, we examine its negatively oriented counterpart, which we refer to as Nash-Sutcliffe loss, defined as $L_{\text{NS}} = 1 - \text{NSE}$. We prove that $L_{\text{NS}}$ is strictly consistent for an elicitable and identifiable multi-dimensional functional, which we name the Nash-Sutcliffe functional. This functional is a data-weighted component-wise mean. The common practice of maximizing the average $\text{NSE}$ across multiple series is the sample analog of minimizing the expected $L_{\text{NS}}$. Consequently, this operation implicitly assumes that all series originate from a single non-stationary, stochastic process. We introduce Nash-Sutcliffe linear regression, a multi-dimensional model estimated by minimizing the average $L_{\text{NS}}$, which reduces to a data-weighted least squares formulation. By reorienting the sample average loss function, we extend the previously proposed evaluation and estimation framework to forecasting multiple stationary dependent time series with differing stochastic properties. This constitutes a more natural empirical implementation of the $\text{NSE}$ than the earlier formulation. Our results establish a decision-theoretic foundation for $\text{NSE}$-based model estimation and forecast evaluation in large datasets, while further clarifying the benefits of global over local machine learning models.

We develop a kernel method for generative modeling within the stochastic interpolant framework, replacing neural network training with linear systems. The drift of the generative SDE is $\hat b_t(x) = \nablaφ(x)^\topη_t$, where $η_t \in \mathbb{R}^P$ solves a $P\times P$ system computable from data, with $P$ independent of the data dimension $d$. Since estimates are inexact, the diffusion coefficient $D_t$ affects sample quality; the optimal $D_t^*$ from Girsanov diverges at $t=0$, but this poses no difficulty and we develop an integrator that handles it seamlessly. The framework accommodates diverse feature maps: scattering transforms, pretrained generative models, etc, enabling generation and model combination without neural network training. We demonstrate the approach on financial time series, turbulence, and image generation.

Time series reasoning tasks often start with a natural language question and require targeted analysis of a time series. Evidence may span the full series or appear in a few short intervals, so the model must decide what to inspect. Most existing approaches encode the entire time series into a fixed representation before inference, regardless of whether or not the entire sequence is relevant. We introduce ARTIST, which formulates time-series reasoning as a sequential decision problem. ARTIST interleaves reasoning with adaptive temporal segment selection. It adopts a controller-reasoner architecture and uses reinforcement learning to train the controller role to select informative segments and the reasoner role to generate segment-conditioned reasoning traces and final answers. During inference, the model actively acquires task-relevant information instead of relying on a static summary of the full sequence. We use a novel hierarchical policy optimization approach for post-training that allows the model to excel in both segment selection and question-answering behavior. We evaluate ARTIST on six time-series reasoning benchmarks and compare it with large language models, vision-language models, and prior time-series reasoning systems. ARTIST improves average accuracy by 6.46 absolute percentage points over the strongest baseline. The largest gains appear on rare event localization and multi-segment reasoning tasks. Supervised fine-tuning improves performance, and reinforcement learning provides additional gains by optimizing question-adaptive segment selection. These results show that selective data use drives effective time-series reasoning.

Modeling multiscale patterns is crucial for long-term time series forecasting (TSF). However, redundancy and noise in time series, together with semantic gaps between non-adjacent scales, make the efficient alignment and integration of multi-scale temporal dependencies challenging. To address this, we propose SEMixer, a lightweight multiscale model designed for long-term TSF. SEMixer features two key components: a Random Attention Mechanism (RAM) and a Multiscale Progressive Mixing Chain (MPMC). RAM captures diverse time-patch interactions during training and aggregates them via dropout ensemble at inference, enhancing patch-level semantics and enabling MLP-Mixer to better model multi-scale dependencies. MPMC further stacks RAM and MLP-Mixer in a memory-efficient manner, achieving more effective temporal mixing. It addresses semantic gaps across scales and facilitates better multiscale modeling and forecasting performance. We not only validate the effectiveness of SEMixer on 10 public datasets, but also on the \textit{2025 CCF AlOps Challenge} based on 21GB real wireless network data, where SEMixer achieves third place. The code is available at the link https://github.com/Meteor-Stars/SEMixer.

Time Series Language Models (TSLMs) promise reasoning over real-world temporal data, but their ability to retrieve and reason over long time-series remains largely untested. We introduce TS-Haystack, a multi-domain retrieval benchmark with ten event-grounded question-answering tasks over contexts from 100 seconds to 24 hours, spanning direct retrieval, temporal reasoning, multi-step reasoning, and contextual anomaly detection. Existing TSLMs exhibit severe long-context degradation: accuracy declines with context length, direct-tokenization models run out of memory beyond 100 seconds on high-rate signals, and time-interval-grounded tasks collapse toward near-zero accuracy when increasing the time-series lengths, aligning with existing literature on text and multi-modal long context retrieval. An agentic retrieval framework using specialized time-series classifier tools matches or outperforms SoTA TSLMs on 9 of 10 tasks, highlighting agentic retrieval as a promising approach for long-context TSLMs.

The contemporary paradigm of trajectory learning operates fundamentally at the level of group dynamics, systematically reducing individual-level complexity to fit group-level models, thus rendering effective patient subtyping difficult and individual-level modeling largely out of reach. We propose a data-driven paradigm that introduces a dedicated individual-level temporal variable to capture \emph{Timing Attention} (i.e., the degree of concentration of an event's timing distribution across the patient cohort), thereby rendering timing a \emph{computable dimension} that enables individualized temporal features in trajectory learning. Instantiated as the Level-of-Individual Time Transformation (LITT) and applied to longitudinal EHR data from 3,276 breast cancer patients, the proposed paradigm demonstrates, for the first time to our knowledge: (1) automatic discovery of clinically significant patient trajectories, and (2) counterfactual timing deduction, that is, a \emph{What-If Machine}. Both results are purely data-driven, requiring no prior domain knowledge. LITT further achieves strong performance on timing prediction and survival analysis tasks.

Short-term forecasting of vegetation dynamics is a key enabler for data-driven decision support in precision agriculture. Normalized Difference Vegetation Index (NDVI) forecasting from satellite observations, however, remains challenging due to sparse and irregular sampling caused by cloud masking, as well as the heterogeneous climatic conditions under which crops evolve. In this work, we propose a probabilistic forecasting framework for field-level NDVI prediction under sparse, irregular clear-sky acquisitions. The architecture separates the encoding of historical NDVI and meteorological observations from future exogenous covariates, fusing both representations for multi-step quantile prediction. To address irregular revisit patterns and horizon-dependent uncertainty, we introduce a temporal-distance weighted quantile loss that aligns the training objective with the effective forecasting horizon. In addition, we incorporate cumulative and extreme-weather feature engineering to capture delayed meteorological effects relevant to vegetation response. Experiments on European satellite data show that the proposed approach outperforms statistical, deep learning, and time-series baselines on both pointwise and probabilistic evaluation metrics. Ablation studies confirm that target history is the primary driver of performance, with meteorological covariates providing additional gains in the full multimodal setting. The code is available at https://github.com/arco-group/ndvi-forecasting.

Credit exposure in Decentralized Finance (DeFi) is often implicit and token-mediated, creating a dense web of inter-protocol dependencies. Thus, a shock to one token may result in significant and uncontrolled contagion effects. As the DeFi ecosystem becomes increasingly linked with traditional financial infrastructure through instruments, such as stablecoins, the risk posed by this dynamic demands more powerful quantification tools. We introduce DeXposure-FM, the first time-series, graph foundation model for measuring and forecasting inter-protocol credit exposure on DeFi networks, to the best of our knowledge. Employing a graph-tabular encoder, with pre-trained weight initialization, and multiple task-specific heads, DeXposure-FM is trained on the DeXposure dataset that has 43.7 million data entries, across 4,300+ protocols on 602 blockchains, covering 24,300+ unique tokens. The training is operationalized for credit-exposure forecasting, predicting the joint dynamics of (1) protocol-level flows, and (2) the topology and weights of credit-exposure links. The DeXposure-FM is empirically validated on two machine learning benchmarks; it consistently outperforms the state-of-the-art approaches, including a graph foundation model and temporal graph neural networks. DeXposure-FM further produces financial economics tools that support macroprudential monitoring and scenario-based DeFi stress testing, by enabling protocol-level systemic-importance scores, sector-level spillover and concentration measures via a forecast-then-measure pipeline. Empirical verification fully supports our financial economics tools. The model and code have been publicly available. Model: https://huggingface.co/EVIEHub/DeXposure-FM. Code: https://github.com/EVIEHub/DeXposure-FM.

Hallucinations remain a major obstacle for large language models (LLMs), especially in safety-critical domains. We present HALT (Hallucination Assessment via Log-probs as Time series), a lightweight hallucination detector that leverages only the top-20 token log-probabilities from LLM generations as a time series. HALT uses a gated recurrent unit model combined with entropy-based features to learn model calibration bias, providing an extremely efficient alternative to large encoders. Unlike white-box approaches, HALT does not require access to hidden states or attention maps, relying only on output log-probabilities. Unlike black-box approaches, it operates on log-probs rather than surface-form text, which enables stronger domain generalization and compatibility with proprietary LLMs without requiring access to internal weights. To benchmark performance, we introduce HUB (Hallucination detection Unified Benchmark), which consolidates prior datasets into ten capabilities covering both reasoning tasks (Algorithmic, Commonsense, Mathematical, Symbolic, Code Generation) and general purpose skills (Chat, Data-to-Text, Question Answering, Summarization, World Knowledge). While being 30x smaller, HALT outperforms Lettuce, a fine-tuned modernBERT-base encoder, achieving a 60x speedup gain on HUB. HALT and HUB together establish an effective framework for hallucination detection across diverse LLM capabilities.

Time Series Foundation Models (TSFMs) leverage extensive pretraining to accurately predict unseen time series during inference, without the need for task-specific fine-tuning. Through large-scale evaluations on standard benchmarks, we find that leading transformer-based TSFMs exhibit redundant components in their intermediate layers. We introduce a set of tools for mechanistic interpretability of TSFMs, including ablations of specific components and direct logit attribution on the residual stream. Our findings are consistent across several leading TSFMs with diverse architectures, and across a diverse set of real-world and synthetic time-series datasets. We discover that all models in our study are robust to ablations of entire layers. Furthermore, we develop a theoretical framework framing transformers as kernel regressors, motivating a purely intrinsic strategy for ablating heads based on the stable rank of the per-head projection matrices. Using this approach, we uncover the specific heads responsible for degenerate phenomena widely observed in TSFMs, such as parroting of motifs from the context and seasonality bias. Our study sheds light on the universal properties of this emerging class of architectures for continuous-time sequence modeling.

Multimodal time series forecasting is crucial in real-world applications, where decisions depend on both numerical data and contextual signals. The core challenge is to effectively combine temporal numerical patterns with the context embedded in other modalities, such as text. While most existing methods align textual features with time-series patterns one step at a time, they neglect the multiscale temporal influences of contextual information such as time-series cycles and dynamic shifts. This mismatch between local alignment and global textual context can be addressed by spectral decomposition, which separates time series into frequency components capturing both short-term changes and long-term trends. In this paper, we propose SpecTF, a simple yet effective framework that integrates the effect of textual data on time series in the frequency domain. Our method extracts textual embeddings, projects them into the frequency domain, and fuses them with the time series' spectral components using a lightweight cross-attention mechanism. This adaptively reweights frequency bands based on textual relevance before mapping the results back to the temporal domain for predictions. Experimental results demonstrate that SpecTF significantly outperforms state-of-the-art models across diverse multi-modal time series datasets while utilizing considerably fewer parameters. Code is available at https://github.com/hiepnh137/SpecTF.

Although recent studies on time-series anomaly detection have increasingly adopted ever-larger neural network architectures such as transformers and foundation models, they incur high computational costs and memory usage, making them impractical for real-time and resource-constrained scenarios. Moreover, they often fail to demonstrate significant performance gains over simpler methods under rigorous evaluation protocols. In this study, we propose Patch-based representation learning for time-series Anomaly detection (PaAno), a lightweight yet effective method for fast and efficient time-series anomaly detection. PaAno extracts short temporal patches from time-series training data and uses a 1D convolutional neural network to embed each patch into a vector representation. The model is trained using a combination of triplet loss and pretext loss to ensure the embeddings capture informative temporal patterns from input patches. During inference, the anomaly score at each time step is computed by comparing the embeddings of its surrounding patches to those of normal patches extracted from the training time-series. Evaluated on the TSB-AD benchmark, PaAno achieved state-of-the-art performance, significantly outperforming existing methods, including those based on heavy architectures, on both univariate and multivariate time-series anomaly detection across various range-wise and point-wise performance measures.

The zero-shot evaluation of time series foundation models (TSFMs) for classification typically uses a frozen encoder followed by a task-specific classifier. However, this practice violates the training-free premise of zero-shot deployment and introduces evaluation bias due to classifier-dependent training choices. To address this issue, we propose TIC-FM, an in-context learning framework that treats the labeled training set as context and predicts labels for all test instances in a single forward pass, without parameter updates. TIC-FM pairs a time series encoder and a lightweight projection adapter with a split-masked latent memory Transformer. We further provide theoretical justification that in-context inference can subsume trained classifiers and can emulate gradient-based classifier training within a single forward pass. Experiments on 128 UCR datasets show strong accuracy, with consistent gains in the extreme low-label situation, highlighting training-free transfer for time series classification.The source code is publicly available at https://github.com/fangjuntao/TIC-FM.

Time series data are essential for a wide range of applications, yet access to high-quality datasets is often constrained by privacy concerns, acquisition costs, and labelling challenges. Synthetic time series generation has emerged as a promising approach to address these limitations. In this work, we investigate the use of complex network mappings for synthetic time series generation, focusing on the Quantile Graph (QG) representation and its inverse. While the inverse QG mapping has been previously proposed, its potential as a general-purpose data generator has not been systematically evaluated. We address this gap through a comprehensive empirical study assessing both the fidelity and utility of synthetic time series generated by the Inverse Quantile Graph (InvQG) framework. The evaluation combines statistical feature analysis, network-based topological characteristics, and performance in downstream clustering and classification tasks, using simulated and real-world datasets. The results show that InvQG effectively preserves marginal distributions and short-term temporal dependencies across a wide range of models, while exhibiting predictable limitations in capturing long-range or higher-order dynamics.

Time series forecasting has witnessed significant progress with deep learning. While prevailing approaches enhance forecasting performance by modifying architectures or introducing novel enhancement strategies, they often fail to dynamically disentangle and leverage the complex, intertwined temporal patterns inherent in time series, thus resulting in the learning of static, averaged representations that lack context-aware capabilities. To address this, we propose the Dual-Prototype Adaptive Disentanglement framework (DPAD), a model-agnostic auxiliary method that equips forecasting models with the ability of pattern disentanglement and context-aware adaptation. Specifically, we construct a Dynamic Dual-Prototype bank (DDP), comprising a common pattern bank with strong temporal priors to capture prevailing trend or seasonal patterns, and a rare pattern bank dynamically memorizing critical yet infrequent events, and then an Dual-Path Context-aware routing (DPC) mechanism is proposed to enhance outputs with selectively retrieved context-specific pattern representations from the DDP. Additionally, we introduce a Disentanglement-Guided Loss (DGLoss) to ensure that each prototype bank specializes in its designated role while maintaining comprehensive coverage. Comprehensive experiments demonstrate that DPAD consistently improves forecasting performance and reliability of state-of-the-art models across diverse real-world benchmarks.

Accurately and efficiently estimating the variance of the Maximum Mean Discrepancy (MMD) remains challenging, particularly for unbalanced sample sizes. In this paper, we derive a finite-sample unbiased estimator of the MMD variance. To overcome the traditional $\mathcal{O}(N^2)$ computational bottleneck, we develop a recursive prefix-suffix accumulation scheme for the Laplace kernel, reducing the computational complexity to $\mathcal{O}(N \log N)$ while requiring $\mathcal{O}(N)$ memory. Experimental results verify the theoretical exactness and numerical stability of the proposed estimator and demonstrate its scalability on large datasets. Furthermore, the method proves effective for monitoring distributional convergence during the training of Time-series Generative Adversarial Networks (TimeGAN).

Time series generation (TSG) is widely used across domains, yet most existing methods assume regular sampling and fixed output resolutions. These assumptions are often violated in practice, where observations are irregular and sparse, while downstream applications require continuous and high-resolution TS. Although Neural Controlled Differential Equation (NCDE) is promising for modeling irregular TS, it is constrained by a single dynamics function, tightly coupled optimization, and limited ability to adapt learned dynamics to newly generated samples from the generative model. We propose Diff-MN, a continuous TSG framework that enhances NCDE with a Mixture-of-Experts (MoE) dynamics function and a decoupled architectural design for dynamics-focused training. To further enable NCDE to generalize to newly generated samples, Diff-MN employs a diffusion model to parameterize the NCDE temporal dynamics parameters (MoE weights), i.e., jointly learn the distribution of TS data and MoE weights. This design allows sample-specific NCDE parameters to be generated for continuous TS generation. Experiments on ten public and synthetic datasets demonstrate that Diff-MN consistently outperforms strong baselines on both irregular-to-regular and irregular-to-continuous TSG tasks. The code is available at the link https://github.com/microsoft/TimeCraft/tree/main/Diff-MN.

Accurate blood glucose forecasting using continuous glucose monitoring (CGM) data can support the early prediction of dysglycemic risk. However, current neural-network-based forecasting models treat CGM data as a purely numerical sequence without integrating the contextual information contained in CGM signal morphology. Recently, large language models (LLMs) have shown promise for time-series forecasting, yet their role as agentic context extractors in diabetes care remains largely unexplored. In this study, we bridge glucose forecasting and LLM-based contextualization by developing GlyRAG, a context-aware, retrieval-augmented forecasting framework that uses an LLM as a contextualization agent to summarize glucose morphology directly from a timed CGM window. The generated CGM-only narrative is embedded and fused with patch-based glucose representations, while a retrieval module incorporates similar historical training episodes through cross-attention. We evaluate GlyRAG on the OhioT1DM and AZT1D datasets for 5-, 30-, and 60-minute forecasting horizons. Compared with strong CGM-only baselines, GPT-4 GlyRAG significantly improves long-horizon root mean square error (RMSE) over PatchTST on both datasets. For example, RMSE decreases from 13.8 to 10.6 at 30 minutes and from 23.1 to 20.2 at 60 minutes on OhioT1DM. LLaMA 3.1 produces smaller but significant long-horizon gains, suggesting that the contextualization pipeline is not limited to GPT-4. Clinical error-grid analyses further show that approximately 85 percent of predictions fall within the clinically acceptable Clarke Error Grid Zones A and B. These results suggest that CGM-derived linguistic context and case-based retrieval can improve long-horizon glucose forecasting without requiring additional sensing modalities.

Traffic forecasting systems rely on fixed sensor networks that frequently exhibit contiguous blackouts. Such outages are usually treated as ignorable missingness, although dropout can depend on unobserved traffic conditions. We study this possibility with an MNAR-aware latent state-space model that combines linear traffic dynamics with a Bernoulli missingness channel whose probability depends on the latent state. Inference uses an Extended Kalman Filter (EKF) followed by Rauch-Tung-Striebel (RTS) smoothing, and parameters are learned by approximate EM. We evaluate Seattle using a leakage-free, month-balanced set of 300 unique all-horizon-aligned blackout windows. On this benchmark, MAR-LDS attains 4.264 mph pooled imputation RMSE and MNAR-LDS improves it to 4.177 (difference -0.086); the detector-cluster bootstrap 95% interval is [-0.182,-0.002]. A causal one-step predicted latent representation raises missingness ROC-AUC from 0.685 using observed-only features to 0.784. We further test whether this compact probabilistic model remains competitive with substantially larger neural time-series architectures under the identical masked-imputation protocol. MNAR-LDS ranks second in pooled RMSE and outperforms 8 of 9 evaluated neural architectures; it is within 1.22% of the best neural result, with no statistically resolved difference under detector-cluster bootstrap, while achieving lower P95 error, lower long-blackout RMSE, and orders of magnitude fewer stored scalar entries. MNAR roughly doubles end-to-end training time relative to MAR and increases EKF+RTS inference time by 41%, making the accuracy-complexity-cost tradeoff explicit. Controlled state-dependent blackouts further show larger gains when dropout is genuinely informative, including a 6.34% reduction in 30-minute forecast RMSE relative to MAR.

Time series extrinsic regression (TSER) refers to the task of predicting a continuous target variable from an input time series. It appears in many domains, including healthcare, finance, environmental monitoring, and engineering. In these settings, accurate predictions and trustworthy reasoning are both essential. Although state-of-the-art TSER models achieve strong predictive performance, they typically operate as black boxes, making it difficult to understand which temporal patterns drive their decisions. Post-hoc interpretability techniques, such as feature attribution, aim to to explain how the model arrives at its predictions, but often produce coarse, noisy, or unstable explanations. Recently, inherently interpretable approaches based on concepts, additive decompositions, or symbolic regression, have emerged as promising alternatives. However, these approaches remain limited: they require explicit supervision on the concepts themselves, often cannot capture interactions between time-series features, lack expressiveness for complex temporal patterns, and struggle to scale to high-dimensional multivariate data. To address these limitations, we propose MAGNETS (Mask-and-AGgregate NEtwork for Time Series), an inherently interpretable neural architecture for TSER. MAGNETS learns a compact set of human-understandable concepts without requiring any annotations. Each concept corresponds to a learned, mask-based aggregation over selected input features, explicitly revealing both which features drive predictions and when they matter in the sequence. Predictions are formed as combinations of these learned concepts through a transparent, additive structure, enabling clear insight into the model's decision process. The code implementation and datasets are publicly available at https://github.com/FlorentF9/MAGNETS.

This study presents a controlled comparison of baseline Kolmogorov-Arnold Networks (KAN), implemented via PyKAN, and Long Short-Term Memory (LSTM) networks for the forecasting of stochastic, non-stationary financial time series. The two architectures are assessed in terms of predictive accuracy, computational efficiency, and interpretability, with accuracy measured by the Root Mean Square Error (RMSE) in normalised feature space. Under a direct multi-output forecasting protocol, LSTM attains clearly superior accuracy across all tested prediction horizons, consistent with its well-established effectiveness for sequential data modelling. Baseline KAN, although offering theoretical interpretability through the Kolmogorov-Arnold representation theorem, exhibits substantially higher error rates and limited practical applicability for time series forecasting in its standard form. Several specialised temporal variants -- including Temporal KAN and Time-Frequency KAN -- have since been proposed to address these sequential modelling limitations, but they lie outside the scope of the present study. KAN is observed to converge faster during training under the configurations tested, although direct runtime comparisons are constrained by methodological factors. These findings support the adoption of LSTM for accuracy-critical financial forecasting and establish an empirical baseline for standard KAN on stochastic sequential data, motivating further investigation of temporally-aware KAN architectures. The study benchmarks baseline KAN against baseline LSTM only; the results do not extend to specialised KAN variants designed for sequential data, nor to the broader family of temporal models.

Foundation models have transformed machine learning for language and vision, but achieving comparable impact in physical simulation remains a challenge. Data heterogeneity and unstable long-term dynamics inhibit learning from sufficiently diverse dynamics, while varying resolutions and dimensionalities challenge efficient training on modern hardware. Through empirical and theoretical analysis, we incorporate new approaches to mitigate these obstacles, including a harmonic-analysis-based stabilization method, load-balanced distributed 2D and 3D training strategies, and compute-adaptive tokenization. Using these tools, we develop Walrus, a transformer-based foundation model developed primarily for fluid-like continuum dynamics. Walrus is pretrained on nineteen diverse scenarios spanning astrophysics, geoscience, rheology, plasma physics, acoustics, and classical fluids. Experiments show that Walrus outperforms prior foundation models on both short and long term prediction horizons on downstream tasks and across the breadth of pretraining data, while ablation studies confirm the value of our contributions to forecast stability, training throughput, and transfer performance over conventional approaches. Code and weights are released for community use.

Modeling continuous-time dynamics from sparse and irregularly-sampled time series remains a fundamental challenge. Neural controlled differential equations provide a principled framework for such tasks, yet their performance is highly sensitive to the choice of control path constructed from discrete observations. Existing methods commonly employ fixed interpolation schemes, which impose simplistic geometric assumptions that often misrepresent the underlying data manifold, particularly under high missingness. We propose FlowPath, a novel approach that learns the geometry of the control path via an invertible neural flow. Rather than merely connecting observations, FlowPath constructs a continuous and data-adaptive manifold, guided by invertibility constraints that enforce information-preserving and well-behaved transformations. This inductive bias distinguishes FlowPath from prior unconstrained learnable path models. Empirical evaluations on 18 benchmark datasets and a real-world case study demonstrate that FlowPath consistently achieves statistically significant improvements in classification accuracy over baselines using fixed interpolants or non-invertible architectures. These results highlight the importance of modeling not only the dynamics along the path but also the geometry of the path itself, offering a robust and generalizable solution for learning from irregular time series.

While Time Series Foundation Models (TSFMs) excel in zero-shot tasks, their behavior under continual fine tuning is poorly understood. We present the first systematic study of catastrophic forgetting in TSFMs (TimesFM-2.0, Chronos-2) versus a specialized SamFormer model across synthetic and real-world energy forecasting benchmarks. Our results show that while fine-tuning improves new task accuracy, it consistently triggers forgetting, though larger models exhibit greater inherent robustness. Notably, employing forgetting mitigation techniques such as DER, levels the playing field: it provides disproportionate gains to smaller models, allowing them to match TSFM performance by the end of the continual learning sequence. These findings suggest that in realistic, non-stationary scenarios, the high computational cost of large foundation models may not be justified over smaller models equipped with effective mitigation strategies.

Benchmark quality is critical for meaningful evaluation and sustained progress in time series forecasting, particularly with the rise of pretrained models. Existing benchmarks often have limited domain coverage or overlook real-world settings such as tasks with covariates. Their aggregation procedures frequently lack statistical rigor, making it unclear whether observed performance differences reflect true improvements or random variation. Many benchmarks lack consistent evaluation infrastructure or are too rigid for integration into existing pipelines. To address these gaps, we propose fev-bench, a benchmark of 100 forecasting tasks across seven domains, including 46 with covariates. Supporting the benchmark, we introduce fev, a lightweight Python library for forecasting evaluation emphasizing reproducibility and integration with existing workflows. Using fev, fev-bench employs principled aggregation with bootstrapped confidence intervals to report performance along two dimensions: win rates and skill scores. We report results on fev-bench for pretrained, statistical, and baseline models and identify promising future research directions.

Electronic health Records (EHRs) have become a cornerstone in modern-day healthcare. They are a crucial part for analyzing the progression of patient health; however, their complexity, characterized by long, multivariate sequences, sparsity, and missing values poses significant challenges in traditional deep learning modeling. While Transformer-based models have demonstrated success in modeling EHR data and predicting clinical outcomes, their quadratic computational complexity and limited context length hinder their efficiency and practical applications. On the other hand, State Space Models (SSMs) like Mamba present a promising alternative offering linear-time sequence modeling and improved efficiency for handling long sequences, but focus mostly on mixing sequence-level information rather than channel-level data. To overcome these challenges, we propose HyMaTE (A Hybrid Mamba and Transformer Model for EHR Representation Learning), a novel hybrid model tailored for representing longitudinal data, combining the strengths of SSMs with advanced attention mechanisms. By testing the model on predictive tasks on multiple clinical datasets, we demonstrate HyMaTE's ability to capture an effective, richer, and more nuanced unified representation of EHR data. Additionally, the interpretability of the outcomes achieved by self-attention illustrates the effectiveness of our model as a scalable and generalizable solution for real-world healthcare applications. Codes are available at: https://github.com/healthylaife/HyMaTE.

Magnitude, obtained as a special case of Euler characteristic of enriched category, represents a sense of the size of metric spaces and is related to classical notions such as cardinality, dimension, and volume. While the studies have explained the meaning of magnitude from various perspectives, continuity also gives a valuable view of magnitude. Based on established results about continuity of magnitude and maximum diversity, this article focuses on continuity of weighting, a distribution whose totality is magnitude, and its variation corresponding to maximum diversity. Meanwhile, recent studies also illuminated the connection between magnitude and data analysis by applying magnitude theory to point clouds representing the data or the set of model parameters. This article will also provide an application for time series analysis by introducing a new kind of invariants of periodic time series, where the invariance follows directly from the continuity results. As a use-case, a simple machine learning experiment is conducted with real-world data, in which the suggested invariants improved the performance.

Handling missing data in time series classification remains a significant challenge in various domains. Traditional methods often rely on imputation, which may introduce bias or fail to capture the underlying temporal dynamics. In this paper, we propose TANDEM (Temporal Attention-guided Neural Differential Equations for Missingness), an attention-guided neural differential equation framework that effectively classifies time series data with missing values. Our approach integrates raw observation, interpolated control path, and continuous latent dynamics through a novel attention mechanism, allowing the model to focus on the most informative aspects of the data. We evaluate TANDEM on 30 benchmark datasets and a real-world medical dataset, demonstrating its superiority over existing state-of-the-art methods. Our framework not only improves classification accuracy but also provides insights into the handling of missing data, making it a valuable tool in practice.

Data augmentation is becoming increasingly important across various areas of time series analysis, including forecasting, classification, and anomaly detection. We introduce the Latent Generative Temporal Augmentation (L-GTA) model, a generative approach based on a Variational Autoencoder with a Bi-LSTM backbone and temporal self-attention. The model learns a latent representation for each timestep and applies controlled perturbations such as jittering, magnitude warping, or drift. We define an equivariance objective to further encourage consistency between latent space and data space transformations. As a result, the augmented samples show predictable and interpretable transformation signatures. We evaluate L-GTA on several real-world datasets against SOTA generative methods, including TimeGAN, TimeVAE, and Diffusion-TS, as well as direct transformation approaches. Across experiments on downstream forecasting, distribution fidelity, and controllability of transformation intensity, L-GTA consistently outperforms competing approaches. In downstream forecasting, it reduces prediction error by up to 26% compared to the strongest generative method and 27% relative to using the original data without augmentation.

Crop type classification from optical satellite time series remains limited in its ability to generalize across growing seasons, particularly when crop phenology shifts due to inter-annual weather variability. This hampers deployment in operational settings where current-year labels are unavailable. In addition, uncertainty quantification is often overlooked, reducing the reliability of such approaches for practical crop monitoring. Inspired by ecophysiological principles, we introduce Thermal Time-based Temporal Sampling ($T^3S$), a simple, model-agnostic method that replaces calendar time with thermal time. By re-indexing satellite observations by cumulative growing degree days, $T^3S$ aligns phenologically equivalent growth stages across years, reducing temporal redundancy while concentrating on the most biologically informative periods. We evaluate $T^3S$ across three architecturally distinct backbones on (i) SwissCrop, a new country-scale, multi-year Sentinel-2 dataset with paired temperature data that we publicly release, and (ii) the cross-region TimeMatch benchmark spanning Denmark and France. Across these settings, $T^3S$ consistently improves cross-year and cross-region crop classification over several state-of-the-art baselines, including thermal positional encoding, with particularly strong gains in uncertainty calibration, robustness under label scarcity, and early-season prediction, while requiring no architectural modification.

When training autoregressive models to forecast dynamical systems, a critical question arises: how far into the future should the model be trained to predict for optimal performance? In this work, we address this question by analyzing the relationship between the geometry of the loss landscape and the training time horizon. Using dynamical systems theory, we prove that loss minima for long horizons generalize well to short-term forecasts, whereas minima found on short horizons result in worse long-term predictions. However, we also prove that the loss landscape becomes rougher as the training horizon grows, making long-horizon training inherently challenging. We validate our theory through numerical experiments and discuss practical implications for selecting training horizons. Our results provide a principled foundation for hyperparameter optimization in autoregressive forecasting models.

We introduce Temporal Variational Implicit Neural Representations (TV-INRs), a probabilistic framework for modeling irregular multivariate time series that enables efficient and accurate individualized imputation and forecasting. By integrating implicit neural representations with latent variable models, TV-INRs learn distributions over time-continuous generator functions conditioned on signal-specific covariates. Unlike existing INR approaches that require extensive training, fine-tuning or meta-learning, our method achieves accurate individualized predictions through a single forward pass. Our experiments demonstrate that with a single TV-INRs instance, we can accurately solve diverse imputation and forecasting tasks, offering a computationally efficient and scalable solution for real-world applications. TV-INRs performs particularly well in low-data regimes, where on several datasets it achieves substantially lower imputation error, including order-of-magnitude improvements.

We propose a framework for generative modeling of continuous-time processes from irregularly and asynchronously recorded data. It is based on the matching of generators and accommodates discontinuous trajectories. Analytical formulas for diffusion and jump bridges yield a family of reference generators that a neural network is trained to match. The key ingredient is that, for our constructed jump bridge, a parametrization of the jump kernel densities by scaled Gaussians admits closed-form expressions for the Kullback-Leibler divergence, allowing simulation-free training.

Time series segmentation assigns a label to each part of a sequence. We formulate dense univariate segmentation as node classification on a graph whose nodes are the original time points. A local window provides node features without setting output granularity. We evaluate the approach on a TSSB-derived inductive benchmark built from disjoint UCR training and test instances. Under one fixed Graph Attention Network (GAT), visibility-based transformations achieve the highest mean ranks among eleven graph constructions. WDPVG, directed NVG, and weighted NVG form a statistically indistinguishable top group after Holm correction. On the 59-dataset Time Series Segmentation Benchmark, WDPVG+GAT reaches a weighted F1 of $0.916$, below seq2point at $0.951$ and statistically indistinguishable from same-feature MLP, random-forest, and 1-NN controls, because at this downsampled resolution each segment is short and the fixed $81$-sample window already spans most of it. At native resolution, where each segment is longer than that window, WDPVG+GAT is less sensitive to feature-window width and remains above the same-feature MLP at every tested window. The graph's advantage over these point-wise classifiers comes from context beyond the local window, which the visibility graph's long-range edges can supply, rather than from better features within it. In a separate resolution sweep, it is statistically tied with a window-searched seq2point while using about $70\times$ fewer parameters and $46\times$ less measured peak memory, although seq2point moves ahead after downsampling. This identifies a practical operating regime for finely sampled series when model size and repeated window tuning matter.

Teleoperation systems must be aware of the human's workload during missions to maintain operator performance. Prior work employed wearable physiological sensor response metrics to estimate current human workload; however, these estimates only enable robots to respond to under- or overload conditions reactively. Current human workload prediction approaches are limited to very short prediction horizons and fail to investigate variable lag horizons' impact on those predictions. This manuscript investigates physiological sensor driven human workload prediction focusing on the impact of lag horizons on both univariate and multivariate time series forecasting models, with longer prediction horizons than the workload prediction state-of-the-art (i.e., > 30 seconds using Long Short-Term Memory networks). Models were trained using data from a 64 participant non-sedentary supervisory environment NASA Multi-Attribute Task Battery-II human subjects evaluation. A key finding is that univariate workload predictions required 240 second lag horizons, whereas multivariate workload predictions sufficed with 120 second lag horizons. This finding indicates additional workload components reduce lag horizon requirements, enabling more efficient models with longer prediction horizons.

Conventional forecasting methods are trained end-to-end on unimodal time series, which limits their ability to exploit textual information and undermines their generalization in data-scarce scenarios. Recently, large language models (LLMs) and time series foundation models (TSFMs) have demonstrated powerful capabilities in complex textual reasoning and zero-shot temporal modeling, respectively. Integrating these strengths to construct a multimodal time series foundation model that jointly leverages temporal and textual information for zero-shot future inference has emerged as a promising research direction. However, the scarcity of large-scale, high-quality multimodal datasets remains a fundamental obstacle. To address this challenge, we propose ChronoSteer, a decoupled agentic framework that learns cross-modal alignment from synthetic paired supervision. Specifically, a pretrained LLM first converts textual events into revision instructions that steer the initial unimodal prediction produced by a frozen TSFM. These revision instructions form an intermediate instruction space that bridges the semantic gap between text and time series while fully leveraging pretrained knowledge. Technically, the instructions are discretized into a compact codebook of instruction anchors, effectively mitigating semantic divergence while reducing the cost of dataset construction. Finally, we adopt a two-stage training strategy to recover the fine-grained magnitude information lost during discretization. Furthermore, we release a leakage-controlled multimodal benchmark constructed with temporal separation and textual context available before the prediction window. When paired with an LLM and trained on synthetic cross-modal alignment data, ChronoSteer achieves a 25.8% improvement in zero-shot prediction accuracy over its unimodal backbone, and outperforms prior state-of-the-art unimodal and multimodal ...

While foundation models have revolutionized various domains, their application to time series classification remains rather under-explored, with existing literature predominantly focused on forecasting. To bridge this gap, we introduce \textbf{Mantis}, a transformer-based foundation model pre-trained exclusively on synthetic data via self-supervised contrastive learning. We demonstrate that effective tokenization is critical to unlocking the full potential of transformers, proposing a novel token generator unit. Furthermore, we introduce an enhanced test-time methodology that bridges the performance gap between Mantis and strong specialized approaches by leveraging intermediate-layer representations, self-ensembling, and cross-model embedding fusion. Extensive experiments demonstrate that Mantis establishes a new state-of-the-art, outperforming existing foundation models across four diverse dataset collections covering various application domains.

We introduce a local surrogate approach for explainable time-series forecasting. An initially non-interpretable predictive model to improve the forecast of a classical time-series 'base model' is used. 'Explainability' of the correction is provided by fitting the base model again to the data from which the error prediction is removed (subtracted), yielding a difference in the model parameters which can be interpreted. We provide illustrative examples to demonstrate the potential of the method to discover and explain underlying patterns in the data.

We introduce a rigorous mathematical framework for Granger causality in extremes, designed to identify causal links from extreme events in time series. Granger causality plays a pivotal role in uncovering directional relationships among time-varying variables. While this notion gains heightened importance during extreme and highly volatile periods, state-of-the-art methods primarily focus on causality within the body of the distribution, often overlooking causal mechanisms that manifest only during extreme events. Our framework is designed to infer causality mainly from extreme events by leveraging the causal tail coefficient. We establish equivalences between causality in extremes and other causal concepts, including (classical) Granger causality, Sims causality, and structural causality. We prove other key properties of Granger causality in extremes and show that the framework is especially helpful under the presence of hidden confounders. We also propose a novel inference method for detecting the presence of Granger causality in extremes from data. Our method is model-free, can handle non-linear and high-dimensional time series, outperforms current state-of-the-art methods in all considered setups, both in performance and speed, and was found to uncover coherent effects when applied to financial and extreme weather observations.

A set of probabilistic forecasts is calibrated if each prediction of the forecaster closely approximates the empirical distribution of outcomes on the subset of timesteps where that prediction was made. We study the fundamental problem of online calibrated forecasting of binary sequences under the standard $\ell_1$ calibration error metric, which was initially studied by Foster & Vohra (1998). They derived an algorithm with $O(T^{2/3})$ calibration error after $T$ time steps, and showed a lower bound of $Ω(T^{1/2})$. These bounds remained stagnant for two decades, until Qiao & Valiant (2021) improved the lower bound to $Ω(T^{0.528})$ by introducing a combinatorial game called sign preservation and showing that lower bounds for this game imply lower bounds for calibration. In this paper, we give the first improvement to the $O(T^{2/3})$ upper bound on calibration error of Foster & Vohra. We do this by introducing a variant of Qiao & Valiant's game that we call sign preservation with reuse (SPR). We prove that the relationship between SPR and calibrated forecasting is bidirectional: not only do lower bounds for SPR translate into lower bounds for calibration, but algorithms for SPR also translate into new algorithms for calibrated forecasting. We then give an improved upper bound for the SPR game, which implies, via our equivalence, a forecasting algorithm with calibration error $O(T^{2/3 - \varepsilon})$ for some $\varepsilon > 0$, improving Foster & Vohra's upper bound for the first time. Using similar ideas, we then prove a slightly stronger lower bound than that of Qiao & Valiant, namely $Ω(T^{0.54389})$. Our lower bound is obtained by an oblivious adversary, marking the first $ω(T^{1/2})$ calibration lower bound for oblivious adversaries.

Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an alternative approach, utilizing neural networks combined with ODE solvers to learn continuous latent representations through parameterized vector fields. Neural Stochastic Differential Equations (Neural SDEs) extend Neural ODEs by incorporating a diffusion term, although this addition is not trivial, particularly when addressing irregular intervals and missing values. Consequently, careful design of drift and diffusion functions is crucial for maintaining stability and enhancing performance, while incautious choices can result in adverse properties such as the absence of strong solutions, stochastic destabilization, or unstable Euler discretizations, significantly affecting Neural SDEs' performance. In this study, we propose three stable classes of Neural SDEs: Langevin-type SDE, Linear Noise SDE, and Geometric SDE. Then, we rigorously demonstrate their robustness in maintaining excellent performance under distribution shift, while effectively preventing overfitting. To assess the effectiveness of our approach, we conduct extensive experiments on four benchmark datasets for interpolation, forecasting, and classification tasks, and analyze the robustness of our methods with 30 public datasets under different missing rates. Our results demonstrate the efficacy of the proposed method in handling real-world irregular time series data.

Real-world time series analysis faces significant challenges when dealing with irregular and incomplete data. While Neural Differential Equation (NDE) based methods have shown promise, they struggle with limited expressiveness, scalability issues, and stability concerns. Conversely, Neural Flows offer stability but falter with irregular data. We introduce 'DualDynamics', a novel framework that synergistically combines NDE-based method and Neural Flow-based method. This approach enhances expressive power while balancing computational demands, addressing critical limitations of existing techniques. We demonstrate DualDynamics' effectiveness across diverse tasks: classification of robustness to dataset shift, irregularly-sampled series analysis, interpolation of missing data, and forecasting with partial observations. Our results show consistent outperformance over state-of-the-art methods, indicating DualDynamics' potential to advance irregular time series analysis significantly.

This paper presents a method to efficiently classify the gastroenterologic section of images derived from Video Capsule Endoscopy (VCE) studies by exploring the combination of a Convolutional Neural Network (CNN) for classification with the time-series analysis properties of a Hidden Markov Model (HMM). It is demonstrated that successive time-series analysis identifies and corrects errors in the CNN output. Our approach achieves an accuracy of $98.04\%$ on the Rhode Island (RI) Gastroenterology dataset. This allows for precise localization within the gastrointestinal (GI) tract while requiring only approximately 1M parameters and thus, provides a method suitable for low power devices

The proliferation of Internet-of-Things (IoT) devices has led to an unprecedented volume of multivariate time series (MTS) data, requiring efficient and accurate processing for timely decision-making in resource-constrained edge environments. Hyperdimensional (HD) computing, with its inherent efficiency and parallelizability, has shown promise in classification tasks but struggles to capture complex temporal patterns, while Transformers excel at sequence modeling but incur high computational and memory overhead. We introduce BiHDTrans, an efficient neurosymbolic binary hyperdimensional Transformer that integrates self-attention into the HD computing paradigm, unifying the representational efficiency of HD computing with the temporal modeling power of Transformers. Empirically, BiHDTrans outperforms state-of-the-art (SOTA) HD computing models by at least 14.47% and achieves 6.67% higher accuracy on average than SOTA binary Transformers. With hardware acceleration on FPGA, our pipelined implementation leverages the independent and identically distributed properties of high-dimensional representations, delivering 39.4 times lower inference latency than SOTA binary Transformers. Theoretical analysis shows that binarizing in holographic high-dimensional space incurs significantly less information distortion than directly binarizing neural networks, explaining BiHDTrans's superior accuracy. Furthermore, dimensionality experiments confirm that BiHDTrans remains competitive even with a 64% reduction in hyperspace dimensionality, surpassing SOTA binary Transformers by 1-2% in accuracy with 4.4 times less model size, as well as further reducing the latency by 49.8% compare to the full-dimensional baseline. Together, these contributions bridge the gap between the expressiveness of Transformers and the efficiency of HD computing, enabling accurate, scalable, and low-latency MTS classification.

Real-world time series exhibit complex and evolving dynamics, making accurate forecasting extremely challenging. Recent multi-modal forecasting methods leverage textual information such as news reports to improve prediction, but most rely on token-level fusion that mixes temporal patches with language tokens in a shared embedding space. However, such fusion can be ill-suited when high-quality time-text pairs are scarce and when time series exhibit substantial variation in characteristics, thus complicating cross-modal alignment. In parallel, mixture-of-experts (MoE) architectures have proven effective for both time series modeling and multi-modal learning, yet many existing MoE-based modality integration methods still depend on token-level fusion. To address this, we propose Expert Modulation, a new mechanism for multi-modal time series prediction that conditions both routing and expert computation on textual signals, enabling direct and efficient cross-modal control over expert behavior. Through theoretical analysis and experiments, our proposed method demonstrates strong improvements in multi-modal time series prediction. The current code implementation is available at https://github.com/BruceZhangReve/MoME

This paper evaluates how reward function choice shapes the performance and behavior of LLM forecasters. We compare five proper scoring rules as training objectives for binary forecasts of resolved real-world events. Although the rules share the same theoretical incentive for truthful probability reporting, the resulting models differ in calibration, probability use, and estimated profiles of bias, information, and noise, with smaller differences in aggregate accuracy and discrimination. The Brier-trained model has the lowest observed Brier score and highest AUC-ROC, while the log-trained model has the highest observed log score and lowest calibration error. Models with similar aggregate performance also reach that performance through different combinations of bias, information, and noise. Proper scoring rules therefore need not behave interchangeably as training objectives. Reward choice may shape not only how well an LLM forecasts, but how its forecasting errors are structured.