Multivariate Time Series Forecasting

This paper presents Naga, a deep State Space Model (SSM) encoding approach inspired by structural concepts from Vedic mathematics. The proposed method introduces a bidirectional representation for time series by jointly processing forward and time-reversed input sequences. These representations are then combined through an element-wise (Hadamard) interaction, resulting in a Vedic-inspired encoding that enhances the model's ability to capture temporal dependencies across distant time steps. We evaluate Naga on multiple long-term time series forecasting (LTSF) benchmarks, including ETTh1, ETTh2, ETTm1, ETTm2, Weather, Traffic, and ILI. The experimental results show that Naga outperforms 28 current state of the art models and demonstrates improved efficiency compared to existing deep SSM-based approaches. The findings suggest that incorporating structured, Vedic-inspired decomposition can provide an interpretable and computationally efficient alternative for long-range sequence modeling.

Attention mechanisms are effective for multivariate time series modeling because they adaptively aggregate information across timestamps and variables. Their quadratic cost, however, limits their use in multivariate and spatio-temporal systems. Linear attention reduces this cost by replacing nonlinear attention mappings with forms that support associative computation. Replacing exponential weighting may weaken the amplification of high-score positions and further bias weakly selective distributions toward uniform aggregation. We propose an entropy-calibrated linear attention module and instantiate it as the ELinFormer forecaster. Our operator decomposes aggregation into a uniform component and a query-dependent correction, whose magnitude is calibrated by a query-specific temperature. We derive a second-order KL proxy from centered query-key scores. The Taylor expansion reduces the proxy to the squared-score energy divided by the squared temperature. This score energy can be computed from shared products of the centered keys without forming the full pairwise score matrix, and the same products support the linear attention output. We design a smooth temperature rule to calibrate the KL proxy: it keeps low-energy residuals vanishing, approximately calibrates moderate-energy queries to a shared KL level, and allows the proxy to continue growing for high-energy queries. Experiments on five PEMS benchmarks show competitive forecasting accuracy. Controlled comparisons with vanilla attention and Linformer demonstrate a favorable accuracy--memory trade-off, while analysis on PEMS08 shows that the proposed rational temperature rule and query-specific calibration achieve lower MAE than a linear rule or shared-temperature alternatives. These results support entropy calibration as an effective mechanism for preserving selective deviations in linear attention.

Standard attention mechanisms in transformers employ static token representations that remain unchanged across all pair-wise computations in each layer. This limits their representational alignment with the potentially diverse relational dynamics of each token-pair interaction. While they excel in domains with relatively homogeneous relationships, standard attention's static relational learning struggles to capture the diverse, heterogeneous inter-channel dependencies of multivariate time series (MTS) data--where different channel-pair interactions within a single system may be governed by entirely different physical laws or temporal dynamics. To better align the attention mechanism for such domain phenomena, we propose attention with dynamic relational priming (prime attention). Unlike standard attention where each token presents an identical representation across all of its pair-wise interactions, prime attention tailors each token dynamically (or per interaction) through learnable modulations to best capture the unique relational dynamics of each token pair, optimizing each pair-wise interaction for that specific relationship. This representational plasticity of prime attention enables effective extraction of relationship-specific information in MTS while maintaining the same asymptotic computational complexity as standard attention. Our results demonstrate that prime attention consistently outperforms standard attention across benchmarks, achieving up to 6.5% improvement in forecasting accuracy. In addition, we find that prime attention achieves comparable or superior performance using up to 40% less sequence length compared to standard attention, further demonstrating its superior relational modeling capabilities.

Rainfall is an important environmental driver of water-quality variations through processes such as runoff, pollutant transport, dilution, and resuspension. Traditional mechanistic models can explicitly describe these processes but often require substantial process specification and site-specific calibration, limiting their flexibility under changing hydrological conditions. In this work, we explore a data-driven alternative by proposing RaiNet to jointly model multiscale water-quality dynamics and station-specific rainfall effects across relative lags and temporal scales. RaiNet employs LocTrend to capture irregular water-quality dynamics, constructs station-oriented rainfall events from gridded precipitation, and introduces XGateFusion for conditional lag-aware fusion across scales. We further release three real-world multimodal datasets comprising over 150,000 temporally aligned water quality observations and gridded precipitation raster images. Experiments show that RaiNet outperforms general time-series, water quality, diffusion-based, and spatiotemporal models by over 20%, while component-wise analyses confirm the distinct contribution of each module.

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.

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 ...