Long-Horizon Forecasting

Reliable disruption prediction is essential for the safe operation of future tokamaks. Existing full-distribution survival methods model the complete residual time-to-disruption distribution, whereas operational decisions primarily depend on disruption risk within a finite prediction horizon. This mismatch motivates introducing Early Event Prediction (EEP) objectives into survival-based disruption prediction. We take Deep Survival Machines (DSM) as the full-distribution baseline and propose applying two established EEP methods to tokamak disruption prediction: Temporal Label Smoothing (TLS), which directly predicts disruption probability within a finite horizon, and survTLS, which additionally models the event-time distribution within that horizon. Using a common causal encoder, we compare these methods on DIII-D, Alcator C-Mod, and EAST. We distinguish threshold-free deadline ranking from validation-selected fixed-policy alarm performance and evaluate prediction horizons and encoder architectures. TLS achieves the best mean alarm performance on DIII-D and EAST, whereas all methods perform poorly on Alcator C-Mod. survTLS does not consistently outperform DSM, suggesting that directly learning horizon-level event probability is more effective than modeling detailed within-horizon event-time distributions in the present setting. Finally, the selected prediction horizons and encoder-ablation results vary across devices, reflecting differences in disruption characteristics.

An Intraoperative Hypotension (IOH) event is a frequent complication during administration of general anaesthesia with serious downstream consequences, yet clinical management remains reactive and not predictive. Existing predictive models, however, ignore drug infusion history as a valuable signal for prediction despite its direct pharmacological relevance. Our model achieves an Area Under the Receiver Operating Characteristic curve (AUROC) of 0.7360 and an Area Under the Precision-Recall Curve (AUPRC) of 0.1794, representing a 2.73-fold lift over the random guessing AUPRC baseline (0.0657), with the removal of propofol and remifentanil effect-site concentrations resulting in a 13.9% AUPRC drop compared to the full model. This is consistent with the hypothesis that pharmacokinetic trajectories encode impending haemodynamic changes before they manifest in the Mean Arterial Pressure (MAP). Additionally, this paper shows that training without lead-gap filtering degraded AUROC by 16.7%, empirically confirming that unfiltered models learn to detect ongoing hypotension rather than predict future events. Finally, a Mamba-based architecture achieves the aforementioned high prediction performance while maintaining a constant memory footprint across a range of sequence lengths, unlike the quadratic VRAM overhead typical of vanilla Transformers, making it the more practical choice for continuous intraoperative deployment.

Quantum long short-term memory (QLSTM) models extend recurrent sequence learning with variational quantum circuits, but their optimization behavior can vary substantially across random initializations and temporal contexts. This paper evaluates a recursive QLSTM architecture against a standard QLSTM for one-step-ahead prediction of daily minimum and maximum temperature. Using daily weather observations from Toronto and identical training settings, we compare convergence, predictive accuracy, and generalization across input windows of 8, 16, and 32 days over 20 random seeds. The recursive model consistently reaches a near-optimal test loss earlier, reduces mean absolute error and root mean squared error, and exhibits a smaller generalization gap. These results indicate that recursive quantum feature transformations can improve stability and out-of-sample performance for compact hybrid quantum--classical temporal models.

Neural PDE solvers provide efficient surrogates for time-dependent physical systems, but autoregressive prediction over long horizons remains challenging because local errors can induce distribution shift and accumulate under recursive deployment. We develop a variational approach to this problem by introducing latent Markov dynamics in which physical states are represented by latent distributions and evolved through probabilistic transitions. The framework is formulated directly on function spaces and specialized to functional Gaussian models, where structured latent perturbations induce a spectral geometry and variational transition alignment regularizes the learned dynamics. We further analyze how these mechanisms affect autoregressive error propagation, providing a theoretical connection between variational training and long-horizon prediction. We instantiate the framework as the Variational Autoencoding Markov Operator (VAMO), which combines spatially resolved latent fields, structured Gaussian perturbations, and a neural-operator transition. Empirically, we demonstrate the effectiveness of VAMO on several fluid-dynamics benchmarks with prediction horizons extending substantially beyond those represented during training, where it consistently reduces error accumulation and improves rollout stability over several deterministic and noise-injection baselines. Overall, these results highlight variational modeling as a complementary approach to robust long-horizon neural PDE dynamics.

Extracting informative representations from longitudinal data that can predict future outcomes remains a critical challenge in medicine. Medical datasets are inherently heterogeneous, consisting of a large number of variables collected from different sources, sampled with different temporal spacings, and representing different aspects of human health status. This requires identifying those variables with predictive value, processing longitudinal information, and integrating multiple variables for outcome prediction. Here, we propose a novel agent-based approach, LongAgent, that can autonomously search over combinations of variable sets, temporal windows and longitudinal aggregation functions, and identify candidates with promising predictive performance. LongAgent utilises a history memory of previous searches and numerical evidence to guide subsequent exploration. On synthetic data, LongAgent achieves a mean prediction RMSE of 1.7376 and improves over the strongest non-agent baseline by 0.0151 (95% CI: [0.0045,0.0260]; p=0.0273). On a real clinical dataset, it performs comparably to the best baseline.

Accurate prediction of equity returns remains a major challenge in computational finance due to the non-stationary, nonlinear, and low signal-to-noise ratio nature of financial time series. This paper proposes a hybrid two-stage architecture that combines a long short-term memory (LSTM) network with an XGBoost gradient-boosted regressor for multi-horizon stock return prediction across a diversified panel of 14 U.S. equities spanning six industry sectors. The LSTM component, comprising two stacked layers with 64 hidden units, processes 60-day sliding windows of five sequential market features to produce 64-dimensional temporal embeddings that encode learned sequential market dynamics. These embeddings are concatenated with 14 hand-crafted technical indicators to form a 78-dimensional hybrid feature vector, which is subsequently passed to an XGBoost regressor tuned via 3-fold cross-validation grid search. The framework is trained on a multi-stock pooled corpus using strict chronological splits and per-stock MinMaxScaling to prevent look-ahead bias, and evaluated across four prediction horizons of 30, 90, 252, and 365 trading days. Experimental results demonstrate that the hybrid model achieves a test RMSE of 0.0949 on the 30-day horizon, roughly one-third that of the standalone LSTM baseline, while marginally matching or surpassing the XGBoost-Only baseline across the majority of stocks. Directional accuracy rises with horizon length, reaching 97.6% at 365 days; we show, however, that this largely tracks the high base rate of positive long-horizon returns in the sample, and we therefore benchmark directional accuracy against a naive always-positive predictor and treat the above-base-rate gap at short horizons as the more informative signal. A composite investment scoring framework derived from multi-horizon predictions is further proposed to support portfolio ranking and decision support.

In autoregressive forecasting, long prediction rollouts provide distant supervision, but backpropagation through time (BPTT) carries gradients from those losses through many autoregressive steps. Repeated Jacobian products can make distant gradients dominate the update while amplifying predictable signal and unpredictable noise together; a large distant gradient therefore need not carry reliable learning signal. Motivated by this observation, we introduce Internal Dual-Wiener routing (Internal-DW), a principled backward-only intervention that preserves the full forward rollout and all horizon losses while reliability-weighting internal gradient routes. At each residual block, we derive bounded Wiener gains for the identity and nonlinear routes that balance preserving predictable learning signal against suppressing unpredictable variation, and estimate them from route-level gradient statistics and an explicit noise model. In a controlled system with known gradient signal-to-noise ratio (SNR), we show that distant gradients can grow even as their SNR falls, and that Internal-DW reduces held-out error in recovering predictable gradient signals and improves forecasting. On four history-dominated, weak-drive testbeds, Internal-DW reduces forecast error by 5.2%-13.8% relative to full BPTT, outperforms gradient clipping and Jacobian regularization on all four, and outperforms validation-selected truncated BPTT (TBPTT) on three. It also extends or preserves the fitted optimal training-horizon range across these four testbeds. Across the full benchmark suite, the current Internal-DW estimator has a clear applicability boundary: its benefit diminishes or reverses when usable history is limited or when the selected sampler fails to represent dominant drive-dependent variation. The results show that retaining long-horizon supervision does not require trusting every backward contribution equally.

Long-horizon predictive maintenance requires models to distinguish slowly evolving degradation from normal operating-regime variation over planning windows measured in days rather than hours. This paper evaluates whether an explicit conditional-quantile representation provides an informative classifier interface for this problem. The proposed TQRNN30d framework combines a dual-stage quantile regression neural network (QRNN) feature extractor with a multi-stream temporal fusion classifier. Each hourly word of 81-channel machine behaviour is mapped to a 324-dimensional quantile-state representation, and 720 ordered hourly words form the 30-day document supplied to the long-horizon model. The classifier fuses quantile states with dynamic covariates, channel-level static metadata, and a 168-hour latent-history stream using gated residual processing, causal recurrent encoding, and metadata-conditioned cross-modal attention. A bounded instability-aware signal derived from sustained one-word-ahead prediction-error divergence provides auxiliary memory modulation at the longest horizon. Evaluation uses a machine-disjoint 43/14/15 train/validation/test allocation across 72 machines in nine manufacturing facilities. At 30 days, TQRNN30d achieves 79.97% F1, 80.18% recall, 81.82% precision, 82.39% accuracy, and 0.820 ROC-AUC. It leads all 18 evaluated baselines at the 7-, 14-, and 30-day fixed-threshold comparisons, with the largest F1 advantage at 14 days. The results support held-out-machine performance within the observed homogeneous nine-facility fleet, but do not establish unseen-site, cross-equipment, or cross-sector generalisation.

Antarctic sea ice concentration (SIC) forecasting is an important yet challenging task due to the coexistence of complex spatial structure, long-range temporal dependencies, and strong seasonal variability. Conventional convolution-based models are effective at capturing local spatial patterns, but often have limited ability to model long-term temporal evolution. To address these challenges, we build on a hybrid Convolutional-Transformer forecasting framework for monthly Antarctic SIC forecasting. This framework combines convolutional encoding for spatial feature extraction with factorised self-attention for spatio-temporal dependency modelling. We further introduce two seasonal prior mechanisms: a month-aware positional encoding that injects calendar-month information into the token representation, and a seasonal temporal bias that encourages attention to periodically related historical states. Experimental results show that the proposed framework achieves better performance than convolutional and recurrent baselines across both classification and regression metrics. Ablation studies further indicate that the seasonal prior mechanisms provide consistent additional gains in both short- and long-horizon prediction. These results demonstrate the value of combining convolutional structures, attention mechanisms, and periodic prior information for Antarctic SIC forecasting.

Forecasting the long-horizon evolution of mechanical systems from position-only observations is a pivotal yet difficult task, as hidden velocities and trajectory-specific physical properties must be inferred simultaneously. Although physics-guided neural networks like Lagrangian Neural Networks (LNNs) guarantee physical plausibility, they generally require complete state inputs and lack adaptability to changing system parameters. To break these limitations, we introduce History-informed Lagrangian Neural Networks (HiLNN). Grounded in the insight that temporal position sequences implicitly encode underlying dynamics, HiLNN employs a recurrent encoder to extract a latent context from history. This context not only reconstructs the unobserved initial velocity but also adaptively modulates the mass matrix, potential energy, and damping coefficients of a structured Lagrangian system. By leveraging a differentiable RK4 rollout scheme, the entire pipeline is optimized end-to-end under multi-step trajectory supervision and energy-consistency regularization. Empirical evaluations across conservative, dissipative, and heterogeneous variable-parameter systems show that HiLNN delivers superior long-term prediction accuracy and maintains precise energy profiles compared to state-of-the-art baselines. The source code is publicly available at https://github.com/yingtian22/History-informed-LNN.

Specialist training beats generalist scale when forecasting financial statements. To our knowledge, no prior work jointly forecasts complete financial statements beyond one year, yet in a discounted-cash-flow valuation most firm value sits past that window. We release ProForma-20Q, a reproducible benchmark for forecasting 78 statement line items 1-20 quarters ahead, for anonymized firms, from past statements and an industry code, scored by change-space $R^2$. On it, Forma, a transformer that reads statements as sets of (account, quarter, value) tuples and maximizes a masked-tuple Gaussian likelihood, beats every competitor we field: classical machine learning, chained gradient boosting, a zero-shot time-series foundation model, and frontier large language models. Its lead widens with horizon, where valuation needs accuracy most, and its Gaussian predictive intervals never under-cover. Forma's forecasts nearly satisfy accounting identities; exact coherence is recoverable at no statistically significant accuracy cost. Its tuple interface supports scenario analysis without retraining, and we show that pinning future revenue paths sharpens the rest of the statement.

Probabilistic forecasting plays an essential role in risk-sensitive decision-making, particularly in long-horizon settings. However, existing approaches often face a fundamental trade-off between distributional flexibility and accurate mean prediction. Traditional parametric methods, such as Mean Variance Estimation (MVE), can suffer from degraded point accuracy when trained under joint Negative Log-Likelihood (NLL) objectives, while modern-flexible generative models, including Normalizing Flows and Diffusion Models, typically rely on costly Monte Carlo sampling and may yield suboptimal mean estimates. To address this limitation, we propose Two-stage Odd Residual Flows (TORF), a framework that decouples mean forecasting from uncertainty estimation. In the first stage, a pre-trained deterministic model is used to produce an accurate mean prediction. In the second stage, a Restricted Normalizing Flow, with strictly odd functions learns flexible residual distributions around the point forecast, guaranteeing mean preservation from the first stage without sampling. Experiments show that TORF achieves state-of-the-art deterministic accuracy (NMAE) while providing strong density estimation performance (CRPS) on short and long-horizon forecasting.

World models are expected to support imagination over extended temporal horizons, yet most are still trained through local few-step prediction objectives and deployed by recursively rolling out their own predictions. This creates a fundamental mismatch: few-step losses optimize local transition fidelity, while long-horizon prediction depends on how errors and gradients propagate through the entire trajectory. As a result, transitions with different downstream influence on the endpoint are treated uniformly during training, and small local errors are amplified through recursive inference. We argue that long-horizon accuracy is better achieved by optimizing directly, through an end-to-end endpoint prediction objective. To instantiate this paradigm, we introduce the Direct Prediction World Model (DPWM), a non-recursive architecture that compresses an action sequence of arbitrary length into a single embedding and predicts the endpoint observation in a single forward pass. This design avoids recurrent rollout in both prediction and gradient propagation, making long-horizon end-to-end training practical at horizons where unrolled autoregressive training becomes unstable. Empirically, DPWM substantially improves long-horizon endpoint prediction over recursive world-model baselines on continuous-control and pixel-based benchmarks, with larger gains as the prediction horizon increases. We further show that recurrent baselines benefit similarly when retrained with the same long-horizon endpoint objective, supporting our central claim that the training objective, rather than the particular backbone choice, is the main driver of long-horizon prediction accuracy. Our results suggest that world models can benefit from being trained and evaluated at the temporal scales where they are ultimately used, shifting the focus from local transition modeling toward long-horizon predictive accuracy.

Proper short-term forecasting of precipitation is crucial in disaster management and preparedness. Nonetheless, the variability and nonlinearity of precipitation make short-term forecasting challenging for meteorologists. Moreover, capturing temporal dependencies in spatiotemporal data is a challenge in precipitation nowcasting. In this article, we introduce a lightweight deep learning model for half-hourly precipitation nowcasting. This model has been designed by incorporating the DenseNet architecture, residual connections, and transformer encoders for effective precipitation nowcasting with reduced model parameters. The North-Eastern region of India has been selected as the area of interest for our study. The region receives the highest precipitation during the months of June-September due to the monsoon season. The proposed model takes the previous five time-steps of half-hourly precipitation as inputs and predicts the precipitation in the next two half-hours. The GPM IMERG precipitation dataset with a 30-minute cadence has been used in this study for training and testing the model. The proposed architecture achieves best MAE of 0.235 millimetres, RMSE of 0.735 millimetres, and KGE score of 0.816 at an interval of 30 minutes.

Commercial grazing systems yield irregular livestock observations, which challenge cattle growth forecasting. This study developed a hybrid machine learning framework for herd level cattle weight forecasting using automated sensing observations collected between 2022 and 2024 in southeastern Australia. Weekly live weight observations, demographic variables, and lagged environmental predictors were integrated into structured forecasting datasets. Herd level forecasting trajectories were generated through temporal aggregation of animal level predictions. Four hybrid architecture families were evaluated, including residual, stacked, cascade, and ensemble assisted frameworks. ARIMA, LSTM, and GRU models were used as comparative baselines. Independent testing demonstrated strong predictive agreement across multiple forecasting horizons. The cascade GB to RF to NN architecture achieved the best performance, with a test R^2 of 0.889, RMSE of 21.319 kg, and MAE of 15.462 kg. Hybrid architectures maintained greater robustness than recurrent sequential models under sparse observation conditions. Forecasting error increased progressively across extended prediction horizons. Feature importance analysis identified animal age, rainfall, and temperature as dominant predictors influencing herd level growth forecasting. The proposed framework may support feed allocation, grazing management, and livestock marketing decisions under heterogeneous sensing environments.

Time series in real-world applications are often generated by nonlinear dynamical systems, making accurate forecasting challenging. Existing approaches that explicitly model system dynamics typically rely on linear assumptions or Koopman-based linearizations, which may inadequately capture complex nonlinear behaviors and lead to error accumulation in long-horizon prediction. To address this limitation, we propose the Neural Bilinear Dynamical Model (NBDM), which models nonlinear system dynamics through a bilinear latent dynamical formulation. Specifically, NBDM leverages Koopman theory to lift the original nonlinear dynamics into a higher-dimensional latent space, where a bilinear dynamical model is constructed to characterize state evolution. To mitigate the approximation error introduced by bilinear representations, we further incorporate a parameterized error compensation term. Within this formulation, control inputs are explicitly integrated into the dynamics, using auxiliary variables when available and learned feedback signals otherwise. To handle scenarios with missing control inputs, we design a memory-enhanced controller that infers latent controls through multiplicative interactions between historical states and control signals. Experiments on five real-world datasets demonstrate that NBDM consistently outperforms competitive baselines in both given-control and missing-control settings, particularly for multi-step and long-horizon forecasting.

Forecasting precise future motion of surrounding agents is essential for reliable autonomous vehicles. However, as the demand for longer prediction horizons increases, existing endpoint-completion or iterative-refine methods increasingly struggle with weak guidance and compounding errors. To tackle the long-horizon prediction challenge, we propose Pivot-Centric Trajectory Prediction (PCTP). By introducing pivots'' and focusing on predicting pivot points along extended trajectories, we divide the long-term prediction task into short-term sub-tasks at various scales. Specifically, PCTP decouples the long-term trajectory predicting process into two processes: pivot prediction and pivot-based trajectory refinement. The pivot prediction process aims to utilize global map context and agent-to-agent interactions to identify these pivot points'', while the pivot-based trajectory refinement process focuses on local map details and refines the short-term trajectory based on predicted ``pivot points''. Compared with existing methods, PCTP provides more intermediate guidance while reducing compounding errors. Moreover, PCTP is a flexible approach that can be integrated into most state-of-the-art trajectory prediction models. Experimental results show that PCTP improves the prediction accuracy of leading models on both Argoverse I and Argoverse II datasets with minimal impact on model size. Specifically, PCTP combined with QCNet outperforms all published ensemble-free methods on the Argoverse II leaderboard at submission.

Modern computing and networking infrastructure emits telemetry continuously, yet operators convert it into decisions with a separate predictor per task, entity, and horizon. One generative model, pretrained once over an operator's own event streams, could replace this fleet, an approach that already scales to high-cardinality streams in recommendation systems. However, point-forecast error on operational telemetry saturates near simple last-value baselines, so lower error alone need not improve the decisions it feeds. To close this gap, we present \sys, a generative foundation model for network and systems telemetry, evaluated by replaying the decisions its calibrated conditional quantiles drive. \sys treats heterogeneous telemetry as event-driven, irregularly timed entity streams and serves flexible forecast horizons in a single pass, requiring no future timestamps. To our knowledge, \sys is the first pretrained telemetry model to improve both HPC scheduling and network provisioning decisions under replay, its runtime estimator transferring zero-shot across months and its pretrained weights across domains from hours of target data. Extensive experiments on HPC job logs and network traffic confirm that \sys lowers the mean bounded slowdown of backfilling by up to approximately $77\%$ over deployed user estimates and roughly halves the deployed rule's violation rate. Our code is available at https://github.com/ZzZTripleZzZ/all-in-one.

Neural operators provide fast surrogates for time-dependent partial differential equations (PDEs) by applying a learned evolution operator recursively to its own predictions, but this autoregressive rollout feeds every prediction error back as input, so local errors accumulate. Existing rollout-training strategies reduce the mismatch between training inputs and self-generated states, yet their supervision still measures only the absolute discrepancy from the ground-truth trajectory. Such supervision is therefore uninformative about whether the operator has overcome the long-horizon failure behaviors it exhibited earlier during optimization. We propose history-enriched rollout training (HERO), which augments conventional absolute trajectory supervision with relative supervision derived from the model's optimization history. HERO ranks detached candidate rollouts from a periodically refreshed lagged operator, the current model, and a perturbed input by rollout error, spectral discrepancy, energy drift, and error growth, and selects the strongest failure trajectory as reference. This reference enters a margin-based objective as a fixed comparison baseline, inducing a bounded, sample-dependent reweighting of the ground-truth rollout gradient rather than an independent gradient direction, which we further analyze theoretically. Experiments on nine PDE benchmarks with spectral and attention-based backbones show that HERO consistently improves long-horizon accuracy, stable rollout length, and out-of-distribution robustness at no inference-time cost. These results indicate that history-enriched relative supervision is effective for stabilizing long-horizon autoregressive prediction.

Neural operators have shown strong potential for learning solution operators of partial differential equations (PDEs). However, long-horizon autoregressive prediction remains challenging: local errors accumulate as spectral inconsistency, phase misalignment, or mean drift. Existing methods mainly improve state representations and operator backbones, while leaving the repeatedly applied latent transition increment weakly structured, allowing spectral errors and unstable channel couplings to accumulate during rollout. To address these issues, we propose a geometry-aware incremental neural operator (GeoIncNO) for stable long-horizon PDE prediction. GeoIncNO predicts latent increments for residual advancement and uses lightweight low-rank projectors to regulate channel coupling within active frequency bands derived from the increment spectral energy distribution. To reduce physical-space reconstruction errors, GeoIncNO further introduces a mean--fluctuation decoupled reconstruction mechanism, where stable mean structures and dynamic fluctuations are fused separately, and phase correction is applied only to the zero-mean fluctuation component. Extensive experiments on six PDE benchmarks, covering 1D, 2D, and 3D dynamical systems, show that GeoIncNO achieves consistently strong prediction accuracy, improved rollout stability, and better spectral fidelity compared with competitive neural-operator baselines.

Phase-field modeling provides a powerful approach for predicting microstructure evolution but becomes computationally prohibitive for multicomponent and multiphase systems over large spatial and temporal scales. This work presents an AE-GCN-LSTM surrogate framework for long-horizon forecasting of microstructure evolution in the multicomponent AlCrFeNi high-entropy alloy system containing coexisting BCC and FCC phases. A multi-head autoencoder compresses the four elemental concentration fields and phase-field order parameter into latent representations, which are formulated as graphs for learning their spatial and temporal evolution. The framework accurately forecasts microstructure evolution over horizons extending to 3,000,000 simulation timesteps. Its robustness is systematically evaluated under previously unseen conditions without retraining, fine-tuning, or parameter adaptation. These evaluations include variations in FCC precipitate size and initial position, microstructures containing one, two, and five FCC precipitates, and complex phase interactions involving precipitate merging and splitting. Although trained only on 100 x 100 computational domains containing a single nominal alloy composition, the framework is successfully transferred to larger 256 x 256 and 512 x 512 systems and to previously unseen AlCrFeNi compositions. Across the evaluated configurations, the model preserves the dominant phase morphology and compositional evolution while providing computational speedups ranging from approximately 7200 to 62300 relative to conventional phase-field simulations. These results demonstrate that latent graph-based AE-GCN-LSTM forecasting provides a scalable and computationally efficient surrogate for long-horizon simulation of multicomponent, multiphase microstructures and offers a promising foundation for high-throughput alloy design.

Long-horizon conversion prediction under delayed feedback creates a two-clock, two-window learning problem in online advertising. A short base observation window releases recent clicks on the click clock before their outcomes mature, whereas conversions continue to arrive on the conversion clock throughout a longer target conversion window. The click clock provides timely but partially observed status supervision. The conversion clock reveals long-tail delays, but the delay composition within an arrival-time slice is weighted by historical click cohorts with different traffic volumes and target-window conversion rates. We present TWICE, a framework that factorizes long-horizon post-click conversion rate (CVR) into a target-window conversion probability and a grouped elapsed-delay cumulative distribution function (CDF). The two clocks provide complementary supervision. Click-clock records train the target-window CVR head through a current-status likelihood over the base observation window. Newly arrived conversions train the delay model on the conversion clock. To account for the cohort mixture, TWICE uses fixed click-time predicted CVR (pCVR) mass as cohort exposure in an arrival-conditioned likelihood. This accounts for differences in cohort traffic and conversion propensity. The resulting aggregate records are self-contained. A single learned CDF produces monotone predictions for all requested horizons up to the target conversion window. Serving requires neither historical lookup nor convolution. Experiments on a public benchmark and an industrial advertising dataset demonstrate the effectiveness of TWICE. In an online A/B test in Kwai's advertising system, TWICE increased expected revenue, revenue, and conversions by 2.486%, 1.858%, and 2.061%, respectively. It was subsequently deployed to full traffic.

Model-based active flow control requires predictive models that are accurate, stable, and fast enough for real-time optimisation. In controlled wake flows, this is often achieved through Reduced-Order Models (ROMs) that first compress high-dimensional velocity snapshots into a latent space and then learn a time- stepping predictor for the dynamics in the latent space. Here, we study how the choice of the spatial encoder affects the predictability of the resulting latent coordinates for wake flows under control inputs. Using two actuated 2D wake configurations, a simplified truck wake and the fluidic pinball, we compare Proper Orthogonal Decomposition (POD) against nonlinear Convolutional Autoencoders (CAEs) and two types of variational autoencoders for compression, and evaluate several temporal predictors based on Long Short-Term Memory networks. CAEs achieve higher compression efficiency and sharper short-term reconstructions, but they produce latent dynamics that are more irregular and with broadband spectral content. As a consequence, long-horizon forecasts degrade faster and show a higher probability of catastrophic divergence than POD-based models. POD yields smoother latent trajectories that are easier to learn and extrapolate, leading to more reliable predictions beyond the short- term regime. These results reveal a clear trade-off between compactness and forecast accuracy, and suggest that the stability of the latent dynamics prediction can outweigh maximal compression. This is particularly relevant for control strategies rooted in forecasts of the dynamics, such as model predictive control and reinforcement learning. The findings provide practical guidance for designing actuation-aware, hardware-feasible predictive ROMs for real-time flow control.

Neural operators provide data-driven mappings for modeling dynamical systems. Extending them to families of systems typically requires explicit conditioning variables such as physical parameters, geometries, or boundary conditions. In many real-world settings, these quantities are unobserved. Here, we formulate neural operator discovery (NOD) as the problem of learning both shared solution operators and system-specific variation directly from heterogeneous trajectories without access to labeled governing factors. We introduce a factorized latent-conditioning formulation that jointly learns a neural operator and a low-dimensional latent representation through factorized prediction, trajectory-decoupled sampling, and dimension selection. Across diverse systems, the learned latent representation captures the intrinsic dimensionality of system variation and organizes system instances in a smooth and approximately invertible latent structure aligned with the underlying governing factors. This organization enables generalization to previously unseen system instances, including zero-shot extrapolation across regimes and stable long-horizon prediction. These results establish an interpretable paradigm for operator learning in the absence of explicit factor supervision.

Long-horizon weather forecasting is a fundamental challenge in atmospheric science, for which autoregressive Deep Learning Weather Prediction (DLWP) has emerged as the primary paradigm. Although the autoregressive pipeline is highly scalable and flexible, its prediction errors grow rapidly over long forecasting horizons. In this work, we study this error growth phenomenon from both theoretical and empirical perspectives. Our analysis reveals that the growth is driven by a feedback loop between output errors and input distribution shifts. Specifically, the autoregressive process amplifies small initial output errors, which progressively corrupt subsequent input distributions, echoing the butterfly effect in atmospheric science and ultimately deteriorating forecasting accuracy over longer horizons. Furthermore, we show that this distributional shift originates at the earliest stage of inference, with out-of-distribution signatures detectable as early as the first autoregressive step. To mitigate this issue, we propose \textbf{Self-Output Fine-Tuning (SOFT)}, a plug-and-play strategy that leverages the model's own one-step predictions to calibrate the biased input distribution encountered at the first step. Extensive experiments demonstrate that, despite its simplicity, SOFT achieves state-of-the-art performance on long-horizon forecasting tasks and substantially reduces both prediction errors and distributional discrepancy. The success of SOFT highlights the importance of reexamining the fundamental pipeline of deep learning weather prediction, representing a critical pipeline advance for atmospheric science.

This study concentrates on predicting stock prices in the Egyptian market, focusing on the EGX30, an influential financial hub in the Middle East. While most research focuses on global stocks, there's a growing need to understand stock trends in developing countries like Egypt. The study compares different machine learning models for forecasting EGX30 trends, covering short and long-term predictions. Using historical EGX30 data, including metrics like root mean squared error, Mean Absolute Percentage Error, and coefficient of determination, models like K-Nearest Neighbours, random forest, extreme gradient boosting, long short-term memory networks, and gated recurrent unit networks were evaluated. The goal is to determine the most effective models for EGX30 prediction, considering Egypt's unique market dynamics. Insights from this study aid investors in making informed decisions. Results show that the Gated Recurrent Unit (GRU) outperformed the other models in the one-week, one-month, and two-months while the eXtreme Gradient Boosting (XGBoost) model outperformed others in the one-day predictions, highlighting their usefulness in predictive analysis for financial markets. The study also showed the importance of using the ensemble techniques, especially in the long-term predictions which proved better results reaching 5 times the GRU in the two-month predictions. Additionally, the study notes the surprisingly good performance of K-Nearest Neighbours (KNN) on long-term predictions, suggesting its enduring relevance and potential for future applications in the fintech domains.

We present a diffusion based model for asynchronous time series prediction, where the goal is to predict the next inter event time and event type. To address the inherent uncertainty of future events, we introduce ReDiTT, a retrieval augmented conditional diffusion transformer that operates in latent space. ReDiTT retrieves structurally similar latent sequences from a memory bank during both training and inference and incorporates them as reference conditions through cross attention. This retrieval based conditioning allows the model to attend to relevant temporal dynamics and provides global structural guidance for generation. As a result, ReDiTT stabilizes long horizon forecasting and improves sample diversity. Experiments on seven real world datasets demonstrate state of the art performance on next event prediction and long horizon forecasting. Our code is available at https://github.com/BorealisAI/ReDiTT.

Real-world time series exhibit complex dynamics characterized by multiple simultaneous temporal patterns: short-term fluctuations, periodic seasonal cycles, long-term trends, and irregular abrupt changes. However, many existing forecasting architectures rely on single-path temporal modeling--transformers capture long-range dependencies but smooth local variations, convolutions capture local patterns but have limited receptive fields, and linear models are efficient but cannot capture nonlinear dynamics. To address this, we introduce RhyMix (RHYthm MIXture), a hybrid neural architecture designed around a parallel dual-path modeling paradigm with adaptive gating mechanisms. RhyMix integrates two complementary encoding branches: (i) a Cyclic Path that incorporates explicit seasonal inductive bias through learnable cyclic embeddings, capturing predictable rhythmic patterns; and (ii) a lightweight Multi-Scale Temporal Convolutional Network with Channel Attention Path that employs multi-scale depthwise dilated convolutions to capture temporal dependencies across different receptive fields. A key innovation is the use of adaptive gating at multiple levels: a path gate dynamically combines four specialized forecasting heads (Direct, Trend-Seasonal Decomposition, Local Convolution, and Periodic Fusion) per sample and channel, while a hybrid gate adaptively balances the Cyclic and MSTCN-CA Paths based on input characteristics. This design ensures the model adapts to specific temporal patterns while maintaining linear complexity in sequence length, channels, and prediction horizon. Across extensive benchmarks on 12 real-world datasets for long-term forecasting, RhyMix achieves state-of-the-art performance on 10 of 12 datasets. The model remains lightweight (~40K params) with linear complexity and low-latency inference (<5ms),suitable for resource-constrained edge devices and real-time deployment.

World models are typically trained to predict discrete-time physical dynamics with a fixed step size baked into the model weights, preventing prediction at variable temporal resolutions. This matters for hierarchical planning, sim-to-real transfer, and scientific or game-engine applications that must query the same dynamics at multiple timescales. Hamiltonian Generative Networks (HGN) offer a principled path forward, grounding predictions in a continuous-time energy function that is, in principle, independent of the observation frame rate. In practice, however, their temporal generalization breaks down in non-conservative settings. We show that in externally forced, dissipative environments, HGN rollouts at step sizes beyond the training regime fail due to distinct failure modes, including latent magnitude growth driven by an unconstrained action-force map, and global truncation error accumulation from an under-resolved integrator. We identify a targeted fix for each mechanism and demonstrate stable dynamics prediction at temporal resolutions well outside the training distribution. In a detailed analysis, we recommend several strategies for enabling temporal generalization in continuous-time video generation.

Accurate long-term forecasting in complex systems is frequently compromised by dataset-level distribution shifts, where diverse underlying behavioral modes and evolving system states drive the dynamic multivariate time-series. While existing methods predominantly focus on local temporal shifts, they fail to explicitly model the global structural challenge where datasets are composites of distinct operational regimes. In this paper, we propose NEST, a specialized framework designed to model and recompose these evolving structures through a two-phase dense MoE architecture. NEST first facilitates structural specialization by partitioning the dataset into distinct operational regimes through unsupervised clustering in a principled moment-entropy space. We introduce a regime-oriented router mechanism that generates initial expert weights based on temporal content, subsequently refined through geometric modulation to regime centroids. Crucially, rather than acting as monolithic predictors, individual experts function as specialized kernels that capture regime-specific dynamics by evolving unique variate-attention patterns. Extensive evaluations on diverse benchmarks, including heterogeneous network traffic and physical phenomena, demonstrate that NEST consistently achieves state-of-the-art performance. Our code and datasets are available at https://github.com/Aaralshin/NEST

Camera-radar (CR) fusion is a practical sensing configuration for autonomous driving, but existing models are typically trained with task-specific supervision, limiting reusable representation learning. We present CRISP, a spatiotemporal CR backbone pretrained through forecasting-based representation learning. Given historical multi-view images and radar sweeps, CRISP learns a unified bird's-eye-view (BEV) representation by predicting future LiDAR point clouds. LiDAR is used only as privileged supervision during pretraining; the deployed model requires only camera and radar. To make forecasting-based pretraining effective for CR fusion, CRISP introduces an enhanced radar encoder, radar-enhanced temporal self-attention, and multimodal feature rendering with modality innovation gating. These components inject radar range and Doppler cues into BEV temporal propagation and allow BEV tokens to selectively incorporate camera and radar evidence. Experiments on nuScenes show that CRISP improves long-horizon point cloud forecasting and transfers effectively to downstream tasks, including 3D detection, tracking, online mapping, motion forecasting, future occupancy prediction, and planning, suggesting that predictive CR pretraining is a promising path toward scalable driving representations under practical sensor configurations. The project website is https://umfieldrobotics.github.io/CRISP.

Long-horizon behavior prediction aims to infer a user's next action based on a lengthy historical sequence, playing a crucial role in artificial intelligence field. The rise of large language models (LLMs) offers a promising direction for sequential behavior prediction, yet LLMs struggle with latent behavioral pattern induction and model-intrinsic cognitive biases when tackling long-horizon behavior prediction. Prior memory management methods follow a context-compression paradigm that attempts to address this task by alleviating the historical sequence burden, yet fail to resolve the core challenges. In this paper, we advocate a paradigm shift that reframes the lengthy historical sequence from a burden into a valuable resource to be exploited, and accordingly propose PraMem, which conducts beforehand practice over the lengthy historical sequence to build an experiential memory, thereby serving as the assisted input for accurate long-horizon behavior prediction. Extensive experiments across diverse tasks demonstrate that PraMem achieves superior performance than prior methods, and more in-depth analyses provide valuable insights into the mechanism and evolution of the experiential memory. Code: https://github.com/icip-cas/PraMem.

Hierarchical state-space models (HSSMs) offer a promising approach to long-horizon prediction by segmenting sequences into temporal chunks. However, their performance hinges on how chunk boundaries are determined. While prior HSSMs typically rely on fixed-length chunking or similarity-based boundary detection, these methods often misalign with the intrinsic temporal structure of the data. We argue that chunking should instead be driven by prediction errors, which more directly indicate when longer-range context becomes necessary. Nevertheless, integrating surprise-based chunking into HSSMs introduces critical challenges, including hierarchical collapse during end-to-end training and the absence of surprise signals during open-loop prediction. To address these issues, we propose Surprise-based Nested Temporal Abstraction (SUNTA), a method that employs a decoupled training strategy to preserve surprise signals and uses internal inconsistency as a top-down surprise metric to determine chunk boundaries within imagined rollouts. Experiments on video prediction tasks in 2D and 3D environments demonstrate that SUNTA outperforms baselines, uniquely maintaining accurate predictions over 250 timesteps, whereas all baselines degrade within the first 10 timesteps.

Different stages of manipulation tasks exhibit varying levels of difficulty, suggesting stage-dependent motion speeds and temporal prediction horizons. However, existing IL-based visuomotor policies typically imitate the execution speed of expert demonstrations and operate with a fixed temporal prediction horizon, limiting flexibility and overall task throughput. In this paper, we introduce AutoSpeed, a model-agnostic learning framework that enables existing visuomotor policies to predict trajectories with stage-adaptive motion speeds, without requiring speed or stage annotations. We treat future trajectories at different speeds as candidate optimization targets, evaluate each candidate using a composite cost that trades off prediction error against prediction horizon, and optimize the policy toward the minimum-cost candidate. With a fixed-length action sequence, speed modulation adjusts the effective temporal prediction horizon: simple stages are executed faster with a longer prediction horizon, whereas complex stages are executed more slowly with a shorter prediction horizon. Specifically, we implement speed modulation in the frequency domain via the discrete cosine transform (DCT), which enables smooth, non-integer speed scaling and thus preserves motion continuity. Extensive evaluations show that AutoSpeed substantially reduces task execution time while also improving success rates. Under the AutoSpeed framework, the inferred motion speeds exhibit a strong correspondence with task stages.

We propose a path-space formulation of prediction in AI world models. Rather than sequences of one-step conditional distributions, we argue that a world model implicitly defines a probability measure over future trajectories. In the local regime where latent dynamics admit an effective Markovian description, this path measure takes the Onsager-Machlup form. Within this framework, prediction (most probable trajectory), planning (constrained optimization), and uncertainty (fluctuations) emerge as operations on a single action functional. We decompose the latent dynamics into reversible and irreversible components and introduce operational measures of entropy production from model rollouts. In controlled small-scale attention-based models, we find that attention asymmetry is acquired during training in proportion to the irreversibility of the data. Symmetrizing the learned attention suppresses entropy production and selectively degrades long-horizon prediction of irreversible dynamics while preserving relaxational prediction. These results suggest that irreversibility may serve as a computational resource for predictive world models. More generally, the fundamental predictive object is a distribution over future paths rather than states.

Demand forecasting at the bottom of a retail hierarchy requires predicting tens of thousands of correlated long-horizon series across products, stores, and regions. Modern systems must scale across massive catalogs, capture shared demand dynamics, and remain interpretable enough to be trusted. Classical statistical methods need a separate model per series and are hard to manage at scale; deep autoregressive models struggle as the joint state grows to tens of thousands of dimensions; and recent graph-based forecasters, while capturing cross-entity dependencies, often produce opaque long-horizon forecasts. We propose GNBAN (Graph Neural Basis Attention Network), an end-to-end architecture combining heterogeneous graph representation learning with an interpretable basis-decomposition head. Retail data are represented directly as a heterogeneous graph derived from the relational schema, so a single model serves the entire catalog. Rather than predicting the horizon directly, GNBAN decomposes each forecast into trend, seasonal, and generic components. Its key innovation is a per-basis attention mechanism: each basis function keeps its own learnable query and retrieves information independently from the entity's historical neighborhood, letting different bases specialize to distinct temporal patterns while preserving interpretability. On two large-scale benchmarks, M5 Walmart and Favorita Grocery Sales, evaluated under matched protocols, GNBAN improves volume-weighted WRMSSE by roughly 4-5% over a matched graph baseline. Qualitative analysis shows the learned decomposition exposes trend, seasonal, and residual demand drivers without post-hoc explanation methods. These results demonstrate that scalable relational forecasting and interpretable forecast decomposition can be achieved together in a unified graph-based framework.

World models are increasingly used for planning, yet most analyses of rollout error assume vector-valued states and scalar error amplification. Many planning environments, however, are naturally graph-structured: agents, tools, skills, routes, and dependencies interact through evolving relations. In this work, we study how prediction errors accumulate in Graph World Models (GWMs). We formulate fixed-edge and dynamic-edge GWM rollouts under a unified state-action transition framework and derive topology-aware error bounds. For fixed-edge rollouts, we show that long-horizon node error separates into a topology factor, governed by the graph spectral radius, and a model factor, governed by layer spectral norms. For dynamic-edge rollouts, we introduce a joint node-edge error operator that captures feedback between feature prediction and structure prediction, revealing when edge errors amplify future message passing. Motivated by these bounds, we propose Error-Aware GWM, a training objective that combines spectral regularization, rollout consistency, and critical-node weighting. Across synthetic graph topologies and heterogeneous agent-graph testbeds, we find that rollout error and planning regret grow with horizon, that dynamic-edge training is necessary when structure evolves, and that Error-Aware GWM improves long-horizon stability without sacrificing one-step accuracy. Our results characterize when graph world models remain reliable under autoregressive planning and when topology makes them fail.

Long-term time series forecasting (LTSF) plays a crucial role in fields such as energy management, finance, and traffic prediction. Transformer-based models have adopted patch-based strategies to capture long-range dependencies, but accurately modeling shape similarities across patches and variables remains challenging due to scale differences. To address this, we introduce patch-mean decoupling (PMD), which separates the trend and residual shape information by subtracting the mean of each patch, preserving the original structure and ensuring that the attention mechanism captures true shape similarities. Futhermore, to more effectively model long-range dependencies and capture cross-variable relationships, we propose Trend Restoration Attention (TRA) and Proximal Variable Attention (PVA). The former module reintegrates the decoupled trend from PMD while calculating attention output. And the latter focuses cross-variable attention on the most relevant, recent time segments to avoid overfitting on outdated correlations. Combining these components, we propose PMDformer, a model designed to effectively capture shape similarity in long-term forecasting scenarios. Extensive experiments indicate that PMDformer outperforms existing state-of-the-art methods in stability and accuracy across multiple LTSF benchmarks. The code is available at https://github.com/aohu1105/PMDformer.

Accurate dynamics models are critical for informed decision-making in robotic systems, particularly for agile aerial vehicles operating under uncertainty. Neural network dynamics models are attractive for capturing complex nonlinear effects, but existing predictive approaches struggle with long-horizon forecasting because their autoregressive rollout mechanism amplifies errors over time. Joint Embedding Predictive Architectures (JEPAs) offer a compelling alternative by modeling dynamics in latent space, yet prior JEPA-style methods for robot navigation have been studied primarily for kinematic-level planning, with limited investigation in high-frequency control. In this work, we introduce the JEPA-style model for real-time quadrotor control. The proposed approach combines a latent dynamics model with a novel physics-inspired prober that maps frozen latents to interpretable state, enabling physically grounded long-horizon prediction. Additionally, we combine the learned model with a sampling-based optimal control solution to take advantage of its predictive capabilities for real-time control on embedded hardware. Finally, to reduce the dependence on expensive and unsafe real-world data collection, we develop a structured pipeline for automated dataset generation. Extensive open-loop and outdoor closed-loop experiments demonstrate accurate prediction, robust zero-shot sim-to-real transfer, and strong generalization across diverse operating conditions.

Recently, world models have emerged as a promising paradigm for building intelligent agents by learning predictive models that estimate future environment states conditioned on observations and actions. In particular, JEPA-style latent world models provide an efficient alternative to pixel space prediction by learning action-conditioned dynamics in compact representation spaces. However, existing latent world models typically rely on one-step prediction and must be recursively rolled out for long-horizon planning, which leads to compounding errors and a mismatch between training objectives and downstream planning tasks. To address this limitation, we propose Variable-length Latent World Models (VLWMs), a framework that learns to predict future latent states conditioned on action sequences of variable lengths. Instead of training only on one-step transitions, VLWMs directly model temporally extended dynamics, allowing the same predictor to evaluate action plans over different horizons. We further introduce a curriculum training strategy that progressively expands the action horizon, stabilizing optimization from short-range dynamics to long-range prediction. At test time, we design planning methods tailored to VLWMs to better exploit their variable-length predictive capabilities. Experiments on long-horizon control tasks show that VLWMs significantly improve latent space world models, achieving 13% average improvement over the state-of-the-art LeWM across different datasets, with especially large gains on tasks requiring extended planning. These results suggest that VLWM provides a simple yet effective paradigm for improving long-horizon prediction and planning in latent world models.

Simple linear and frequency-domain models remain surprisingly competitive in long-horizon time-series forecasting, and recent mechanistic evidence suggests that standard forecasting benchmarks may not require the dense superposed representations that make transformers powerful in other domains. This raises a substrate-level question: if the core forecasting operator is often low-complexity and approximately linear, does it need to be implemented as learned digital temporal mixing? We introduce HAMON, a passive diffractive optical forecasting core in which historical values are encoded onto an optical aperture, future positions are left dark, and cascaded trainable phase masks with free-space diffraction shape the forecast directly in the output field. At inference, prediction is performed by a single passive optical propagation pass with no trainable digital sequence-mixing layer. Across standard benchmarks, HAMON outperforms the strongest digital baselines considered on ETTm2 at all horizons and on ETTh2 at all but the longest horizon, improving MSE by up to 14% and doing so consistently across horizons rather than at isolated points. It is competitive on Weather and trails the strongest baselines on the remaining ETT settings and on the high-channel-count Traffic and Electricity datasets. Phase encoding, intensity-compatible readout, and phase-scrambling ablations, together with a TorchOptics cross-simulator check, indicate that the forecasts arise from the data-bearing optical field rather than from a digital forecasting head. Because the passive core uses standard Fourier optics, HAMON defines a concrete target for optical hardware and for passive physical sequence mixing.

Recent research is exploring self-organised traffic management as a solution for scaling to complex real-world networks. In such a system, trains predict their neighbourhood, produce traffic plan hypotheses, and agree via consensus with neighbours on a future traffic plan to be implemented. This paper investigates a structural parameter within this pipeline: the predictive neighbourhood horizon. The horizon is used by trains to identify future potential conflicts with neighbours, and to establish the local interaction topology, that is, the subset of trains to negotiate with. As the primary design variable, the horizon directly determines the size and density of the social interaction graph, whereas its impact on the complexity of local sub-problems and the distributed consensus dynamics represents a trade-off to be explored. Through a closed-loop simulation framework the study evaluates how variations of the horizon impact the overall decentralised coordination process, from initial conflict detection to distributed schedule consensus. The analysis focuses on investigating the potential trade-off introduced by the horizon choice: balancing local tractability and computational responsiveness with the need for global schedule coherence and feasibility in safety-critical environments. Contrary to intuition, our empirical results indicate that the short time horizons suffice, while long values compromise local tractability and computational responsiveness with no gain in global schedule optimality.

Robotic table tennis is a representative benchmark for high-speed, closed-loop robotic control in dynamic environments, where accurate and fast prediction of ball states is critical for reliable planning and control. Physics-based approaches rely heavily on accurate parameter identification and precise initial state, while learning-based methods often struggle to capture long-range temporal dependencies and are typically trained on limited or simulated data. We propose a transformer-based framework for table tennis ball state prediction that leverages attention mechanisms to model long-range temporal correlations directly from historical observations, without relying on explicit flight or bounce models. To support robust learning and generalization, we collected a large-scale real-world dataset from players of varying skill levels and diverse ball cannon configurations. The combination of a high-capacity transformer architecture and extensive real-world data enables accurate long-horizon forecasting. Building on this capability, we introduce a plug-and-play sim-to-real transfer strategy, Swap Predictor at Deployment (SPAD), which replaces the physics-based simulator used during training with the proposed real-world-trained predictor at deployment, improving the sim-to-real transferability of the policy without requiring retraining. We demonstrate that this simple substitution effectively narrows the sim-to-real gap while preserving the efficiency and scalability of simulation-based training.

Action chunking has become a standard design in modern robot policies, from diffusion/flow policies to vision-language-action models, where the policy predicts a sequence of actions and executes a fixed number of them instead of acting one step at a time. However, this paradigm relies on a key assumption: a fixed execution horizon. During chunk execution, the policy operates open-loop, which is particularly problematic for fine-grained manipulation tasks that require frequent replanning. In practice, the execution horizon is typically chosen through empirical tuning and is highly task-dependent. To this end, we propose Dynamic Execution Horizon Prediction (DEHP), an effective method that trains a lightweight execution-horizon prediction branch using online reinforcement learning while keeping the pretrained chunk policy completely frozen. This makes the method compatible with black-box chunk policies and isolates the effect of adapting the execution horizon from changes to the underlying action generator. Across our evaluations, DEHP improves the success rate of different high-precision and long-horizon manipulation tasks by a large margin. Our qualitative analysis further shows that DEHP predicts shorter execution horizons during fine-grained stages of the task and longer horizons during free-space motion. In this way, DEHP balances the efficiency of open-loop chunk execution with the reactivity of closed-loop single-step control. Project page: https://dehp-chunking.github.io/

Long-horizon autoregressive forecasting of oscillatory physical signals, such as seismograms, gravitational-wave strain, and similar wavefields is limited by error accumulation: as a causal model is fed its own outputs over hundreds of steps, small per-step errors compound into phase drift that pointwise metrics fail to detect. We ask when such rollout stays stable, using synthetic three-component seismograms as a physically structured testbed and the \textsc{SeismoGPT} autoregressive forecaster as the model under study. Through controlled, intra-architecture ablations evaluated on free-running rollout with paired significance tests, we isolate the contribution of each design choice. Multi-token prediction is the dominant stabilizer, accounting for almost the entire improvement over a single-token baseline ($+0.040$ median NCC); a horizon-embedding hybrid prediction head and a cross-horizon STFT-magnitude coherence loss each add a small but consistent further gain. Performance depends sharply on a context-ratio threshold near one, roughly the full P-S interval of observed signal, below which rollout generalization collapses. The dominant residual failure is a polarity inversion that a magnitude-based spectral loss cannot, by construction, penalize, identifying phase-aware objectives as the natural next step. We frame this as a controlled study of rollout stability on oscillatory wavefields, not a benchmark of forecasting architectures.

Reduced-order modeling of high-dimensional dynamical systems is often hindered by closure effects arising from unresolved variables, which can introduce non-Markovian dependence into the resolved dynamics. Motivated by the history-dependent memory term arising in the Mori--Zwanzig formalism, we recast non-Markovian closure modeling as a sequence modeling problem and propose the Mamba-Assisted Closure (MAC) framework. MAC employs a Mamba-based sequence model to predict the closure from the resolved trajectory and couples the learned closure with the reduced-order governing equations through a numerical integrator to advance the resolved variables in time. During training, the selective scan mechanism in Mamba enables efficient parallel sequence processing with linear scaling in sequence length, while autoregressive inference proceeds through recurrent state updates at essentially constant per-step cost. We evaluate MAC on four benchmark systems with complementary characteristics: the viscous Burgers' equation, the chaotic two-scale Lorenz '96 system, the 3-bus DeMarco--Zheng power-grid system, and the dispersive Korteweg--de Vries equation. Across these benchmarks, MAC consistently improves predictive accuracy and long-time rollout stability relative to the comparison models, demonstrating an effective and computationally scalable approach to non-Markovian closure modeling.

Multi-step time series forecasting (MSF) is commonly evaluated using point-wise error metrics such as mean squared error (MSE), implicitly treating the conditional mean as a sufficient target. We show that this can be misleading under conditional uncertainty, where the conditional expectation becomes unrepresentative of typical realized values at longer horizons. We formalize this effect through a conditional uncertainty gap and prove that whenever this gap is nonzero, no deterministic predictor can simultaneously minimize MSE and match the marginal distribution of realized futures. This establishes a fundamental, model-agnostic trade-off between point accuracy and marginal realism in MSF evaluation. Using controlled stochastic dynamical systems and nine real-world forecasting benchmarks, we empirically characterize the resulting accuracy--realism frontier and \textbf{quantify the practical cost of MSE-only model selection}. As conditional uncertainty increases with forecast horizon, the attainable set expands into a pronounced Pareto front, separating MSE-optimal but under-dispersed predictors from methods that trade accuracy for realistic marginal variability. \textbf{Across benchmarks, we find that small relaxations in MSE ($\boldsymbol{\le 5\%}$) frequently unlock disproportionate gains in marginal realism, with median improvements of $\mathbf{17.3\%}$ and gains exceeding $\mathbf{30\%}$ in some datasets.} We further show that common forecasting strategies systematically occupy different regions of this frontier: direct multi-output predictors concentrate near the accuracy-optimal extreme, while recursive strategies and sample-based inference favors marginal realism. Together, these results expose a structural failure mode of MSE-based evaluation in long-horizon forecasting and recast strategy and inference selection as navigation of an unavoidable accuracy--realism trade-off.

Time series forecasting has advanced rapidly, especially with the emergence of foundation models that show strong zero-shot performance on numerical extrapolation. However, in real-world forecasting settings, a statistically plausible baseline is rarely the final forecast used in practice. Before a forecast becomes decision-ready, it often needs to be revised using weakly structured business context such as holiday effects, campaign plans, external events, historical analogs, and expert feedback. This practical stage remains underexplored in the forecasting literature. In this paper, we formulate this stage as the \textbf{last-mile forecasting} problem and present an LLM-agent framework that sits on top of a forecasting backbone. Our system maintains a unified forecast workspace, invokes tools to retrieve contextual evidence, and converts reasoning trajectories into explicit forecast revision actions under structural safety constraints. It also supports long-horizon forecasting through map-reduce-style decomposition and post-hoc reflection through a memory bank. The resulting system is designed to be controllable and auditable. Through real-world case studies, we show how LLM agents can bridge the gap between statistical prediction and business-ready forecasting.

The diffusion based robot navigation world models are typically trained using parallel supervision, while autoregressive inference is employed during path planning. This results in a distribution shift between training and inference, which destabilizes the performance over long-horizon prediction. We propose AR Forcing, an autoregressive training strategy, which integrates the standard diffusion loss into the autoregressive training loop. At each step, the model uses its own predictions to update the context and optimize the single step noise prediction objective, thereby explicitly exposing the model to the inference state distribution during training. Our method does not require additional discriminators or distribution-matching losses, retains the original diffusion framework and sampler, and is easy to integrate. Experiments on multi-domain navigation datasets (RECON, SCAND, HuRoN, TartanDrive) show that compared with strong baselines, AR Forcing improved the consistency of generated images during long-horizon navigation and the accuracy of predicted trajectories, enhancing robustness of the model in complex known and unknown environments. We will release the code soon.

Non-prehensile robot manipulation is challenging due to discontinuous, long-horizon interactions between the robot and the objects it manipulates. Sampling-based model predictive control methods are effective with discontinuous contact but face challenges with finding promising trajectories in long-horizon planning. We propose a closed-loop object-informed (CLOI) method that splits the problem into object-level planning to find long-horizon object poses that lead the object to its goal, and robot-level planning to select robot actions that follow those poses. We use model predictive path integral (MPPI) control to solve the subproblems and couple their solutions through consensus on the object poses using the alternating direction method of multipliers (ADMM). The object plan is revised toward robot-realizable object trajectories, while the robot plan is aligned with the object poses the task requires. In planar pushing tasks with obstacles using an xArm6 manipulator, CLOI increases the success rate by 35% in simulation and 43% on hardware, compared to standard MPPI given the same computational budget.

While AI weather models excel at short-to-medium range forecasts (up to 15 days), they frequently suffer from ill-defined "instabilities" when rolled out over longer horizons. This work addresses the lack of a formal taxonomy by categorizing these failures into three distinct regimes: blow-up, drift, and loss of seasonality, through year-long rollouts of nine state-of-the-art AI weather models. Our analysis reveals that stability hinges on the treatment of small spatio-temporal scales: unstable models amplify high-frequency energy, while stable models act as denoisers when noise is added to their inputs. Far from reducing these models to mere stochastic parrots, our findings highlight that stable models generate unique weather trajectories, conditioned on the initial state. We verify our findings through ablation studies on architectural design choices, conducted using state-of-the-art Vision Transformer (ViT) AI weather model architectures.

Accurate long-range prediction of geophysical systems is difficult due to strongly nonlinear dynamics, the high computational cost of full-physics simulations, and the error accumulation that arise when one-step autoregressive surrogates are rolled out over decades. Deep neural network can serve as efficient emulators, but most are trained only for next-step prediction and often drift or become unstable as the forecast horizon grows. We propose a multi-horizon graph neural network emulator that learns state-to-state transitions from a single current time to multiple future lead times within one unified model. The physical domain is represented as a graph, where nodes correspond to spatial locations with time-varying geophysical attributes and edges encode local spatial interactions. Given the current graph state, the model predicts the future evolution of key fields, ice thickness and ice velocities at all nodes, using a shared graph backbone with separate output branches for each target variable. To improve stability, the network predicts state increments relative to the current state, which are then added back to reconstruct future states. Training jointly optimizes all lead times with a unified regression objective, and inference uses a coarse-to-fine rollout that advances with larger jumps and selectively refines with shorter jumps to reduce drift and avoid redundant computation. Experiments on multi-decadal Pine Island Glacier simulations show that our approach achieves higher long-range accuracy and improved stability than both (i) an initial-state baseline that predicts each future time directly from the starting state and (ii) a standard single-step autoregressive rollout, producing a more reliable emulator for downstream climate and sea-level studies.

Multi-step-ahead forecasts are often updated as new observations become available, since shorter forecast horizons typically improve forecast quality. However, such improvements come at the cost of forecast instability, i.e., variability in forecasts for the same target period. This instability can trigger costly changes to plans formulated based on the forecasts and may erode trust in the forecasting system. In this work, we integrate forecast stability alongside forecast quality into the training of distribution-free probabilistic time-series forecasting models, allowing us to control this trade-off. We propose a method for generating stabilized forecasted conditional quantile functions using regression splines parameterized by a neural network. This approach enables joint optimization of quality and stability, as it allows us to directly penalize dissimilarities arising from forecast updates. Furthermore, it allows assigning varying importance to stabilizing different parts of the forecast distributions (e.g., central parts vs. tails) to focus on the parts most relevant for the intended downstream use (e.g., the upper tail for inventory management). We empirically evaluate the proposed method on two datasets with different statistical properties and show that it can effectively reduce forecast instability without a substantial loss in forecast quality, and that it can target stabilization effort toward specific parts of the forecast distributions.

Learning-based surrogates have become increasingly effective for wave-field prediction, and neural operators in particular have shown strong performance within observed frequency regimes. However, higher-frequency prediction under scarce target supervision remains comparatively underexplored, especially in wave problems where higher-frequency data are substantially more expensive to simulate or measure than lower-frequency data. A central difficulty is that cross-frequency transfer is inherently asymmetric: coarse amplitude structure remains relatively stable across frequencies, whereas phase-sensitive oscillatory structure deteriorates much more rapidly as frequency increases. Motivated by this asymmetry, we propose APEX, Amplitude-anchored and Phase-prior-guided Enhancement from eXtrapolated coarse predictions, a framework for target-scarce higher-frequency wave-field prediction. A lower-frequency neural operator first provides a coarse prediction in the target-frequency regime, from which we retain only the amplitude as a transferable structural anchor. A conditional flow-matching enhancer then reconstructs the target higher-frequency field under the guidance of a Green's-function-inspired phase prior. Experiments on SimpleWave, Helmholtz, and Maxwell benchmarks show that APEX consistently outperforms direct lower-to-higher extrapolation, target-adapted operator, and joint generative baselines under limited target-frequency supervision. Our results suggest that reliable higher-frequency prediction of oscillatory wave fields should not rely on direct end-to-end transfer of the full complex field, but instead on explicitly reusing transferable coarse structure while separately recovering the missing oscillatory detail.

Long-horizon decision problems with cumulative damage couple locally attractive actions to globally adverse outcomes. We identify two orthogonal failure modes for policy-gradient methods on this class and propose a decomposition that separates them: \emph{completion} (reaching the terminal horizon rather than exiting via an implicit terminal constraint) and \emph{optimality} (matching the dynamic-programming reference given completion). Under PPO with a linear soft penalty, granting horizon access alone reduces the completion rate: the penalty's equilibrium drives the dominant-activity share to zero, while action-space restriction combined with horizon access achieves completion but leaves an optimality gap ($ΔM_{\text{final}} = 0.271$) that we trace to first-phase greedy commitment at the damage origin. We derive four testable predictions and evaluate them in two separately calibrated environments that share the same abstract structure but differ in domain, horizon, activity set, and calibration data: a 49-step bricklayer career and a 20-season NBA power-forward career. All four predictions replicate qualitatively. The horizon-invariance prediction is met at three of four tested horizons, with the exception at $H = 15$ consistent with the $H^*$ boundary ($H^* \in [6, 14]$ under the NBA parameters).

Learned physics simulators are often evaluated by one-step or short-horizon prediction error, but these metrics can miss failures in temporal composition and long-horizon rollout. For autonomous, state-complete systems, exact solution maps satisfy a semigroup law: direct evolution over $s+t$ should agree with evolution over $s$ followed by $t$. We propose normalized semigroup error as a post hoc, model-agnostic diagnostic comparing these direct and composed learned predictions. On one-dimensional heat and Burgers dynamics with time-conditioned ConvNet and FNO baselines, semigroup error is positively associated with rollout degradation, with trajectory-level Spearman correlation $ρ= 0.635$ and $95$ CI $[0.621, 0.649]$. Semigroup regularization has mixed effects, supporting semigroup consistency primarily as an evaluation diagnostic rather than a universally beneficial training objective.

Neural operators learn mappings from function-dependent inputs to solutions, providing an effective framework for solving partial differential equations (PDEs). For time-dependent PDEs, existing methods typically perform long-horizon prediction through autoregressive rollout directly in high-dimensional physical field spaces, where each predicted state is recursively fed back as the input for the next step. Although effective for short-term prediction, this autoregressive rollout and the lack of continuous-time modeling lead to progressive error accumulation over long-horizon rollouts. In this work, we propose Autoregression-Free Neural Operators (AFNO), which map the time evolution of PDEs into a latent space and model continuous-time vector fields within it. AFNO uses flow matching to learn the latent vector field, thereby enabling continuous evolution over extended horizons, avoiding autoregressive rollout and capturing dynamics under varying parameter configurations through explicit conditioning on physical parameters. Theoretical analysis and extensive experiments on six PDEs demonstrate that AFNO improves long-horizon prediction stability and consistently reduces rollout errors compared with the baselines.

Temporal surrogate models are effective for predicting chaotic dynamical systems where computational cost can be prohibitive. Several deep neural network architectures can be used for such purposes. In this work, a few commonly used architectures are compared using a common training protocol. The objective is to fairly assess the impact of model architectures for long-horizon prediction stability. Experiments are carried out for three problems, the double pendulum, the Kuramoto-Sivashinsky equations, and the Kolmogorov flow. The experiments are carried out with matching model capacity. Analysis is also carried out for a scenario where each model is individually optimized. It is observed that in both scenarios, the models exhibit categorical differences in long-horizon rollouts. For a concrete quantification, stepwise error injections and perturbation amplifications are analyzed using metrics such as local jacobian, relative one-step bias, and finite-time Lyapunov growth. Additionally, an attractor analysis is also conducted to assess how well the learned models replicate the underlying system geometry. An ablation study to isolate the impact of each component of a continuous-update architecture is also carried out. It is concluded that models that having integrator-like updates show lower bias and perturbation amplification yielding stable long-horizon rollout and more accurate predictions.

Irregular multivariate time series impose a trade-off for long-horizon forecasting: discrete methods can distort temporal structure via re-gridding, while continuous-time models often require sequential solvers prone to drift. To bridge this gap, we present 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 utilizing a stable modal parameterization motivated by stochastic port-Hamiltonian dynamics, and parameterize its mean evolution in the Laplace domain via learnable complex-conjugate poles, enabling direct evaluation over irregular timestamps. We also link continuous dynamics to irregular observations through renewal-averaging analysis, which maps sampling gaps to effective event-domain poles and motivates a gap-aware history summarizer. Extensive experiments show that LLapDiff improves over baselines in long-horizon forecasting, and its continuous-time generative nature supports missing-value imputation by querying the same model at historical timestamps. Code is available at https://github.com/pixelhero98/LLapDiffusion.

The rapid global expansion of solar photovoltaic (PV) capacity-reaching a record 597 GW in 2024-highlights the urgent need for robust forecasting models to mitigate the grid instability caused by the intermittent nature of solar irradiance. While deep learning-based direct forecasting using ground-based sky images (GSI) has emerged as a dominant approach, existing literature is often constrained by single-architecture evaluations and an exclusive focus on single-horizon (point) prediction. This paper proposes a transition from traditional single-horizon estimation toward a multi-horizon forecasting framework, leading to an architecture-independent improvement in accuracy. We hypothesize and demonstrate experimentally that joint optimization over a sequence of future values allows deep neural networks to better capture latent inter-step temporal dependencies by avoiding precocious convergence of the network in terms of both weight gradients and filter diversity. Leveraging this architecture-independent improvement that integrates sequential sky imagery with historical PV generation data, we evaluate the models' abilities to predict power output across multiple discrete future time steps simultaneously. Our methodology is validated through a comparative analysis across diverse deep learning architectures. The results demonstrate that this multi-horizon approach significantly enhances predictive accuracy and robustness across the entire forecast horizon while maintaining computational parsimony. By achieving superior performance with negligible overhead compared to single-horizon models, this work provides a scalable and efficient solution to improve the resilience of modern power grids.