The PUR-1 Cyber-Physical Digital Twin

Digital twin technologies have the potential to improve operational flexibility and responsiveness capabilities of nuclear systems. To provide decision support, cyber event characterization, state estimation, predictive control, and real-time dynamic processing of operational data, however, an efficient digital twin needs to integrate multiple models (data-driven as well as physics-based) with explainability while at the same time maintain two-way synchronization with the physical facility at a time constant less than its operational cycle. In this work, we present the Purdue University Reactor One Digital Twin (PUR-1 DT), a cyber-physical digital twin with a complete high-fidelity physics-based and AI-driven virtual model stack (neutronics, thermal-hydraulics, point kinetics) which provides closed-loop explainable diagnostics, forecasting, predictive control, and action recommendation back to the reactor via two-way communications and a cyber-physical testbed. We demonstrate real-time synchronized state estimation and short-term forecasting over a full reactor operational cycle and conduct a series of benchmarking experiments to validate accuracy and latency. Our results show good agreement with experimental results and lay the groundwork for further development and experimental demonstration of DT-enabled functionalities in real-world facilities.

Sparse Koopman Autoencoders Identify Local Dynamical Regimes in Multibasin Systems

Koopman autoencoders (KAEs) seek a higher-dimensional latent representation in which nonlinear dynamics evolve linearly. However, many interesting systems have multiple basins of attraction, and both theoretical and empirical work has shown these multibasin systems cannot generally admit a single finite-dimensional global Koopman embedding under standard assumptions. We posit that encoders with a sparsity-inducing objective encouraging few active latent coefficients will provide latent supports as an inspectable basin-modeling principle for Koopman autoencoders. We use these encoders producing sparse latents in training Sparse Koopman Autoencoders (SKAEs) without basin labels or other regime annotations, and treat the learned latent supports as model-produced regime variables after training. Across a range of procedurally generated multibasin systems and chaotic flows, we show that SKAEs have superior forecasting performance compared to dense-latent KAEs. We also perform a mechanistic study that shows latent supports produced by SKAEs are both essential for the quality of the representation and useful for identifying basins on held-out basin interior states, whereas dense-latent KAEs collapse to an uninformative single family. These results identify sparse latents and their corresponding supports as label-free, interpretable regime variables for Koopman learning in nonlinear systems with multiple local dynamical laws.

How Proper Scoring Rules Shape LLM Forecasting

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

What Will This Copper Look Like Later? Forecasting Surface Appearance and Rendering It as a PBR Material

Digital design requires predicting how a metal surface will look later in its oxidation; this paper presents such a pipeline for copper. Given a fixed-camera observation, the system forecasts appearance 10 accelerated units ahead and converts it into the albedo, normal, roughness and metallic maps a renderer consumes. Forecasting is evaluated as an authoring tool would use it, on a copper specimen the system has not observed: an entire recording is held out, so training and checkpoint selection use one specimen and the test set is the whole of a second, recorded on a different day and condition. Under this protocol a learned spatio-temporal model with a monotone oxidation state, the most accurate forecaster within a single recording, is less accurate than copying the last observed frame on an unseen specimen, in both directions, as are three further trained architectures. The only forecaster that transfers is a closed-form global color extrapolation with no trained parameters, improving on copy-last-frame by 13.4% and 50.6%, with a margin that increases with horizon to +16.7% and +55.5% at t+10. Two controls qualify this: correcting every frame for the photometric drift measured on a non-oxidizing reference region leaves both margins intact, ruling out uncontrolled exposure as their source, and a moving-block bootstrap over the 6 independent windows each recording contains separates the larger margin from zero but leaves the smaller one not individually significant. The mechanism is measured: a learned susceptibility map encodes where corrosion begins on the training specimen and misleads on a new one, whereas the global color trajectory is what specimens share. The pipeline therefore deploys the closed-form forecaster for unseen specimens and the learned model only for continuing one already observed. Code, splits, protocol and leakage audit are released.

Technical Comparative Benchmarking Study: Advanced AI Hybrid Methods for Renewable Energy Farm Optimization and Forecasting

This study provides a comprehensive benchmarking of conventional machine learning (ML), ensemble learning, deep neural networks, recurrent architectures, Transformers, graph based models, and hybrid ensemble deep learning approaches under complementary renewable energy scenarios. Three datasets are considered: a large scale WEC dataset, a 16 WEC dataset, and operational 10 min SCADA measurements at the Penmanshiel wind farm. For structured WEC layout data, tree ensembles exhibited a clear advantage over conventional ML and neural predictors because randomized partitioning and boosting efficiently captured nonlinear layout power interactions without requiring explicit feature representation learning. The Extra Trees was the strongest model, achieving considerable results. Relative to the MLP baseline, this corresponds to an approximately 63.7% reduction in MAE, demonstrating the suitability of randomized tree ensembles for high dimensional structured WEC data. Also, STGCN reduced the MAE to approximately 167.0 kW and achieved R = 0.93 by explicitly learning spatial and temporal turbine interactions. The best overall forecasting accuracy was obtained by the RF BiLSTM hybrid, with an MAE=150.5 kW. Compared with standalone LSTM, this represents an approximately 75% reduction in MAE, while improving on STGCN by approximately 10.0%. Finally, the experiments reveal that no single AI architecture is universally optimal: randomized and boosted ensembles are particularly effective for structured WEC surrogate modeling, graph networks become advantageous when explicit spatial interactions dominate, and ensemble recurrent hybrids provide the strongest balance when nonlinear tabular relationships and temporal dynamics coexist.

LLM Agents for Time-Series: A Survey

LLM-based agents are increasingly being developed for time-series problems, but their design choices vary substantially across task settings. This survey adopts a problem-driven taxonomy that organizes these systems by the time-series problems they address rather than by isolated technical components. We group existing systems into four categories: forecasting and reasoning, augmentation and synthesis, anomaly detection and diagnosis, and decision support. Within each category, we examine how task requirements shape agent architecture, tool use, and memory design. We further summarize representative datasets and environments, and compare reported model performance under shared or closely related settings. Overall, this survey offers a task-oriented guide to designing LLM-based agents for time-series problems and identifies open gaps for future work.

NVExplain: Explaining Time Series Forecasting with Latent Trajectory Analysis and Structure-Preserving Surrogates

Time series forecasting models are widely used in high-stakes settings, yet their predictions remain difficult to interpret because existing post-hoc methods often ignore temporal dependence and fail to provide horizon-specific explanations. We propose a model-agnostic explainability framework that explains forecasting predictions by attributing each forecast horizon to temporally relevant historical lags. The framework models forecasting as a latent trajectory and introduces semantic flow to quantify how information evolves across time in the model's internal representations. By aggregating semantic flow, it constructs a lag-horizon attribution matrix that captures horizon-resolved temporal influence. To improve explainability, we further generate structure-preserving perturbations and fit sparse local surrogate models, producing human-readable and temporally coherent explanations. We evaluate the method using faithfulness and stability diagnostics across multiple benchmark datasets. Results show that the semantic-flow variant achieves competitive or superior faithfulness compared to standard post-hoc baselines, while being substantially more computationally efficient. Stability analysis further demonstrates that the explanations are robust and identifies regimes where interpretation should be applied with caution.

LLM-based Agents for Forecasting and Prediction: Methods, Training, Evaluation, and Applications

Large language models (LLMs) now support forecasting systems that combine language-based reasoning with temporal data, evidence retrieval, external tools, and iterative prediction. We investigate LLM-based forecasting agents, meaning systems in which a language model contributes to a scored prediction about a future or currently unobserved target. We organize architectures into three groups. Standalone LLM workflows operate on encoded time series or event context. Tool- and retrieval-augmented agents incorporate external evidence. Hybrid systems pair LLMs with statistical or foundation models. We then review training methods and evaluation protocols. We examine negative as well as positive evidence, including sensitivity to small input perturbations, ablations in which the LLM component does not improve accuracy, and benchmark gains that may reflect contamination instead of temporal reasoning. We cover applications in finance, weather, health, energy, and operations, and we summarize the benchmarks and datasets used for evaluation. The evidence indicates that measurement is a central limitation. Future work requires calibration under distribution shift, contamination-resistant live evaluation, explicit reporting of cost and accuracy together, and methods for handling feedback between deployed forecasts and the outcomes being forecast.

Do Time-Series Foundation Models Pay Off for Industrial Monitoring? A Cost-Aware Empirical Study

Industrial monitoring models must detect operationally relevant deviations while satisfying target-specific data, calibration, and resource constraints. Time-series foundation models (TSFMs) promise reusable representations and zero-shot forecasts, yet evidence for their deployment value remains mixed when task definitions are heterogeneous and lightweight baselines are competitive. This work presents a protocol-aware empirical assessment across three settings: a C-MAPSS degradation-risk proxy, normal-only training for anomalous-sound detection on MIMII, and BDG2 forecasting-residual diagnostics with synthetic target perturbations. We assess classical one-class methods, compact neural autoencoders, residual forecasters, MOMENT-small, Chronos-T5, and TimesFM 2.5 in terms of anomaly-ranking performance, risk-horizon sensitivity, residual forecasting and perturbation sensitivity, and local implementation cost. Across 100 C-MAPSS engines evaluated out of fold, TCN-AE reaches fold-weighted AUROC/AUPRC 0.9570/0.8960, compared with 0.7310/0.3080 for MOMENT reconstruction; paired engine-cluster bootstrap confidence intervals exclude zero for both differences. Across five matched MIMII pump evaluations, OCSVM also exceeds MOMENT reconstruction in AUROC and AUPRC. On a fixed 12-meter BDG2 panel, TimesFM 2.5 has the lowest aligned forecast error and the highest synthetic AUROC point estimate, although synthetic AUPRC is similar across TSFM and fitted residual models. Same-device measurements show that MOMENT incurs higher latency, peak allocated VRAM, and serialized state-dictionary size than TCN-AE. Under the evaluated frozen and zero-shot settings, TSFMs are task-dependent deployment options rather than default replacements for fitted lightweight models.

DAW: Dynamics-Aware Weighting for Deep Learning Forecasts of Chaotic Systems

Deep learning surrogates for forecasting chaotic dynamical systems suffer from catastrophic error accumulation over long-term autoregressive rollouts. This behavior is partly tied to the underlying systems: chaotic spatiotemporal systems, such as the Kuramoto-Sivashinsky (KS) equation, visit phase space unevenly - dominated by recurrent, low-dimensional quiescent states (e.g., near-laminar flows) and punctuated by rare, dynamically complex topological transitions (e.g., wave-merging events). Under a sample-wise uniform objective, standard neural surrogates allocate their finite capacity to the statistically numerous quiescent states, under-representing the transient regimes that trigger disproportionate, localized errors. Existing imbalanced-regression methods reweight samples by target-space density. However, statistical target-space rarity need not coincide with the intrinsic dynamical rarity - the recurrence geometry of the attractor that is the source of the imbalance. To address this, we introduce Dynamics-Aware Weighting (DAW), a data-centric objective reweighting framework. Using the local dimension $d$ from dynamical systems theory as an a priori measure of a state's active degrees of freedom, DAW reshapes the loss landscape to allocate representational capacity toward the sparse, high-$d$ regimes where forecast errors are systematically large. On the chaotic KS equation, DAW consistently outperforms uniform training, purely statistical density weighting, and its randomly permuted ablation, reducing long-term autoregressive error relative to all baselines. Event-level analysis shows that DAW achieves this by suppressing the localized error amplifications incurred during sharp jumps in $d$, which accompany complex physical processes such as wave-merging in the KS system.

Empirical Characterization of Learning Geometry in Hybrid Quantum Forecasting Models

We characterize the learning dynamics of a compact hybrid quantum forecasting model through comparison with a structurally aligned classical baseline. Using stationary harmonic-mixture and nonstationary chirp benchmarks with controlled spectral complexity and data availability, we analyze empirical Neural Tangent Kernel dynamics through kernel-target alignment, kernel drift, spectral concentration, and training loss. The classical model exhibits stronger early target alignment, whereas the hybrid model generally develops a less concentrated kernel spectrum and smaller kernel drift. Despite these distinct optimization geometries, both architectures attain similar held-out performance across the evaluated regimes. Notably, the hybrid model uses 125 trainable parameters compared with 281 for the classical baseline and reaches its validation-selected checkpoint earlier in 15 of 18 frequency conditions. A Fourier-augmented classical baseline does not reproduce the observed training behavior, while a controlled re-uploading ablation shows that repeated encoding systematically modifies both optimization and kernel geometry. These results demonstrate that comparable generalization can emerge from substantially different learning trajectories and that individual NTK diagnostics do not provide monotonic predictors of validation convergence. Rather than claiming a general quantum advantage, the study identifies architecture-dependent learning behavior that is masked by endpoint accuracy alone.

HLSR: Hybrid Live Forecast Selective Dynamic Vehicle Rerouting for Real-Time Congestion Avoidance

Urban traffic congestion reduces productivity and increases travel cost and emissions. Network-wide live travel-time shortest-path rerouting can be highly effective in simulation, but assumes that essentially every on-road vehicle is replanned every decision period. We propose HLSR, a selective hybrid live--forecast vehicle rerouting framework that fuses live edge speeds with short-horizon forecasts under limited intervention scope. Building on dual-threshold congestion detection, calibrated upstream selection, and driver-tailored travel-time prediction, HLSR further introduces approaching-vehicle expansion, travel-time-weighted k-shortest-path generation, and a horizon-dependent hybrid live--forecast segment speed used in multi-cost route allocation.

Causal Local States: Scalable Simultaneous Causal Network Inference and Forecasting for Dynamical Systems

Machine learning methods predict many real-world systems with remarkable accuracy, but they are typically treated as black boxes that offer no insight into which interactions drive the dynamics. Causal discovery methods reconstruct the interaction network from observational data, but without regard to whether the inferred structure supports prediction. Existing approaches combining both tasks rely on a single global hyperparameter, such as a causal threshold or a fixed neighborhood size, which cannot recover the structure of heterogeneous systems. Here we introduce causal local states (CLS), a framework that simultaneously infers an approximate Granger-causal interaction network and forecasts the system dynamics. For each node independently, we select the smallest set of neighbors that allows a predictive model to forecast the node near-optimally, and the resulting neighborhoods are then combined for a forecast of the full system. On three benchmarks of increasing difficulty, we achieve reconstruction of the underlying networks with high fidelity and forecasts on par with a model that is supplied with the true network, providing a step toward explainable and scalable forecasting of complex systems.

Rethinking Irregular Time Series Forecasting from the Perspective of Basis Functions

Irregular time series forecasting is crucial in many domains, such as healthcare and meteorological observation. However, due to the inherent characteristics of irregular time series, including sparse observations and non-uniform sampling, accurately predicting future dynamics remains challenging. In light of these two characteristics, many existing methods aggregate irregular observations into fixed-dimensional estimated response coefficients through predefined basis functions and use these coefficients as sequence representations. Nevertheless, this modeling paradigm still suffers from two key limitations: (i) a potential non-vanishing asymptotic bias caused by ignoring the sampling density of timestamps; and (ii) the limited adaptability of predefined basis functions to diverse temporal patterns. In this study, we propose a Debiased Neural Basis-Function Network (DNBNet) to address these challenges. Its core is a debiased neural basis-function response mechanism, which corrects asymptotic bias through importance sampling while parameterizing basis functions with neural networks to adapt to diverse temporal patterns. In addition, considering the sparsity of irregular data, we design a novel multi-scale decomposition module based on average pooling, together with a mass-aware fusion mechanism, to obtain richer representations. Finally, a dual-branch decoder is employed for forecasting. Extensive experiments on multiple real-world datasets demonstrate the effectiveness of DNBNet and its strong generalizability across diverse irregular time series scenarios. Our code can be obtained at https://github.com/hnu-vis/DNBNet.

Supervised Mixed-Frequency Learning for Macro-Financial Forecasting When Factors are Weak

Factor-MIDAS regressions forecast a low-frequency target by extracting common factors from a large panel of high-frequency predictors via principal component analysis (PCA). While PCA mitigates the curse of dimensionality, it relies on factor pervasiveness, an assumption often violated when factors are weak, as is common in macro-financial forecasting. We propose SsPCA-MIDAS, which integrates supervised scaled PCA (SsPCA) into the mixed-data sampling framework. We establish consistency and asymptotic normality under weak factors, permitting inference on the prediction target. Simulations show that SsPCA-MIDAS outperforms competing PCA-based and supervised methods, especially when weak factors are prevalent. Applying machine-learning techniques such as boosting to the cleaner factors it extracts yields further gains. An extensive application to U.S. macro-financial forecasting shows that SsPCA-MIDAS selects economically meaningful predictors and improves forecasts of GDP, inflation, unemployment, asset prices, and volatility.

Do Time-Series Forecasters Use the Right History: Recoverability, Recovery, and Functional Use of Temporal Delays

Forecast accuracy does not tell us which past inputs produced a prediction. We separate three questions for time-series models with known delay structure: can the true delay be recovered from the observed data, does the model report it, and does the forecast actually use the same history? We first derive input-conditioned recoverability measures that separate intrinsic ambiguity from model error. We then prove that a delay report can become arbitrarily reliable while forecast risk approaches the oracle even though the predictor still uses the wrong lag. This failure also appears in finite samples on the point-delay task: among forecasts with a correct delay report and normalized excess risk within 10\% of the oracle, the reported history is functionally unused under our matched masking test in 55.4\% of N-HiTS cases and 92.7\% of TCN cases. Finally, we show that routing the prediction through the reported history removes off-report bypass paths; a hard one-hot control achieves exact fixed-report alignment. The main conclusion is simple: a good forecast, even with a correct delay report, does not show that the model used the right history.

Predicting blood clot growth from sparse post-onset measurements with latent neural differential equations

Computational models of blood clotting improve understanding of thrombus formation, but their clinical application remains limited because many model inputs are difficult to measure and patient-specific data are often sparse. We present a computational framework based on latent neural differential equations that infers unknown model parameters from sparse measurements and forecasts thrombosis progression. We demonstrate the framework using data generated from a multiphysics blood-clotting model in which clot growth is governed by the coagulation cascade and diffusion. Four known biochemical inputs (fibrinogen and factors IX, VIII, and V), together with sparse early clot-size observations, are used to infer the tissue-factor parameter and predict subsequent clot growth. We compare seven probabilistic methods: stochastic neural ordinary differential equations (SNODE), stochastic neural functional differential equations (SNFDE), a latent neural-process baseline, a monotone probabilistic deep ensemble, empirical trajectory retrieval, PCA-ridge Gaussian posterior, and Gompertz-curve retrieval. SNODE achieved the best performance in inferring the unknown input and forecasting future clot-growth trajectories. SNFDE performed similarly and consistently outperformed the other non-differential models. Prediction accuracy improved as more observations became available, whereas longer forecasting horizons increased uncertainty and decreased accuracy. Latent neural differential equations thus effectively combine parameter inference and clot-growth forecasting from sparse measurements, providing a promising foundation for personalized thrombosis modeling.

WorldCup Arena: Prospective, Leakage-Free Evaluation of Frontier LLMs on a Live Tournament

Benchmarks that measure the forecasting ability of large language models are almost always retrospective: the event has happened, the answer is somewhere on the Web, and the evaluation must defend itself against memorisation. We report the opposite design. Over the 39 days of the 2026 FIFA World Cup, six frontier LLMs -- all with extended thinking and native server-side web search -- were asked before every kickoff, one match at a time, to fill in a seven-market prediction card for all 104 matches, plus 12 group winners and a pre-tournament outright pool; no answer existed when the question was asked, so the evaluation is leakage-free by construction rather than by filtering, and the frozen archive holds 4,494 scored predictions. What the tournament establishes is a set of behaviours the six systems share. On match outcome they average 63.9%, level with backing the bookmaker's favourite -- which is in fact what they usually do. They agree with one another far more often than they are right, so a majority vote adds nothing. They under-commit to draws and to goals, and crowd their scoreline picks onto a single prototypical result. Accuracy tracks how lopsided a fixture is rather than how much is known about it: it collapses in the closest ties, where the dossiers are richest, while questions about the tournament as a whole are answered well. On this task the current generation of frontier systems is not sharply differentiated: the standings hold up at the top and the bottom across the run and churn in the middle, and the margins stay narrow throughout. The briefing dossiers, fixtures and official results are released as a benchmark, together with the scoring code.

Traceable Multi-Agent System for Knowledge-Based Forecasting

Enterprise forecasting increasingly relies on autonomous agents that interpret documents, search for data, generate code, and revise models. While this autonomy helps build adaptive forecasting pipelines, it also makes it difficult for practitioners to inspect why a forecast changed, which evidence supported the change, and how data and modeling choices were revised. We present TraceMAS, an interactive demo system for traceable multi-agent forecasting. TraceMAS organizes agent outputs around two causal-loop representations: an Ideal Causal Loop Diagram (Ideal CLD), which captures key factors and their causal relations extracted from domain documents, and a Data-Grounded Causal Loop Diagram (Data-Grounded CLD), which links those factors to internal variables, external data, or documented proxies. The Data-Grounded CLD guides feature construction and model design while preserving the connection between textual evidence, data choices, and model revisions. We demonstrate TraceMAS on crude oil price forecasting. The demo interface allows users to compare forecasting iterations, inspect agent-level revisions, explore causal maps, review feature-data mappings and model architecture, and connect scenario forecasts to market narratives. This demonstration shows how autonomous forecasting agents can retain flexibility while making the evidence-to-forecast process inspectable.

Forecasting Revenue with its Customer-Base Drivers: When and Why Coordination Helps

Revenue forecasts guide acquisition budgets, demand planning, and customer-based valuations, yet an aggregate forecast does not show whether change reflects acquisition, repeat purchasing, spending per order, or offsetting movements. Using weekly transaction panels for 966 companies in 25 industries, the authors develop the Customer-Based Multi-task Transformer (CBMT), which learns shared structure, retains separate primitive forecasts, and aligns their combination with downstream revenue. CBMT's mean total-sales error is 30% below the strongest representative established customer-base benchmark. It is also 2.65% below a Transformer that forecasts total sales directly, although the paired difference is not statistically significant (p=.222), and it beats separately estimated single-task forecasts for 74.3% of firms. CBMT's source MAE is lower in 23 of 24 benchmark-by-outcome comparisons, with the remaining difference not statistically distinguishable from zero. Firms whose primitives co-move more strongly are more likely to benefit from joint forecasting; selected-family scenario-3 comparisons are consistent with gains from shared representation and revenue alignment but remain diagnostic rather than causal. Accuracy deteriorates for all models when customer-base dynamics are highly volatile, and CBMT's advantage narrows there. Calibration-period routing rules do not improve average accuracy over always deploying CBMT. The results show how coordinated customer-base forecasts support revenue planning and when they warrant greater caution.

Enhancing Irregular Time Series Forecasting with Continuous-Time Modeling Framework

Irregular multivariate time series are widely encountered in applications such as healthcare monitoring, human activity recognition, and environmental sensing. Their core challenges stem from asynchronous observations, non-uniform sampling intervals, and the fact that temporal patterns themselves carry critical dynamic information. Existing approaches either rely on discretization-based preprocessing (e.g., interpolation, imputation, or aggregation), which disrupts the underlying continuous-time semantics, or adopt continuous-time modeling via ODE-based frameworks, which typically require specialized architectures and incur substantial computational overhead due to numerical solvers. To address these limitations, we propose WrapFlow, a continuous-time modeling framework for irregular time series forecasting. On the input side, WrapFlow introduces Continuous-Time Tokenization, which directly encodes raw observation events and explicitly models long unobserved intervals via gap-aware tokens. The resulting continuous-time tokens are then processed by a standard Transformer backbone to capture long-range temporal dependencies. On the output side, we develop a simulation-free training paradigm for Residual Flow Matching, which learns conditional residual vector fields around base predictions while avoiding numerical-solver simulation and backpropagation during training. This design enables high-quality continuous forecasting using only a small number of fixed rollout steps at inference. Extensive experiments on multiple real-world datasets demonstrate that WrapFlow achieves state-of-the-art performance.

Complementary Matrix-Gated QKAN Fast-Weight Programmers for Quantum Dynamics Forecasting

Sequence models must decide what to write into memory and what to retain. In quantum and quantum-inspired sequence learning, nonlinear recurrent updates often require repeated circuit evaluations and sequential backpropagation through time, making long contexts costly. Gated fast-weight programmers (FWPs) based on quantum-inspired Kolmogorov-Arnold networks (QKANs) alleviate this bottleneck by storing context in time-varying fast parameters. However, their scalar gate applies one retention-write balance to every fast-state coordinate, forcing all parameters to share a memory timescale. We introduce Self-Modulating QKAN-based FWPs, which replace this broadcast gate with low-rank-generated element-wise modulation of the new-proposal branch, a bounded old-state branch, or both. We further propose Complementary Matrix Gating (CMG), which uses one sigmoid matrix gate to retain the old state and its complement to write the new proposal. CMG provides coordinate-wise memory control while preserving the bounded convex update and affine prefix-scan structure of scalar gating, at the modulation-head cost of a single-branch rule. We compare four self-modulating rules with scalar gating across four FWP architectures combining classical and QKAN-based slow and fast programmers. Across seven single-step forecasting benchmarks and five sequence lengths, CMG gives the most consistent improvements for architectures whose fast programmer incorporates a QKAN-based module. In direct multi-step forecasting of Jaynes-Cummings and transmon-resonator dynamics simulated with CUDA-Q Dynamics, CMG models maintain mean-squared errors on the order of 0.001 or lower across forecasting horizons of 4, 8, and 16 steps, while improving on their scalar-gated counterparts by at least 91.2%. These results establish coordinate-wise complementary modulation as a stable and effective update for QKAN-based FWPs.

LLM-SoccerArena: Benchmarking LLMs on Real-World Predictions in Sports

Large language models (LLMs) increasingly support decisions about uncertain future events, yet evaluating their ability to forecast real-world outcomes remains difficult. In particular, existing benchmarks are typically static and retrospective, and therefore cannot test how information is synthesized by LLMs to predict future events under uncertainty. We introduce LLM-SoccerArena (https://llm-soccerarena.com), a prospective live benchmark that evaluates how well LLMs forecast real-world sports events before the outcomes are known. LLM-SoccerArena provides (1) a prospective live benchmark protocol, (2) a public open-source platform, and (3) a factorial benchmark design together with tournament-related questions (e.g., which team will win). LLM-SoccerArena automatically records timestamped, schema-validated forecasts of unresolved events, together with prompts, model versions, tool traces, and costs. The factorial design varies along four dimensions: (1) model version (e.g., GPT-5.5, Claude Opus 4.8); (2) information access; (3) prompting strategy, and (4) forecast horizon. We demonstrate LLM-SoccerArena through a large-scale evaluation of the 2026 FIFA World Cup, in which seven LLMs generated forecasts for all 104 matches and 15 tournament-related questions. We provide a detailed analysis of model performance across information access, prompting strategy, and forecast horizon. As a result, LLM-SoccerArena provides new evidence about the forecasting performance of state-of-the-art LLMs. For example, LLMs with web access outperform those without, but only by a small margin (i.e., a 0.023 improvement in Brier score). Overall, LLM-SoccerArena provides a flexible, open-source platform for prospective benchmarking of unresolved events. LLM-SoccerArena will be continuously updated, and can be directly applied to future national and international tournaments and league competitions.

Adaptive Multi-Scale Forecasting and Gate-Localized Conformal Prediction for Multivariate Nonstationary Time Series

We propose ABF-T-GLCP, a model-agnostic framework for forecasting and uncertainty quantification in nonstationary multivariate time series. The central idea is to learn an adaptive predictive state representation for point forecasting and reuse it for conformal calibration. The forecasting module combines horizon-specific temporal experts through a learned gate and refines predictions using sparse predictive transfer across related series. The uncertainty module, Gate-Localized Conformal Prediction (GLCP), uses the learned gate state, together with temporal recency, to select locally relevant calibration residuals, thereby coupling uncertainty calibration to the predictive regimes used by the forecasting model. This shared representation allows point forecasts and prediction intervals to adapt consistently under evolving temporal dynamics while retaining the model-agnostic nature of conformal prediction and yielding approximate local coverage under mild stability conditions. Experiments on a large-scale high-frequency commodity forecasting benchmark show consistent gains in point forecasting accuracy and substantially narrower prediction intervals with empirical coverage close to the nominal level. Additional results indicate that the framework extends beyond the motivating financial application.

MissHyper: Restoring Clinical Synchronicity in Missingness-Guided Hypergraph Forecasting

Clinical irregular multivariate time series are shaped not only by physiological dynamics but also by the measurement process that determines when and what to observe. In event-centric models, however, co-timestamp structure can be flattened too early: measurements acquired at the same timestamp are embedded as isolated nodes, leaving local patient-state context unavailable until later message-passing layers. We study this pre-propagation representation bottleneck and address it by restoring co-timestamp context before message passing begins. We propose MissHyper, a missingness-guided hypergraph forecasting model with pre-propagation synchronicity restoration. MissHyper augments each event with a local support-density cue, aggregates co-timestamp records to recover patient-state context, and uses a missingness-guided gate to adaptively fuse node-specific evidence with the recovered context. Across PhysioNet 2012, MIMIC-III, and MIMIC-IV, MissHyper achieves consistent gains in multi-step forecasting and outperforms a strong hypergraph baseline. These results suggest that improving event initialization can benefit sparse clinical forecasting without requiring a redesigned downstream propagation architecture. Ablations indicate that snapshot restoration, adaptive fusion, and support-density encoding all contribute, pointing to event initialization as a critical design axis for sparse clinical forecasting.

Transformer-based Diffusion models for Hydrological Time Series Probabilistic Imputation and Forecasting

The modeling of hydrometeorological time series with limited observations is a key challenge in the monitoring of hydro-systems and water resources, as well as for flood or drought risk assessment. Due to the high variability of the underlying processes and the sparsity of available measurements, traditional statistical approaches often struggle to accurately represent their dynamics. In this context, recent advances in deep learning offer a promising direction for improving the representation and generation of complex temporal processes sampled at several observation sites. This study investigates the application of transformer-based diffusion models to the simulation and reconstruction of hydrological time series. The proposed framework is applied to the joint modeling of water quantity and quality at six sites spread across three adjacent headwater catchments located in North-East France on a limestone plateau covered by forests and field crops. The model is calibrated and validated using available observational data, which has been quality controlled and corrected for sensor drift and malfunction through collaborative efforts by LNE metrology expertise and Andra monthly quality control over more than 15 years. Its performance is compared with several established baseline approaches commonly used for time series modeling. Quantitative evaluation metrics are employed to assess the ability of the proposed method to reproduce key temporal characteristics of the observed signals in two settings: the imputation of incomplete time series and the forecasting of upcoming hydrological conditions. Results support the effectiveness of the transformer-based approach and highlight its capacity to capture and simulate the complex patterns present in hydrological data. In particular, the results indicate that diffusion models can efficiently sample realistic time series distributions under observation settings with variable missing data for both forecasting and imputation.

Zero-Shot Heart Rate Variability Forecasting from Consumer Wearables Using Time Series Foundation Models

Short-term Heart Rate Variability (HRV) forecasting could provide clinicians with actionable lead time for detecting autonomic dysfunction and adverse cardiac events. Consumer wearable devices generate fragmented, artifact-rich HRV signals that challenge conventional forecasting approaches. In this study, we evaluated the forecasting ability of three Time Series Foundation Models (TSFMs), TimesFM, Chronos, and MOIRAI, against traditional baselines (Mean, Exponential Smoothing, and Exponentially Weighted Moving Average) on real-world wearable data collected from 49 healthy individuals. To address data fragmentation, we introduce a variability-preserving imputation method that augments linear interpolation with locally adaptive stochastic noise, retaining physiological dynamics essential for accurate forecasting. The results show that TSFMs outperformed all baselines without fine-tuning, achieving average Mean Absolute Scaled Error (MASE) between 0.81 and 0.87 across TSFMs and both context lengths (32 and 64 time steps), with Chronos and TimesFM as the top models, though MOIRAI showed limited gains over baselines. With up to a 2-hour forecast horizon, the results establish a baseline for TSFMs' performance on a real-world dataset, highlighting domain-specific fine-tuning as a promising direction for clinical deployment.

Black-Mamba: Biologically-Inspired Leaky Accumulation for Conceptual Knowledge under Distribution Drift

Forecasting under real-world conditions is inherently non-stationary, as the conditional distribution of future observations evolves over time. Recent test-time adaptive sequence models address this challenge by updating internal states during inference, but tie adaptation to instantaneous prediction errors or surprise. This coupling can conflate persistent distribution shift with stochastic innovations, leading to unnecessary updates and inefficient adaptation. We introduce Black-Mamba, a test-time adaptive forecasting architecture that formulates online adaptation as evidence-gated state tracking under distribution drift. The model augments a base predictor with a dynamic memory updated when temporally accumulated surprisal provides sufficient evidence of a regime change. This turns adaptation into a selective, event-driven process rather than a continuous one. Across multiple forecasting benchmarks with non-stationary dynamics, Black-Mamba achieves competitive or improved predictive performance compared to existing test-time adaptation methods while significantly reducing the number of memory updates during inference. Together with mathematical analysis and biological evidence, these results suggest that accumulated surprisal provides a principled signal for distinguishing persistent drift from transient noise, yielding more efficient and robust adaptation.

FIFA World Cup 2026 as a Contamination-Free Benchmark for LLM Forecasting Agents: Four Models, a Bookmaker, and 104 Matches

We introduce WC2026-Agents, a benchmark and dataset for evaluating large language models (LLMs) as autonomous forecasting agents on real, future events. For every one of the 104 matches of the 2026 FIFA World Cup, four frontier models -- Claude Opus 4.8, ChatGPT (GPT-5.5, high reasoning), Gemini 3.1 Pro, and Grok (Expert Mode) -- ran an identical search-act-reflect loop: gather evidence with a web tool, commit to a 1X2 (team-A win / draw / team-B win) distribution and a virtual 100-USD bet, and, after the match, reflect given only the final score. Because every match kicked off after the models' training cutoffs, the benchmark is contamination-free by construction. Crucially, we pair the four agents with a fifth competitor drawn from the same information environment -- the pre-match betting market -- collected as per-match 1X2 odds, giving an economically grounded baseline and letting us score not just what an agent predicts but what it does with money. The release contains 416 forecasts and 414 reflections with verbatim reasoning, ground truth (including penalty shootouts), odds, and a reproducible evaluation suite. A reference evaluation surfaces findings that raw accuracy hides: the four agents issue an identical top pick in 92% of matches and none beats the market's Brier score; indeed, a naive flat stake on the market favorite out-earns all four agents. Yet the agents diverge sharply as decision-makers: betting return-on-investment ranges from -18% to +10%, fading the market is unprofitable for all four, the share of forecasts that cite the market ranges from 12% to 100%, and self-reported error rates on wrong picks range from 36% to 86%. The benchmark thus measures calibration, decision quality, and self-knowledge -- axes on which frontier models differ even when their predictions do not. Data and code: https://github.com/graphuofm/FIFA2026LLM

Hindcast: Replaying Prediction Markets to Evaluate LLM Forecasters

Forecasters are evaluated by backtesting, which replays resolved questions and grades the probability the system would have assigned before the outcome was known. For LLMs, two channels leak the answer into this test. A model that retrieves can surface reports written after the event, turning forecasting into a lookup, and each new model is trained on data closer to the event, so a question that lay in the future for last year's models sits inside this year's training data. Either way, the test grades recall while claiming to grade foresight. We introduce Hindcast, which closes both leaks by grading a model as if it stood at a chosen past date $t_0$, before the outcome existed in either channel. Hindcast replays resolved Polymarket prediction markets against a frozen snapshot of public Reddit, lets the model read only posts written before $t_0$, and scores each forecast against both what happened and the market's own price at $t_0$, itself a human forecast made from the same past information. Because the cutoff is set per market and the snapshot never changes, the evaluation re-runs on new markets as models improve, without going stale. Once the leak is closed, retrieval still helps most models, but only where Reddit discussed the event beforehand. Where the archive carried only speculation, retrieval hurts.