Multi-Modal Time Series Prediction via Mixture of Modulated Experts

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

Echo State Networks for Time Series Forecasting: Hyperparameter Sweep and Benchmarking

This paper investigates the forecasting performance of Echo State Networks (ESNs) for univariate time series forecasting using a subset of the M4 Forecasting Competition dataset. Focusing on monthly and quarterly time series with at most 20 years of historical data, we evaluate whether a fully automatic, purely feedback-driven ESN can serve as a competitive alternative to widely used statistical forecasting methods. The study adopts a rigorous two-stage evaluation approach: a Parameter dataset is used to conduct an extensive hyperparameter sweep covering leakage rate, spectral radius, reservoir size, and information criteria for regularization, resulting in over four million ESN model fits; a disjoint Forecast dataset is then used for out-of-sample accuracy assessment. Forecast accuracy is measured using MASE and sMAPE and benchmarked against simple benchmarks like drift and seasonal naive and statistical models like ARIMA, ETS, and TBATS. The hyperparameter analysis reveals consistent and interpretable patterns, with monthly series favoring moderately persistent reservoirs and quarterly series favoring more contractive dynamics. Across both frequencies, high leakage rates are preferred, while optimal spectral radii and reservoir sizes vary with temporal resolution. In the out-of-sample evaluation, the ESN performs on par with ARIMA and TBATS for monthly data and achieves the lowest mean MASE for quarterly data, while requiring lower computational cost than the more complex statistical models. Overall, the results demonstrate that ESNs offer a compelling balance between predictive accuracy, robustness, and computational efficiency, positioning them as a practical option for automated time series forecasting.

Bonnet: Ultra-fast whole-body bone segmentation from CT scans

This work proposes Bonnet, an ultra-fast sparse-volume pipeline for whole-body bone segmentation from CT scans. Accurate bone segmentation is important for surgical planning and anatomical analysis, but existing 3D voxel-based models such as nnU-Net and STU-Net require heavy computation and often take several minutes per scan, which limits time-critical use. The proposed Bonnet addresses this by integrating a series of novel framework components including HU-based bone thresholding, patch-wise inference with a sparse spconv-based U-Net, and multi-window fusion into a full-volume prediction. Trained on TotalSegmentator and evaluated without additional tuning on RibSeg, CT-Pelvic1K, and CT-Spine1K, Bonnet achieves high Dice across ribs, pelvis, and spine while running in only 2.69 seconds per scan on an RTX A6000. Compared to strong voxel baselines, Bonnet attains a similar accuracy but reduces inference time by roughly 25x on the same hardware and tiling setup. The toolkit and pre-trained models will be released at https://github.com/HINTLab/Bonnet.

Learnable Koopman-Enhanced Transformer-Based Time Series Forecasting with Spectral Control

This paper proposes a unified family of learnable Koopman operator parameterizations that integrate linear dynamical systems theory with modern deep learning forecasting architectures. We introduce four learnable Koopman variants-scalar-gated, per-mode gated, MLP-shaped spectral mapping, and low-rank Koopman operators which generalize and interpolate between strictly stable Koopman operators and unconstrained linear latent dynamics. Our formulation enables explicit control over the spectrum, stability, and rank of the linear transition operator while retaining compatibility with expressive nonlinear backbones such as Patchtst, Autoformer, and Informer. We evaluate the proposed operators in a large-scale benchmark that also includes LSTM, DLinear, and simple diagonal State-Space Models (SSMs), as well as lightweight transformer variants. Experiments across multiple horizons and patch lengths show that learnable Koopman models provide a favorable bias-variance trade-off, improved conditioning, and more interpretable latent dynamics. We provide a full spectral analysis, including eigenvalue trajectories, stability envelopes, and learned spectral distributions. Our results demonstrate that learnable Koopman operators are effective, stable, and theoretically principled components for deep forecasting.

LLM-Assisted Logic Rule Learning: Scaling Human Expertise for Time Series Anomaly Detection

Time series anomaly detection is critical for supply chain management to take proactive operations, but faces challenges: classical unsupervised anomaly detection based on exploiting data patterns often yields results misaligned with business requirements and domain knowledge, while manual expert analysis cannot scale to millions of products in the supply chain. We propose a framework that leverages large language models (LLMs) to systematically encode human expertise into interpretable, logic-based rules for detecting anomaly patterns in supply chain time series data. Our approach operates in three stages: 1) LLM-based labeling of training data instructed by domain knowledge, 2) automated generation and iterative improvements of symbolic rules through LLM-driven optimization, and 3) rule augmentation with business-relevant anomaly categories supported by LLMs to enhance interpretability. The experiment results showcase that our approach outperforms the unsupervised learning methods in both detection accuracy and interpretability. Furthermore, compared to direct LLM deployment for time series anomaly detection, our approach provides consistent, deterministic results with low computational latency and cost, making it ideal for production deployment. The proposed framework thus demonstrates how LLMs can bridge the gap between scalable automation and expert-driven decision-making in operational settings.

ParalESN: Enabling parallel information processing in Reservoir Computing

Reservoir Computing (RC) has established itself as an efficient paradigm for temporal processing. However, its scalability remains severely constrained by (i) the necessity of processing temporal data sequentially and (ii) the prohibitive memory footprint of high-dimensional reservoirs. In this work, we revisit RC through the lens of structured operators and state space modeling to address these limitations, introducing Parallel Echo State Network (ParalESN). ParalESN enables the construction of high-dimensional and efficient reservoirs based on diagonal linear recurrence in the complex space, enabling parallel processing of temporal data. We provide a theoretical analysis demonstrating that ParalESN preserves the Echo State Property and the universality guarantees of traditional Echo State Networks while admitting an equivalent representation of arbitrary linear reservoirs in the complex diagonal form. Empirically, ParalESN matches the predictive accuracy of traditional RC on time series benchmarks, while delivering substantial computational savings. On 1-D pixel-level classification tasks, ParalESN achieves competitive accuracy with fully trainable neural networks while reducing computational costs and energy consumption by orders of magnitude. Overall, ParalESN offers a promising, scalable, and principled pathway for integrating RC within the deep learning landscape.

Do Not Waste Your Rollouts: Recycling Search Experience for Efficient Test-Time Scaling

Test-Time Scaling enhances the reasoning capabilities of Large Language Models by allocating additional inference compute to broaden the exploration of the solution space. However, existing search strategies typically treat rollouts as disposable samples, where valuable intermediate insights are effectively discarded after each trial. This systemic memorylessness leads to massive computational redundancy, as models repeatedly re-derive discovered conclusions and revisit known dead ends across extensive attempts. To bridge this gap, we propose \textbf{Recycling Search Experience (RSE)}, a self-guided, training-free strategy that turns test-time search from a series of isolated trials into a cumulative process. By actively distilling raw trajectories into a shared experience bank, RSE enables positive recycling of intermediate conclusions to shortcut redundant derivations and negative recycling of failure patterns to prune encountered dead ends. Theoretically, we provide an analysis that formalizes the efficiency gains of RSE, validating its advantage over independent sampling in solving complex reasoning tasks. Empirically, extensive experiments on HMMT24, HMMT25, IMO-Bench, and HLE show that RSE consistently outperforms strong baselines with comparable computational cost, achieving state-of-the-art scaling efficiency.

From Observations to States: Latent Time Series Forecasting

Deep learning has achieved strong performance in Time Series Forecasting (TSF). However, we identify a critical representation paradox, termed Latent Chaos: models with accurate predictions often learn latent representations that are temporally disordered and lack continuity. We attribute this phenomenon to the dominant observation-space forecasting paradigm. Most TSF models minimize point-wise errors on noisy and partially observed data, which encourages shortcut solutions instead of the recovery of underlying system dynamics. To address this issue, we propose Latent Time Series Forecasting (LatentTSF), a novel paradigm that shifts TSF from observation regression to latent state prediction. Specifically, LatentTSF employs an AutoEncoder to project observations at each time step into a higher-dimensional latent state space. This expanded representation aims to capture underlying system variables and impose a smoother temporal structure. Forecasting is then performed entirely in the latent space, allowing the model to focus on learning structured temporal dynamics. Theoretical analysis demonstrates that our proposed latent objectives implicitly maximize mutual information between predicted latent states and ground-truth states and observations. Extensive experiments on widely-used benchmarks confirm that LatentTSF effectively mitigates latent chaos, achieving superior performance. Our code is available in https://github.com/Muyiiiii/LatentTSF.

TimeMar: Multi-Scale Autoregressive Modeling for Unconditional Time Series Generation

Generative modeling offers a promising solution to data scarcity and privacy challenges in time series analysis. However, the structural complexity of time series, characterized by multi-scale temporal patterns and heterogeneous components, remains insufficiently addressed. In this work, we propose a structure-disentangled multiscale generation framework for time series. Our approach encodes sequences into discrete tokens at multiple temporal resolutions and performs autoregressive generation in a coarse-to-fine manner, thereby preserving hierarchical dependencies. To tackle structural heterogeneity, we introduce a dual-path VQ-VAE that disentangles trend and seasonal components, enabling the learning of semantically consistent latent representations. Additionally, we present a guidance-based reconstruction strategy, where coarse seasonal signals are utilized as priors to guide the reconstruction of fine-grained seasonal patterns. Experiments on six datasets show that our approach produces higher-quality time series than existing methods. Notably, our model achieves strong performance with a significantly reduced parameter count and exhibits superior capability in generating high-quality long-term sequences. Our implementation is available at https://anonymous.4open.science/r/TimeMAR-BC5B.

ACFormer: Mitigating Non-linearity with Auto Convolutional Encoder for Time Series Forecasting

Time series forecasting (TSF) faces challenges in modeling complex intra-channel temporal dependencies and inter-channel correlations. Although recent research has highlighted the efficiency of linear architectures in capturing global trends, these models often struggle with non-linear signals. To address this gap, we conducted a systematic receptive field analysis of convolutional neural network (CNN) TSF models. We introduce the "individual receptive field" to uncover granular structural dependencies, revealing that convolutional layers act as feature extractors that mirror channel-wise attention while exhibiting superior robustness to non-linear fluctuations. Based on these insights, we propose ACFormer, an architecture designed to reconcile the efficiency of linear projections with the non-linear feature-extraction power of convolutions. ACFormer captures fine-grained information through a shared compression module, preserves temporal locality via gated attention, and reconstructs variable-specific temporal patterns using an independent patch expansion layer. Extensive experiments on multiple benchmark datasets demonstrate that ACFormer consistently achieves state-of-the-art performance, effectively mitigating the inherent drawbacks of linear models in capturing high-frequency components.