Daily Papers

Understanding diffuse Galactic radio emission is interesting both in its own right and for minimizing foreground contamination of cosmological measurements. Cosmic Microwave Background experiments have focused on frequencies > 10 GHz, whereas 21 cm tomography of the high redshift universe will mainly focus on < 0.2 GHz, for which less is currently known about Galactic emission. Motivated by this, we present a global sky model derived from all publicly available total power large-area radio surveys, digitized with optical character recognition when necessary and compiled into a uniform format, as well as the new Villa Elisa data extending the 1.4 GHz map to the entire sky. We quantify statistical and systematic uncertainties in these surveys by comparing them with various global multi-frequency model fits. We find that a principal component based model with only three components can fit the 11 most accurate data sets (at 10, 22, 45 & 408 MHz and 1.4, 2.3, 23, 33, 41, 61, 94 GHz) to an accuracy around 1%-10% depending on frequency and sky region. Both our data compilation and our software returning a predicted all-sky map at any frequency from 10 MHz to 100 GHz are publicly available at http://space.mit.edu/home/angelica/gsm .

In this paper, we introduce FITS, a lightweight yet powerful model for time series analysis. Unlike existing models that directly process raw time-domain data, FITS operates on the principle that time series can be manipulated through interpolation in the complex frequency domain. By discarding high-frequency components with negligible impact on time series data, FITS achieves performance comparable to state-of-the-art models for time series forecasting and anomaly detection tasks, while having a remarkably compact size of only approximately 10k parameters. Such a lightweight model can be easily trained and deployed in edge devices, creating opportunities for various applications. The code is available in: https://github.com/VEWOXIC/FITS

Missing values, irregularly collected samples, and multi-resolution signals commonly occur in multivariate time series data, making predictive tasks difficult. These challenges are especially prevalent in the healthcare domain, where patients' vital signs and electronic records are collected at different frequencies and have occasionally missing information due to the imperfections in equipment or patient circumstances. Researchers have handled each of these issues differently, often handling missing data through mean value imputation and then using sequence models over the multivariate signals while ignoring the different resolution of signals. We propose a unified model named Multi-resolution Flexible Irregular Time series Network (Multi-FIT). The building block for Multi-FIT is the FIT network. The FIT network creates an informative dense representation at each time step using signal information such as last observed value, time difference since the last observed time stamp and overall mean for the signal. Vertical FIT (FIT-V) is a variant of FIT which also models the relationship between different temporal signals while creating the informative dense representations for the signal. The multi-FIT model uses multiple FIT networks for sets of signals with different resolutions, further facilitating the construction of flexible representations. Our model has three main contributions: a.) it does not impute values but rather creates informative representations to provide flexibility to the model for creating task-specific representations b.) it models the relationship between different signals in the form of support signals c.) it models different resolutions in parallel before merging them for the final prediction task. The FIT, FIT-V and Multi-FIT networks improve upon the state-of-the-art models for three predictive tasks, including the forecasting of patient survival.

Time series foundation models have demonstrated impressive performance as zero-shot forecasters. However, achieving effectively unified training on time series remains an open challenge. Existing approaches introduce some level of model specialization to account for the highly heterogeneous nature of time series data. For instance, Moirai pursues unified training by employing multiple input/output projection layers, each tailored to handle time series at a specific frequency. Similarly, TimesFM maintains a frequency embedding dictionary for this purpose. We identify two major drawbacks to this human-imposed frequency-level model specialization: (1) Frequency is not a reliable indicator of the underlying patterns in time series. For example, time series with different frequencies can display similar patterns, while those with the same frequency may exhibit varied patterns. (2) Non-stationarity is an inherent property of real-world time series, leading to varied distributions even within a short context window of a single time series. Frequency-level specialization is too coarse-grained to capture this level of diversity. To address these limitations, this paper introduces Moirai-MoE, using a single input/output projection layer while delegating the modeling of diverse time series patterns to the sparse mixture of experts (MoE) within Transformers. With these designs, Moirai-MoE reduces reliance on human-defined heuristics and enables automatic token-level specialization. Extensive experiments on 39 datasets demonstrate the superiority of Moirai-MoE over existing foundation models in both in-distribution and zero-shot scenarios. Furthermore, this study conducts comprehensive model analyses to explore the inner workings of time series MoE foundation models and provides valuable insights for future research.

Long-term Time Series Forecasting (LTSF) is critical for numerous real-world applications, such as electricity consumption planning, financial forecasting, and disease propagation analysis. LTSF requires capturing long-range dependencies between inputs and outputs, which poses significant challenges due to complex temporal dynamics and high computational demands. While linear models reduce model complexity by employing frequency domain decomposition, current approaches often assume stationarity and filter out high-frequency components that may contain crucial short-term fluctuations. In this paper, we introduce MMFNet, a novel model designed to enhance long-term multivariate forecasting by leveraging a multi-scale masked frequency decomposition approach. MMFNet captures fine, intermediate, and coarse-grained temporal patterns by converting time series into frequency segments at varying scales while employing a learnable mask to filter out irrelevant components adaptively. Extensive experimentation with benchmark datasets shows that MMFNet not only addresses the limitations of the existing methods but also consistently achieves good performance. Specifically, MMFNet achieves up to 6.0% reductions in the Mean Squared Error (MSE) compared to state-of-the-art models designed for multivariate forecasting tasks.

Recent years have witnessed the emergence of multivariate modeling using time series foundation models (TSFMs), which achieve advanced zero-shot generalization. Modern multivariate TSFMs are predominantly pretrained on multivariate synthetic data, which is easier to scale but may fail to capture the complex temporal dynamics and cross-variable relationships present in real-world time series. This raises a key question: Whether and to what extent the leading TSFMs trained with the real-world corpus perform better than those trained with synthetic data? To answer this, we establish the RMISC corpus, a considerably large-scale, high-quality, openly accessible, real-world, and multivariate time series archive that contains around 200 datasets and 142 billion time points across diverse domains. Furthermore, we pretrain four advanced TSFMs on univariate, synthetic multivariate, and real-world multivariate data and evaluate their zero-shot generalization capabilities on standard in-distribution and out-of-distribution benchmarks. Experimental results show that incorporating real-world multivariate data predominantly improves the generalization performance for both univariate and multivariate TSFMs. These results provide a deeper understanding of how real-world multivariate data contributes to the development of stronger TSFMs.

Pre-trained foundation models (FMs) have shown exceptional performance in univariate time series forecasting tasks. However, several practical challenges persist, including managing intricate dependencies among features and quantifying uncertainty in predictions. This study aims to tackle these critical limitations by introducing adapters; feature-space transformations that facilitate the effective use of pre-trained univariate time series FMs for multivariate tasks. Adapters operate by projecting multivariate inputs into a suitable latent space and applying the FM independently to each dimension. Inspired by the literature on representation learning and partially stochastic Bayesian neural networks, we present a range of adapters and optimization/inference strategies. Experiments conducted on both synthetic and real-world datasets confirm the efficacy of adapters, demonstrating substantial enhancements in forecasting accuracy and uncertainty quantification compared to baseline methods. Our framework, AdaPTS, positions adapters as a modular, scalable, and effective solution for leveraging time series FMs in multivariate contexts, thereby promoting their wider adoption in real-world applications. We release the code at https://github.com/abenechehab/AdaPTS.

Time-series forecasting is crucial for numerous real-world applications including weather prediction and financial market modeling. While temporal-domain methods remain prevalent, frequency-domain approaches can effectively capture multi-scale periodic patterns, reduce sequence dependencies, and naturally denoise signals. However, existing approaches typically train model components for all frequencies under a unified training objective, often leading to mismatched learning speeds: high-frequency components converge faster and risk overfitting, while low-frequency components underfit due to insufficient training time. To deal with this challenge, we propose BEAT (Balanced frEquency Adaptive Tuning), a novel framework that dynamically monitors the training status for each frequency and adaptively adjusts their gradient updates. By recognizing convergence, overfitting, or underfitting for each frequency, BEAT dynamically reallocates learning priorities, moderating gradients for rapid learners and increasing those for slower ones, alleviating the tension between competing objectives across frequencies and synchronizing the overall learning process. Extensive experiments on seven real-world datasets demonstrate that BEAT consistently outperforms state-of-the-art approaches.

Existing video recognition algorithms always conduct different training pipelines for inputs with different frame numbers, which requires repetitive training operations and multiplying storage costs. If we evaluate the model using other frames which are not used in training, we observe the performance will drop significantly (see Fig.1), which is summarized as Temporal Frequency Deviation phenomenon. To fix this issue, we propose a general framework, named Frame Flexible Network (FFN), which not only enables the model to be evaluated at different frames to adjust its computation, but also reduces the memory costs of storing multiple models significantly. Concretely, FFN integrates several sets of training sequences, involves Multi-Frequency Alignment (MFAL) to learn temporal frequency invariant representations, and leverages Multi-Frequency Adaptation (MFAD) to further strengthen the representation abilities. Comprehensive empirical validations using various architectures and popular benchmarks solidly demonstrate the effectiveness and generalization of FFN (e.g., 7.08/5.15/2.17% performance gain at Frame 4/8/16 on Something-Something V1 dataset over Uniformer). Code is available at https://github.com/BeSpontaneous/FFN.

Accurate and efficient long-term multivariate time series forecasting requires capturing recurring temporal structure while keeping inference cheap across many variables and horizons. Frequency-space models represent long-range and periodic variation compactly, but they typically process the real and imaginary spectral components as weakly coupled streams and treat periodic cues as ordinary input features, even when such cues are unreliable. This paper proposes FRWKV-Plus, a lightweight periodic-aware frequency-space forecasting model built on the efficient FRWKV backbone. FRWKV-Plus introduces a cross-branch spectral gate that reweights each spectral branch using a summary of its sibling branch, and a trust-gated residual correction that converts compact within-period context into a bounded, sign-flexible adjustment of these gates under a learned, data-dependent trust score. By construction, the correction is identity-preserving at initialization and strictly bounded, so periodic evidence can refine but never dominate or invert the base interaction. On seven standard benchmarks, FRWKV-Plus is consistently competitive with strong linear, frequency-domain, recurrent-style, and Transformer-based forecasters while preserving the lightweight profile of the backbone. Controlled three-seed ablations show that each component contributes, that the benefit is modest on strongly periodic data and pronounced on the harder Exchange and ILI datasets, and that the within-period context is the most influential single component. The implementation is publicly available at https://github.com/yangqingyuan-byte/FRWKV-plus.

Frequency analysis is useful for understanding the mechanisms of representation learning in neural networks (NNs). Most research in this area focuses on the learning dynamics of NNs for regression tasks, while little for classification. This study empirically investigates the latter and expands the understanding of frequency shortcuts. First, we perform experiments on synthetic datasets, designed to have a bias in different frequency bands. Our results demonstrate that NNs tend to find simple solutions for classification, and what they learn first during training depends on the most distinctive frequency characteristics, which can be either low- or high-frequencies. Second, we confirm this phenomenon on natural images. We propose a metric to measure class-wise frequency characteristics and a method to identify frequency shortcuts. The results show that frequency shortcuts can be texture-based or shape-based, depending on what best simplifies the objective. Third, we validate the transferability of frequency shortcuts on out-of-distribution (OOD) test sets. Our results suggest that frequency shortcuts can be transferred across datasets and cannot be fully avoided by larger model capacity and data augmentation. We recommend that future research should focus on effective training schemes mitigating frequency shortcut learning.

Multivariate time series forecasting (MTSF) seeks to model temporal dynamics among variables to predict future trends. Transformer-based models and large language models (LLMs) have shown promise due to their ability to capture long-range dependencies and patterns. However, current methods often rely on rigid inductive biases, ignore intervariable interactions, or apply static fusion strategies that limit adaptability across forecast horizons. These limitations create bottlenecks in capturing nuanced, horizon-specific relationships in time-series data. To solve this problem, we propose T3Time, a novel trimodal framework consisting of time, spectral, and prompt branches, where the dedicated frequency encoding branch captures the periodic structures along with a gating mechanism that learns prioritization between temporal and spectral features based on the prediction horizon. We also proposed a mechanism which adaptively aggregates multiple cross-modal alignment heads by dynamically weighting the importance of each head based on the features. Extensive experiments on benchmark datasets demonstrate that our model consistently outperforms state-of-the-art baselines, achieving an average reduction of 3.28% in MSE and 2.29% in MAE. Furthermore, it shows strong generalization in few-shot learning settings: with 5% training data, we see a reduction in MSE and MAE by 4.13% and 1.91%, respectively; and with 10% data, by 3.62% and 1.98% on average. Code - https://github.com/monaf-chowdhury/T3Time/

With the rapid deployment of SCADA systems, how to effectively analyze industrial signals and detect abnormal states is an urgent need for the industry. Due to the significant heterogeneity of these signals, which we summarize as the M5 problem, previous works only focus on small sub-problems and employ specialized models, failing to utilize the synergies between modalities and the powerful scaling law. However, we argue that the M5 signals can be modeled in a unified manner due to the intrinsic similarity. As a result, we propose FISHER, a Foundation model for multi-modal Industrial Signal compreHEnsive Representation. To support arbitrary sampling rates, FISHER considers the increment of sampling rate as the concatenation of sub-band information. Specifically, FISHER takes the STFT sub-band as the modeling unit and adopts a teacher student SSL framework for pre-training. We also develop the RMIS benchmark, which evaluates the representations of M5 industrial signals on multiple health management tasks. Compared with top SSL models, FISHER showcases versatile and outstanding capabilities with a general performance gain up to 5.03%, along with much more efficient scaling curves. We also investigate the scaling law on downstream tasks and derive potential avenues for future works. FISHER is now open-sourced on https://github.com/jianganbai/FISHER

Pretrained time series foundation models (TSFMs) have enabled zero-shot forecasting on unseen target series. However, existing TSFMs often incur high computational cost and provide limited support for diverse variable types, often failing to account for covariates that exogenously influence target variability. To address these challenges, we propose CITRAS-FM, a tiny 7M-parameter TSFM that supports univariate, multivariate, and covariate-informed zero-shot forecasting with real-time CPU inference. Built on a patch-based, decoder-only Transformer, CITRAS-FM introduces Shifted Attention into the cross-variate module to effectively exploit known covariates accessible throughout the forecast horizon. Moreover, to enable covariate-aware pretraining despite the scarcity of covariate-rich corpora, we propose CovSynth, which synthesizes realistic covariates from decomposed components of target series. Experiments on fev-bench, spanning 100 tasks across various settings, demonstrate that CITRAS-FM achieves state-of-the-art zero-shot accuracy among sub-10M TSFMs while delivering sub-0.1-second CPU inference, offering a strong balance between forecasting accuracy and real-time deployability.

Diffusion models have achieved remarkable success in generative modeling, yet how to effectively adapt large pretrained models to new tasks remains challenging. We revisit the reconstruction behavior of diffusion models during denoising to unveil the underlying frequency energy mechanism governing this process. Building upon this observation, we propose FeRA, a frequency driven fine tuning framework that aligns parameter updates with the intrinsic frequency energy progression of diffusion. FeRA establishes a comprehensive frequency energy framework for effective diffusion adaptation fine tuning, comprising three synergistic components: (i) a compact frequency energy indicator that characterizes the latent bandwise energy distribution, (ii) a soft frequency router that adaptively fuses multiple frequency specific adapter experts, and (iii) a frequency energy consistency regularization that stabilizes diffusion optimization and ensures coherent adaptation across bands. Routing operates in both training and inference, with inference time routing dynamically determined by the latent frequency energy. It integrates seamlessly with adapter based tuning schemes and generalizes well across diffusion backbones and resolutions. By aligning adaptation with the frequency energy mechanism, FeRA provides a simple, stable, and compatible paradigm for effective and robust diffusion model adaptation.

We introduce TiRex-2, a recurrent xLSTM-based time series foundation model that generalizes the univariate TiRex to multivariate forecasting with both past and future covariates. Real-world forecasting is inherently sequential: observations arrive continuously, variables evolve jointly, and a subset of covariates is known ahead of time. Existing Transformer-based time series foundation models capture cross-variate dependencies but incur quadratic complexity in context length and require full-history recomputation as new observations arrive. TiRex-2 addresses these limitations through a memory-centric recurrent design that operates at constant per-patch cost under streaming. The model combines a bidirectional time mixer with an asymmetric grouped-attention variate mixer, enabling the integration of future-known covariates while preserving strict causality over target variables. To our knowledge, this is the first time series foundation model that achieves this combination of properties. To support scalable multivariate pretraining, we propose a synthetic coupling pipeline that composes diverse multivariate samples on the fly from large univariate corpora. Empirically, TiRex-2 achieves state-of-the-art zero-shot performance on GIFT-Eval and fev-bench, remains stable when streamed to arbitrary context lengths, and maintains constant inference cost per patch. The model uses 38.4M active parameters in univariate mode, with an additional 44.1M parameters activated for multivariate forecasting.

Periodic signals play an important role in daily lives. Although conventional sequential models have shown remarkable success in various fields, they still come short in modeling periodicity; they either collapse, diverge or ignore details. In this paper, we introduce a novel framework inspired by Fourier series to generate periodic signals. We first decompose the given signals into multiple sines and cosines and then conditionally generate periodic signals with the output components. We have shown our model efficacy on three tasks: reconstruction, imputation and conditional generation. Our model outperforms baselines in all tasks and shows more stable and refined results.

Time series foundation models have shown impressive performance on a variety of tasks, across a wide range of domains, even in zero-shot settings. However, most of these models are designed to handle short univariate time series as an input. This limits their practical use, especially in domains such as healthcare with copious amounts of long and multivariate data with strong temporal and intra-variate dependencies. Our study bridges this gap by cataloging and systematically comparing various context expansion techniques from both language and time series domains, and introducing a novel compressive memory mechanism to allow encoder-only TSFMs to effectively model intra-variate dependencies. We demonstrate the benefits of our approach by imbuing MOMENT, a recent family of multi-task time series foundation models, with the multivariate context.

The performance of transformers for time-series forecasting has improved significantly. Recent architectures learn complex temporal patterns by segmenting a time-series into patches and using the patches as tokens. The patch size controls the ability of transformers to learn the temporal patterns at different frequencies: shorter patches are effective for learning localized, high-frequency patterns, whereas mining long-term seasonalities and trends requires longer patches. Inspired by this observation, we propose a novel framework, Multi-resolution Time-Series Transformer (MTST), which consists of a multi-branch architecture for simultaneous modeling of diverse temporal patterns at different resolutions. In contrast to many existing time-series transformers, we employ relative positional encoding, which is better suited for extracting periodic components at different scales. Extensive experiments on several real-world datasets demonstrate the effectiveness of MTST in comparison to state-of-the-art forecasting techniques.

Inferring atmospheric properties of exoplanets from observed spectra is key to understanding their formation, evolution, and habitability. Since traditional Bayesian approaches to atmospheric retrieval (e.g., nested sampling) are computationally expensive, a growing number of machine learning (ML) methods such as neural posterior estimation (NPE) have been proposed. We seek to make ML-based atmospheric retrieval (1) more reliable and accurate with verified results, and (2) more flexible with respect to the underlying neural networks and the choice of the assumed noise models. First, we adopt flow matching posterior estimation (FMPE) as a new ML approach to atmospheric retrieval. FMPE maintains many advantages of NPE, but provides greater architectural flexibility and scalability. Second, we use importance sampling (IS) to verify and correct ML results, and to compute an estimate of the Bayesian evidence. Third, we condition our ML models on the assumed noise level of a spectrum (i.e., error bars), thus making them adaptable to different noise models. Both our noise level-conditional FMPE and NPE models perform on par with nested sampling across a range of noise levels when tested on simulated data. FMPE trains about 3 times faster than NPE and yields higher IS efficiencies. IS successfully corrects inaccurate ML results, identifies model failures via low efficiencies, and provides accurate estimates of the Bayesian evidence. FMPE is a powerful alternative to NPE for fast, amortized, and parallelizable atmospheric retrieval. IS can verify results, thus helping to build confidence in ML-based approaches, while also facilitating model comparison via the evidence ratio. Noise level conditioning allows design studies for future instruments to be scaled up, for example, in terms of the range of signal-to-noise ratios.

Parameter-efficient fine-tuning (PEFT) has emerged as a crucial paradigm for adapting large language models (LLMs) under constrained computational budgets. However, standard PEFT methods often struggle in multi-task fine-tuning settings, where diverse optimization objectives induce task interference and limited parameter budgets lead to representational deficiency. While recent approaches incorporate mixture-of-experts (MoE) to alleviate these issues, they predominantly operate in the spatial domain, which may introduce structural redundancy and parameter overhead. To overcome these limitations, we reformulate adaptation in the spectral domain. Our spectral analysis reveals that different tasks exhibit distinct frequency energy distributions, and that LLM layers display heterogeneous frequency sensitivities. Motivated by these insights, we propose FourierMoE, which integrates the MoE architecture with the inverse discrete Fourier transform (IDFT) for frequency-aware adaptation. Specifically, FourierMoE employs a frequency-adaptive router to dispatch tokens to experts specialized in distinct frequency bands. Each expert learns a set of conjugate-symmetric complex coefficients, preserving complete phase and amplitude information while theoretically guaranteeing lossless IDFT reconstruction into real-valued spatial weights. Extensive evaluations across 28 benchmarks, multiple model architectures, and scales demonstrate that FourierMoE consistently outperforms competitive baselines in both single-task and multi-task settings while using significantly fewer trainable parameters. These results highlight the promise of spectral-domain expert adaptation as an effective and parameter-efficient paradigm for LLM fine-tuning.

We introduce the Cisco Time Series Model, a univariate zero-shot forecaster. This time series foundation model is the result of a general architectural innovation to a time series model enabling it to accept multiresolution input, applied to a popular decoder-only time series model (TimesFM). The resulting multiresolution decoder-only model is trained on over 300B unique data points, with more than half coming from the observability domain. Quantitative and qualitative evaluations demonstrate that the resulting model achieves superior performance on observability datasets while retaining very similar performance on a standard general-purpose forecasting benchmark (GIFT-Eval), and suggest that the multiresolution structure enables the model to make more accurate predictions on long context input.

Global climate models parameterize a range of atmospheric-oceanic processes like gravity waves, clouds, moist convection, and turbulence that cannot be sufficiently resolved. These subgrid-scale closures for unresolved processes are a leading source of model uncertainty. Here, we present a new approach to developing machine learning parameterizations of small-scale climate processes by fine-tuning a pre-trained AI foundation model (FM). FMs are largely unexplored in climate research. A pre-trained encoder-decoder from a 2.3 billion parameter FM (NASA and IBM Research's Prithvi WxC) -- which contains a latent probabilistic representation of atmospheric evolution -- is fine-tuned (or reused) to create a deep learning parameterization for atmospheric gravity waves (GWs). The parameterization captures GW effects for a coarse-resolution climate model by learning the fluxes from an atmospheric reanalysis with 10 times finer resolution. A comparison of monthly averages and instantaneous evolution with a machine learning model baseline (an Attention U-Net) reveals superior predictive performance of the FM parameterization throughout the atmosphere, even in regions excluded from pre-training. This performance boost is quantified using the Hellinger distance, which is 0.11 for the baseline and 0.06 for the fine-tuned model. Our findings emphasize the versatility and reusability of FMs, which could be used to accomplish a range of atmosphere- and climate-related applications, leading the way for the creation of observations-driven and physically accurate parameterizations for more earth-system processes.

The performance of time series forecasting has recently been greatly improved by the introduction of transformers. In this paper, we propose a general multi-scale framework that can be applied to the state-of-the-art transformer-based time series forecasting models (FEDformer, Autoformer, etc.). By iteratively refining a forecasted time series at multiple scales with shared weights, introducing architecture adaptations, and a specially-designed normalization scheme, we are able to achieve significant performance improvements, from 5.5% to 38.5% across datasets and transformer architectures, with minimal additional computational overhead. Via detailed ablation studies, we demonstrate the effectiveness of each of our contributions across the architecture and methodology. Furthermore, our experiments on various public datasets demonstrate that the proposed improvements outperform their corresponding baseline counterparts. Our code is publicly available in https://github.com/BorealisAI/scaleformer.

Large Language Models (LLMs) and Foundation Models (FMs) have recently become prevalent for time series forecasting tasks. While fine-tuning LLMs enables domain adaptation, they often struggle to generalize across diverse and unseen datasets. Moreover, existing Time Series Foundation Models (TSFMs) still face challenges in handling non-stationary dynamics and distribution shifts, largely due to the lack of effective mechanisms for adaptation. To this end, we present TS-RAG, a retrieval-augmented generation framework for time series forecasting that enhances the generalization and interpretability of TSFMs. Specifically, TS-RAG leverages pre-trained time series encoders to retrieve semantically relevant segments from a dedicated knowledge base, enriching the contextual representation of the input query. Furthermore, we propose an Adaptive Retrieval Mixer (ARM) module that dynamically fuses the retrieved patterns with the TSFM's internal representation, improving forecasting accuracy without requiring task-specific fine-tuning. Thorough empirical studies on seven public benchmark datasets demonstrate that TS-RAG achieves state-of-the-art zero-shot forecasting performance, outperforming the existing TSFMs by up to 6.84% across diverse domains while also providing desirable interpretability. Our code and data are available at: https://github.com/UConn-DSIS/TS-RAG

Foundation models (FMs) for the Earth system learn statistical relationships between physical variables across massive datasets to enable versatile downstream applications through finetuning, separating them from task-specific weather models. Here, we introduce Earth System Foundation Model (ESFM), a fully open model building on the 3D Swin UNet backbone of the pioneering Aurora model. ESFM introduces extensions that increase functionality and foster adoption in climate sciences. First, the encoding scheme and training protocols have been extended to handle diverse datasets, including those containing missing values across all spatio-temporal dimensions such as satellite data, as well as station data, all under one backbone. Axial attention is introduced to capture inter-variable dependencies. As a result ESFM skillfully predicts variables in regions or on pressure levels where no data is present at the initial time, while preserving inter-variable relationships, for example between temperature, pressure, and humidity. Individual variable tokenization enables different sets of variables to be shuffled during training and simplifies the process of building extensions for new downstream tasks. Adaptive layer norm-based ensembles allow for a simple yet effective way to transform deterministic ESFM to a probabilistic FM. We present findings using dense gridded data (ERA5, CMIP6), regionally masked dense data, sparse gridded MODIS satellite data, and station data. Results demonstrate competitive or superior performance relative to state-of-the-art benchmarks. Case studies of Super Typhoon Doksuri (2023) and 2024 sudden stratospheric warming events show accurate positional and magnitude estimations of extreme weather. ESFM retains the strengths of previous foundation models, such as long-term stability, but facilitates application to a variety of downstream tasks.

Spectrograms are pivotal in time-frequency signal analysis, widely used in audio processing and computational neuroscience. Chirp-like patterns in electroencephalogram (EEG) spectrograms (marked by linear or exponential frequency sweep) are key biomarkers for seizure dynamics, but automated tools for their detection, localization, and feature extraction are lacking. This study bridges this gap by fine-tuning a Vision Transformer (ViT) model on synthetic spectrograms, augmented with Low-Rank Adaptation (LoRA) to boost adaptability. We generated 100000 synthetic spectrograms with chirp parameters, creating the first large-scale benchmark for chirp localization. These spectrograms mimic neural chirps using linear or exponential frequency sweep, Gaussian noise, and smoothing. A ViT model, adapted for regression, predicted chirp parameters. LoRA fine-tuned the attention layers, enabling efficient updates to the pre-trained backbone. Training used MSE loss and the AdamW optimizer, with a learning rate scheduler and early stopping to curb overfitting. Only three features were targeted: Chirp Start Time (Onset Time), Chirp Start Frequency (Onset Frequency), and Chirp End Frequency (Offset Frequency). Performance was evaluated via Pearson correlation between predicted and actual labels. Results showed strong alignment: 0.9841 correlation for chirp start time, with stable inference times (137 to 140s) and minimal bias in error distributions. This approach offers a tool for chirp analysis in EEG time-frequency representation, filling a critical methodological void.

This paper introduces a structural equation formulation that gives rise to a new family of quasi-periodic Gaussian processes, useful to process a broad class of natural and physiological signals. The proposed formulation simplifies generation and forecasting, and provides hyperparameter estimates, which we exploit in a convergent and consistent iterative estimation algorithm. A bootstrap approach for standard error estimation and confidence intervals is also provided. We demonstrate the computational and scaling benefits of the proposed approach on a broad class of problems, including water level tidal analysis, CO_{2} emission data, and sunspot numbers data. By leveraging the structural equations, our method reduces the cost of likelihood evaluations and predictions from O(k^2 p^2) to O(p^2), significantly improving scalability.

Recent progress in neural forecasting accelerated improvements in the performance of large-scale forecasting systems. Yet, long-horizon forecasting remains a very difficult task. Two common challenges afflicting the task are the volatility of the predictions and their computational complexity. We introduce N-HiTS, a model which addresses both challenges by incorporating novel hierarchical interpolation and multi-rate data sampling techniques. These techniques enable the proposed method to assemble its predictions sequentially, emphasizing components with different frequencies and scales while decomposing the input signal and synthesizing the forecast. We prove that the hierarchical interpolation technique can efficiently approximate arbitrarily long horizons in the presence of smoothness. Additionally, we conduct extensive large-scale dataset experiments from the long-horizon forecasting literature, demonstrating the advantages of our method over the state-of-the-art methods, where N-HiTS provides an average accuracy improvement of almost 20% over the latest Transformer architectures while reducing the computation time by an order of magnitude (50 times). Our code is available at bit.ly/3VA5DoT

We present Masked Frequency Modeling (MFM), a unified frequency-domain-based approach for self-supervised pre-training of visual models. Instead of randomly inserting mask tokens to the input embeddings in the spatial domain, in this paper, we shift the perspective to the frequency domain. Specifically, MFM first masks out a portion of frequency components of the input image and then predicts the missing frequencies on the frequency spectrum. Our key insight is that predicting masked components in the frequency domain is more ideal to reveal underlying image patterns rather than predicting masked patches in the spatial domain, due to the heavy spatial redundancy. Our findings suggest that with the right configuration of mask-and-predict strategy, both the structural information within high-frequency components and the low-level statistics among low-frequency counterparts are useful in learning good representations. For the first time, MFM demonstrates that, for both ViT and CNN, a simple non-Siamese framework can learn meaningful representations even using none of the following: (i) extra data, (ii) extra model, (iii) mask token. Experimental results on image classification and semantic segmentation, as well as several robustness benchmarks show the competitive performance and advanced robustness of MFM compared with recent masked image modeling approaches. Furthermore, we also comprehensively investigate the effectiveness of classical image restoration tasks for representation learning from a unified frequency perspective and reveal their intriguing relations with our MFM approach.

Triggered by the realization that AI emulators can rival the performance of traditional numerical weather prediction models running on HPC systems, there is now an increasing number of large AI models that address use cases such as forecasting, downscaling, or nowcasting. While the parallel developments in the AI literature focus on foundation models -- models that can be effectively tuned to address multiple, different use cases -- the developments on the weather and climate side largely focus on single-use cases with particular emphasis on mid-range forecasting. We close this gap by introducing Prithvi WxC, a 2.3 billion parameter foundation model developed using 160 variables from the Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA-2). Prithvi WxC employs an encoder-decoder-based architecture, incorporating concepts from various recent transformer models to effectively capture both regional and global dependencies in the input data. The model has been designed to accommodate large token counts to model weather phenomena in different topologies at fine resolutions. Furthermore, it is trained with a mixed objective that combines the paradigms of masked reconstruction with forecasting. We test the model on a set of challenging downstream tasks namely: Autoregressive rollout forecasting, Downscaling, Gravity wave flux parameterization, and Extreme events estimation. The pretrained model with 2.3 billion parameters, along with the associated fine-tuning workflows, has been publicly released as an open-source contribution via Hugging Face.

This paper introduces the multi-freq-ldpy Python package for multiple frequency estimation under Local Differential Privacy (LDP) guarantees. LDP is a gold standard for achieving local privacy with several real-world implementations by big tech companies such as Google, Apple, and Microsoft. The primary application of LDP is frequency (or histogram) estimation, in which the aggregator estimates the number of times each value has been reported. The presented package provides an easy-to-use and fast implementation of state-of-the-art solutions and LDP protocols for frequency estimation of: single attribute (i.e., the building blocks), multiple attributes (i.e., multidimensional data), multiple collections (i.e., longitudinal data), and both multiple attributes/collections. Multi-freq-ldpy is built on the well-established Numpy package -- a de facto standard for scientific computing in Python -- and the Numba package for fast execution. These features are described and illustrated in this paper with four worked examples. This package is open-source and publicly available under an MIT license via GitHub (https://github.com/hharcolezi/multi-freq-ldpy) and can be installed via PyPI (https://pypi.org/project/multi-freq-ldpy/).

Time series foundation models (TSFMs) are increasingly being adopted as highly-capable general-purpose time series representation learners. Although their training corpora are vast, they exclude astronomical time series data. Observations of stars produce peta-scale time series with unique challenges including irregular sampling and heteroskedasticity. We introduce StarEmbed, the first public benchmark for rigorous and standardized evaluation of state-of-the-art TSFMs on stellar time series observations (``light curves''). We benchmark on three scientifically-motivated downstream tasks: unsupervised clustering, supervised classification, and out-of-distribution source detection. StarEmbed integrates a catalog of expert-vetted labels with multi-variate light curves from the Zwicky Transient Facility, yielding ~40k hand-labeled light curves spread across seven astrophysical classes. We evaluate the zero-shot representation capabilities of three TSFMs (MOIRAI, Chronos, Chronos-Bolt) and a domain-specific transformer (Astromer) against handcrafted feature extraction, the long-standing baseline in the astrophysics literature. Our results demonstrate that these TSFMs, especially the Chronos models, which are trained on data completely unlike the astronomical observations, can outperform established astrophysics-specific baselines in some tasks and effectively generalize to entirely new data. In particular, TSFMs deliver state-of-the-art performance on our out-of-distribution source detection benchmark. With the first benchmark of TSFMs on astronomical time series data, we test the limits of their generalization and motivate a paradigm shift in time-domain astronomy from using task-specific, fully supervised pipelines toward adopting generic foundation model representations for the analysis of peta-scale datasets from forthcoming observatories.

Electroencephalography foundation models (EEG-FMs) have advanced brain signal analysis, but the lack of standardized evaluation benchmarks impedes model comparison and scientific progress. Current evaluations rely on inconsistent protocols that render cross-model comparisons unreliable, while a lack of diagnostic analyses obscures the internal mechanisms driving transfer efficiency and scaling behaviors. To address this, we introduce EEG-FM-Bench, a unified system for the standardized evaluation of EEG-FMs. The benchmark integrates 14 datasets across 10 paradigms and incorporates diverse experimental settings, including multiple fine-tuning strategies, task organizations, and classifier configurations, supported by tools for gradient and representation analysis. Our experiments and analysis reveal several critical insights: (1) multi-task learning acts as a critical regularizer to mitigate overfitting in data-scarce EEG contexts; (2) pre-training efficiency is currently limited by gradient conflicts between reconstruction objectives and downstream tasks; (3) model scaling deviates from typical laws, as compact architectures with domain-specific inductive biases consistently outperform significantly larger models. This benchmark enables fair comparison and reproducible analysis, shifting the field from fragmented results to interpretable advances. Code is available at https://github.com/xw1216/EEG-FM-Bench.

We derive a Fast Multipole Method (FMM) where a low-rank approximation of the kernel is obtained using the Empirical Interpolation Method (EIM). Contrary to classical interpolation-based FMM, where the interpolation points and basis are fixed beforehand, the EIM is a nonlinear approximation method which constructs interpolation points and basis which are adapted to the kernel under consideration. The basis functions are obtained using evaluations of the kernel itself. We restrict ourselves to translation-invariant kernels, for which a modified version of the EIM approximation can be used in a multilevel FMM context; we call the obtained algorithm Empirical Interpolation Fast Multipole Method (EIFMM). An important feature of the EIFMM is a built-in error estimation of the interpolation error made by the low-rank approximation of the far-field behavior of the kernel: the algorithm selects the optimal number of interpolation points required to ensure a given accuracy for the result, leading to important gains for inhomogeneous kernels.

Recently, multi-band spectrogram-based approaches such as Band-Split RNN (BSRNN) have demonstrated promising results for music source separation. In our recent work, we introduce the BS-RoFormer model which inherits the idea of band-split scheme in BSRNN at the front-end, and then uses the hierarchical Transformer with Rotary Position Embedding (RoPE) to model the inner-band and inter-band sequences for multi-band mask estimation. This model has achieved state-of-the-art performance, but the band-split scheme is defined empirically, without analytic supports from the literature. In this paper, we propose Mel-RoFormer, which adopts the Mel-band scheme that maps the frequency bins into overlapped subbands according to the mel scale. In contract, the band-split mapping in BSRNN and BS-RoFormer is non-overlapping and designed based on heuristics. Using the MUSDB18HQ dataset for experiments, we demonstrate that Mel-RoFormer outperforms BS-RoFormer in the separation tasks of vocals, drums, and other stems.

Time series forecasting is widely used in extensive applications, such as traffic planning and weather forecasting. However, real-world time series usually present intricate temporal variations, making forecasting extremely challenging. Going beyond the mainstream paradigms of plain decomposition and multiperiodicity analysis, we analyze temporal variations in a novel view of multiscale-mixing, which is based on an intuitive but important observation that time series present distinct patterns in different sampling scales. The microscopic and the macroscopic information are reflected in fine and coarse scales respectively, and thereby complex variations can be inherently disentangled. Based on this observation, we propose TimeMixer as a fully MLP-based architecture with Past-Decomposable-Mixing (PDM) and Future-Multipredictor-Mixing (FMM) blocks to take full advantage of disentangled multiscale series in both past extraction and future prediction phases. Concretely, PDM applies the decomposition to multiscale series and further mixes the decomposed seasonal and trend components in fine-to-coarse and coarse-to-fine directions separately, which successively aggregates the microscopic seasonal and macroscopic trend information. FMM further ensembles multiple predictors to utilize complementary forecasting capabilities in multiscale observations. Consequently, TimeMixer is able to achieve consistent state-of-the-art performances in both long-term and short-term forecasting tasks with favorable run-time efficiency.

Transformer-based foundation models have emerged as a dominant paradigm in time series analysis, offering unprecedented capabilities in tasks such as forecasting, anomaly detection, classification, trend analysis and many more time series analytical tasks. This survey provides a comprehensive overview of the current state of the art pre-trained foundation models, introducing a novel taxonomy to categorize them across several dimensions. Specifically, we classify models by their architecture design, distinguishing between those leveraging patch-based representations and those operating directly on raw sequences. The taxonomy further includes whether the models provide probabilistic or deterministic predictions, and whether they are designed to work with univariate time series or can handle multivariate time series out of the box. Additionally, the taxonomy encompasses model scale and complexity, highlighting differences between lightweight architectures and large-scale foundation models. A unique aspect of this survey is its categorization by the type of objective function employed during training phase. By synthesizing these perspectives, this survey serves as a resource for researchers and practitioners, providing insights into current trends and identifying promising directions for future research in transformer-based time series modeling.

Long-term time series forecasting requires models that simultaneously capture rapid oscillations, medium-range periodicities, and slowly evolving macro-trends from a fixed look-back window. Existing lightweight MLP-based models typically operate on a single temporal resolution, limiting their ability to explicitly model patterns at multiple scales. We propose MSMixer, a channel-independent multi-scale MLP architecture that addresses this limitation through three complementary innovations: (i) three parallel scale branches at down-sample factors {1x, 4x, 16x} with independent MLP blocks, (ii) a learnable softmax gate that dynamically weighs branch outputs, and (iii) a DLinear complementary shortcut that provides full-window trend and seasonality context. MSMixer contains only 112K parameters at H=96 and runs at O(T) complexity. Evaluated on four ETT benchmarks with standard chronological splits and three random seeds, MSMixer achieves the lowest average MSE (0.357) among lightweight models, outperforming DLinear (0.386, -7.4%) and NLinear (0.365, -2.1%), winning 12 of 16 configurations. Against five Transformer-based baselines from the literature, MSMixer achieves best or second-best MSE in 9 of 16 configurations while using 5x fewer parameters than PatchTST. Ablation and sensitivity analyses confirm the complementary contributions of the multi-scale branches and the DLinear shortcut.

Anomaly detection in multivariate time series is challenging as heterogeneous subsequence anomalies may occur. Reconstruction-based methods, which focus on learning normal patterns in the frequency domain to detect diverse abnormal subsequences, achieve promising results, while still falling short on capturing fine-grained frequency characteristics and channel correlations. To contend with the limitations, we introduce CATCH, a framework based on frequency patching. We propose to patchify the frequency domain into frequency bands, which enhances its ability to capture fine-grained frequency characteristics. To perceive appropriate channel correlations, we propose a Channel Fusion Module (CFM), which features a patch-wise mask generator and a masked-attention mechanism. Driven by a bi-level multi-objective optimization algorithm, the CFM is encouraged to iteratively discover appropriate patch-wise channel correlations, and to cluster relevant channels while isolating adverse effects from irrelevant channels. Extensive experiments on 10 real-world datasets and 12 synthetic datasets demonstrate that CATCH achieves state-of-the-art performance. We make our code and datasets available at https://github.com/decisionintelligence/CATCH.

Irregular Multivariate Time Series (IMTS) forecasting is challenging due to the unaligned nature of multi-channel signals and the prevalence of extensive missing data. Existing methods struggle to capture reliable temporal patterns from such data due to significant missing values. While pre-trained foundation models show potential for addressing these challenges, they are typically designed for Regularly Sampled Time Series (RTS). Motivated by the visual Mask AutoEncoder's (MAE) powerful capability for modeling sparse multi-channel information and its success in RTS forecasting, we propose VIMTS, a framework adapting Visual MAE for IMTS forecasting. To mitigate the effect of missing values, VIMTS first processes IMTS along the timeline into feature patches at equal intervals. These patches are then complemented using learned cross-channel dependencies. Then it leverages visual MAE's capability in handling sparse multichannel data for patch reconstruction, followed by a coarse-to-fine technique to generate precise predictions from focused contexts. In addition, we integrate self-supervised learning for improved IMTS modeling by adapting the visual MAE to IMTS data. Extensive experiments demonstrate VIMTS's superior performance and few-shot capability, advancing the application of visual foundation models in more general time series tasks. Our code is available at https://github.com/WHU-HZY/VIMTS.

We present a multi-modal foundation model for astrophysical galaxy data, designed to map between simulation- and observation-based galactic features. Our encoder-only transformer flexibly ingests scalar quantities (e.g., redshifts, galaxy masses) and vectors (e.g., star formation histories, spectra), supporting multi-task training that includes within-modality reconstruction and cross-modality prediction. With a dynamic masking strategy, the model can query arbitrary galaxy properties from partial inputs -- including predicting spectra from redshift and mass, or estimating photometric redshifts from broadband magnitudes -- while also recovering missing segments within a modality. Trained on 185,000 simulated galaxies from a gigaparsec-scale Cosmology simulation, the model yields a 50% improvement in redshift estimation when combining LSST and SPHEREx photometry over LSST photometry alone, and a 63% improvement in stellar mass inference when combining late-time SFH with LSST photometry over early-time SFH with LSST photometry. The model demonstrates strong generalization across multi-modal tasks and lays the groundwork for future integration of higher-dimensional and structured data such as images, merger trees, and 3D fields. This approach provides a unified framework for connecting simulations and observations, advancing the development of generalizable astrophysical foundation models.

Spectral analysis provides one of the most effective paradigms for information-preserving dimensionality reduction, as simple descriptions of naturally occurring signals are often obtained via few terms of periodic basis functions. In this work, we study deep neural networks designed to harness the structure in frequency domain for efficient learning of long-range correlations in space or time: frequency-domain models (FDMs). Existing FDMs are based on complex-valued transforms i.e. Fourier Transforms (FT), and layers that perform computation on the spectrum and input data separately. This design introduces considerable computational overhead: for each layer, a forward and inverse FT. Instead, this work introduces a blueprint for frequency domain learning through a single transform: transform once (T1). To enable efficient, direct learning in the frequency domain we derive a variance-preserving weight initialization scheme and investigate methods for frequency selection in reduced-order FDMs. Our results noticeably streamline the design process of FDMs, pruning redundant transforms, and leading to speedups of 3x to 10x that increase with data resolution and model size. We perform extensive experiments on learning the solution operator of spatio-temporal dynamics, including incompressible Navier-Stokes, turbulent flows around airfoils and high-resolution video of smoke. T1 models improve on the test performance of FDMs while requiring significantly less computation (5 hours instead of 32 for our large-scale experiment), with over 20% reduction in average predictive error across tasks.

We present Zeus, a unified tuning-free Time Series Foundation Model (TSFM) that delivers superior performance across diverse analysis tasks without any task-specific fine-tuning. Unlike prior studies that primarily focus on zero-shot forecasting but require task-specific tuning for other tasks, Zeus bridges this gap by addressing two fundamental challenges in multi-task generalization. First, to reconcile point-level granularity with long-sequence scalability, Zeus incorporates a multi-scale Transformer featuring point-wise tokenization and a U-shaped hierarchy, effectively balancing fine-grained fidelity with computational efficiency. Second, to accommodate varying inductive biases across different tasks, Zeus introduces Multi-Objective Temporal Masking (MOTM), a unified strategy that supports heterogeneous tasks (e.g., extrapolation, interpolation, and global abstraction) within a single framework. Extensive experiments across five representative tasks demonstrate that Zeus consistently achieves competitive results in tuning-free settings, underscoring its potential as a general-purpose TSFM.

Time series forecasting with pretrained foundation models has demonstrated strong zero-shot capabilities. However, achieving optimal performance on time series with short or negligible historical data in domain-specific applications typically requires adaptation via either fine-tuning or RAG. While fine-tuning is effective, it incurs substantial computational costs. This work explores RAG within univariate time series (Retrieval Augmented Generation) as a more efficient alternative, in particular RAF (Retrieval Augmented Forecasting), and introduces RAEF (Retrieval-Augmented Extended Forecasting), a model-agnostic method built upon RAF. RAEF incorporates key refinements to the retrieval and aggregation mechanisms: (1) direct retrieval in input-space rather than embedding-space, reducing inference overhead, and (2) concatenation-based aggregation that preserves temporal structure instead of averaging. Empirical evaluation across multiple benchmark datasets demonstrates that RAEF outperforms RAF in both accuracy and inference overhead. Furthermore, comprehensive comparisons with zero-shot and fine-tuned foundation models show that RAEF achieves competitive or superior performance to fine-tuning while avoiding its computational burden, establishing it as a practical and scalable approach for domain adaptation in time series forecasting.

Time series foundation models (TSFMs) pretrained on data from multiple domains have shown strong performance on diverse modeling tasks. Various efforts have been made to develop foundation models specific to electroencephalography (EEG) data, which records brain electrical activity as time series. However, no comparative analysis of EEG-specific foundation models (EEGFMs) versus general TSFMs has been performed on EEG-specific tasks. We introduce a novel Spatial-Temporal Adapter with Multi-Head Pooling (STAMP), which leverages univariate embeddings produced by a general TSFM, implicitly models spatial-temporal characteristics of EEG data, and achieves performance comparable to state-of-the-art EEGFMs. A comprehensive analysis is performed on 8 benchmark datasets of clinical tasks using EEG for classification, along with ablation studies. Our proposed adapter is lightweight in trainable parameters and flexible in the inputs it can accommodate, supporting easy modeling of EEG data using TSFMs.

We present a novel type of neural fields that uses general radial bases for signal representation. State-of-the-art neural fields typically rely on grid-based representations for storing local neural features and N-dimensional linear kernels for interpolating features at continuous query points. The spatial positions of their neural features are fixed on grid nodes and cannot well adapt to target signals. Our method instead builds upon general radial bases with flexible kernel position and shape, which have higher spatial adaptivity and can more closely fit target signals. To further improve the channel-wise capacity of radial basis functions, we propose to compose them with multi-frequency sinusoid functions. This technique extends a radial basis to multiple Fourier radial bases of different frequency bands without requiring extra parameters, facilitating the representation of details. Moreover, by marrying adaptive radial bases with grid-based ones, our hybrid combination inherits both adaptivity and interpolation smoothness. We carefully designed weighting schemes to let radial bases adapt to different types of signals effectively. Our experiments on 2D image and 3D signed distance field representation demonstrate the higher accuracy and compactness of our method than prior arts. When applied to neural radiance field reconstruction, our method achieves state-of-the-art rendering quality, with small model size and comparable training speed.

Pan-sharpening involves reconstructing missing high-frequency information in multi-spectral images with low spatial resolution, using a higher-resolution panchromatic image as guidance. Although the inborn connection with frequency domain, existing pan-sharpening research has not almost investigated the potential solution upon frequency domain. To this end, we propose a novel Frequency Adaptive Mixture of Experts (FAME) learning framework for pan-sharpening, which consists of three key components: the Adaptive Frequency Separation Prediction Module, the Sub-Frequency Learning Expert Module, and the Expert Mixture Module. In detail, the first leverages the discrete cosine transform to perform frequency separation by predicting the frequency mask. On the basis of generated mask, the second with low-frequency MOE and high-frequency MOE takes account for enabling the effective low-frequency and high-frequency information reconstruction. Followed by, the final fusion module dynamically weights high-frequency and low-frequency MOE knowledge to adapt to remote sensing images with significant content variations. Quantitative and qualitative experiments over multiple datasets demonstrate that our method performs the best against other state-of-the-art ones and comprises a strong generalization ability for real-world scenes. Code will be made publicly at https://github.com/alexhe101/FAME-Net.

Time series modeling presents unique challenges due to autocorrelation in both historical data and future sequences. While current research predominantly addresses autocorrelation within historical data, the correlations among future labels are often overlooked. Specifically, modern forecasting models primarily adhere to the Direct Forecast (DF) paradigm, generating multi-step forecasts independently and disregarding label autocorrelation over time. In this work, we demonstrate that the learning objective of DF is biased in the presence of label autocorrelation. To address this issue, we propose the Frequency-enhanced Direct Forecast (FreDF), which mitigates label autocorrelation by learning to forecast in the frequency domain, thereby reducing estimation bias. Our experiments show that FreDF significantly outperforms existing state-of-the-art methods and is compatible with a variety of forecast models. Code is available at https://github.com/Master-PLC/FreDF.

The short-time Fourier transform (STFT) is widely used for analyzing non-stationary signals. However, its performance is highly sensitive to its parameters, and manual or heuristic tuning often yields suboptimal results. To overcome this limitation, we propose a unified differentiable formulation of the STFT that enables gradient-based optimization of its parameters. This approach addresses the limitations of traditional STFT parameter tuning methods, which often rely on computationally intensive discrete searches. It enables fine-tuning of the time-frequency representation (TFR) based on any desired criterion. Moreover, our approach integrates seamlessly with neural networks, allowing joint optimization of the STFT parameters and network weights. The efficacy of the proposed differentiable STFT in enhancing TFRs and improving performance in downstream tasks is demonstrated through experiments on both simulated and real-world data.

Non-linear activation functions are crucial in Convolutional Neural Networks. However, until now they have not been well described in the frequency domain. In this work, we study the spectral behavior of ReLU, a popular activation function. We use the ReLU's Taylor expansion to derive its frequency domain behavior. We demonstrate that ReLU introduces higher frequency oscillations in the signal and a constant DC component. Furthermore, we investigate the importance of this DC component, where we demonstrate that it helps the model extract meaningful features related to the input frequency content. We accompany our theoretical derivations with experiments and real-world examples. First, we numerically validate our frequency response model. Then we observe ReLU's spectral behavior on two example models and a real-world one. Finally, we experimentally investigate the role of the DC component introduced by ReLU in the CNN's representations. Our results indicate that the DC helps to converge to a weight configuration that is close to the initial random weights.

Although Kolmogorov-Arnold based interpretable networks (KAN) have strong theoretical expressiveness, they face significant parameter explosion and high-frequency feature capture challenges in high-dimensional tasks. To address this issue, we propose the Kolmogorov-Arnold-Fourier Network (KAF), which effectively integrates trainable Random Fourier Features (RFF) and a novel hybrid GELU-Fourier activation mechanism to balance parameter efficiency and spectral representation capabilities. Our key technical contributions include: (1) merging KAN's dual-matrix structure through matrix association properties to substantially reduce parameters; (2) introducing learnable RFF initialization strategies to eliminate spectral distortion in high-dimensional approximation tasks; (3) implementing an adaptive hybrid activation function that progressively enhances frequency representation during the training process. Comprehensive experiments demonstrate the superiority of our KAF across various domains including vision, NLP, audio processing, and differential equation-solving tasks, effectively combining theoretical interpretability with practical utility and computational efficiency.

Wireless foundation models (WFMs) have recently demonstrated promising capabilities, jointly performing multiple wireless functions and adapting effectively to new environments. However, while current WFMs process only one modality, depending on the task and operating conditions, the most informative modality changes and no single modality is best for all tasks. WFMs should therefore be designed to accept multiple modalities to enable a broader and more diverse range of tasks and scenarios. In this work, we propose and build the first multimodal wireless foundation model capable of processing both raw IQ streams and image-like wireless modalities (e.g., spectrograms and CSI) and performing multiple tasks across both. We introduce masked wireless modeling for the multimodal setting, a self-supervised objective and pretraining recipe that learns a joint representation from IQ streams and image-like wireless modalities. We evaluate the model on five tasks across both modality families: image-based (human activity sensing, RF signal classification, 5G NR positioning) and IQ-based (RF device fingerprinting, interference detection/classification). The multimodal WFM is competitive with single-modality WFMs, and in several cases surpasses their performance. Our results demonstrates the strong potential of developing multimodal WFMs that support diverse wireless tasks across different modalities. We believe this provides a concrete step toward both AI-native 6G and the vision of joint sensing, communication, and localization.

Time-series forecasting in real-world applications such as finance and energy often faces challenges due to limited training data and complex, noisy temporal dynamics. Existing deep forecasting models typically supervise predictions using full-length temporal windows, which include substantial high-frequency noise and obscure long-term trends. Moreover, auxiliary variables containing rich domain-specific information are often underutilized, especially in few-shot settings. To address these challenges, we propose LoFT-LLM, a frequency-aware forecasting pipeline that integrates low-frequency learning with semantic calibration via a large language model (LLM). Firstly, a Patch Low-Frequency forecasting Module (PLFM) extracts stable low-frequency trends from localized spectral patches. Secondly, a residual learner then models high-frequency variations. Finally, a fine-tuned LLM refines the predictions by incorporating auxiliary context and domain knowledge through structured natural language prompts. Extensive experiments on financial and energy datasets demonstrate that LoFT-LLM significantly outperforms strong baselines under both full-data and few-shot regimes, delivering superior accuracy, robustness, and interpretability.

This survey delves into the realm of Parameter-Efficient Fine-Tuning (PEFT) within the context of Foundation Models (FMs). PEFT, a cost-effective fine-tuning technique, minimizes parameters and computational complexity while striving for optimal downstream task performance. FMs, like ChatGPT, DALL-E, and LLaVA specialize in language understanding, generative tasks, and multimodal tasks, trained on diverse datasets spanning text, images, and videos. The diversity of FMs guides various adaptation strategies for PEFT. Therefore, this survey aims to provide a comprehensive overview of PEFT techniques applied to diverse FMs and address critical gaps in understanding the techniques, trends, and applications. We start by providing a detailed development of FMs and PEFT. Subsequently, we systematically review the key categories and core mechanisms of PEFT across diverse FMs to offer a comprehensive understanding of trends. We also explore the most recent applications across various FMs to demonstrate the versatility of PEFT, shedding light on the integration of systematic PEFT methods with a range of FMs. Furthermore, we identify potential research and development directions for improving PEFTs in the future. This survey provides a valuable resource for both newcomers and experts seeking to understand and use the power of PEFT across FMs. All reviewed papers are listed at https://github.com/THUDM/Awesome-Parameter-Efficient-Fine-Tuning-for-Foundation-Models.

Implicit Neural Representations (INRs) have recently gained attention as a powerful approach for continuously representing signals such as images, videos, and 3D shapes using multilayer perceptrons (MLPs). However, MLPs are known to exhibit a low-frequency bias, limiting their ability to capture high-frequency details accurately. This limitation is typically addressed by incorporating high-frequency input embeddings or specialized activation layers. In this work, we demonstrate that these embeddings and activations are often configured with hyperparameters that perform well on average but are suboptimal for specific input signals under consideration, necessitating a costly grid search to identify optimal settings. Our key observation is that the initial frequency spectrum of an untrained model's output correlates strongly with the model's eventual performance on a given target signal. Leveraging this insight, we propose frequency shifting (or FreSh), a method that selects embedding hyperparameters to align the frequency spectrum of the model's initial output with that of the target signal. We show that this simple initialization technique improves performance across various neural representation methods and tasks, achieving results comparable to extensive hyperparameter sweeps but with only marginal computational overhead compared to training a single model with default hyperparameters.

In recent years, there has been increasing interest in developing foundation models for time series data that can generalize across diverse downstream tasks. While numerous forecasting-oriented foundation models have been introduced, there is a notable scarcity of models tailored for time series classification. To address this gap, we present Mantis, a new open-source foundation model for time series classification based on the Vision Transformer (ViT) architecture that has been pre-trained using a contrastive learning approach. Our experimental results show that Mantis outperforms existing foundation models both when the backbone is frozen and when fine-tuned, while achieving the lowest calibration error. In addition, we propose several adapters to handle the multivariate setting, reducing memory requirements and modeling channel interdependence.

In this paper we explore the possibility of maximizing the information represented in spectrograms by making the spectrogram basis functions trainable. We experiment with two different tasks, namely keyword spotting (KWS) and automatic speech recognition (ASR). For most neural network models, the architecture and hyperparameters are typically fine-tuned and optimized in experiments. Input features, however, are often treated as fixed. In the case of audio, signals can be mainly expressed in two main ways: raw waveforms (time-domain) or spectrograms (time-frequency-domain). In addition, different spectrogram types are often used and tailored to fit different applications. In our experiments, we allow for this tailoring directly as part of the network. Our experimental results show that using trainable basis functions can boost the accuracy of Keyword Spotting (KWS) by 14.2 percentage points, and lower the Phone Error Rate (PER) by 9.5 percentage points. Although models using trainable basis functions become less effective as the model complexity increases, the trained filter shapes could still provide us with insights on which frequency bins are important for that specific task. From our experiments, we can conclude that trainable basis functions are a useful tool to boost the performance when the model complexity is limited.

Transformer models are deployed in a wide range of settings, from multi-accelerator clusters to standalone mobile phones. The diverse inference constraints in these scenarios necessitate practitioners to train foundation models such as PaLM 2, Llama, & ViTs as a series of models of varying sizes. Due to significant training costs, only a select few model sizes are trained and supported, limiting more fine-grained control over relevant tradeoffs, including latency, cost, and accuracy. This work introduces MatFormer, a nested Transformer architecture designed to offer elasticity in a variety of deployment constraints. Each Feed Forward Network (FFN) block of a MatFormer model is jointly optimized with a few nested smaller FFN blocks. This training procedure allows for the Mix'n'Match of model granularities across layers -- i.e., a trained universal MatFormer model enables extraction of hundreds of accurate smaller models, which were never explicitly optimized. We empirically demonstrate MatFormer's effectiveness across different model classes (decoders & encoders), modalities (language & vision), and scales (up to 2.6B parameters). We find that a 2.6B decoder-only MatFormer language model (MatLM) allows us to extract smaller models spanning from 1.5B to 2.6B, each exhibiting comparable validation loss and one-shot downstream evaluations to their independently trained counterparts. Furthermore, we observe that smaller encoders extracted from a universal MatFormer-based ViT (MatViT) encoder preserve the metric-space structure for adaptive large-scale retrieval. Finally, we showcase that speculative decoding with the accurate and consistent submodels extracted from MatFormer can further reduce inference latency.

We present TimeFound, an encoder-decoder transformer-based time series foundation model for out-of-the-box zero-shot forecasting. To handle time series data from various domains, TimeFound employs a multi-resolution patching strategy to capture complex temporal patterns at multiple scales. We pre-train our model with two sizes (200M and 710M parameters) on a large time-series corpus comprising both real-world and synthetic datasets. Over a collection of unseen datasets across diverse domains and forecasting horizons, our empirical evaluations suggest that TimeFound can achieve superior or competitive zero-shot forecasting performance, compared to state-of-the-art time series foundation models.

Time series foundation models (TSFMs) have emerged as a powerful paradigm for time series analysis, driven by large-scale pretraining on diverse data corpora. However, time series inherently exhibit heterogeneous information density over time, influenced by system states and signal complexity, presenting significant modeling challenges especially in a zero-shot scenario. Current TSFMs rely on non-adaptive processing pipelines that fail to capture this dynamic nature. For example, common tokenization strategies such as fixed-size patching enforce rigid observational granularity, limiting their ability to adapt to varying information densities. Similarly, conventional positional encodings impose a uniform temporal scale, making it difficult to model diverse periodicities and trends across series. To overcome these limitations, we propose Kairos, a flexible TSFM framework that integrates a dynamic patching tokenizer and an instance-adaptive positional embedding. Kairos adaptively selects tokenization granularity and tailors positional encodings to the unique characteristics of each time series instance. Trained on a large-scale Predictability-Stratified Time Series (PreSTS) corpus comprising over 300 billion time points and adopting a multi-patch prediction strategy in the inference stage, Kairos achieves superior performance with much fewer parameters on two common zero-shot benchmarks, GIFT-Eval and the Time-Series-Library benchmark, consistently outperforming established methods across diverse tasks. The project page is at https://foundation-model-research.github.io/Kairos .

Recently, there has been a growing interest in Long-term Time Series Forecasting (LTSF), which involves predicting long-term future values by analyzing a large amount of historical time-series data to identify patterns and trends. There exist significant challenges in LTSF due to its complex temporal dependencies and high computational demands. Although Transformer-based models offer high forecasting accuracy, they are often too compute-intensive to be deployed on devices with hardware constraints. On the other hand, the linear models aim to reduce the computational overhead by employing either decomposition methods in the time domain or compact representations in the frequency domain. In this paper, we propose MixLinear, an ultra-lightweight multivariate time series forecasting model specifically designed for resource-constrained devices. MixLinear effectively captures both temporal and frequency domain features by modeling intra-segment and inter-segment variations in the time domain and extracting frequency variations from a low-dimensional latent space in the frequency domain. By reducing the parameter scale of a downsampled n-length input/output one-layer linear model from O(n^2) to O(n), MixLinear achieves efficient computation without sacrificing accuracy. Extensive evaluations with four benchmark datasets show that MixLinear attains forecasting performance comparable to, or surpassing, state-of-the-art models with significantly fewer parameters (0.1K), which makes it well-suited for deployment on devices with limited computational capacity.

Real-world multivariate time series can exhibit intricate multi-scale structures, including global trends, local periodicities, and non-stationary regimes, which makes long-horizon forecasting challenging. Although sparse Mixture-of-Experts (MoE) approaches improve scalability and specialization, they typically rely on homogeneous MLP experts that poorly capture the diverse temporal dynamics of time series data. We address these limitations with MoHETS, an encoder-only Transformer that integrates sparse Mixture-of-Heterogeneous-Experts (MoHE) layers. MoHE routes temporal patches to a small subset of expert networks, combining a shared depthwise-convolution expert for sequence-level continuity with routed Fourier-based experts for patch-level periodic structures. MoHETS further improves robustness to non-stationary dynamics by incorporating exogenous information via cross-attention over covariate patch embeddings. Finally, we replace parameter-heavy linear projection heads with a lightweight convolutional patch decoder, improving parameter efficiency, reducing training instability, and allowing a single model to generalize across arbitrary forecast horizons. We validate across seven multivariate benchmarks and multiple horizons, with MoHETS consistently achieving state-of-the-art performance, reducing the average MSE by 12% compared to strong recent baselines, demonstrating effective heterogeneous specialization for long-term forecasting.

Existing few-shot medical image segmentation (FSMIS) models fail to address a practical issue in medical imaging: the domain shift caused by different imaging techniques, which limits the applicability to current FSMIS tasks. To overcome this limitation, we focus on the cross-domain few-shot medical image segmentation (CD-FSMIS) task, aiming to develop a generalized model capable of adapting to a broader range of medical image segmentation scenarios with limited labeled data from the novel target domain. Inspired by the characteristics of frequency domain similarity across different domains, we propose a Frequency-aware Matching Network (FAMNet), which includes two key components: a Frequency-aware Matching (FAM) module and a Multi-Spectral Fusion (MSF) module. The FAM module tackles two problems during the meta-learning phase: 1) intra-domain variance caused by the inherent support-query bias, due to the different appearances of organs and lesions, and 2) inter-domain variance caused by different medical imaging techniques. Additionally, we design an MSF module to integrate the different frequency features decoupled by the FAM module, and further mitigate the impact of inter-domain variance on the model's segmentation performance. Combining these two modules, our FAMNet surpasses existing FSMIS models and Cross-domain Few-shot Semantic Segmentation models on three cross-domain datasets, achieving state-of-the-art performance in the CD-FSMIS task.

Pansharpening aims to combine a high-resolution panchromatic (PAN) image with a low-resolution multispectral (LRMS) image to produce a high-resolution multispectral (HRMS) image. Although pansharpening in the frequency domain offers clear advantages, most existing methods either continue to operate solely in the spatial domain or fail to fully exploit the benefits of the frequency domain. To address this issue, we innovatively propose Multi-Frequency Fusion Attention (MFFA), which leverages wavelet transforms to cleanly separate frequencies and enable lossless reconstruction across different frequency domains. Then, we generate Frequency-Query, Spatial-Key, and Fusion-Value based on the physical meanings represented by different features, which enables a more effective capture of specific information in the frequency domain. Additionally, we focus on the preservation of frequency features across different operations. On a broader level, our network employs a wavelet pyramid to progressively fuse information across multiple scales. Compared to previous frequency domain approaches, our network better prevents confusion and loss of different frequency features during the fusion process. Quantitative and qualitative experiments on multiple datasets demonstrate that our method outperforms existing approaches and shows significant generalization capabilities for real-world scenarios.

We propose PROSE-FD, a zero-shot multimodal PDE foundational model for simultaneous prediction of heterogeneous two-dimensional physical systems related to distinct fluid dynamics settings. These systems include shallow water equations and the Navier-Stokes equations with incompressible and compressible flow, regular and complex geometries, and different buoyancy settings. This work presents a new transformer-based multi-operator learning approach that fuses symbolic information to perform operator-based data prediction, i.e. non-autoregressive. By incorporating multiple modalities in the inputs, the PDE foundation model builds in a pathway for including mathematical descriptions of the physical behavior. We pre-train our foundation model on 6 parametric families of equations collected from 13 datasets, including over 60K trajectories. Our model outperforms popular operator learning, computer vision, and multi-physics models, in benchmark forward prediction tasks. We test our architecture choices with ablation studies.

Remote Sensing Large Multi-Modal Models (RSLMMs) are developing rapidly and showcase significant capabilities in remote sensing imagery (RSI) comprehension. However, due to the limitations of existing datasets, RSLMMs have shortcomings in understanding the rich semantic relations among objects in complex remote sensing scenes. To unlock RSLMMs' complex comprehension ability, we propose a large-scale instruction tuning dataset FIT-RS, containing 1,800,851 instruction samples. FIT-RS covers common interpretation tasks and innovatively introduces several complex comprehension tasks of escalating difficulty, ranging from relation reasoning to image-level scene graph generation. Based on FIT-RS, we build the FIT-RSFG benchmark. Furthermore, we establish a new benchmark to evaluate the fine-grained relation comprehension capabilities of LMMs, named FIT-RSRC. Based on combined instruction data, we propose SkySenseGPT, which achieves outstanding performance on both public datasets and FIT-RSFG, surpassing existing RSLMMs. We hope the FIT-RS dataset can enhance the relation comprehension capability of RSLMMs and provide a large-scale fine-grained data source for the remote sensing community. The dataset will be available at https://github.com/Luo-Z13/SkySenseGPT

Precipitation nowcasting is critical for disaster mitigation and aviation safety. However, radar-only models frequently suffer from a lack of large-scale atmospheric context, leading to performance degradation at longer lead times. While integrating meteorological variables predicted by weather foundation models offers a potential remedy, existing architectures fail to reconcile the profound representational heterogeneities between radar imagery and meteorological data. To bridge this gap, we propose PW-FouCast, a novel frequency-domain fusion framework that leverages Pangu-Weather forecasts as spectral priors within a Fourier-based backbone. Our architecture introduces three key innovations: (i) Pangu-Weather-guided Frequency Modulation to align spectral magnitudes and phases with meteorological priors; (ii) Frequency Memory to correct phase discrepancies and preserve temporal evolution; and (iii) Inverted Frequency Attention to reconstruct high-frequency details typically lost in spectral filtering. Extensive experiments on the SEVIR and MeteoNet benchmarks demonstrate that PW-FouCast achieves state-of-the-art performance, effectively extending the reliable forecast horizon while maintaining structural fidelity. Our code is available at https://github.com/Onemissed/PW-FouCast.

Machine learning based solvers have garnered much attention in physical simulation and scientific computing, with a prominent example, physics-informed neural networks (PINNs). However, PINNs often struggle to solve high-frequency and multi-scale PDEs, which can be due to spectral bias during neural network training. To address this problem, we resort to the Gaussian process (GP) framework. To flexibly capture the dominant frequencies, we model the power spectrum of the PDE solution with a student t mixture or Gaussian mixture. We apply the inverse Fourier transform to obtain the covariance function (by Wiener-Khinchin theorem). The covariance derived from the Gaussian mixture spectrum corresponds to the known spectral mixture kernel. Next, we estimate the mixture weights in the log domain, which we show is equivalent to placing a Jeffreys prior. It automatically induces sparsity, prunes excessive frequencies, and adjusts the remaining toward the ground truth. Third, to enable efficient and scalable computation on massive collocation points, which are critical to capture high frequencies, we place the collocation points on a grid, and multiply our covariance function at each input dimension. We use the GP conditional mean to predict the solution and its derivatives so as to fit the boundary condition and the equation itself. As a result, we can derive a Kronecker product structure in the covariance matrix. We use Kronecker product properties and multilinear algebra to promote computational efficiency and scalability, without low-rank approximations. We show the advantage of our method in systematic experiments. The code is released at https://github.com/xuangu-fang/Gaussian-Process-Slover-for-High-Freq-PDE.

Time series foundation models (TSFMs) are transforming the forecasting paradigm through large-scale cross-domain pretraining. However, most existing TSFMs remain univariate, and recent efforts to enable cross-variate modeling still operate directly within the raw variate space. This design introduces fundamental limitations in semantic alignment and relational expressivity. Specifically, raw-space group mixing lacks a dedicated mechanism to align heterogeneous physical quantities, while standard non-negative attention fails to capture the complex synergistic and antagonistic interactions ubiquitous in real-world systems. To address these challenges, we propose Falcon-X, decouples variates from the raw space and maps them into a unified latent prototype space. Falcon-X employs a Unified Prototype Diff-Attention mechanism that explicitly evaluates both positive and negative semantic affinities to explicitly align heterogeneous variates. Cross-variate interactions are then efficiently performed within this shared space via Latent Entity Attention, naturally facilitating zero-shot structural transfer. Finally, a Variate Reassembly Router robustly reconstructs variate-specific trajectories via a request-and-dispatch mechanism. Extensive evaluations on the GIFT-Eval and fev-bench benchmarks demonstrate that Falcon-X achieves state-of-the-art forecasting performance, offering a principled and scalable paradigm for complex multivariate environments. Falcon-X is publicly released to support future research.

This paper thoroughly analyses the effect of different input representations on polyphonic multi-instrument music transcription. We use our own GPU based spectrogram extraction tool, nnAudio, to investigate the influence of using a linear-frequency spectrogram, log-frequency spectrogram, Mel spectrogram, and constant-Q transform (CQT). Our results show that a 8.33% increase in transcription accuracy and a 9.39% reduction in error can be obtained by choosing the appropriate input representation (log-frequency spectrogram with STFT window length 4,096 and 2,048 frequency bins in the spectrogram) without changing the neural network design (single layer fully connected). Our experiments also show that Mel spectrogram is a compact representation for which we can reduce the number of frequency bins to only 512 while still keeping a relatively high music transcription accuracy.

Following its success for vision and text, the "foundation model" (FM) paradigm -- pretraining large models on massive data, then fine-tuning on target tasks -- has rapidly expanded to domains in the sciences, engineering, healthcare, and beyond. Has this achieved what the original FMs accomplished, i.e. the supplanting of traditional supervised learning in their domains? To answer we look at three modalities -- genomics, satellite imaging, and time series -- with multiple recent FMs and compare them to a standard supervised learning workflow: model development, hyperparameter tuning, and training, all using only data from the target task. Across these three specialized domains, we find that it is consistently possible to train simple supervised models -- no more complicated than a lightly modified wide ResNet or UNet -- that match or even outperform the latest foundation models. Our work demonstrates that the benefits of large-scale pretraining have yet to be realized in many specialized areas, reinforces the need to compare new FMs to strong, well-tuned baselines, and introduces two new, easy-to-use, open-source, and automated workflows for doing so.

In this work we propose an analytical model that reproduces the core-bounds phase of gravitational waves (GW) of Rapidly Rotating (RR) from Core Collapse Supernovae (CCSNe), as a function of three parameters, the arrival time tau, the ratio of the kinetic and potential energy beta and a phenomenological parameter alpha related to rotation and equation of state (EOS). To validate the model we use 126 waveforms from the Richers catalog Richers_2017 selected with the criteria of exploring a range of rotation profiles, and involving EOS. To quantify the degree of accuracy of the proposed model, with a particular focus on the rotation parameter beta, we show that the average Fitting Factor (FF) between the simulated waveforms with the templates is 94.4\%. In order to estimate the parameters we propose a frequentist matched filtering approach in real interferometric noise which does not require assigning any priors. We use the Matched Filter (MF) technique, where we inject a bank of templates considering simulated colored Gaussian noise and the real noise of O3L1. For example for A300w6.00\_BHBLP at 10Kpc we obtain a standar deviation of sigma = 3.34times 10^{-3} for simulated colored Gaussian noise and sigma= 1.46times 10^{-2} for real noise. On the other hand, from the asymptotic expansion of the variance we obtain the theoretical minimum error for beta at 10 kpc and optimal orientation. The estimation error in this case is from 10^{-2} to 10^{-3} as beta increases. We show that the results of the estimation error of beta for the 3-parameter space (3D) is consistent with the single-parameter space (1D), which allows us to conclude that beta is decoupled from the others two parameters.

Recently, universal waveform generation tasks have been investigated conditioned on various out-of-distribution scenarios. Although GAN-based methods have shown their strength in fast waveform generation, they are vulnerable to train-inference mismatch scenarios such as two-stage text-to-speech. Meanwhile, diffusion-based models have shown their powerful generative performance in other domains; however, they stay out of the limelight due to slow inference speed in waveform generation tasks. Above all, there is no generator architecture that can explicitly disentangle the natural periodic features of high-resolution waveform signals. In this paper, we propose PeriodWave, a novel universal waveform generation model. First, we introduce a period-aware flow matching estimator that can capture the periodic features of the waveform signal when estimating the vector fields. Additionally, we utilize a multi-period estimator that avoids overlaps to capture different periodic features of waveform signals. Although increasing the number of periods can improve the performance significantly, this requires more computational costs. To reduce this issue, we also propose a single period-conditional universal estimator that can feed-forward parallel by period-wise batch inference. Additionally, we utilize discrete wavelet transform to losslessly disentangle the frequency information of waveform signals for high-frequency modeling, and introduce FreeU to reduce the high-frequency noise for waveform generation. The experimental results demonstrated that our model outperforms the previous models both in Mel-spectrogram reconstruction and text-to-speech tasks. All source code will be available at https://github.com/sh-lee-prml/PeriodWave.

Acoustic beamforming models typically assume wide-sense stationarity of speech signals within short time frames. However, voiced speech is better modeled as a cyclostationary (CS) process, a random process whose mean and autocorrelation are T_1-periodic, where alpha_1=1/T_1 corresponds to the fundamental frequency of vowels. Higher harmonic frequencies are found at integer multiples of the fundamental. This work introduces a cyclic multichannel Wiener filter (cMWF) for speech enhancement derived from a cyclostationary model. This beamformer exploits spectral correlation across the harmonic frequencies of the signal to further reduce the mean-squared error (MSE) between the target and the processed input. The proposed cMWF is optimal in the MSE sense and reduces to the MWF when the target is wide-sense stationary. Experiments on simulated data demonstrate considerable improvements in scale-invariant signal-to-distortion ratio (SI-SDR) on synthetic data but also indicate high sensitivity to the accuracy of the estimated fundamental frequency alpha_1, which limits effectiveness on real data.

Recent advances in foundation models have shown great promise in domains such as natural language processing and computer vision, and similar efforts are now emerging in the Earth Observation community. These models aim to generalize across tasks with limited supervision, reducing the need for training separate models for each task. However, current strategies, which largely focus on scaling model size and dataset volume, require prohibitive computational and data resources, limiting accessibility to only a few large institutions. Moreover, this paradigm of ever-larger models stands in stark contrast with the principles of sustainable and environmentally responsible AI, as it leads to immense carbon footprints and resource inefficiency. In this work, we present a novel and efficient alternative: an Ensemble-of-Specialists framework for building Remote Sensing Foundation Models (RSFMs). Our method decomposes the training process into lightweight, task-specific ConvNeXtV2 specialists that can be frozen and reused. This modular approach offers strong advantages in efficiency, interpretability, and extensibility. Moreover, it naturally supports federated training, pruning, and continuous specialist integration, making it particularly well-suited for collaborative and resource-constrained settings. Our framework sets a new direction for building scalable and efficient RSFMs. All codes and pretrained models are available at https://github.com/pierreadorni/EoS-FM.

Parameter-Efficient Fine-Tuning (PEFT) is a technique that allows us to adapt powerful Foundation Models (FMs) to diverse downstream tasks while preserving and unleashing their inherent capabilities. However, we have observed that existing PEFT methods, which are often designed with natural imagery in mind, struggle when applied to Remote Sensing (RS) scenarios. This is primarily due to their inability to handle artifact influences, a problem particularly severe in RS image features. To tackle this challenge, we introduce Earth-Adapter, the first PEFT method specifically designed for RS artifacts conquering. Earth-Adapter introduces a novel Mixture of Frequency Adaptation process that combines a Mixture of Adapter (MoA) with Discrete Fourier Transformation (DFT). By utilizing DFT, Earth-Adapter can decompose features into different frequency components, precisely separating artifacts from original features. The MoA then dynamically assigns weights to each adapter expert, allowing for the combination of features across various frequency domains. These simple-yet-effective approaches enable Earth-Adapter to more efficiently overcome the disturbances caused by artifacts than previous PEFT methods, significantly enhancing the FMs' performance on RS scenarios. Experiments on Domain Adaptation (DA), and Domain Generalization (DG) semantic segmentation benchmarks showcase the Earth-Adapter's effectiveness. Compared with baseline Rein, Earth-Adapter significantly improves 9.0% mIoU in DA and 3.1% mIoU in DG benchmarks. Our code will be released at https://github.com/VisionXLab/Earth-Adapter.

We present a systematic investigation of Multi-modal Retrieval Augmented Multi-modal Generation (M^2RAG), a novel task that enables foundation models to process multi-modal web content and generate multi-modal responses, which exhibits better information density and readability. Despite its potential impact, M^2RAG remains understudied, lacking comprehensive analysis and high-quality data resources. To address this gap, we establish a comprehensive benchmark through a rigorous data curation pipeline, and employ text-modal metrics and multi-modal metrics based on foundation models for evaluation. We further propose several strategies for foundation models to process M^2RAG effectively and construct a training set by filtering high-quality samples using designed metrics. Our extensive experiments demonstrate the reliability of our proposed metrics, a landscape of model performance within our designed strategies, and show that our fine-tuned 7B-8B models outperform the state-of-the-art GPT-4o model. Additionally, we perform fine-grained analyses across diverse domains and validate the effectiveness of our designs in data curation pipeline. All resources, including codes, datasets, and model weights, will be publicly released.

Long-term time series forecasting (LTSF) is important for various domains but is confronted by challenges in handling the complex temporal-contextual relationships. As multivariate input models underperforming some recent univariate counterparts, we posit that the issue lies in the inefficiency of existing multivariate LTSF Transformers to model series-wise relationships: the characteristic differences between series are often captured incorrectly. To address this, we introduce ARM: a multivariate temporal-contextual adaptive learning method, which is an enhanced architecture specifically designed for multivariate LTSF modelling. ARM employs Adaptive Univariate Effect Learning (AUEL), Random Dropping (RD) training strategy, and Multi-kernel Local Smoothing (MKLS), to better handle individual series temporal patterns and correctly learn inter-series dependencies. ARM demonstrates superior performance on multiple benchmarks without significantly increasing computational costs compared to vanilla Transformer, thereby advancing the state-of-the-art in LTSF. ARM is also generally applicable to other LTSF architecture beyond vanilla Transformer.

Deep learning (e.g., Transformer) has been widely and successfully used in multivariate time series forecasting (MTSF). Unlike existing methods that focus on training models from a single modal of time series input, large language models (LLMs) based MTSF methods with cross-modal text and time series input have recently shown great superiority, especially with limited temporal data. However, current LLM-based MTSF methods usually focus on adapting and fine-tuning LLMs, while neglecting the distribution discrepancy between textual and temporal input tokens, thus leading to sub-optimal performance. To address this issue, we propose a novel Cross-Modal LLM Fine-Tuning (CALF) framework for MTSF by reducing the distribution discrepancy between textual and temporal data, which mainly consists of the temporal target branch with temporal input and the textual source branch with aligned textual input. To reduce the distribution discrepancy, we develop the cross-modal match module to first align cross-modal input distributions. Additionally, to minimize the modality distribution gap in both feature and output spaces, feature regularization loss is developed to align the intermediate features between the two branches for better weight updates, while output consistency loss is introduced to allow the output representations of both branches to correspond effectively. Thanks to the modality alignment, CALF establishes state-of-the-art performance for both long-term and short-term forecasting tasks with low computational complexity, and exhibiting favorable few-shot and zero-shot abilities similar to that in LLMs. Code is available at https://github.com/Hank0626/LLaTA.

Long-term time-series forecasting needs models that are accurate yet efficient enough for commodity hardware. Lightweight linear forecasters are remarkably strong in this regime, yet they leave two openings: reversible instance normalization (RevIN) de-normalizes the entire horizon with a single lookback statistic, which is inaccurate under non-stationarity, and time-domain trend/seasonal decomposition relies on a fixed, non-adaptive filter. We present FreqLite, an ultra-lightweight, channel-independent frequency-decomposed linear forecaster: a learnable, lossless, partition-of-unity spectral filter splits the input into bands that are forecast by per-band linear heads and, unlike low-pass-truncation approaches, the high-frequency band is retained and modeled. FreqLite is the best lightweight model on the standard long-term forecasting benchmarks and, at long lookback (L=336), attains a lower average error than a PatchTST Transformer (0.3244 vs. 0.3587 MSE) while using 4x fewer parameters, 2.2x less memory, and 2.2x less time per epoch on a single 4 GB laptop GPU; although modest in magnitude, its improvements are statistically significant under paired Wilcoxon tests across all matched cells (p < 1e-5). We further introduce Adaptive Reversible Instance Normalization (A-RevIN), a regime-adaptive reversible normalization that strictly generalizes RevIN (recovered exactly when its gate is closed), engages under non-stationarity, and reduces to RevIN without harm on stationary data. We validate this on both a real strongly non-stationary dataset (ILI, up to ~5% MSE reduction) and a controlled synthetic drift sweep in which A-RevIN's benefit and its learned gate both rise monotonically with injected non-stationarity. Every component is independently ablatable (Linear and RLinear are special cases of FreqLite), and all results are reproducible on commodity hardware.

A handful of visual foundation models (VFMs) have recently emerged as the backbones for numerous downstream tasks. VFMs like CLIP, DINOv2, SAM are trained with distinct objectives, exhibiting unique characteristics for various downstream tasks. We find that despite their conceptual differences, these models can be effectively merged into a unified model through multi-teacher distillation. We name this approach AM-RADIO (Agglomerative Model -- Reduce All Domains Into One). This integrative approach not only surpasses the performance of individual teacher models but also amalgamates their distinctive features, such as zero-shot vision-language comprehension, detailed pixel-level understanding, and open vocabulary segmentation capabilities. In pursuit of the most hardware-efficient backbone, we evaluated numerous architectures in our multi-teacher distillation pipeline using the same training recipe. This led to the development of a novel architecture (E-RADIO) that exceeds the performance of its predecessors and is at least 7x faster than the teacher models. Our comprehensive benchmarking process covers downstream tasks including ImageNet classification, ADE20k semantic segmentation, COCO object detection and LLaVa-1.5 framework. Code: https://github.com/NVlabs/RADIO

In time series forecasting, effectively disentangling intricate temporal patterns is crucial. While recent works endeavor to combine decomposition techniques with deep learning, multiple frequencies may still be mixed in the decomposed components, e.g., trend and seasonal. Furthermore, frequency domain analysis methods, e.g., Fourier and wavelet transforms, have limitations in resolution in the time domain and adaptability. In this paper, we propose D-PAD, a deep-shallow multi-frequency patterns disentangling neural network for time series forecasting. Specifically, a multi-component decomposing (MCD) block is introduced to decompose the series into components with different frequency ranges, corresponding to the "shallow" aspect. A decomposition-reconstruction-decomposition (D-R-D) module is proposed to progressively extract the information of frequencies mixed in the components, corresponding to the "deep" aspect. After that, an interaction and fusion (IF) module is used to further analyze the components. Extensive experiments on seven real-world datasets demonstrate that D-PAD achieves the state-of-the-art performance, outperforming the best baseline by an average of 9.48% and 7.15% in MSE and MAE, respectively.

We present an efficient frequency-based neural representation termed PREF: a shallow MLP augmented with a phasor volume that covers significant border spectra than previous Fourier feature mapping or Positional Encoding. At the core is our compact 3D phasor volume where frequencies distribute uniformly along a 2D plane and dilate along a 1D axis. To this end, we develop a tailored and efficient Fourier transform that combines both Fast Fourier transform and local interpolation to accelerate na\"ive Fourier mapping. We also introduce a Parsvel regularizer that stables frequency-based learning. In these ways, Our PREF reduces the costly MLP in the frequency-based representation, thereby significantly closing the efficiency gap between it and other hybrid representations, and improving its interpretability. Comprehensive experiments demonstrate that our PREF is able to capture high-frequency details while remaining compact and robust, including 2D image generalization, 3D signed distance function regression and 5D neural radiance field reconstruction.

Continuous-latent audio autoencoders form the backbone of latent music generators, yet decoders at high compression rates commonly exhibit three failure modes: high-frequency loss, phase incoherence, and stereo-image collapse. These share a structural root: waveform autoencoders lack an explicit frequency axis, leaving no handle for targeted per-band correction. Among five matched-budget representations, the complex STFT achieves the lowest full-band and high-frequency spectral distances, providing direct access to magnitude and phase at every bin. Building on this, we present ear-VAE2, a complex-spectral autoencoder with cross-channel interaction. Spec-SnakeBeta learns a periodic activation per frequency bin with frequency-dependent initialization, outperforming other activation variants while using fewer parameters than the fully independent variant. Duplex-Aware Refiner applies band-specific corrections to magnitude and phase following duplex theory of sound localization. On the 546-track Song Describer Dataset, ear-VAE2 achieves the best point estimates on five of seven reconstruction metrics. The Duplex-Aware Refiner reduces Mel Distance by 19.4% and uses ~45% fewer residual-output dimensions than the Unconstrained Refiner, while also lowering spectral distances, spatial-cue errors, and receiving higher ratings from professional engineers. The downstream generator using ear-VAE2 latents achieves better point estimates on all 12 automatic metrics.Demo page is available at https://eps-acoustic-revolution-lab.github.io/EAR_VAE2/.

When solving forecasting problems including multiple time-series features, existing approaches often fall into two extreme categories, depending on whether to utilize inter-feature information: univariate and complete-multivariate models. Unlike univariate cases which ignore the information, complete-multivariate models compute relationships among a complete set of features. However, despite the potential advantage of leveraging the additional information, complete-multivariate models sometimes underperform univariate ones. Therefore, our research aims to explore a middle ground between these two by introducing what we term Partial-Multivariate models where a neural network captures only partial relationships, that is, dependencies within subsets of all features. To this end, we propose PMformer, a Transformer-based partial-multivariate model, with its training algorithm. We demonstrate that PMformer outperforms various univariate and complete-multivariate models, providing a theoretical rationale and empirical analysis for its superiority. Additionally, by proposing an inference technique for PMformer, the forecasting accuracy is further enhanced. Finally, we highlight other advantages of PMformer: efficiency and robustness under missing features.

The scientific reasoning ability of large language models (LLMs) has recently attracted significant attention. Time series, as a fundamental modality in scientific data, presents unique challenges that are often overlooked in current multimodal LLMs, which either encode numerical sequences as text or convert them into images. Such approaches may be insufficient for comprehensive scientific time series understanding and generation. Existing unified time series models typically specialise in either forecasting or analysis, and their effectiveness on non-periodic, heterogeneous scientific signals remains unclear. To address these gaps, we introduce SciTS, a benchmark spanning 12 scientific domains and 43 tasks, with over 50k+ instances, both univariate and multivariate signals ranging from 10^0 to 10^7 in length and up to 10~MHz in frequency. We benchmark 17 models, including text-only LLMs, multimodal LLMs, and unified time series models, and find that general-purpose LLMs exhibit stronger generalisability than specialised time series models, while representing time series as text or images limits their performance due to excessively long sequences and loss of numerical precision, respectively. We then introduce TimeOmni, a framework that equips LLMs with the ability to understand and generate time series while remaining compatible with general-purpose LLM training. This work fills a gap in both dedicated benchmarks and modelling frameworks for scientific time series, paving the way for LLMs to understand and generate complex temporal scientific data.

Developing a versatile deep neural network to model music audio is crucial in MIR. This task is challenging due to the intricate spectral variations inherent in music signals, which convey melody, harmonics, and timbres of diverse instruments. In this paper, we introduce Mel-RoFormer, a spectrogram-based model featuring two key designs: a novel Mel-band Projection module at the front-end to enhance the model's capability to capture informative features across multiple frequency bands, and interleaved RoPE Transformers to explicitly model the frequency and time dimensions as two separate sequences. We apply Mel-RoFormer to tackle two essential MIR tasks: vocal separation and vocal melody transcription, aimed at isolating singing voices from audio mixtures and transcribing their lead melodies, respectively. Despite their shared focus on singing signals, these tasks possess distinct optimization objectives. Instead of training a unified model, we adopt a two-step approach. Initially, we train a vocal separation model, which subsequently serves as a foundation model for fine-tuning for vocal melody transcription. Through extensive experiments conducted on benchmark datasets, we showcase that our models achieve state-of-the-art performance in both vocal separation and melody transcription tasks, underscoring the efficacy and versatility of Mel-RoFormer in modeling complex music audio signals.

General speech restoration demands techniques that can interpret complex speech structures under various distortions. While State-Space Models like SEMamba have advanced the state-of-the-art in speech denoising, they are not inherently optimized for critical speech characteristics, such as spectral periodicity or multi-resolution frequency analysis. In this work, we introduce an architecture tailored to incorporate speech-specific features as inductive biases. In particular, we propose Frequency GLP, a frequency feature extraction block that effectively and efficiently leverages the properties of frequency bins. Then, we design a multi-resolution parallel time-frequency dual-processing block to capture diverse spectral patterns, and a learnable mapping to further enhance model performance. With all our ideas combined, the proposed SEMamba++ achieves the best performance among multiple baseline models while remaining computationally efficient.

Implicit Neural Representations (INRs) have emerged as a powerful paradigm for representing signals such as images, audio, and 3D scenes. However, existing INR frameworks -- including MLPs with Fourier features, SIREN, and multiresolution hash grids -- implicitly assume a global and stationary spectral basis. This assumption is fundamentally misaligned with real-world signals whose frequency characteristics vary significantly across space, exhibiting local high-frequency textures, smooth regions, and frequency drift phenomena. We propose Neural Spectral Transport Representation (NSTR), the first INR framework that explicitly models a spatially varying local frequency field. NSTR introduces a learnable frequency transport equation, a PDE that governs how local spectral compositions evolve across space. Given a learnable local spectrum field S(x) and a frequency transport network F_θ enforcing nabla S(x) approx F_θ(x, S(x)), NSTR reconstructs signals by spatially modulating a compact set of global sinusoidal bases. This formulation enables strong local adaptivity and offers a new level of interpretability via visualizing frequency flows. Experiments on 2D image regression, audio reconstruction, and implicit 3D geometry show that NSTR achieves significantly better accuracy-parameter trade-offs than SIREN, Fourier-feature MLPs, and Instant-NGP. NSTR requires fewer global frequencies, converges faster, and naturally explains signal structure through spectral transport fields. We believe NSTR opens a new direction in INR research by introducing explicit modeling of space-varying spectrum.

Recently, deep learning has driven significant advancements in multivariate time series forecasting (MTSF) tasks. However, much of the current research in MTSF tends to evaluate models from a holistic perspective, which obscures the individual contributions and leaves critical issues unaddressed. Adhering to the current modeling paradigms, this work bridges these gaps by systematically decomposing deep MTSF methods into their core, fine-grained components like series-patching tokenization, channel-independent strategy, attention modules, or even Large Language Models and Time-series Foundation Models. Through extensive experiments and component-level analysis, our work offers more profound insights than previous benchmarks that typically discuss models as a whole. Furthermore, we propose a novel automated solution called TSGym for MTSF tasks. Unlike traditional hyperparameter tuning, neural architecture searching or fixed model selection, TSGym performs fine-grained component selection and automated model construction, which enables the creation of more effective solutions tailored to diverse time series data, therefore enhancing model transferability across different data sources and robustness against distribution shifts. Extensive experiments indicate that TSGym significantly outperforms existing state-of-the-art MTSF and AutoML methods. All code is publicly available on https://github.com/SUFE-AILAB/TSGym.

Foundation models offer a promising route to compress multi-modal physiological signals into compact representations of human health, with broad applications across sleep medicine, cardiology, neurology and other healthcare domains. Existing models have typically been trained with masked-reconstruction or contrastive objectives. However, masked reconstruction may be poorly suited to the stochastic nature of these signals, while contrastive approaches rely on positive-pair definitions despite the semantic invariances of physiological signals being poorly understood. In this work, we show that next-token prediction is a simple and scalable alternative. We develop Hypnos, a multi-modal sleep foundation model trained using eight different sensing modalities (e.g. EEG, ECG, respiratory signals) drawn from over 20,000 overnight polysomnography recordings. We tokenize each modality into streams of discrete tokens using residual vector quantization, then train a large auto-regressive RQ-Transformer to jointly predict the next token across all modalities in parallel. After training, Hypnos can be applied to continuous streams of sensor data from any subset of supported modalities, generating embeddings for downstream tasks. Across a range of benchmarks, Hypnos significantly outperforms existing foundation models. In sleep stage classification, we match the performance of strong supervised baselines on held-out test sets whilst using \(100\times\) less labelled data. Hypnos even generalises to daytime physiology, surpassing a dedicated ECG foundation model at detecting atrial fibrillation. Our results demonstrate that next-token prediction is a strong self-supervised objective for representation learning from multi-modal physiological signals.

The recent surge in Time Series Foundation Models has rapidly advanced the field, yet the heterogeneous training setups across studies make it difficult to attribute improvements to architectural innovations versus data engineering. In this work, we investigate the potential of a standard patch Transformer, demonstrating that this generic architecture achieves state-of-the-art zero-shot forecasting performance using a straightforward training protocol. We conduct a comprehensive ablation study that covers model scaling, data composition, and training techniques to isolate the essential ingredients for high performance. Our findings identify the key drivers of performance, while confirming that the generic architecture itself demonstrates excellent scalability. By strictly controlling these variables, we provide comprehensive empirical results on model scaling across multiple dimensions. We release our open-source model and detailed findings to establish a transparent, reproducible baseline for future research.

Machine learning models in astrophysics are often limited in scope and cannot adapt to data from new instruments or tasks. We introduce SpectraFM, a Transformer-based foundation model architecture that can be pre-trained on stellar spectra from any wavelength range and instrument. SpectraFM excels in generalization by combining flexibility with knowledge transfer from pre-training, allowing it to outperform traditional machine learning methods, especially in scenarios with limited training data. Our model is pre-trained on approximately 90k examples of synthetic spectra to predict the chemical abundances (Fe, Mg, O), temperature, and specific gravity of stars. We then fine-tune the model on real spectra to adapt it to observational data before fine-tuning it further on a restricted 100-star training set in a different wavelength range to predict iron abundance. Despite a small iron-rich training set of real spectra, transfer learning from the synthetic spectra pre-training enables the model to perform well on iron-poor stars. In contrast, a neural network trained from scratch fails at this task. We investigate the Transformer attention mechanism and find that the wavelengths receiving attention carry physical information about chemical composition. By leveraging the knowledge from pre-training and its ability to handle non-spectra inputs, SpectraFM reduces the need for large training datasets and enables cross-instrument and cross-domain research. Its adaptability makes it well-suited for tackling emerging challenges in astrophysics, like extracting insights from multi-modal datasets.

In this work, we aim to estimate the stellar parameters of the primary (Aa) by performing asteroseismic analysis on its period-spacing pattern. We use the C-3PO neural network to perform asteroseismic modelling of the g-mode period-spacing pattern of Aa, discussing the interplay of this information with external constraints from spectroscopy (T_{rm eff} and log(g)) and eclipse modelling (R). To estimate the level of uncertainty due to different frequency extraction and pattern identification processes, we consider four different variations on the period-spacing patterns. To better understand the correlations between and the uncertainty structure of our parameter estimates, we also employed a classical, parameter-based MCMC grid search on four different stellar grids. The best-fitting, externally constrained model to the period-spacing pattern arrives at estimates of the stellar properties for Aa of: M=1.51 pm 0.05 M_odot, X_c =0.43 pm 0.04, R=1.66 pm 0.1 R_odot, f_{rm ov}=0.010, Omega_c=1.58 pm 0.01 d^{-1} with rigid rotation to within the measurement errors, log(T_{rm eff})=3.856 pm 0.008 dex, log(g)=4.18 pm 0.04 dex, and log(L)=0.809 pm 0.005 dex, which agree well with previous measurements from eclipse modelling, spectroscopy, and the Gaia DR3 luminosity. We find that the near-core properties of the best-fitting asteroseismic models are consistent with external constraints from eclipse modelling and spectroscopy. Aa appears to be a typical example of a gamma Dor star, fitting well within existing populations. We find that Aa is quasi-rigidly rotating to within the uncertainties, and note that the asteroseismic age estimate for Aa (1100 pm 100 Myr) is considerably older than the young (35 Myr) age implied by previous isochrone fits to the B binary in the literature. Our MCMC parameter-based grid-search agrees well with our pattern-modelling approach.

Recent works propose complex multi-modal models that handle both time series and language, ultimately claiming high performance on complex tasks like time series reasoning and cross-modal question-answering. However, they skip evaluations of simple and important foundational tasks, which complex models should reliably master. They also lack direct, head-to-head comparisons with other popular approaches. So we ask a simple question: Can recent models even produce generic visual descriptions of time series data? In response, we propose three new tasks, posing that successful multi-modal models should be able to recognize, differentiate, and generate language descriptions of time series. We then create BEDTime, the first benchmark dataset to assess models on each task, comprising four datasets reformatted for these tasks across multiple modalities. Using BEDTime, we evaluate 13 state-of-the-art models, and find that (1) surprisingly, dedicated time series foundation models severely underperform, despite being designed for similar tasks, (2) vision-language models are quite capable, (3) language-only methods perform worst, despite many lauding their potential, and (4) all approaches are clearly fragile to a range of realistic robustness tests, indicating avenues for future work.

The objective of this study is to evaluate the potential for History Matching (HM) to tune a climate system with multi-scale dynamics. By considering a toy climate model, namely, the two-scale Lorenz96 model and producing experiments in perfect-model setting, we explore in detail how several built-in choices need to be carefully tested. We also demonstrate the importance of introducing physical expertise in the range of parameters, a priori to running HM. Finally we revisit a classical procedure in climate model tuning, that consists of tuning the slow and fast components separately. By doing so in the Lorenz96 model, we illustrate the non-uniqueness of plausible parameters and highlight the specificity of metrics emerging from the coupling. This paper contributes also to bridging the communities of uncertainty quantification, machine learning and climate modeling, by making connections between the terms used by each community for the same concept and presenting promising collaboration avenues that would benefit climate modeling research.

Despite the rapid advancements in Artificial Intelligence (AI), Stochastic Differential Equations (SDEs) remain the gold-standard formalism for modeling systems under uncertainty. However, applying SDEs in practice is fraught with challenges: modeling risk is high, calibration is often brittle, and high-fidelity simulations are computationally expensive. This technical report introduces JointFM, a foundation model that inverts this paradigm. Instead of fitting SDEs to data, we sample an infinite stream of synthetic SDEs to train a generic model to predict future joint probability distributions directly. This approach establishes JointFM as the first foundation model for distributional predictions of coupled time series - requiring no task-specific calibration or finetuning. Despite operating in a purely zero-shot setting, JointFM reduces the energy loss by 14.2% relative to the strongest baseline when recovering oracle joint distributions generated by unseen synthetic SDEs.

Foundation models (FMs) have transformed natural language processing, but their success has not yet translated to time series forecasting. Existing time series foundation models (TSFMs), often based on transformer variants, struggle with generalization across varying context and target lengths, lack adaptability to different sampling rates, and are computationally inefficient. We introduce FlowState, a novel TSFM architecture that addresses these challenges through two key innovations: a state space model (SSM) based encoder and a functional basis decoder. This design enables continuous-time modeling and dynamic time-scale adjustment, allowing FlowState to inherently generalize across all possible temporal resolutions, and dynamically adjust the forecasting horizons. In contrast to other state-of-the-art TSFMs, which require training data across all possible sampling rates to memorize patterns at each scale, FlowState inherently adapts its internal dynamics to the input scale, enabling smaller models, reduced data requirements, and improved efficiency. We further propose an efficient pretraining strategy that improves robustness and accelerates training. Despite being the smallest model, FlowState outperforms all other models and is state-of-the-art for the GIFT-ZS and the Chronos-ZS benchmarks. Ablation studies confirm the effectiveness of its components, and we demonstrate its unique ability to adapt online to varying input sampling rates.

We assess the impact of a multi-scale loss formulation for training probabilistic machine-learned weather forecasting models. The multi-scale loss is tested in AIFS-CRPS, a machine-learned weather forecasting model developed at the European Centre for Medium-Range Weather Forecasts (ECMWF). AIFS-CRPS is trained by directly optimising the almost fair continuous ranked probability score (afCRPS). The multi-scale loss better constrains small scale variability without negatively impacting forecast skill. This opens up promising directions for future work in scale-aware model training.

Deep learning-based methods have been widely researched in the areas of language and vision, demonstrating their capacity to understand long sequences of data and their usefulness in numerous helio-physics applications. Foundation models (FMs), which are pre-trained on a large-scale datasets, form the basis for a variety of downstream tasks. These models, especially those based on transformers in vision and language, show exceptional potential for adapting to a wide range of downstream applications. In this paper, we provide our perspective on the criteria for designing an FM for heliophysics and associated challenges and applications using the Solar Dynamics Observatory (SDO) dataset. We believe that this is the first study to design an FM in the domain of heliophysics.

Current language model training commonly applies multi-task Supervised Fine-Tuning (SFT) using a homogeneous compute budget across all sub-datasets. This approach is fundamentally sub-optimal: heterogeneous learning dynamics cause faster-learning tasks to overfit early while slower ones remain under-fitted. To address this, we introduce mSFT, an iterative, overfitting-aware search algorithm for multi-task data mixtures. mSFT trains the model on an active mixture, identifies and excludes the earliest overfitting sub-dataset, and reverts to that specific optimal checkpoint before continuing. Extensive evaluations demonstrate that mSFT consistently outperforms 4 baselines across 10 benchmarks and 6 base models. Further analysis confirms mSFT maintains robust gains across diverse dataset sizes, task granularities, and is insensitive to its single new hyperparameter (compute budget). Notably, at low compute budget, mSFT can improve performance while lowering training FLOPs. Ultimately, mSFT establishes a practical overfitting-aware algorithm for multi-task SFT that maximizes the potential of models across diverse data mixtures.

Time series classification (TSC) on multivariate time series is a critical problem. We propose a novel multi-view approach integrating frequency-domain and time-domain features to provide complementary contexts for TSC. Our method fuses continuous wavelet transform spectral features with temporal convolutional or multilayer perceptron features. We leverage the Mamba state space model for efficient and scalable sequence modeling. We also introduce a novel tango scanning scheme to better model sequence relationships. Experiments on 10 standard benchmark datasets demonstrate our approach achieves an average 6.45% accuracy improvement over state-of-the-art TSC models.

Time series data are ubiquitous across a wide range of real-world domains. While real-world time series analysis (TSA) requires human experts to integrate numerical series data with multimodal domain-specific knowledge, most existing TSA models rely solely on numerical data, overlooking the significance of information beyond numerical series. This oversight is due to the untapped potential of textual series data and the absence of a comprehensive, high-quality multimodal dataset. To overcome this obstacle, we introduce Time-MMD, the first multi-domain, multimodal time series dataset covering 9 primary data domains. Time-MMD ensures fine-grained modality alignment, eliminates data contamination, and provides high usability. Additionally, we develop MM-TSFlib, the first multimodal time-series forecasting (TSF) library, seamlessly pipelining multimodal TSF evaluations based on Time-MMD for in-depth analyses. Extensive experiments conducted on Time-MMD through MM-TSFlib demonstrate significant performance enhancements by extending unimodal TSF to multimodality, evidenced by over 15% mean squared error reduction in general, and up to 40% in domains with rich textual data. More importantly, our datasets and library revolutionize broader applications, impacts, research topics to advance TSA. The dataset and library are available at https://github.com/AdityaLab/Time-MMD and https://github.com/AdityaLab/MM-TSFlib.

Time series forecasting plays a crucial role in data mining, driving rapid advancements across numerous industries. With the emergence of large models, time series foundation models (TSFMs) have exhibited remarkable generalization capabilities, such as zero-shot learning, through large-scale pre-training. Meanwhile, Retrieval-Augmented Generation (RAG) methods have been widely employed to enhance the performance of foundation models on unseen data, allowing models to access to external knowledge. In this paper, we introduce TimeRAF, a Retrieval-Augmented Forecasting model that enhance zero-shot time series forecasting through retrieval-augmented techniques. We develop customized time series knowledge bases that are tailored to the specific forecasting tasks. TimeRAF employs an end-to-end learnable retriever to extract valuable information from the knowledge base. Additionally, we propose Channel Prompting for knowledge integration, which effectively extracts relevant information from the retrieved knowledge along the channel dimension. Extensive experiments demonstrate the effectiveness of our model, showing significant improvement across various domains and datasets.

Gravitational-wave data analysis relies on accurate and efficient methods to extract physical information from noisy detector signals, yet the increasing rate and complexity of observations represent a growing challenge. Deep learning provides a powerful alternative to traditional inference, but existing neural models typically lack the flexibility to handle variations in data analysis settings. Such variations accommodate imperfect observations or are required for specialized tests, and could include changes in detector configurations, overall frequency ranges, or localized cuts. We introduce a flexible transformer-based architecture paired with a training strategy that enables adaptation to diverse analysis settings at inference time. Applied to parameter estimation, we demonstrate that a single flexible model -- called Dingo-T1 -- can (i) analyze 48 gravitational-wave events from the third LIGO-Virgo-KAGRA Observing Run under a wide range of analysis configurations, (ii) enable systematic studies of how detector and frequency configurations impact inferred posteriors, and (iii) perform inspiral-merger-ringdown consistency tests probing general relativity. Dingo-T1 also improves median sample efficiency on real events from a baseline of 1.4% to 4.2%. Our approach thus demonstrates flexible and scalable inference with a principled framework for handling missing or incomplete data -- key capabilities for current and next-generation observatories.

This paper introduces Mamba4Cast, a zero-shot foundation model for time series forecasting. Based on the Mamba architecture and inspired by Prior-data Fitted Networks (PFNs), Mamba4Cast generalizes robustly across diverse time series tasks without the need for dataset specific fine-tuning. Mamba4Cast's key innovation lies in its ability to achieve strong zero-shot performance on real-world datasets while having much lower inference times than time series foundation models based on the transformer architecture. Trained solely on synthetic data, the model generates forecasts for entire horizons in a single pass, outpacing traditional auto-regressive approaches. Our experiments show that Mamba4Cast performs competitively against other state-of-the-art foundation models in various data sets while scaling significantly better with the prediction length. The source code can be accessed at https://github.com/automl/Mamba4Cast.

Time series data in real-world applications such as healthcare, climate modeling, and finance are often irregular, multimodal, and messy, with varying sampling rates, asynchronous modalities, and pervasive missingness. However, existing benchmarks typically assume clean, regularly sampled, unimodal data, creating a significant gap between research and real-world deployment. We introduce Time-IMM, a dataset specifically designed to capture cause-driven irregularity in multimodal multivariate time series. Time-IMM represents nine distinct types of time series irregularity, categorized into trigger-based, constraint-based, and artifact-based mechanisms. Complementing the dataset, we introduce IMM-TSF, a benchmark library for forecasting on irregular multimodal time series, enabling asynchronous integration and realistic evaluation. IMM-TSF includes specialized fusion modules, including a timestamp-to-text fusion module and a multimodality fusion module, which support both recency-aware averaging and attention-based integration strategies. Empirical results demonstrate that explicitly modeling multimodality on irregular time series data leads to substantial gains in forecasting performance. Time-IMM and IMM-TSF provide a foundation for advancing time series analysis under real-world conditions. The dataset is publicly available at https://github.com/blacksnail789521/Time-IMM, and the benchmark library can be accessed at https://github.com/blacksnail789521/IMM-TSF. Project page: https://blacksnail789521.github.io/time-imm-project-page/

This paper investigates foundation models tailored for music informatics, a domain currently challenged by the scarcity of labeled data and generalization issues. To this end, we conduct an in-depth comparative study among various foundation model variants, examining key determinants such as model architectures, tokenization methods, temporal resolution, data, and model scalability. This research aims to bridge the existing knowledge gap by elucidating how these individual factors contribute to the success of foundation models in music informatics. Employing a careful evaluation framework, we assess the performance of these models across diverse downstream tasks in music information retrieval, with a particular focus on token-level and sequence-level classification. Our results reveal that our model demonstrates robust performance, surpassing existing models in specific key metrics. These findings contribute to the understanding of self-supervised learning in music informatics and pave the way for developing more effective and versatile foundation models in the field. A pretrained version of our model is publicly available to foster reproducibility and future research.

Diffusion models typically suffer from error accumulation during iterative sampling, commonly referred to as exposure bias. We reveal systematic frequency-dependent discrepancies between training and inference, which can be interpreted as frequency-dependent SNR error. Crucially, the direction of this mismatch varies across models and timesteps, indicating that fixed correction rules do not generalize. We propose Spectral Alignment (SPA), a lightweight, guidance-based method that calibrates the power spectrum of intermediate predictions to a pre-computed prior. Our approach consists of two stages: (1) offline fitting of a parametric spectrum model from training data, and (2) inference-time guidance via efficient FFT-based gradient computation. SPA introduces minimal computational overhead (3-4\%) and is complementary to Classifier-Free Guidance (CFG). We demonstrate consistent improvements across diverse architectures, from pixel-space models (DDPM, ADM) to latent diffusion models (SD2.0, SDXL) and flow-matching models (SD3.5, FLUX). Our implementation is available at https://github.com/SonyResearch/SPA.

Time series analysis stands as a focal point within the data mining community, serving as a cornerstone for extracting valuable insights crucial to a myriad of real-world applications. Recent advances in Foundation Models (FMs) have fundamentally reshaped the paradigm of model design for time series analysis, boosting various downstream tasks in practice. These innovative approaches often leverage pre-trained or fine-tuned FMs to harness generalized knowledge tailored for time series analysis. This survey aims to furnish a comprehensive and up-to-date overview of FMs for time series analysis. While prior surveys have predominantly focused on either application or pipeline aspects of FMs in time series analysis, they have often lacked an in-depth understanding of the underlying mechanisms that elucidate why and how FMs benefit time series analysis. To address this gap, our survey adopts a methodology-centric classification, delineating various pivotal elements of time-series FMs, including model architectures, pre-training techniques, adaptation methods, and data modalities. Overall, this survey serves to consolidate the latest advancements in FMs pertinent to time series analysis, accentuating their theoretical underpinnings, recent strides in development, and avenues for future exploration.

Learning time series foundation models has been shown to be a promising approach for zero-shot time series forecasting across diverse time series domains. Insofar as scaling has been a critical driver of performance of foundation models in other modalities such as language and vision, much recent work on time series foundation modeling has focused on scaling. This has resulted in time series foundation models with hundreds of millions of parameters that are, while performant, inefficient and expensive to use in practice. This paper describes a simple recipe for learning efficient foundation models for zero-shot time series forecasting that are orders of magnitude smaller. We show that large-scale transformers are not necessary: small hybrid models that interleave long convolution and linear RNN layers (in particular DeltaNet layers) can match the performance of larger transformer-based models while being more than a hundred times smaller. We also describe several data augmentation and inference strategies that further improve performance. This recipe results in Reverso, a family of efficient time series foundation models for zero-shot forecasting that significantly push the performance-efficiency Pareto frontier.

The performance of single image super-resolution depends heavily on how to generate and complement high-frequency details to low-resolution images. Recently, diffusion-based models exhibit great potential in generating high-quality images for super-resolution tasks. However, existing models encounter difficulties in directly predicting high-frequency information of wide bandwidth by solely utilizing the high-resolution ground truth as the target for all sampling timesteps. To tackle this problem and achieve higher-quality super-resolution, we propose a novel Frequency Domain-guided multiscale Diffusion model (FDDiff), which decomposes the high-frequency information complementing process into finer-grained steps. In particular, a wavelet packet-based frequency complement chain is developed to provide multiscale intermediate targets with increasing bandwidth for reverse diffusion process. Then FDDiff guides reverse diffusion process to progressively complement the missing high-frequency details over timesteps. Moreover, we design a multiscale frequency refinement network to predict the required high-frequency components at multiple scales within one unified network. Comprehensive evaluations on popular benchmarks are conducted, and demonstrate that FDDiff outperforms prior generative methods with higher-fidelity super-resolution results.

Time series forecasting is a foundational task across domains, such as finance, healthcare, and environmental monitoring. While recent advances in Time Series Foundation Models (TSFMs) have demonstrated strong generalisation through large-scale pretraining, existing models operate predominantly in a unimodal setting, ignoring the rich multimodal context, such as visual and textual signals, that often accompanies time series data in real-world scenarios. This paper introduces a novel parameter-efficient multimodal framework, UniCast, that extends TSFMs to jointly leverage time series, vision, and text modalities for enhanced forecasting performance. Our method integrates modality-specific embeddings from pretrained Vision and Text Encoders with a frozen TSFM via soft prompt tuning, enabling efficient adaptation with minimal parameter updates. This design not only preserves the generalisation strength of the foundation model but also enables effective cross-modal interaction. Extensive experiments across diverse time-series forecasting benchmarks demonstrate that UniCast consistently and significantly outperforms all existing TSFM baselines. The findings highlight the critical role of multimodal context in advancing the next generation of general-purpose time series forecasters.

Accurate Multivariate Time Series (MTS) forecasting is crucial for collaborative design of complex systems, Digital Twin building, and maintenance ahead of time. However, the collaborative industrial environment presents new challenges for MTS forecasting models: models should decouple complex inter-variable dependencies while addressing non-stationary distribution shift brought by environmental changes. To address these challenges and improve collaborative sensing reliability, we propose a Patch-Based Dual-Branch Channel-Temporal Forecasting Network (D-CTNet). Particularly, with a parallel dual-branch design incorporating linear temporal modeling layer and channel attention mechanism, our method explicitly decouples and jointly learns intra-channel temporal evolution patterns and dynamic multivariate correlations. Furthermore, a global patch attention fusion module goes beyond the local window scope to model long range dependencies. Most importantly, aiming at non-stationarity, a Frequency-Domain Stationarity Correction mechanism adaptively suppresses distribution shift impacts from environment change by spectrum alignment. Evaluations on seven benchmark datasets show that our model achieves better forecasting accuracy and robustness compared with state-of-the-art methods. Our work shows great promise as a new forecasting engine for industrial collaborative systems.

Hyperparameter tuning almost always means search: fit the model at every value on a grid, score each by cross-validation, and keep the winner. For spline regression that search is unnecessary. The optimal resolution can be solved for in closed form, to the accuracy an exhaustive search reaches, at a fraction of the compute. Three ingredients make this possible: classical approximation theory pins the squared bias to a known power of the resolution G, exactly the Kolmogorov n-width of the smoothness class; the basis dimension is an explicit polynomial in G; and leave-one-out error follows from a single fit via the PRESS identity. Balancing the two known curves gives the minimizer analytically. We extend this calculus to many coordinates by replacing ambient input dimension with interaction order, the number of active low-order components in an ANOVA decomposition, yielding a scaling law in which the optimal resolution and error are power functions of the effective density (sample size per active component), with input dimension absent from the exponent. The law becomes an algorithm. KORE (Kolmogorov-optimal Order-aware Resolution Estimation) fits two pilot resolutions, solves a leverage-calibrated 2x2 system for the bias and noise scales, and evaluates the closed-form plug-in resolution with a tiny leave-one-out certificate: about a dozen fits instead of a full grid sweep, with a consistency guarantee as the sample grows. Across additive and sparse pairwise targets up to 80 input dimensions, KORE matches exhaustive 3-fold cross-validation and the full classical ladder (GCV, Mallows' Cp, AIC, BIC) while fitting roughly 8x fewer models; on 36 real tabular datasets it ranks first among 21 methods in accuracy per unit of compute, ahead of tuned boosters and kernel machines. When complexity lives in low interaction order, solving for the resolution beats searching for it.

Time series classification (TSC) performance depends not only on architectural design but also on the diversity of input representations. In this work, we propose a scalable multi-scale convolutional framework that systematically integrates structured multi-representation inputs for univariate time series. We introduce two architectures: MRMS-Net, a hierarchical multi-scale convolutional network optimized for robustness and calibration, and LMRMS-Net, a lightweight variant designed for efficiency-aware deployment. In addition, we adapt LiteMV -- originally developed for multivariate inputs -- to operate on multi-representation univariate signals, enabling cross-representation interaction. We evaluate all models across 142 benchmark datasets under a unified experimental protocol. Critical Difference (CD) analysis confirms statistically significant performance differences among the top models. Results show that LiteMV achieves the highest mean accuracy, MRMS-Net provides superior probabilistic calibration (lowest NLL), and LMRMS-Net offers the best efficiency-accuracy tradeoff. Pareto analysis further demonstrates that multi-representation multi-scale modeling yields a flexible design space that can be tuned for accuracy-oriented, calibration-oriented, or resource-constrained settings. These findings establish scalable multi-representation multi-scale learning as a principled and practical direction for modern TSC. Reference implementation of MRMS-Net and LMRMS-Net is available at: https://github.com/alagoz/mrmsnet-tsc

Foundation models have transformed natural language processing and computer vision, and a rapidly growing literature on time-series foundation models (TSFMs) seeks to replicate this success in forecasting. While recent open-source models demonstrate the promise of TSFMs, the field lacks a comprehensive and community-accepted model evaluation framework. We see at least four major issues impeding progress on the development of such a framework. First, existing evaluation frameworks comprise benchmark forecasting tasks derived from often outdated datasets (e.g., M3), many of which lack clear metadata and overlap with the corpora used to pre-train TSFMs. Second, these frameworks evaluate models along a narrowly defined set of benchmark forecasting tasks, such as forecast horizon length or domain, but overlook core statistical properties such as non-stationarity and seasonality. Third, domain-specific models (e.g., XGBoost) are often compared unfairly, as existing frameworks do not enforce a systematic and consistent hyperparameter tuning convention for all models. Fourth, visualization tools for interpreting comparative performance are lacking. To address these issues, we introduce TempusBench, an open-source evaluation framework for TSFMs. TempusBench consists of 1) new datasets which are not included in existing TSFM pretraining corpora, 2) a set of novel benchmark tasks that go beyond existing ones, 3) a model evaluation pipeline with a standardized hyperparameter tuning protocol, and 4) a tensorboard-based visualization interface. We provide access to our code on GitHub: https://github.com/Smlcrm/TempusBench and maintain a live leaderboard at https://benchmark.smlcrm.com/.

Financial time series forecasting is central to trading, portfolio optimization, and risk management, yet it remains challenging due to noisy, non-stationary, and heterogeneous data. Recent advances in time series foundation models (TSFMs), inspired by large language models, offer a new paradigm for learning generalizable temporal representations from large and diverse datasets. This paper presents the first comprehensive empirical study of TSFMs in global financial markets. Using a large-scale dataset of daily excess returns across diverse markets, we evaluate zero-shot inference, fine-tuning, and pre-training from scratch against strong benchmark models. We find that off-the-shelf pre-trained TSFMs perform poorly in zero-shot and fine-tuning settings, whereas models pre-trained from scratch on financial data achieve substantial forecasting and economic improvements, underscoring the value of domain-specific adaptation. Increasing the dataset size, incorporating synthetic data augmentation, and applying hyperparameter tuning further enhance performance.

We present results from an analysis of all data taken by the BICEP2, Keck Array and BICEP3 CMB polarization experiments up to and including the 2018 observing season. We add additional Keck Array observations at 220 GHz and BICEP3 observations at 95 GHz to the previous 95/150/220 GHz data set. The Q/U maps now reach depths of 2.8, 2.8 and 8.8 μ{mathrm K}_{cmb} arcmin at 95, 150 and 220 GHz respectively over an effective area of approx 600 square degrees at 95 GHz and approx 400 square degrees at 150 & 220 GHz. The 220 GHz maps now achieve a signal-to-noise on polarized dust emission exceeding that of Planck at 353 GHz. We take auto- and cross-spectra between these maps and publicly available WMAP and Planck maps at frequencies from 23 to 353 GHz and evaluate the joint likelihood of the spectra versus a multicomponent model of lensed-ΛCDM+r+dust+synchrotron+noise. The foreground model has seven parameters, and no longer requires a prior on the frequency spectral index of the dust emission taken from measurements on other regions of the sky. This model is an adequate description of the data at the current noise levels. The likelihood analysis yields the constraint r_{0.05}<0.036 at 95% confidence. Running maximum likelihood search on simulations we obtain unbiased results and find that σ(r)=0.009. These are the strongest constraints to date on primordial gravitational waves.