Theoretical Foundation of Flow-Based Time Series Generation: Provable Approximation, Generalization, and Efficiency

Recent studies suggest utilizing generative models instead of traditional auto-regressive algorithms for time series forecasting (TSF) tasks. These non-auto-regressive approaches involving different generative methods, including GAN, Diffusion, and Flow Matching for time series, have empirically demonstrated high-quality generation capability and accuracy. However, we still lack an appropriate understanding of how it processes approximation and generalization. This paper presents the first theoretical framework from the perspective of flow-based generative models to relieve the knowledge of limitations. In particular, we provide our insights with strict guarantees from three perspectives: $\textbf{Approximation}$, $\textbf{Generalization}$ and $\textbf{Efficiency}$. In detail, our analysis achieves the contributions as follows: $\bullet$ By assuming a general data model, the fitting of the flow-based generative models is confirmed to converge to arbitrary error under the universal approximation of Diffusion Transformer (DiT). $\bullet$ Introducing a polynomial-based regularization for flow matching, the generalization error thus be bounded since the generalization of polynomial approximation. $\bullet$ The sampling for generation is considered as an optimization process, we demonstrate its fast convergence with updating standard first-order gradient descent of some objective.

Time-varying Factor Augmented Vector Autoregression with Grouped Sparse Autoencoder

Recent economic events, including the global financial crisis and COVID-19 pandemic, have exposed limitations in linear Factor Augmented Vector Autoregressive (FAVAR) models for forecasting and structural analysis. Nonlinear dimension techniques, particularly autoencoders, have emerged as promising alternatives in a FAVAR framework, but challenges remain in identifiability, interpretability, and integration with traditional nonlinear time series methods. We address these challenges through two contributions. First, we introduce a Grouped Sparse autoencoder that employs the Spike-and-Slab Lasso prior, with parameters under this prior being shared across variables of the same economic category, thereby achieving semi-identifiability and enhancing model interpretability. Second, we incorporate time-varying parameters into the VAR component to better capture evolving economic dynamics. Our empirical application to the US economy demonstrates that the Grouped Sparse autoencoder produces more interpretable factors through its parsimonious structure; and its combination with time-varying parameter VAR shows superior performance in both point and density forecasting. Impulse response analysis reveals that monetary policy shocks during recessions generate more moderate responses with higher uncertainty compared to expansionary periods.

TS-LIF: A Temporal Segment Spiking Neuron Network for Time Series Forecasting

Spiking Neural Networks (SNNs) offer a promising, biologically inspired approach for processing spatiotemporal data, particularly for time series forecasting. However, conventional neuron models like the Leaky Integrate-and-Fire (LIF) struggle to capture long-term dependencies and effectively process multi-scale temporal dynamics. To overcome these limitations, we introduce the Temporal Segment Leaky Integrate-and-Fire (TS-LIF) model, featuring a novel dual-compartment architecture. The dendritic and somatic compartments specialize in capturing distinct frequency components, providing functional heterogeneity that enhances the neuron's ability to process both low- and high-frequency information. Furthermore, the newly introduced direct somatic current injection reduces information loss during intra-neuronal transmission, while dendritic spike generation improves multi-scale information extraction. We provide a theoretical stability analysis of the TS-LIF model and explain how each compartment contributes to distinct frequency response characteristics. Experimental results show that TS-LIF outperforms traditional SNNs in time series forecasting, demonstrating better accuracy and robustness, even with missing data. TS-LIF advances the application of SNNs in time-series forecasting, providing a biologically inspired approach that captures complex temporal dynamics and offers potential for practical implementation in diverse forecasting scenarios. The source code is available at https://github.com/kkking-kk/TS-LIF.

Data Foundations for Large Scale Multimodal Clinical Foundation Models

Recent advances in clinical AI have enabled remarkable progress across many clinical domains. However, existing benchmarks and models are primarily limited to a small set of modalities and tasks, which hinders the development of large-scale multimodal methods that can make holistic assessments of patient health and well-being. To bridge this gap, we introduce Clinical Large-Scale Integrative Multimodal Benchmark (CLIMB), a comprehensive clinical benchmark unifying diverse clinical data across imaging, language, temporal, and graph modalities. CLIMB comprises 4.51 million patient samples totaling 19.01 terabytes distributed across 2D imaging, 3D video, time series, graphs, and multimodal data. Through extensive empirical evaluation, we demonstrate that multitask pretraining significantly improves performance on understudied domains, achieving up to 29% improvement in ultrasound and 23% in ECG analysis over single-task learning. Pretraining on CLIMB also effectively improves models' generalization capability to new tasks, and strong unimodal encoder performance translates well to multimodal performance when paired with task-appropriate fusion strategies. Our findings provide a foundation for new architecture designs and pretraining strategies to advance clinical AI research. Code is released at https://github.com/DDVD233/climb.

SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild

DeepSeek-R1 has shown that long chain-of-thought (CoT) reasoning can naturally emerge through a simple reinforcement learning (RL) framework with rule-based rewards, where the training may directly start from the base models-a paradigm referred to as zero RL training. Most recent efforts to reproduce zero RL training have primarily focused on the Qwen2.5 model series, which may not be representative as we find the base models already exhibit strong instruction-following and self-reflection abilities. In this work, we investigate zero RL training across 10 diverse base models, spanning different families and sizes including LLama3-8B, Mistral-7B/24B, DeepSeek-Math-7B, Qwen2.5-math-7B, and all Qwen2.5 models from 0.5B to 32B. Leveraging several key design strategies-such as adjusting format reward and controlling query difficulty-we achieve substantial improvements in both reasoning accuracy and response length across most settings. However, by carefully monitoring the training dynamics, we observe that different base models exhibit distinct patterns during training. For instance, the increased response length does not always correlate with the emergence of certain cognitive behaviors such as verification (i.e., the "aha moment"). Notably, we observe the "aha moment" for the first time in small models not from the Qwen family. We share the key designs that enable successful zero RL training, along with our findings and practices. To facilitate further research, we open-source the code, models, and analysis tools.

FinTMMBench: Benchmarking Temporal-Aware Multi-Modal RAG in Finance

Finance decision-making often relies on in-depth data analysis across various data sources, including financial tables, news articles, stock prices, etc. In this work, we introduce FinTMMBench, the first comprehensive benchmark for evaluating temporal-aware multi-modal Retrieval-Augmented Generation (RAG) systems in finance. Built from heterologous data of NASDAQ 100 companies, FinTMMBench offers three significant advantages. 1) Multi-modal Corpus: It encompasses a hybrid of financial tables, news articles, daily stock prices, and visual technical charts as the corpus. 2) Temporal-aware Questions: Each question requires the retrieval and interpretation of its relevant data over a specific time period, including daily, weekly, monthly, quarterly, and annual periods. 3) Diverse Financial Analysis Tasks: The questions involve 10 different tasks, including information extraction, trend analysis, sentiment analysis and event detection, etc. We further propose a novel TMMHybridRAG method, which first leverages LLMs to convert data from other modalities (e.g., tabular, visual and time-series data) into textual format and then incorporates temporal information in each node when constructing graphs and dense indexes. Its effectiveness has been validated in extensive experiments, but notable gaps remain, highlighting the challenges presented by our FinTMMBench.

Dynamical Mode Recognition of Turbulent Flames in a Swirl-stabilized Annular Combustor by a Time-series Learning Approach

Thermoacoustic instability in annular combustors, essential to aero engines and modern gas turbines, can severely impair operational stability and efficiency, accurately recognizing and understanding various combustion modes is the prerequisite for understanding and controlling combustion instabilities. However, the high-dimensional spatial-temporal dynamics of turbulent flames typically pose considerable challenges to mode recognition. Based on the bidirectional temporal and nonlinear dimensionality reduction models, this study introduces a two-layer bidirectional long short-term memory variational autoencoder, Bi-LSTM-VAE model, to effectively recognize dynamical modes in annular combustion systems. Specifically, leveraging 16 pressure signals from a swirl-stabilized annular combustor, the model maps complex dynamics into a low-dimensional latent space while preserving temporal dependency and nonlinear behavior features through the recurrent neural network structure. The results show that the novel Bi-LSTM-VAE method enables a clear representation of combustion states in two-dimensional state space. Analysis of latent variable distributions reveals distinct patterns corresponding to a wide range of equivalence ratios and premixed fuel and air mass flow rates, offering novel insights into mode classification and transitions, highlighting this model's potential for deciphering complex thermoacoustic phenomena.

TS-OOD: Evaluating Time-Series Out-of-Distribution Detection and Prospective Directions for Progress

Detecting out-of-distribution (OOD) data is a fundamental challenge in the deployment of machine learning models. From a security standpoint, this is particularly important because OOD test data can result in misleadingly confident yet erroneous predictions, which undermine the reliability of the deployed model. Although numerous models for OOD detection have been developed in computer vision and language, their adaptability to the time-series data domain remains limited and under-explored. Yet, time-series data is ubiquitous across manufacturing and security applications for which OOD is essential. This paper seeks to address this research gap by conducting a comprehensive analysis of modality-agnostic OOD detection algorithms. We evaluate over several multivariate time-series datasets, deep learning architectures, time-series specific data augmentations, and loss functions. Our results demonstrate that: 1) the majority of state-of-the-art OOD methods exhibit limited performance on time-series data, and 2) OOD methods based on deep feature modeling may offer greater advantages for time-series OOD detection, highlighting a promising direction for future time-series OOD detection algorithm development.

Spatiotemporal Forecasting in Climate Data Using EOFs and Machine Learning Models: A Case Study in Chile

Effective resource management and environmental planning in regions with high climatic variability, such as Chile, demand advanced predictive tools. This study addresses this challenge by employing an innovative and computationally efficient hybrid methodology that integrates machine learning (ML) methods for time series forecasting with established statistical techniques. The spatiotemporal data undergo decomposition using time-dependent Empirical Orthogonal Functions (EOFs), denoted as \(\phi_{k}(t)\), and their corresponding spatial coefficients, \(\alpha_{k}(s)\), to reduce dimensionality. Wavelet analysis provides high-resolution time and frequency information from the \(\phi_{k}(t)\) functions, while neural networks forecast these functions within a medium-range horizon \(h\). By utilizing various ML models, particularly a Wavelet - ANN hybrid model, we forecast \(\phi_{k}(t+h)\) up to a time horizon \(h\), and subsequently reconstruct the spatiotemporal data using these extended EOFs. This methodology is applied to a grid of climate data covering the territory of Chile. It transitions from a high-dimensional multivariate spatiotemporal data forecasting problem to a low-dimensional univariate forecasting problem. Additionally, cluster analysis with Dynamic Time Warping for defining similarities between rainfall time series, along with spatial coherence and predictability assessments, has been instrumental in identifying geographic areas where model performance is enhanced. This approach also elucidates the reasons behind poor forecast performance in regions or clusters with low spatial coherence and predictability. By utilizing cluster medoids, the forecasting process becomes more practical and efficient. This compound approach significantly reduces computational complexity while generating forecasts of reasonable accuracy and utility.

Optimal Stochastic Trace Estimation in Generative Modeling

Hutchinson estimators are widely employed in training divergence-based likelihoods for diffusion models to ensure optimal transport (OT) properties. However, this estimator often suffers from high variance and scalability concerns. To address these challenges, we investigate Hutch++, an optimal stochastic trace estimator for generative models, designed to minimize training variance while maintaining transport optimality. Hutch++ is particularly effective for handling ill-conditioned matrices with large condition numbers, which commonly arise when high-dimensional data exhibits a low-dimensional structure. To mitigate the need for frequent and costly QR decompositions, we propose practical schemes that balance frequency and accuracy, backed by theoretical guarantees. Our analysis demonstrates that Hutch++ leads to generations of higher quality. Furthermore, this method exhibits effective variance reduction in various applications, including simulations, conditional time series forecasts, and image generation.