An Analysis of Temporal Dropout in Earth Observation Time Series for Regression Tasks

Missing instances in time series data impose a significant challenge to deep learning models, particularly in regression tasks. In the Earth Observation field, satellite failure or cloud occlusion frequently results in missing time-steps, introducing uncertainties in the predicted output and causing a decline in predictive performance. While many studies address missing time-steps through data augmentation to improve model robustness, the uncertainty arising at the input level is commonly overlooked. To address this gap, we introduce Monte Carlo Temporal Dropout (MC-TD), a method that explicitly accounts for input-level uncertainty by randomly dropping time-steps during inference using a predefined dropout ratio, thereby simulating the effect of missing data. To bypass the need for costly searches for the optimal dropout ratio, we extend this approach with Monte Carlo Concrete Temporal Dropout (MC-ConcTD), a method that learns the optimal dropout distribution directly. Both MC-TD and MC-ConcTD are applied during inference, leveraging Monte Carlo sampling for uncertainty quantification. Experiments on three EO time-series datasets demonstrate that MC-ConcTD improves predictive performance and uncertainty calibration compared to existing approaches. Additionally, we highlight the advantages of adaptive dropout tuning over manual selection, making uncertainty quantification more robust and accessible for EO applications.

Learning the Simplest Neural ODE

Since the advent of the ``Neural Ordinary Differential Equation (Neural ODE)'' paper, learning ODEs with deep learning has been applied to system identification, time-series forecasting, and related areas. Exploiting the diffeomorphic nature of ODE solution maps, neural ODEs has also enabled their use in generative modeling. Despite the rich potential to incorporate various kinds of physical information, training Neural ODEs remains challenging in practice. This study demonstrates, through the simplest one-dimensional linear model, why training Neural ODEs is difficult. We then propose a new stabilization method and provide an analytical convergence analysis. The insights and techniques presented here serve as a concise tutorial for researchers beginning work on Neural ODEs.

Reach-Avoid-Stabilize Using Admissible Control Sets

Hamilton-Jacobi Reachability (HJR) analysis has been successfully used in many robotics and control tasks, and is especially effective in computing reach-avoid sets and control laws that enable an agent to reach a goal while satisfying state constraints. However, the original HJR formulation provides no guarantees of safety after a) the prescribed time horizon, or b) goal satisfaction. The reach-avoid-stabilize (RAS) problem has therefore gained a lot of focus: find the set of initial states (the RAS set), such that the trajectory can reach the target, and stabilize to some point of interest (POI) while avoiding obstacles. Solving RAS problems using HJR usually requires defining a new value function, whose zero sub-level set is the RAS set. The existing methods do not consider the problem when there are a series of targets to reach and/or obstacles to avoid. We propose a method that uses the idea of admissible control sets; we guarantee that the system will reach each target while avoiding obstacles as prescribed by the given time series. Moreover, we guarantee that the trajectory ultimately stabilizes to the POI. The proposed method provides an under-approximation of the RAS set, guaranteeing safety. Numerical examples are provided to validate the theory.

Nearest Neighbor Multivariate Time Series Forecasting

Multivariate time series (MTS) forecasting has a wide range of applications in both industry and academia. Recently, spatial-temporal graph neural networks (STGNNs) have gained popularity as MTS forecasting methods. However, current STGNNs can only use the finite length of MTS input data due to the computational complexity. Moreover, they lack the ability to identify similar patterns throughout the entire dataset and struggle with data that exhibit sparsely and discontinuously distributed correlations among variables over an extensive historical period, resulting in only marginal improvements. In this article, we introduce a simple yet effective k-nearest neighbor MTS forecasting ( kNN-MTS) framework, which forecasts with a nearest neighbor retrieval mechanism over a large datastore of cached series, using representations from the MTS model for similarity search. This approach requires no additional training and scales to give the MTS model direct access to the whole dataset at test time, resulting in a highly expressive model that consistently improves performance, and has the ability to extract sparse distributed but similar patterns spanning over multivariables from the entire dataset. Furthermore, a hybrid spatial-temporal encoder (HSTEncoder) is designed for kNN-MTS which can capture both long-term temporal and short-term spatial-temporal dependencies and is shown to provide accurate representation for kNN-MTSfor better forecasting. Experimental results on several real-world datasets show a significant improvement in the forecasting performance of kNN-MTS. The quantitative analysis also illustrates the interpretability and efficiency of kNN-MTS, showing better application prospects and opening up a new path for efficiently using the large dataset in MTS models.

Learning from Peers in Reasoning Models

Large Reasoning Models (LRMs) have the ability to self-correct even when they make mistakes in their reasoning paths. However, our study reveals that when the reasoning process starts with a short but poor beginning, it becomes difficult for the model to recover. We refer to this phenomenon as the "Prefix Dominance Trap". Inspired by psychological findings that peer interaction can promote self-correction without negatively impacting already accurate individuals, we propose **Learning from Peers** (LeaP) to address this phenomenon. Specifically, every tokens, each reasoning path summarizes its intermediate reasoning and shares it with others through a routing mechanism, enabling paths to incorporate peer insights during inference. However, we observe that smaller models sometimes fail to follow summarization and reflection instructions effectively. To address this, we fine-tune them into our **LeaP-T** model series. Experiments on AIME 2024, AIME 2025, AIMO 2025, and GPQA Diamond show that LeaP provides substantial improvements. For instance, QwQ-32B with LeaP achieves nearly 5 absolute points higher than the baseline on average, and surpasses DeepSeek-R1-671B on three math benchmarks with an average gain of 3.3 points. Notably, our fine-tuned LeaP-T-7B matches the performance of DeepSeek-R1-Distill-Qwen-14B on AIME 2024. In-depth analysis reveals LeaP's robust error correction by timely peer insights, showing strong error tolerance and handling varied task difficulty. LeaP marks a milestone by enabling LRMs to collaborate during reasoning. Our code, datasets, and models are available at https://learning-from-peers.github.io/ .

FRIREN: Beyond Trajectories -- A Spectral Lens on Time

Long-term time-series forecasting (LTSF) models are often presented as general-purpose solutions that can be applied across domains, implicitly assuming that all data is pointwise predictable. Using chaotic systems such as Lorenz-63 as a case study, we argue that geometric structure - not pointwise prediction - is the right abstraction for a dynamic-agnostic foundational model. Minimizing the Wasserstein-2 distance (W2), which captures geometric changes, and providing a spectral view of dynamics are essential for long-horizon forecasting. Our model, FRIREN (Flow-inspired Representations via Interpretable Eigen-networks), implements an augmented normalizing-flow block that embeds data into a normally distributed latent representation. It then generates a W2-efficient optimal path that can be decomposed into rotation, scaling, inverse rotation, and translation. This architecture yields locally generated, geometry-preserving predictions that are independent of the underlying dynamics, and a global spectral representation that functions as a finite Koopman operator with a small modification. This enables practitioners to identify which modes grow, decay, or oscillate, both locally and system-wide. FRIREN achieves an MSE of 11.4, MAE of 1.6, and SWD of 0.96 on Lorenz-63 in a 336-in, 336-out, dt=0.01 setting, surpassing TimeMixer (MSE 27.3, MAE 2.8, SWD 2.1). The model maintains effective prediction for 274 out of 336 steps, approximately 2.5 Lyapunov times. On Rossler (96-in, 336-out), FRIREN achieves an MSE of 0.0349, MAE of 0.0953, and SWD of 0.0170, outperforming TimeMixer's MSE of 4.3988, MAE of 0.886, and SWD of 3.2065. FRIREN is also competitive on standard LTSF datasets such as ETT and Weather. By connecting modern generative flows with classical spectral analysis, FRIREN makes long-term forecasting both accurate and interpretable, setting a new benchmark for LTSF model design.

LLM4FTS: Enhancing Large Language Models for Financial Time Series Prediction

Predicting financial time series presents significant challenges due to inherent low signal-to-noise ratios and intricate temporal patterns. Traditional machine learning models exhibit limitations in this forecasting task constrained by their restricted model capacity. Recent advances in large language models (LLMs), with their greatly expanded parameter spaces, demonstrate promising potential for modeling complex dependencies in temporal sequences. However, existing LLM-based approaches typically focus on fixed-length patch analysis due to the Transformer architecture, ignoring market data's multi-scale pattern characteristics. In this study, we propose $LLM4FTS$, a novel framework that enhances LLM capabilities for temporal sequence modeling through learnable patch segmentation and dynamic wavelet convolution modules. Specifically,we first employ K-means++ clustering based on DTW distance to identify scale-invariant patterns in market data. Building upon pattern recognition results, we introduce adaptive patch segmentation that partitions temporal sequences while preserving maximal pattern integrity. To accommodate time-varying frequency characteristics, we devise a dynamic wavelet convolution module that emulates discrete wavelet transformation with enhanced flexibility in capturing time-frequency features. These three modules work together to improve large language model's ability to handle scale-invariant patterns in financial time series. Extensive experiments on real-world financial datasets substantiate the framework's efficacy, demonstrating superior performance in capturing complex market patterns and achieving state-of-the-art results in stock return prediction. The successful deployment in practical trading systems confirms its real-world applicability, representing a significant advancement in LLM applications for financial forecasting.

The Multimodal Paradox: How Added and Missing Modalities Shape Bias and Performance in Multimodal AI

Multimodal learning, which integrates diverse data sources such as images, text, and structured data, has proven superior to unimodal counterparts in high-stakes decision-making. However, while performance gains remain the gold standard for evaluating multimodal systems, concerns around bias and robustness are frequently overlooked. In this context, this paper explores two key research questions (RQs): (i) RQ1 examines whether adding a modality con-sistently enhances performance and investigates its role in shaping fairness measures, assessing whether it mitigates or amplifies bias in multimodal models; (ii) RQ2 investigates the impact of missing modalities at inference time, analyzing how multimodal models generalize in terms of both performance and fairness. Our analysis reveals that incorporating new modalities during training consistently enhances the performance of multimodal models, while fairness trends exhibit variability across different evaluation measures and datasets. Additionally, the absence of modalities at inference degrades performance and fairness, raising concerns about its robustness in real-world deployment. We conduct extensive experiments using multimodal healthcare datasets containing images, time series, and structured information to validate our findings.

TSP-OCS: A Time-Series Prediction for Optimal Camera Selection in Multi-Viewpoint Surgical Video Analysis

Recording the open surgery process is essential for educational and medical evaluation purposes; however, traditional single-camera methods often face challenges such as occlusions caused by the surgeon's head and body, as well as limitations due to fixed camera angles, which reduce comprehensibility of the video content. This study addresses these limitations by employing a multi-viewpoint camera recording system, capturing the surgical procedure from six different angles to mitigate occlusions. We propose a fully supervised learning-based time series prediction method to choose the best shot sequences from multiple simultaneously recorded video streams, ensuring optimal viewpoints at each moment. Our time series prediction model forecasts future camera selections by extracting and fusing visual and semantic features from surgical videos using pre-trained models. These features are processed by a temporal prediction network with TimeBlocks to capture sequential dependencies. A linear embedding layer reduces dimensionality, and a Softmax classifier selects the optimal camera view based on the highest probability. In our experiments, we created five groups of open thyroidectomy videos, each with simultaneous recordings from six different angles. The results demonstrate that our method achieves competitive accuracy compared to traditional supervised methods, even when predicting over longer time horizons. Furthermore, our approach outperforms state-of-the-art time series prediction techniques on our dataset. This manuscript makes a unique contribution by presenting an innovative framework that advances surgical video analysis techniques, with significant implications for improving surgical education and patient safety.

AI-assisted Automatic Jump Detection and Height Estimation in Volleyball Using a Waist-worn IMU

The physical load of jumps plays a critical role in injury prevention for volleyball players. However, manual video analysis of jump activities is time-intensive and costly, requiring significant effort and expensive hardware setups. The advent of the inertial measurement unit (IMU) and machine learning algorithms offers a convenient and efficient alternative. Despite this, previous research has largely focused on either jump classification or physical load estimation, leaving a gap in integrated solutions. This study aims to present a pipeline to automatically detect jumps and predict heights using data from a waist-worn IMU. The pipeline leverages a Multi-Stage Temporal Convolutional Network (MS-TCN) to detect jump segments in time-series data and classify the specific jump category. Subsequently, jump heights are estimated using three downstream regression machine learning models based on the identified segments. Our method is verified on a dataset comprising 10 players and 337 jumps. Compared to the result of VERT in height estimation (R-squared=-1.53), a commercial device commonly used in jump landing tasks, our method not only accurately identifies jump activities and their specific types (F1-score=0.90) but also demonstrates superior performance in height prediction (R-squared=0.50). This integrated solution offers a promising tool for monitoring physical load and mitigating injury risk in volleyball players.