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.

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/ .

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.

Forecasting from Clinical Textual Time Series: Adaptations of the Encoder and Decoder Language Model Families

Clinical case reports encode rich, temporal patient trajectories that are often underexploited by traditional machine learning methods relying on structured data. In this work, we introduce the forecasting problem from textual time series, where timestamped clinical findings--extracted via an LLM-assisted annotation pipeline--serve as the primary input for prediction. We systematically evaluate a diverse suite of models, including fine-tuned decoder-based large language models and encoder-based transformers, on tasks of event occurrence prediction, temporal ordering, and survival analysis. Our experiments reveal that encoder-based models consistently achieve higher F1 scores and superior temporal concordance for short- and long-horizon event forecasting, while fine-tuned masking approaches enhance ranking performance. In contrast, instruction-tuned decoder models demonstrate a relative advantage in survival analysis, especially in early prognosis settings. Our sensitivity analyses further demonstrate the importance of time ordering, which requires clinical time series construction, as compared to text ordering, the format of the text inputs that LLMs are classically trained on. This highlights the additional benefit that can be ascertained from time-ordered corpora, with implications for temporal tasks in the era of widespread LLM use.

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.

A Physically Driven Long Short Term Memory Model for Estimating Snow Water Equivalent over the Continental United States

Snow is an essential input for various land surface models. Seasonal snow estimates are available as snow water equivalent (SWE) from process-based reanalysis products or locally from in situ measurements. While the reanalysis products are computationally expensive and available at only fixed spatial and temporal resolutions, the in situ measurements are highly localized and sparse. To address these issues and enable the analysis of the effect of a large suite of physical, morphological, and geological conditions on the presence and amount of snow, we build a Long Short-Term Memory (LSTM) network, which is able to estimate the SWE based on time series input of the various physical/meteorological factors as well static spatial/morphological factors. Specifically, this model breaks down the SWE estimation into two separate tasks: (i) a classification task that indicates the presence/absence of snow on a specific day and (ii) a regression task that indicates the height of the SWE on a specific day in the case of snow presence. The model is trained using physical/in situ SWE measurements from the SNOw TELemetry (SNOTEL) snow pillows in the western United States. We will show that trained LSTM models have a classification accuracy of $\geq 93\%$ for the presence of snow and a coefficient of correlation of $\sim 0.9$ concerning their SWE estimates. We will also demonstrate that the models can generalize both spatially and temporally to previously unseen data.

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.

FreCT: Frequency-augmented Convolutional Transformer for Robust Time Series Anomaly Detection

Time series anomaly detection is critical for system monitoring and risk identification, across various domains, such as finance and healthcare. However, for most reconstruction-based approaches, detecting anomalies remains a challenge due to the complexity of sequential patterns in time series data. On the one hand, reconstruction-based techniques are susceptible to computational deviation stemming from anomalies, which can lead to impure representations of normal sequence patterns. On the other hand, they often focus on the time-domain dependencies of time series, while ignoring the alignment of frequency information beyond the time domain. To address these challenges, we propose a novel Frequency-augmented Convolutional Transformer (FreCT). FreCT utilizes patch operations to generate contrastive views and employs an improved Transformer architecture integrated with a convolution module to capture long-term dependencies while preserving local topology information. The introduced frequency analysis based on Fourier transformation could enhance the model's ability to capture crucial characteristics beyond the time domain. To protect the training quality from anomalies and improve the robustness, FreCT deploys stop-gradient Kullback-Leibler (KL) divergence and absolute error to optimize consistency information in both time and frequency domains. Extensive experiments on four public datasets demonstrate that FreCT outperforms existing methods in identifying anomalies.

Waymo Driverless Car Data Analysis and Driving Modeling using CNN and LSTM

Self driving cars has been the biggest innovation in the automotive industry, but to achieve human level accuracy or near human level accuracy is the biggest challenge that research scientists are facing today. Unlike humans autonomous vehicles do not work on instincts rather they make a decision based on the training data that has been fed to them using machine learning models using which they can make decisions in different conditions they face in the real world. With the advancements in machine learning especially deep learning the self driving car research skyrocketed. In this project we have presented multiple ways to predict acceleration of the autonomous vehicle using Waymo's open dataset. Our main approach was to using CNN to mimic human action and LSTM to treat this as a time series problem.

Explainability by design: an experimental analysis of the legal coding process

Behind a set of rules in Deontic Defeasible Logic, there is a mapping process of normative background fragments. This process goes from text to rules and implicitly encompasses an explanation of the coded fragments. In this paper we deliver a methodology for \textit{legal coding} that starts with a fragment and goes onto a set of Deontic Defeasible Logic rules, involving a set of \textit{scenarios} to test the correctness of the coded fragments. The methodology is illustrated by the coding process of an example text. We then show the results of a series of experiments conducted with humans encoding a variety of normative backgrounds and corresponding cases in which we have measured the efforts made in the coding process, as related to some measurable features. To process these examples, a recently developed technology, Houdini, that allows reasoning in Deontic Defeasible Logic, has been employed. Finally we provide a technique to forecast time required in coding, that depends on factors such as knowledge of the legal domain, knowledge of the coding processes, length of the text, and a measure of \textit{depth} that refers to the length of the paths of legal references.