Tree-Ring Watermarking is a significant technique for authenticating AI-generated images. However, its effectiveness in rectified flow-based models remains unexplored, particularly given the inherent challenges of these models with noise latent inversion. Through extensive experimentation, we evaluated and compared the detection and separability of watermarks between SD 2.1 and FLUX.1-dev models. By analyzing various text guidance configurations and augmentation attacks, we demonstrate how inversion limitations affect both watermark recovery and the statistical separation between watermarked and unwatermarked images. Our findings provide valuable insights into the current limitations of Tree-Ring Watermarking in the current SOTA models and highlight the critical need for improved inversion methods to achieve reliable watermark detection and separability. The official implementation, dataset release and all experimental results are available at this \href{https://github.com/dsgiitr/flux-watermarking}{\textbf{link}}.

We revisit the optimal transport problem over angular velocity dynamics given by the controlled Euler equation. The solution of this problem enables stochastic guidance of spin states of a rigid body (e.g., spacecraft) over hard deadline constraint by transferring a given initial state statistics to a desired terminal state statistics. This is an instance of generalized optimal transport over a nonlinear dynamical system. While prior work has reported existence-uniqueness and numerical solution of this dynamical optimal transport problem, here we present structural results about the equivalent Kantorovich a.k.a. optimal coupling formulation. Specifically, we focus on deriving the ground cost for the associated Kantorovich optimal coupling formulation. The ground cost equals to the cost of transporting unit amount of mass from a specific realization of the initial or source joint probability measure to a realization of the terminal or target joint probability measure, and determines the Kantorovich formulation. Finding the ground cost leads to solving a structured deterministic nonlinear optimal control problem, which is shown to be amenable to an analysis technique pioneered by Athans et. al. We show that such techniques have broader applicability in determining the ground cost (thus Kantorovich formulation) for a class of generalized optimal mass transport problems involving nonlinear dynamics with translated norm-invariant drift.

Modeling and forecasting interval-valued time series (ITS) have attracted considerable attention due to their growing presence in various contexts. To the best of our knowledge, there have been no efforts to model large-scale ITS. In this paper, we propose a feature extraction procedure for large-scale ITS, which involves key steps such as auto-segmentation and clustering, and feature transfer learning. This procedure can be seamlessly integrated with any suitable prediction models for forecasting purposes. Specifically, we transform the automatic segmentation and clustering of ITS into the estimation of Toeplitz sparse precision matrices and assignment set. The majorization-minimization algorithm is employed to convert this highly non-convex optimization problem into two subproblems. We derive efficient dynamic programming and alternating direction method to solve these two subproblems alternately and establish their convergence properties. By employing the Joint Recurrence Plot (JRP) to image subsequence and assigning a class label to each cluster, an image dataset is constructed. Then, an appropriate neural network is chosen to train on this image dataset and used to extract features for the next step of forecasting. Real data applications demonstrate that the proposed method can effectively obtain invariant representations of the raw data and enhance forecasting performance.

--Autonomous vehicle path planning has reached a stage where safety and regulatory compliance are crucial. This paper presents an approach that integrates a motion planner with a deep reinforcement learning model to predict potential traffic rule violations. Our main innovation is replacing the standard actor network in an actor-critic method with a motion planning module, which ensures both stable and interpretable trajectory generation. In this setup, we use traffic rule robustness as the reward to train a reinforcement learning agent's critic, and the output of the critic is directly used as the cost function of the motion planner, which guides the choices of the trajectory. We incorporate some key interstate rules from the German Road Traffic Regulation into a rule book and use a graph-based state representation to handle complex traffic information. Experiments on an open German highway dataset show that the model can predict and prevent traffic rule violations beyond the planning horizon, increasing safety and rule compliance in challenging traffic scenarios. HE field of autonomous driving has advanced substantially over the past five years. Although perception and prediction modules have become more reliable, planning systems still face challenges, particularly regarding safety assurance and operational robustness. Furthermore, traffic rule compliance remains a fundamental prerequisite for autonomous vehicles, both to protect road users and to satisfy legal certification standards. Recent research has effectively applied temporal logic to formalize traffic rules, enabling automated online monitoring systems [1]-[3] to continuously monitor the compliance of traffic rules. These approaches use the concept of rule robustness--a quantitative metric indicating how thoroughly specific traffic rules are satisfied or violated.

In stochastic optimal control and conditional generative modelling, a central computational task is to modify a reference diffusion process to maximise a given terminal-time reward. Most existing methods require this reward to be differentiable, using gradients to steer the diffusion towards favourable outcomes. However, in many practical settings, like diffusion bridges, the reward is singular, taking an infinite value if the target is hit and zero otherwise. We introduce a novel framework, based on Malliavin calculus and path-space integration by parts, that enables the development of methods robust to such singular rewards. This allows our approach to handle a broad range of applications, including classification, diffusion bridges, and conditioning without the need for artificial observational noise. We demonstrate that our approach offers stable and reliable training, outperforming existing techniques.

In recent years, the modeling and analysis of interval-valued time series have garnered significant attention in the fields of econometrics and statistics. However, the existing literature primarily focuses on regression tasks while neglecting classification aspects. In this paper, we propose an adaptive approach for interval-valued time series classification. Specifically, we represent interval-valued time series using convex combinations of upper and lower bounds of intervals and transform these representations into images based on point-valued time series imaging methods. We utilize a fine-grained image classification neural network to classify these images, to achieve the goal of classifying the original interval-valued time series. This proposed method is applicable to both univariate and multivariate interval-valued time series. On the optimization front, we treat the convex combination coefficients as learnable parameters similar to the parameters of the neural network and provide an efficient estimation method based on the alternating direction method of multipliers (ADMM). On the theoretical front, under specific conditions, we establish a margin-based multiclass generalization bound for generic CNNs composed of basic blocks involving convolution, pooling, and fully connected layers. Through simulation studies and real data applications, we validate the effectiveness of the proposed method and compare its performance against a wide range of point-valued time series classification methods. Introduction Interval-valued time series have attracted significant attention in the fields of statistics and econometrics in recent years [1, 2, 3, 4, 5, 6], as they can simultaneously capture variation and level information. In practical applications, interval-valued time series are quite common. For example, in macroeconomics, the minimum and maximum annualized monthly GDP growth rates form interval-valued data for annual GDP growth rate. In meteorology, interval-valued time series are widely used to describe daily weather conditions, such as pollutant concentrations and temperature. In general, interval-valued time series modeling offers two main advantages over point-valued time series [6]. Firstly, within the same time period, interval-valued time series contain more variation and level information [4, 5, 6], which means that modeling interval-valued time series can lead to more efficient estimation and powerful inference. Secondly, specific disturbances, which may be considered noise in point-valued time series modeling and have adverse effects, can be addressed through modeling interval-valued time series. Over the past three decades, numerous methods for modeling and analyzing univari-ate and multivariate interval-valued time series, particularly focusing on regression, have been proposed.

While most modern machine learning methods offer speed and accuracy, few promise interpretability or explainability -- two key features necessary for highly sensitive industries, like medicine, finance, and engineering. Using eight datasets representative of one especially sensitive industry, nuclear power, this work compares a traditional feedforward neural network (FNN) to a Kolmogorov-Arnold Network (KAN). We consider not only model performance and accuracy, but also interpretability through model architecture and explainability through a post-hoc SHAP analysis. In terms of accuracy, we find KANs and FNNs comparable across all datasets, when output dimensionality is limited. KANs, which transform into symbolic equations after training, yield perfectly interpretable models while FNNs remain black-boxes. Finally, using the post-hoc explainability results from Kernel SHAP, we find that KANs learn real, physical relations from experimental data, while FNNs simply produce statistically accurate results. Overall, this analysis finds KANs a promising alternative to traditional machine learning methods, particularly in applications requiring both accuracy and comprehensibility.

Importance Sampling (IS) is a widely used variance reduction technique for enhancing the efficiency of Monte Carlo methods, particularly in rare-event simulation and related applications. Despite its power, the performance of IS is often highly sensitive to the choice of the proposal distribution and frequently requires stochastic calibration techniques. While the design and analysis of IS have been extensively studied in estimation settings, applying IS within stochastic optimization introduces a unique challenge: the decision and the IS distribution are mutually dependent, creating a circular optimization structure. This interdependence complicates both the analysis of convergence for decision iterates and the efficiency of the IS scheme. In this paper, we propose an iterative gradient-based algorithm that jointly updates the decision variable and the IS distribution without requiring time-scale separation between the two. Our method achieves the lowest possible asymptotic variance and guarantees global convergence under convexity of the objective and mild assumptions on the IS distribution family. Furthermore, we show that these properties are preserved under linear constraints by incorporating a recent variant of Nesterov's dual averaging method.

Earthquakes cause harm not only through direct ground shaking but also by triggering secondary ground failures such as landslides and liquefaction. These combined effects lead to devastating consequences, including structural damage and human casualties. A striking illustration is the 2021 Haiti earthquake, which initiated over 7,000 landslides covering more than 80 square kilometers. This catastrophic event resulted in damage or destruction to over 130,000 buildings, claimed 2,248 lives, and left more than 12,200 people injured [1]. Rapidly identifying where and how severely ground failures and structural damage have occurred following an earthquake is essential for effective victim rescue operations within the crucial "Golden 72 Hour" window, and plays a vital role in developing effective post-disaster recovery plans [2, 3]. Over the years, researchers have developed various approaches for estimating the location and intensity of earthquake-induced ground failures and building damage.

Complex systems with intricate causal dependencies challenge accurate prediction. Effective modeling requires precise physical process representation, integration of interdependent factors, and incorporation of multi-resolution observational data. These systems manifest in both static scenarios with instantaneous causal chains and temporal scenarios with evolving dynamics, complicating modeling efforts. Current methods struggle to simultaneously handle varying resolutions, capture physical relationships, model causal dependencies, and incorporate temporal dynamics, especially with inconsistently sampled data from diverse sources. We introduce Temporal-SVGDM: Score-based Variational Graphical Diffusion Model for Multi-resolution observations. Our framework constructs individual SDEs for each variable at its native resolution, then couples these SDEs through a causal score mechanism where parent nodes inform child nodes' evolution. This enables unified modeling of both immediate causal effects in static scenarios and evolving dependencies in temporal scenarios. In temporal models, state representations are processed through a sequence prediction model to predict future states based on historical patterns and causal relationships. Experiments on real-world datasets demonstrate improved prediction accuracy and causal understanding compared to existing methods, with robust performance under varying levels of background knowledge. Our model exhibits graceful degradation across different disaster types, successfully handling both static earthquake scenarios and temporal hurricane and wildfire scenarios, while maintaining superior performance even with limited data.