Vision-language models (VLMs) now rival human performance on many multimodal tasks, yet they still hallucinate objects or generate unsafe text. Current hallucination detectors, e.g., single-token linear probing (LP) and PTrue, typically analyze only the logit of the first generated token or just its highest-scoring component, overlooking richer signals embedded within earlier token distributions. We demonstrate that analyzing the complete sequence of early logits potentially provides substantially more diagnostic information. We emphasize that hallucinations may only emerge after several tokens, as subtle inconsistencies accumulate over time. By analyzing the Kullback-Leibler (KL) divergence between logits corresponding to hallucinated and non-hallucinated tokens, we underscore the importance of incorporating later-token logits to more accurately capture the reliability dynamics of VLMs. In response, we introduce Multi-Token Reliability Estimation (MTRE), a lightweight, white-box method that aggregates logits from the first ten tokens using multi-token log-likelihood ratios and self-attention. Despite the challenges posed by large vocabulary sizes and long logit sequences, MTRE remains efficient and tractable. Across MAD-Bench, MM-SafetyBench, MathVista, and four compositional-geometry benchmarks, MTRE achieves a 9.4% gain in accuracy and a 14.8% gain in AUROC over standard detection methods, establishing a new state of the art in hallucination detection for open-source VLMs.

Modeling hierarchical latent dynamics behind time series data is critical for capturing temporal dependencies across multiple levels of abstraction in real-world tasks. However, existing temporal causal representation learning methods fail to capture such dynamics, as they fail to recover the joint distribution of hierarchical latent variables from \textit{single-timestep observed variables}. Interestingly, we find that the joint distribution of hierarchical latent variables can be uniquely determined using three conditionally independent observations. Building on this insight, we propose a Causally Hierarchical Latent Dynamic (CHiLD) identification framework. Our approach first employs temporal contextual observed variables to identify the joint distribution of multi-layer latent variables. Sequentially, we exploit the natural sparsity of the hierarchical structure among latent variables to identify latent variables within each layer. Guided by the theoretical results, we develop a time series generative model grounded in variational inference. This model incorporates a contextual encoder to reconstruct multi-layer latent variables and normalize flow-based hierarchical prior networks to impose the independent noise condition of hierarchical latent dynamics. Empirical evaluations on both synthetic and real-world datasets validate our theoretical claims and demonstrate the effectiveness of CHiLD in modeling hierarchical latent dynamics.

In this paper, we investigate the utility of datasets and whether more data or the 'right' data is advantageous for robot learning. In particular, we are interested on quantifying the utility of contact-based data as contact holds significant information for robot learning. Our approach derives a contact-aware objective function for learning object dynamics and shape from pose and contact data. We show that the contact-aware Fisher-information metric can be used to rank and curate contact-data based on how informative data is for learning. In addition, we find that selecting a reduced dataset based on this ranking improves the learning task while also making learning a deterministic process. Interestingly, our results show that more data is not necessarily advantageous, and rather, less but informative data can accelerate learning, especially depending on the contact interactions. Last, we show how our metric can be used to provide initial guidance on data curation for contact-based robot learning.

In this paper, we generalize Pearl's do-calculus to an Intuitionistic setting called $j$-stable causal inference inside a topos of sheaves. Our framework is an elaboration of the recently proposed framework of Topos Causal Models (TCMs), where causal interventions are defined as subobjects. We generalize the original setting of TCM using the Lawvere-Tierney topology on a topos, defined by a modal operator $j$ on the subobject classifier $Ω$. We introduce $j$-do-calculus, where we replace global truth with local truth defined by Kripke-Joyal semantics, and formalize causal reasoning as structure-preserving morphisms that are stable along $j$-covers. $j$-do-calculus is a sound rule system whose premises and conclusions are formulas of the internal Intuitionistic logic of the causal topos. We define $j$-stability for conditional independences and interventional claims as local truth in the internal logic of the causal topos. We give three inference rules that mirror Pearl's insertion/deletion and action/observation exchange, and we prove soundness in the Kripke-Joyal semantics. A companion paper in preparation will describe how to estimate the required entities from data and instantiate $j$-do with standard discovery procedures (e.g., score-based and constraint-based methods), and will include experimental results on how to (i) form data-driven $j$-covers (via regime/section constructions), (ii) compute chartwise conditional independences after graph surgeries, and (iii) glue them to certify the premises of the $j$-do rules in practice

In this work, we introduce MUSE (Model-based Uncertainty-aware Similarity Estimation), a training-free framework designed for model-based zero-shot 2D object detection and segmentation. MUSE leverages 2D multi-view templates rendered from 3D unseen objects and 2D object proposals extracted from input query images. In the embedding stage, it integrates class and patch embeddings, where the patch embeddings are normalized using generalized mean pooling (GeM) to capture both global and local representations efficiently. During the matching stage, MUSE employs a joint similarity metric that combines absolute and relative similarity scores, enhancing the robustness of matching under challenging scenarios. Finally, the similarity score is refined through an uncertainty-aware object prior that adjusts for proposal reliability. Without any additional training or fine-tuning, MUSE achieves state-of-the-art performance on the BOP Challenge 2025, ranking first across the Classic Core, H3, and Industrial tracks. These results demonstrate that MUSE offers a powerful and generalizable framework for zero-shot 2D object detection and segmentation.

Inference in dynamic probabilistic models is a complex task involving expensive operations. In particular, for Hidden Markov Models, the whole state space has to be enumerated for advancing in time. Even states with negligible probabilities are considered, resulting in computational inefficiency and increased noise due to the propagation of unlikely probability mass. We propose to denoise the future and speed up inference by using only the top-p states, i.e., the most probable states with accumulated probability p. We show that the error introduced by using only the top-p states is bound by p and the so-called minimal mixing rate of the underlying model. Moreover, in our empirical evaluation, we show that we can expect speedups of at least an order of magnitude, while the error in terms of total variation distance is below 0.09.

While Variational Inference (VI) is central to modern generative models like Variational Autoencoders (VAEs) and Denoising Diffusion Models (DDMs), its pedagogical treatment is split across disciplines. In statistics, VI is typically framed as a Bayesian method for posterior approximation. In machine learning, however, VAEs and DDMs are developed from a Frequentist viewpoint, where VI is used to approximate a maximum likelihood estimator. This creates a barrier for statisticians, as the principles behind VAEs and DDMs are hard to contextualize without a corresponding Frequentist introduction to VI. This paper provides that introduction: we explain the theory for VI, VAEs, and DDMs from a purely Frequentist perspective, starting with the classical Expectation-Maximization (EM) algorithm. We show how VI arises as a scalable solution for intractable E-steps and how VAEs and DDMs are natural, deep-learning-based extensions of this framework, thereby bridging the gap between classical statistical inference and modern generative AI.

The intricate dynamics of stock markets have led to extensive research on models that are able to effectively explain their inherent complexities. This study leverages the econometrics literature to explore the dynamic factor model as an interpretable model with sufficient predictive capabilities for capturing essential market phenomena. Although the model has been extensively applied for predictive purposes, this study focuses on analyzing the extracted loadings and common factors as an alternative framework for understanding stock price dynamics. The results reveal novel insights into traditional market theories when applied to the Philippine Stock Exchange using the Kalman method and maximum likelihood estimation, with subsequent validation against the capital asset pricing model. Notably, a one-factor model extracts a common factor representing systematic or market dynamics similar to the composite index, whereas a two-factor model extracts common factors representing market trends and volatility. Furthermore, an application of the model for nowcasting the growth rates of the Philippine gross domestic product highlights the potential of the extracted common factors as viable real-time market indicators, yielding over a 34% decrease in the out-of-sample prediction error. Overall, the results underscore the value of dynamic factor analysis in gaining a deeper understanding of market price movement dynamics.

Detecting symmetry from data is a fundamental problem in signal analysis, providing insight into underlying structure and constraints. When data emerge as trajectories of dynamical systems, symmetries encode structural properties of the dynamics that enable model reduction, principled comparison across conditions, and detection of regime changes. While recent optimal transport methods provide practical tools for data-driven symmetry detection in this setting, they rely on deterministic thresholds and lack uncertainty quantification, limiting robustness to noise and ability to resolve hierarchical symmetry structures. We present a Bayesian framework that formulates symmetry detection as probabilistic model selection over a lattice of candidate subgroups, using a Gibbs posterior constructed from Wasserstein distances between observed data and group-transformed copies. We establish three theoretical guarantees: $(i)$ a Bayesian Occam's razor favoring minimal symmetry consistent with data, $(ii)$ conjugation equivariance ensuring frame-independence, and $(iii)$ stability bounds under perturbations for robustness to noise. Posterior inference is performed via Metropolis-Hastings sampling and numerical experiments on equivariant dynamical systems and synthetic point clouds demonstrate accurate symmetry recovery under high noise and small sample sizes. An application to human gait dynamics reveals symmetry changes induced by mechanical constraints, demonstrating the framework's utility for statistical inference in biomechanical and dynamical systems.

Timely and reliable decision-making is vital for flood emergency response, yet it remains severely hindered by limited and imprecise situational awareness due to various budget and data accessibility constraints. Traditional flood management systems often rely on in-situ sensors to calibrate remote sensing-based large-scale flood depth forecasting models, and further take flood depth estimates to optimize flood response decisions. However, these approaches often take fixed, decision task-agnostic strategies to decide where to put in-situ sensors (e.g., maximize overall information gain) and train flood forecasting models (e.g., minimize average forecasting errors), but overlook that systems with the same sensing gain and average forecasting errors may lead to distinct decisions. To address this, we introduce a novel decision-focused framework that strategically selects locations for in-situ sensor placement and optimize spatio-temporal flood forecasting models to optimize downstream flood response decision regrets. Our end-to-end pipeline integrates four components: a contextual scoring network, a differentiable sensor selection module under hard budget constraints, a spatio-temporal flood reconstruction and forecasting model, and a differentiable decision layer tailored to task-specific objectives. Central to our approach is the incorporation of Implicit Maximum Likelihood Estimation (I-MLE) to enable gradient-based learning over discrete sensor configurations, and probabilistic decision heads to enable differentiable approximation to various constrained disaster response tasks.