Large language models perform near-Bayesian inference yet violate permutation invariance on exchangeable data. We resolve this by showing transformers minimize expected conditional description length (cross-entropy) over orderings, $\mathbb{E}_π[\ell(Y \mid Γ_π(X))]$, which admits a Kolmogorov-complexity interpretation up to additive constants, rather than the permutation-invariant description length $\ell(Y \mid X)$. This makes them Bayesian in expectation, not in realization. We derive (i) a Quantified Martingale Violation bound showing order-induced deviations scale as $O(\log n)$ with constants; (ii) the Expectation-level Decompression Law linking information budgets to reliability for Bernoulli predicates; and (iii) deployable planners (B2T/RoH/ISR) for answer/abstain decisions. Empirically, permutation dispersion follows $a+b\ln n$ (Qwen2-7B $b \approx 0.377$, Llama-3.1-8B $b \approx 0.147$); permutation mixtures improve ground-truth likelihood/accuracy; and randomized dose-response shows hallucinations drop by $\sim 0.13$ per additional nat. A pre-specified audit with a fixed ISR=1.0 achieves near-0\% hallucinations via calibrated refusal at 24\% abstention. The framework turns hallucinations into predictable compression failures and enables principled information budgeting.

Evaluating tabular generators remains a challenging problem, as the unique causal structural prior of heterogeneous tabular data does not lend itself to intuitive human inspection. Recent work has introduced structural fidelity as a tabular-specific evaluation dimension to assess whether synthetic data complies with the causal structures of real data. However, existing benchmarks often neglect the interplay between structural fidelity and conventional evaluation dimensions, thus failing to provide a holistic understanding of model performance. Moreover, they are typically limited to toy datasets, as quantifying existing structural fidelity metrics requires access to ground-truth causal structures, which are rarely available for real-world datasets. In this paper, we propose a novel evaluation framework that jointly considers structural fidelity and conventional evaluation dimensions. We introduce a new evaluation metric, $\textbf{global utility}$, which enables the assessment of structural fidelity even in the absence of ground-truth causal structures. In addition, we present $\textbf{TabStruct}$, a comprehensive evaluation benchmark offering large-scale quantitative analysis on 13 tabular generators from nine distinct categories, across 29 datasets. Our results demonstrate that global utility provides a task-independent, domain-agnostic lens for tabular generator performance. We release the TabStruct benchmark suite, including all datasets, evaluation pipelines, and raw results. Code is available at https://github.com/SilenceX12138/TabStruct.

Abstract-- Autonomous multi-finger grasping is a fundamental capability in robotic manipulation. Optimization-based approaches show strong performance, but tend to be sensitive to initialization and are potentially time-consuming. As an alternative, the generator-evaluator-planner framework has been proposed. A generator generates grasp candidates, an evaluator ranks the proposed grasps, and a motion planner plans a trajectory to the highest-ranked grasp. If the planner doesn't find a trajectory, a new trajectory optimization is started with the next-best grasp as the target and so on. However, executing lower-ranked grasps means a lower chance of grasp success, and multiple trajectory optimizations are time-consuming. Alternatively, relaxing the threshold for motion planning accuracy allows for easier computation of a successful trajectory but implies lower accuracy in estimating grasp success likelihood. It's a lose-lose proposition: either spend more time finding a successful trajectory or have a worse estimate of grasp success. We propose a framework that plans trajectories to a set of generated grasp targets in parallel, the evaluator estimates the grasp success likelihood of the resulting trajectories, and the robot executes the trajectory most likely to succeed. T o plan trajectories to different targets efficiently, we propose the use of a vectorized motion planner . Our experiments show our approach improves over the traditional generator-evaluator-planner framework across different objects, generators, and motion planners, and successfully generalizes to novel environments in the real world, including different shelves and table heights.

Complex networks have become essential tools for understanding diverse phenomena in social systems, traffic systems, biomolecular systems, and financial systems. Identifying critical nodes is a central theme in contemporary research, serving as a vital bridge between theoretical foundations and practical applications. Nevertheless, the intrinsic complexity and structural heterogeneity characterizing real-world networks, with particular emphasis on dynamic and higher-order networks, present substantial obstacles to the development of universal frameworks for critical node identification. This paper provides a comprehensive review of critical node identification techniques, categorizing them into seven main classes: centrality, critical nodes deletion problem, influence maximization, network control, artificial intelligence, higher-order and dynamic methods. Our review bridges the gaps in existing surveys by systematically classifying methods based on their methodological foundations and practical implications, and by highlighting their strengths, limitations, and applicability across different network types. Our work enhances the understanding of critical node research by identifying key challenges, such as algorithmic universality, real-time evaluation in dynamic networks, analysis of higher-order structures, and computational efficiency in large-scale networks. The structured synthesis consolidates current progress and highlights open questions, particularly in modeling temporal dynamics, advancing efficient algorithms, integrating machine learning approaches, and developing scalable and interpretable metrics for complex systems.

This paper addresses 6-DOF (degree-of-freedom) tactile localization, i.e. the pose estimation of tridimensional objects given tactile measurements. This estimation problem is fundamental for the operation of autonomous robots that are often required to manipulate and grasp objects whose pose is a-priori unknown. The nature of tactile measurements, the strict time requirements for real-time operation and the multimodality of the involved probability distributions pose remarkable challenges and call for advanced nonlinear filtering techniques. Following a Bayesian approach, this paper proposes a novel and effective algorithm, named Memory Unscented Particle Filter (MUPF), which solves the 6-DOF localization problem recursively in real-time by only exploiting contact point measurements. MUPF combines a modified particle filter that incorporates a sliding memory of past measurements to better handle multimodal distributions, along with the unscented Kalman filter that moves the particles towards regions of the search space that are more likely with the measurements. The performance of the proposed MUPF algorithm has been assessed both in simulation and on a real robotic system equipped with tactile sensors (i.e., the iCub humanoid robot). The experiments show that the algorithm provides accurate and reliable localization even with a low number of particles and, hence, is compatible with real-time requirements.

Anomaly detection in dynamic graphs is essential for identifying malicious activities, fraud, and unexpected behaviors in real-world systems such as cybersecurity and power grids. However, existing approaches struggle with scalability, probabilistic interpretability, and adaptability to evolving traffic patterns. In this paper, we propose ADAPTIVE-GRAPHSKETCH, a lightweight and scalable framework for real-time anomaly detection in streaming edge data. Our method integrates temporal multi-tensor sketching with Count-Min Sketch using Conservative Update (CMS-CU) to compactly track edge frequency patterns with bounded memory, while mitigating hash collision issues. We incorporate Bayesian inference for probabilistic anomaly scoring and apply Exponentially Weighted Moving Average (EWMA) for adaptive thresholding tuned to burst intensity. Extensive experiments on four real-world intrusion detection datasets demonstrate that ADAPTIVE-GRAPHSKETCH outperforms state-of-the-art baselines such as ANOEDGE-G/L, MIDAS-R, and F-FADE, achieving up to 6.5% AUC gain on CIC-IDS2018 and up to 15.6% on CIC-DDoS2019, while processing 20 million edges in under 3.4 seconds using only 10 hash functions. Our results show that ADAPTIVE-GRAPHSKETCH is practical and effective for fast, accurate anomaly detection in large-scale streaming graphs. Keywords: Anomaly Detection, Streaming, Real-time, Dynamic Graphs, Edge Streams, Tensor Sketching

We show that ensembles of deep neural networks, called deep ensembles, can be used to perform quantum parameter estimation while also providing a means for quantifying uncertainty in parameter estimates, which is a key advantage of using Bayesian inference for parameter estimation. These models are shown to be more robust to noise in the measurement results used to perform the parameter estimation as well as noise in the data used to train them. We also show that much less data is needed to achieve comparable performance to Bayesian inference based estimation, which is known to reach the ultimate precision limit as more data is collected, than was used in previous proposals.

Sequential fine-tuning of transformers is useful when new data arrive sequentially, especially with shifting distributions. Unlike batch learning, sequential learning demands that training be stabilized despite a small amount of data by balancing new information and previously learned knowledge in the pre-trained models. This challenge is further complicated when training is to be completed in latency-critical environments and learning must additionally quantify and be mediated by uncertainty. Motivated by these challenges, we propose a novel method that frames sequential fine-tuning as a posterior inference problem within a Bayesian framework. Our approach integrates closed-form moment propagation of random variables, Kalman Bayesian Neural Networks, and Taylor approximations of the moments of softmax functions. By explicitly accounting for pre-trained models as priors and adaptively balancing them against new information based on quantified uncertainty, our method achieves robust and data-efficient sequential learning. The effectiveness of our method is demonstrated through numerical simulations involving sequential adaptation of a decision transformer to tasks characterized by distribution shifts and limited memory resources.

Air pollution in cities and the possibilities of reducing this pollution represents one of the most important factors that today's society has to deal with. This paper focuses on a systemic approach to traffic emissions with their relation to meteorological conditions, analyzing the effect of weather on the quantity and dispersion of traffic emissions in a city. Using fuzzy inference systems (FIS) the model for prediction of changes in emissions depending on various conditions is developed. The proposed model is based on traffic, meteorology and emission data measured in Prague, Czech Republic. The main objective of the work is to provide insight into how urban planners and policymakers can plan and manage urban transport more effectively with environmental protection in mind.

Several emerging post-Bayesian methods target a probability distribution for which an entropy-regularised variational objective is minimised. This increased flexibility introduces a computational challenge, as one loses access to an explicit unnormalised density for the target. To mitigate this difficulty, we introduce a novel measure of suboptimality called 'gradient discrepancy', and in particular a 'kernel gradient discrepancy' (KGD) that can be explicitly computed. In the standard Bayesian context, KGD coincides with the kernel Stein discrepancy (KSD), and we obtain a novel charasterisation of KSD as measuring the size of a variational gradient. Outside this familiar setting, KGD enables novel sampling algorithms to be developed and compared, even when unnormalised densities cannot be obtained. To illustrate this point several novel algorithms are proposed, including a natural generalisation of Stein variational gradient descent, with applications to mean-field neural networks and prediction-centric uncertainty quantification presented. On the theoretical side, our principal contribution is to establish sufficient conditions for desirable properties of KGD, such as continuity and convergence control.