Personalized Bayesian federated learning (PBFL) handles non-i.i.d. client data and quantifies uncertainty by combining personalization with Bayesian inference. However, existing PBFL methods face two limitations: restrictive parametric assumptions in client posterior inference and naive parameter averaging for server aggregation. To overcome these issues, we propose FedWBA, a novel PBFL method that enhances both local inference and global aggregation. At the client level, we use particle-based variational inference for nonparametric posterior representation. At the server level, we introduce particle-based Wasserstein barycenter aggregation, offering a more geometrically meaningful approach. Theoretically, we provide local and global convergence guarantees for FedWBA. Locally, we prove a KL divergence decrease lower bound per iteration for variational inference convergence. Globally, we show that the Wasserstein barycenter converges to the true parameter as the client data size increases. Empirically, experiments show that FedWBA outperforms baselines in prediction accuracy, uncertainty calibration, and convergence rate, with ablation studies confirming its robustness.

Priors are vital for planning under partial observability, yet difficult to obtain in practice. We present a sampling-based pipeline that leverages large-scale pretrained generative models to produce probabilistic priors capturing environmental uncertainty and spatio-semantic relationships in a zero-shot manner. Conditioned on partial observations, the pipeline recovers complete RGB-D point cloud samples with occupancy and target semantics, formulated to be directly useful in configuration-space planning. We establish a Matterport3D benchmark of rooms partially visible through doorways, where a robot must navigate to an unobserved target object. Effective priors for this setting must represent both occupancy and target-location uncertainty in unobserved regions. Experiments show that our approach recovers commonsense spatial semantics consistent with ground truth, yielding diverse, clean 3D point clouds usable in motion planning, highlight the promise of generative models as a rich source of priors for robotic planning.

Random permutation set (RPS) is a recently proposed framework designed to represent order-structured uncertain information. Measuring the distance between permutation mass functions is a key research topic in RPS theory (RPST). This paper conducts an in-depth analysis of distances between RPSs from two different perspectives: random finite set (RFS) and transferable belief model (TBM). Adopting the layer-2 belief structure interpretation of RPS, we regard RPST as a refinement of TBM, where the order in the ordered focus set represents qualitative propensity. Starting from the permutation, we introduce a new definition of the cumulative Jaccard index to quantify the similarity between two permutations and further propose a distance measure method for RPSs based on the cumulative Jaccard index matrix. The metric and structural properties of the proposed distance measure are investigated, including the positive definiteness analysis of the cumulative Jaccard index matrix, and a correction scheme is provided. The proposed method has a natural top-weightiness property: inconsistencies between higher-ranked elements tend to result in greater distance values. Two parameters are provided to the decision-maker to adjust the weight and truncation depth. Several numerical examples are used to compare the proposed method with the existing method. The experimental results show that the proposed method not only overcomes the shortcomings of the existing method and is compatible with the Jousselme distance, but also has higher sensitivity and flexibility.

Belief systems are rarely globally consistent, yet effective reasoning often persists locally. We propose a novel graph-theoretic framework that cleanly separates credibility--external, a priori trust in sources--from confidence--an internal, emergent valuation induced by network structure. Beliefs are nodes in a directed, signed, weighted graph whose edges encode support and contradiction. Confidence is obtained by a contractive propagation process that mixes a stated prior with structure-aware influence and guarantees a unique, stable solution. Within this dynamics, we define reasoning zones: high-confidence, structurally balanced subgraphs on which classical inference is safe despite global contradictions. We provide a near-linear procedure that seeds zones by confidence, tests balance using a parity-based coloring, and applies a greedy, locality-preserving repair with Jaccard de-duplication to build a compact atlas. To model belief change, we introduce shock updates that locally downscale support and elevate targeted contradictions while preserving contractivity via a simple backtracking rule. Re-propagation yields localized reconfiguration-zones may shrink, split, or collapse--without destabilizing the entire graph. We outline an empirical protocol on synthetic signed graphs with planted zones, reporting zone recovery, stability under shocks, and runtime. The result is a principled foundation for contradiction-tolerant reasoning that activates classical logic precisely where structure supports it.

Frontier large language models such as GPT-5 and Claude Sonnet remain prone to overconfidence even after alignment through Reinforcement Learning with Human Feedback (RLHF) and Direct Preference Optimization (DPO). For instance, they tend to offer the same conservative answer "No" to both questions "Can I eat the [food / potato chips] that has been left out overnight?" despite the latter requiring no refridgeration for safe consumption. We find that this failure is potentially attributed to a limitation of existing preference learning: it emphasizes selecting the correct response for a given prompt, while neglecting counterfactual prompts that should alter the response. To address this limitation, we propose abductive preference learning, a fine-tuning paradigm that reverses the conventional conditioning by learning preferences over prompts given a response. To validate this idea, we construct an abductive dataset derived from the HaluEval QA benchmark with 1,001 entries, implementing abductive DPO and its variant DPOP. Experiments reveal complementary strengths: standard methods improve response selection, abductive methods improve prompt discrimination, while a multitask objective unifies both. On the abductive dataset, multitask DPOP boosts accuracy from $90.0\%$ to $99.5\%$ in response selection and $54.7\%$ to $85.0\%$ in prompt discrimination, with qualitative evidence highlighting improved sensitivity to prompt differences. Finally, evaluation on AlpacaEval shows multitask DPOP improves win rate (from $5.26\%$ to $6.17\%$), confirming that abductive preference learning preserves the benefits of conventional preference optimization while addressing the overlooked challenge of counterfactual prompts.

Causal discovery from observational data is fundamental to scientific fields like biology, where controlled experiments are often impractical. However, existing methods, including constraint-based (e.g., PC, causalMGM) and score-based approaches (e.g., NOTEARS), face significant limitations. These include an inability to resolve causal direction, restrictions to linear associations, sensitivity to violations of the faithfulness assumption, and inefficiency in searching vast hypothesis spaces. While large language models (LLMs) offer powerful reasoning capabilities, their application is hindered by a fundamental discrepancy: they are designed for text, while most causal data is tabular. To address these challenges, we introduce CALM, a novel causal analysis language model specifically designed for tabular data in complex systems. CALM leverages a Mamba-based architecture to classify causal patterns from pairwise variable relationships. It integrates a comprehensive suite of evidence, including local causal scores, conditional independence tests, and relational attributes, to capture a wide spectrum of linear, nonlinear, and conditional causal mechanisms. Trained on a diverse corpus of synthetic data (from linear, mixed, and nonlinear models) and 10 real-world biological datasets with rigorously validated causal relationships, our model ensures robustness and generalizability. Empirical evaluation demonstrates that CALM significantly outperforms existing methods in both simulation studies, achieving over 91% accuracy, and in a real-world application identifying causal factors in Hepatitis C virus progression. This work represents a significant step towards accurate and generalizable causal discovery by successfully adapting the pattern recognition capabilities of language models to the intricacies of tabular data.

While large language models (LLMs) excel in mathematical and code reasoning, we observe they struggle with social reasoning tasks, exhibiting cognitive confusion, logical inconsistencies, and conflation between objective world states and subjective belief states. Through deteiled analysis of DeepSeek-R1's reasoning trajectories, we find that LLMs frequently encounter reasoning impasses and tend to output contradictory terms like "tricky" and "confused" when processing scenarios with multiple participants and timelines, leading to erroneous reasoning or infinite loops. The core issue is their inability to disentangle objective reality from agents' subjective beliefs. To address this, we propose an adaptive world model-enhanced reasoning mechanism that constructs a dynamic textual world model to track entity states and temporal sequences. It dynamically monitors reasoning trajectories for confusion indicators and promptly intervenes by providing clear world state descriptions, helping models navigate through cognitive dilemmas. The mechanism mimics how humans use implicit world models to distinguish between external events and internal beliefs. Evaluations on three social benchmarks demonstrate significant improvements in accuracy (e.g., +10% in Hi-ToM) while reducing computational costs (up to 33.8% token reduction), offering a simple yet effective solution for deploying LLMs in social contexts.

Diffusion Posterior Sampling (DPS) provides a principled Bayesian approach to inverse problems by sampling from $p(x_0 \mid y)$. However, in practice, the goal of inverse problem solving is not to cover the posterior but to recover the most accurate reconstruction, where optimization-based diffusion solvers often excel despite lacking a clear probabilistic foundation. We introduce Local MAP Sampling (LMAPS), a new inference framework that iteratively solving local MAP subproblems along the diffusion trajectory. This perspective clarifies their connection to global MAP estimation and DPS, offering a unified probabilistic interpretation for optimization-based methods. Building on this foundation, we develop practical algorithms with a probabilistically interpretable covariance approximation, a reformulated objective for stability and interpretability, and a gradient approximation for non-differentiable operators. Across a broad set of image restoration and scientific tasks, LMAPS achieves state-of-the-art performance, including $\geq 2$ dB gains on motion deblurring, JPEG restoration, and quantization, and $>1.5$ dB improvements on inverse scattering benchmarks.

Modern preference alignment techniques, such as Best-of-N (BoN) sampling, rely on reward models trained with pairwise comparison data. While effective at learning relative preferences, this paradigm fails to capture a signal of response acceptability, leaving systems vulnerable to selecting the least bad of many unacceptable options. This is particularly problematic for hard prompts, where the risk of such false acceptances increases with the number of samples. In this paper, we address this critical reliability gap by introducing a new data collection and modeling framework. By augmenting preference data with an outside option, inspired by discrete choice models, we train a reward model that can distinguish not just what is better, but what is good enough. We leverage this capability to create an adaptive inference strategy, best of mini-N in-loop, which partitions the generation budget into sequential loops with a calibrated, early-exit condition. Our experiments show that when tuned as an alignment guardrail, it reduces reliability failures by 70%, and when tuned as an inference accelerator, it improves average inference speed by over 22% in IMDB-sentiment setting. We thus provide a principled and flexible framework for practitioners to explicitly manage the trade-off between reliability and computational efficiency.

This paper proposes a synergy of amortised and particle-based methods for sampling from distributions defined by unnormalised density functions. We state a connection between sequential Monte Carlo (SMC) and neural sequential samplers trained by maximum-entropy reinforcement learning (MaxEnt RL), wherein learnt sampling policies and value functions define proposal kernels and twist functions. Exploiting this connection, we introduce an off-policy RL training procedure for the sampler that uses samples from SMC -- using the learnt sampler as a proposal -- as a behaviour policy that better explores the target distribution. We describe techniques for stable joint training of proposals and twist functions and an adaptive weight tempering scheme to reduce training signal variance. Furthermore, building upon past attempts to use experience replay to guide the training of neural samplers, we derive a way to combine historical samples with annealed importance sampling weights within a replay buffer. On synthetic multi-modal targets (in both continuous and discrete spaces) and the Boltzmann distribution of alanine dipeptide conformations, we demonstrate improvements in approximating the true distribution as well as training stability compared to both amortised and Monte Carlo methods.