We propose a new framework to systematically incorporate data uncertainty in Gaussian Splatting. Being the new paradigm of neural rendering, Gaussian Splatting has been investigated in many applications, with the main effort in extending its representation, improving its optimization process, and accelerating its speed. However, one orthogonal, much needed, but under-explored area is data uncertainty. In standard 4D Gaussian Splatting, data uncertainty can manifest as view sparsity, missing frames, camera asynchronization, etc. So far, there has been little research to holistically incorporating various types of data uncertainty under a single framework. To this end, we propose Graphical X Splatting, or GraphiXS, a new probabilistic framework that considers multiple types of data uncertainty, aiming for a fundamental augmentation of the current 4D Gaussian Splatting paradigm into a probabilistic setting. GraphiXS is general and can be instantiated with a range of primitives, e.g. Gaussians, Student’s-t. Furthermore, GraphiXS can be used to ‘upgrade’ existing methods to accommodate data uncertainty. Through exhaustive evaluation and comparison, we demonstrate that GraphiXS can systematically model various uncertainties in data, outperform existing methods in many settings where data are missing or polluted in space and time, and therefore is a major generalization of the current 4D Gaussian Splatting research.
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Active retrieval-augmented generation (RAG) triggers external knowledge retrieval during generation based on model-side uncertainty signals to support knowledge-intensive, multi-hop reasoning. However, existing methods often retrieve only after producing a complete answer, failing to surface and fill information gaps in time; moreover, relying on a single internal signal as the trigger cannot adequately capture the multifaceted nature of uncertainty. We therefore propose a conflict-aware active RAG framework. We first decompose complex questions into a sequence of step-level sub-problems. At each step, we quantify local distributional uncertainty via a sliding-window peak token entropy, and estimate cross-sample consensus via the variation ratio computed over multiple Monte Carlo samples. After calibrating both signals onto a probabilistic scale, we quantify their conflict using a symmetric, bounded divergence over Bernoulli parameters, and fuse the three quantities into a single uncertainty score that gates retrieval. Experiments demonstrate the effectiveness of our framework.
While Large Language Models (LLMs) excel at many reasoning tasks, their native inability to produce calibrated, multi-class probability distributions limits their use in high-stakes Web applications like content moderation and fraud detection. Existing methods to elicit probabilities from LLMs either sacrifice their crucial Chain-of-Thought (CoT) reasoning capabilities or suffer from poor calibration. To address this, we introduce a new paradigm, Verbalized Probability Distribution, and a novel training framework, RLVP (Reinforcement Learning with Verbalized Probabilities). RLVP fine-tunes an LLM to generate both an interpretable CoT and a complete, verbalized probability distribution. We overcome the ''insufficient reward granularity'' problem in standard Reinforcement Learning (RL) for classification by using soft probabilities from expert tabular models as a dense reward curriculum. Through large-scale joint training on 169 tabular tasks, we demonstrate that a single RLVP-trained model can surpass a strong, task-specific XGBoost baseline on up to 55% of tasks. More importantly, the trained model achieves state-of-the-art few-shot performance on unseen, heterogeneous Web benchmarks that mix structured data with free text, achieving performance comparable to or superior than expert models trained on the same limited data. This showcases a strong capability for generalization and knowledge transfer to complex Web data. Our work presents a viable path toward building general-purpose, probabilistically-sound, and interpretable foundation models for the Web.
Active feature acquisition (AFA) studies how a predictive system can sequentially choose which feature values to obtain for each instance to balance predictive accuracy against feature acquisition cost. This survey provides the first unified treatment of modern AFA through a partially observable Markov decision process (POMDP) formulation, showing that most existing methods can be understood as different approximations of the same underlying sequential decision problem. The survey proposes an up-to-date taxonomy organizing AFA into four categories: (i) embedded cost-aware predictors (notably cost-sensitive decision trees and ensembles), (ii) model-based methods that plan using learned probabilistic components, (iii) model-free methods that learn acquisition policies from simulated episodes, and (iv) hybrid methods that combine the strengths of model-based and model-free approaches. We argue that this POMDP-centric view clarifies connections among existing methods and motivates more principled algorithm design. Since much prior work is heuristic and lacks formal guarantees, we also outline routes to guarantees by connecting AFA to adaptive stochastic optimization. We conclude by highlighting open challenges and promising directions for future research.
Numerical weather prediction (NWP) models remain the cornerstone of atmospheric sciences. Yet, deep learning (DL) is challenging this paradigm by its ability to capture intricate spatio-temporal patterns and deliver ultra-fast predictions. Analogous to the foundation models (e.g., ChatGPT) in natural language processing, foundation models in the weather/climate domain have also been developed. This paper reviews DL and foundation models for weather prediction by highlighting their strengths and limitations. In particular, we carefully examine them from the perspective of their training paradigms: deterministic predictive learning, probabilistic generative learning, and pre-training & fine-tuning. For each paradigm, we summarize the underlying model architectures, training methods, and respective features. To facilitate further study, we provide a curated repository featuring categorized papers, open-source code, and benchmark datasets. Finally, we discuss and suggest potential research directions across new tasks and models in weather data storage and management, and operational deployment, further inspiring innovations in this rapidly evolving field. GitHub: https://github.com/JimengShi/DL-Foundation-Models-Weather.
Recent developments in brain recording are driving a demand for machine learning tools capable of decoding the latent structure of large populations of neurons. In this paper, we provide a comprehensive survey that outlines the trajectory of Latent Variable Models (LVMs) from early state-space models to more recent deep generative models. We organize the literature into three closely related domains: (1) Single-Region Latent Dynamics, which includes models such as linear dynamical systems to more complex dynamics represented by Recurrent Neural Networks (RNNs) and Neural Ordinary Differential Equations (ODEs); (2) Multi-Region Communication, which employs probabilistic as well as subspace methods to study how information is transfered across different brain areas considering synaptic propagation delays and network connectivity; and (3) Behavior-Aligned Modeling, which seeks to disentangle neural activity related to task performance from other internal states via supervised or contrastive learning. Finally, we conclude and discuss benchmarks, evaluation criteria, and open challenges, such as the ability to identify causal links or directionality of communication, to facilitate future research for bridging interpretable brain dynamics with reliable neural decoding.
Reinforcement learning (RL) is increasingly applied in complex, safety-critical domains, yet the lack of rigorous behavioral guarantees for neural network-based policies remains a major barrier to deployment. Recent advances in policy expressiveness and scale have intensified this challenge, leading to a rapidly growing but conceptually fragmented body of work on RL policy verification. This survey provides a unifying perspective on RL verification methods. We introduce a taxonomy that clarifies relationships among existing approaches along three axes: verification paradigm (formal versus probabilistic), temporal scope (step-wise versus multi-step), and guarantees strength. Beyond taxonomy, we unify underlying theoretical foundations, make implicit assumptions and limitations explicit, and identify emerging directions.
Understanding underlying agent attributes such as goals, preferences, beliefs, and ability level is key to explaining decision-making and predicting behaviour in complex environments. While goal recognition (GR) has produced effective methods for inferring goals, recent work has begun to explore reinforcement learning (RL)-based approaches to attribute recognition (AR), which generalises GR by inferring a wider range of agent attributes beyond goals. Existing frameworks treat attributes as discrete variables and typically require separate models for each attribute. In reality, many agent attributes vary continuously rather than as discrete values, making continuous representations crucial for capturing subtle variations in behaviour. We introduce a multivariate RL-based AR framework that jointly infers multiple continuous-valued attributes from observed behaviour using a single attribute-conditioned policy and continuous probabilistic inference. Our experiments demonstrate that the proposed framework achieves stable and fine-grained inference, offering improved flexibility and generality compared to existing approaches.
LLMs' overconfidence, particularly when hallucinating, poses a significant challenge for the deployment of the models in safety-critical settings and makes a reliable estimation of uncertainty necessary. Existing approaches for uncertainty quantification typically prioritize lexical or probabilistic measures; however, these techniques often ignore the semantic variance of different responses with similar meaning. In this paper, we propose Adaptive Conformal Semantic Entropy (ACSE), a method for estimating prompt-level uncertainty by adaptively measuring semantic dispersion in LLMs outputs. Our uncertainty scoring function is based on clustering semantic entropy of multiple diverse responses to the same prompt. The function adaptively adjusts the uncertainty score based on semantic features of each cluster. To ensure statistical reliability of our score, we use conformal calibration to apply a decision rule to accept/abstain the prompts, providing a finite-sample, distribution-free guarantee such that the error rate among the accepted responses remains bounded by a user-specified tolerance. Our extensive experimental evaluations using different LLMs and datasets, demonstrate that our approach consistently outperforms state-of-the-art uncertainty quantification baselines using discriminative performance, acceptance rate, conformal guarantees, and probabilistic calibration indicators. As a highlight, for TriviaQA dataset, AUROC of our approach is 0.88 compared to 0.65 produced by the token entropy approach.
Spatio-temporal graph networks form the foundation of modern traffic prediction, yet their deployment is fundamentally challenged by the pervasive reality of distribution shifts. While out-of-distribution (OOD) learning holds promise for robustness, existing methods rely on static graph structures, failing to capture the inherent topological dynamics of real-world traffic systems and thus limiting long-term deployment reliability. To bridge this gap, we propose DynaSTar, a Dynamic Spatio-Temporal Graph Invariant Learning model designed for reliable out-of-time (OOT) traffic prediction under evolving topologies. Our model employs a dynamic probabilistic graph structure, which is continuously refined through momentum-based updates and differentiable sparse sampling to model evolving inter-node dependencies. Besides, it utilizes node-level environment construction and modulated prediction to extract representations invariant to heterogeneous neighborhood fluctuations, enabling robust generalization. Comprehensive experiments on large-scale, long-term real-world datasets demonstrate that by effectively tracking evolving topological shifts, DynaSTar consistently outperforms state-of-the-art baselines across various OOT scenarios.
Asset pricing and portfolio recommendation are two closely related fundamental tasks in quantitative investment, for which machine learning methods have attracted significant attention in both academia and industry. In particular, nonlinear asset pricing models based on deep learning architectures that learn risk factors and risk exposures (betas) conditioned on high-dimensional asset characteristics have become widely used in the field. Despite their popularity, three challenges remain for portfolio recommendation: (i) their static risk pricing structure constrains predictive performance for expected returns; (ii) their representation learning is typically deterministic or fails to account for the inherent distributional uncertainty in the feature space arising from noisy returns and heterogeneous characteristics; and (iii) the sparse factor structure of asset returns and the diversity of characteristics make it difficult to identify incremental predictive information. To address these issues and bridge the gap to practical applications, we propose a novel multi-task dynamic factor model that jointly performs asset pricing and portfolio recommendation. Specifically, we introduce dual-adversarial trainers into the variational prior-posterior learning framework for Factor and Beta Networks, augmented with probabilistic equivariance regularization and dual adaptive spatio-temporal clustering. These components filter redundant information and enhance the model's ability to adapt to changing market conditions. Extensive experiments on a comprehensive open-source stock market dataset demonstrate that our model achieves strong and robust performance relative to baseline methods in the literature.
Prototype-based federated learning enables efficient knowledge sharing by exchanging class prototypes rather than full model parameters. However, heterogeneous client data and limited local samples increase prototype estimation variance, making many client prototypes unreliable. Existing methods usually treat prototypes as deterministic point estimates and cannot quantify their reliability, which may contaminate global prototypes and cause negative transfer. To address these challenges, we propose FedUP, an uncertainty-aware personalized federated learning framework that models prototypes as probability distributions. FedUP captures both aleatoric and epistemic uncertainty on a probabilistic simplex to guide local training and global aggregation. It further uses global probabilistic prototypes as class-conditional priors for feature augmentation, alleviating client-side data sparsity. Finally, FedUP aggregates prototype distributions through reliability-informed barycenters on the statistical manifold, suppressing unreliable contributions while preserving geometric structure. Experiments on natural and medical benchmarks demonstrate that FedUP consistently outperforms state-of-the-art methods.
We introduce QUINTIC, a general algorithm for actively learning quantitative automata from preferences. Quantitative automata evaluate input sequences by applying a valuation function---such as sum, product, or average---to the output labels of the states visited. Such models naturally arise in use cases ranging from probabilistic verification, sequence classification, and sequential decision making. However, existing learning approaches, such as variants of L*, weighted‐automata learning algorithms, and active learning preference‐driven methods, either assume finite output alphabets or restrict the valuation function to particular forms. QUINTIC utilizes a symbolic observation table and applies deductive reasoning with the assistance of an SMT solver to identify the correct minimal state, transition, and state label combination of the quantitative automaton. The deductive reasoning relies on the minimal combination of theories determined by the valuation function and output alphabet. Consequently, QUINTIC has completeness, minimalism, and query complexity guarantees, and learns quantitative automata across finite, integer, and rational outputs. Our extensive experiments show how QUINTIC scales under weak or strong feedback, and alternative MaxSMT objectives.
Survival models on networks describe the time-evolving dynamics of complex systems, but existing frameworks suffer from two key limitations: First, many past approaches implicitly assume independent censoring, which can introduce substantial bias. Second, point-process-based models often emphasize only sending behavior and overlook shared latent structure between interacting nodes. Recent work has incorporated copulas into deep survival models to mitigate censoring bias, but these methods do not capture topological role structure. Another line of research combines survival analysis with the Mixed-Membership Stochastic Blockmodel (MMSB) to model heterogeneity via role-specific hazard rates; however, it typically assumes structural independence and therefore misses important correlations between roles. To bridge these gaps, we apply an improved Copula–MMSB mechanism and propose the first Survival Fully-Collapsed Copula Mixed Membership Blockmodel. Our framework jointly models time-to-event dynamics and complex dependencies among latent roles. On the Enron benchmark, it surpasses state-of-the-art survival blockmodels in both predictive likelihood and structural interpretability. Additionally, the model admits an exact closed-form discrete distribution over role pairs, which enables a fully collapsed Gibbs sampler and avoids the slow mixing and poor convergence common in non-conjugate inference. In simulations, this yields a 100× improvement in sampling efficiency over semi-collapsed baselines.
Responsibility allocation---determining the extent to which agents are accountable for outcomes---is a fundamental challenge in the design and analysis of multi-agent systems. In this work, we model such systems as concurrent stochastic multi-player games and introduce a notion of retrospective (backward) counterfactual responsibility, which quantifies an agent's accountability for outcomes resulting from a given strategy profile. To allocate responsibility among agents, we utilise the Shapley value and formally show that this method satisfies key desirable properties, including fairness and consistency. Building on this foundation, we propose a formal framework that supports both verification and strategic reasoning in responsibility-aware multi-agent systems. Furthermore, by adopting Nash equilibrium as the solution concept, we demonstrate how to compute stable strategy profiles in which agents trade off responsibility against expected reward.
Model counting of Disjunctive Normal Form (DNF) formulas is a critical problem in applications such as probabilistic inference and network reliability. For example, it is often used for query evaluation in probabilistic databases. Due to the computational intractability of exact DNF counting, there has been a line of research into a variety of approximation algorithms. We develop a new Monte Carlo approach with an adaptive stopping rule and short-circuit formula evaluation. We prove it achieves Probably Approximately Correct (PAC) learning bounds and has asymptotically improved time and randomness complexity compared to previous methods. We also show experimentally that it out-performs prior algorithms by at least three orders of magnitude in running time and scalability.
Probabilistic time series forecasting seeks to quantify the uncertainty of future observations. While recent works introduce latent variables to alleviate the spurious dependencies caused by hidden confounders, thereby reducing overly wide confidence intervals, simply incorporating latent factors is not sufficient. When the underlying latent dynamics evolve at multiple temporal scales, existing methods may entangle temporally coarse and fine latent dynamics, which introduces spurious latent transitions and in turn amplifies predictive uncertainty. Therefore, disentangling temporally coarse and fine latent dynamics is essential for achieving sharper and more reliable probabilistic forecasting results. Building on this insight, we propose COFE (COarse And FinE latent dynamics disentanglement), a variational autoencoder–based framework that models the temporal distribution by disentangling and modeling the rapidly changing and slowly varying latent dynamics simultaneously. In particular, the proposed COFE harnesses the independence of estimated noises between adjacent latent states as well as a sparsity constraint on estimated noise to disentangle latent dynamics across different scales effectively. More specifically, we show that the multi-scale latent dynamics are disentangled with rigorous theoretical guarantees. Extensive experiments on 15 benchmark datasets, compared against 12 state-of-the-art baselines, demonstrate that COFE achieves superior uncertainty quantification, validating its effectiveness in a wide range of real-world scenarios. Code is available at https://github.com/polars8948/COFE
Identifying cancer driver genes (CDGs) requires integrating heterogeneous biological networks, each encoding distinct mechanistic insights into tumorigenesis. Existing multi-network methods typically fuse views at the feature level or enforce uniform representations, which obscures network-specific signals and limits interpretability. To address this, we propose LogicFusion, a novel differentiable framework that treats each biological network as an independent probabilistic evidence source and explicitly learns how to combine them using logical reasoning. Specifically, LogicFusion maps the output of each view into probabilistic space as independent evidence, and learns a set of logical rules in a differentiable manner. These rules adaptively select and fuse these view evidences through logical conjunction (AND) and disjunction (OR). The final prediction is then obtained via gene-specific weighting. LogicFusion enables both high-accuracy CDG identification and interpretable attribution of predictions to specific networks. Experiments on pan-cancer and cancer-specific datasets show that LogicFusion consistently outperforms state-of-the-art methods, while providing transparency in multi-view genomic reasoning through learned logical rules.
Explainable AI (XAI) seeks to answer the question: which features of the data led a model to make its decision? Sufficient reasons are an important concept for understanding the behaviour of machine learning models, as they identify the key characteristics responsible for the prediction of an individual instance. Recent work introduced probabilistic global sufficient reasons, extending sufficient reasons from the single-instance level to all instances in the feature domain, thereby providing a global understanding of the classifier. However, prior work on this notion has been purely theoretical, without empirical evaluation. In this paper, we aim to fill this gap by developing practical methods for computing probabilistic global sufficient reasons and evaluating them on decision trees and circuit-based models.
PRIMP: PRobabilistically-Informed Motion Primitives for Efficient Affordance Learning from Demonstration (Abstract Reprint)
PDF ↗This paper proposes a learning-from-demonstration (LfD) method using probability densities on the workspaces of robot manipulators. The method, named PRobabilistically-Informed Motion Primitives (PRIMP), learns the probability distribution of the end effector trajectories in the 6D workspace that includes both positions and orientations. It is able to adapt to new situations such as novel via points with uncertainty and a change of viewing frame. The method itself is robot-agnostic, in that the learned distribution can be transferred to another robot with the adaptation to its workspace density. Workspace-STOMP, a new version of the existing STOMP motion planner, is also introduced, which can be used as a post-process to improve the performance of PRIMP and any other reachability-based LfD method. The combination of PRIMP and Workspace-STOMP can further help the robot avoid novel obstacles that are not present during the demonstration process. The proposed methods are evaluated with several sets of benchmark experiments. PRIMP runs more than 5 times faster than existing state-of-the-art methods while generalizing trajectories more than twice as close to both the demonstrations and novel desired poses. They are then combined with our lab’s robot imagination method that learns object affordances, illustrating the applicability to learn tool use through physical experiments.