Kinodynamic motion planning for a multirobot system with different dynamics and actuation limits is a challenging problem. The difficulty increases with the presence of aerodynamic interaction forces that occur when aerial robots fly in close proximity. Due to these complexities, existing planners either rely on simplified assumptions (like ignoring robot dynamics and interaction forces) or produce highly suboptimal solutions. This article presents a kinodynamic motion planner for a heterogeneous team of robots that respects robot dynamics, scales well to 16 robots, and directly reasons about interaction forces between aerial robots operating in close proximity. Our method, db-ECBS, generalizes the multiagent path-finding method Enhanced Conflict-Based Search (ECBS) to the continuous domain by using the single-robot kinodynamic motion planner discontinuity-bounded A. The planner db-ECBS operates on three levels. Initially, individual robot trajectories are computed using a graph search that allows bounded discontinuities between precomputed motion primitives. The second level identifies interrobot collisions or interaction force violations and resolves them by imposing constraints on the first level. The third and final level uses the resulting solution with discontinuities as an initial guess for a joint-space trajectory optimization. The procedure is repeated with a reduced discontinuity bound, resulting in an anytime, probabilistically complete, and asymptotically bounded suboptimal planner. We provide a benchmark of 65 problems with six different dynamics. We demonstrate that db-ECBS produces trajectories that are less than half the cost of existing planners. We show that the interaction-awareness is particularly important for very dense scenarios.
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Linguistic steganography (stego) seeks to conceal secret information within natural language text. However, existing methods often struggle to balance stego text quality with embedding efficiency, largely due to limitations in generation strategies and coding mechanisms. We propose SA-ANS, a self-adaptive linguistic steganography framework based on a self-adjusting Asymmetric Numeral System. SA-ANS allows user-specified embedding rates and uses probabilistic coding with adaptive candidate selection, dynamically tailoring the token pool to the language model’s probability distribution. This design produces fluent, semantically coherent stego text while preserving statistical indistinguishability from natural language. Extensive experiments on multiple benchmark datasets, evaluated across embedding efficiency, linguistic quality, statistical similarity, robustness to steganalysis, and human judgment, show that SA-ANS consistently outperforms state-of-the-art methods, demonstrating both effectiveness and practicality.
Coastal flooding poses increasing threats to communities worldwide, necessitating accurate and hyper-local inundation forecasting for effective emergency response. However, real-world deployment of forecasting systems is often constrained by sparse sensor networks, where only a limited subset of locations may have sensors due to budget constraints. To approach this challenge, we present Diff-Sparse, a masked conditional diffusion model designed for probabilistic coastal inundation forecasting from sparse sensor observations. Diff-Sparse primarily utilizes the inundation history of a location and its neighboring locations from a context time window as spatiotemporal context. The fundamental challenge of spatiotemporal prediction based on sparse observations in the context window is addressed by introducing a novel masking strategy during training. Digital elevation data and temporal co-variates are utilized as additional spatial and temporal contexts, respectively. A convolutional neural network and a conditional UNet architecture with cross-attention mechanism are employed to capture the spatiotemporal dynamics in the data. We trained and tested Diff-Sparse on coastal inundation data from the Eastern Shore of Virginia and systematically assessed the performance of Diff-Sparse across different sparsity levels (0%, 50%, 95% missing observations). Our experiment results show that Diff-Sparse achieves upto 62% improvement in terms of two forecasting performance metrics compared to existing methods, at 95% sparsity level. Moreover, our ablation studies reveal that digital elevation data becomes more useful at high sparsity levels compared to temporal co-variates.
GraphVSSM: Graph Variational State-Space Model for Probabilistic Spatiotemporal Inference of Dynamic Exposure and Vulnerability for Regional Disaster Resilience Assessment
PDF ↗Regional disaster resilience quantifies the changing nature of physical risks to inform policy instruments ranging from local immediate recovery to international sustainable development. While many existing state-of-practice methods have greatly advanced the dynamic mapping of exposure and hazard, our understanding of large-scale physical vulnerability has remained static, costly, limited, region-specific, coarse-grained, overly aggregated, and inadequately calibrated. With the significant growth in the availability of time-series satellite imagery and derived products for exposure and hazard, we focus our work on the equally important yet challenging element of the risk equation: physical vulnerability. Given this unique problem, we leverage machine learning methods that flexibly capture spatial contextual relationships, limited temporal observations, and uncertainty in a unified probabilistic spatiotemporal inference framework. We therefore introduce Graph Variational State-Space Model (GraphVSSM), a novel modular spatiotemporal approach that uniquely integrates graph deep learning, state-space modeling, and variational inference using time-series data and prior expert belief systems in a weakly supervised or coarse-to-fine-grained manner. We present three major results: a city-wide demonstration in Quezon City, Philippines; an investigation of sudden changes in the cyclone-impacted coastal Khurushkul community (Bangladesh) and the mudslide-affected Freetown (Sierra Leone); and an open geospatial dataset, METEOR 2.5D, that spatiotemporally enhances the existing global static dataset for 46 UN-recognized Least Developed Countries (as of 2020). Beyond advancing the practice of regional disaster resilience assessment and improving our understanding of global progress in disaster risk reduction, our method also offers a probabilistic deep learning approach, contributing to broader urban studies that require compositional data analysis in weakly supervised settings.
Meta-learning for Bayesian optimization accelerates optimization by leveraging knowledge from previous tasks, but existing methods optimize for average performance and fail on challenging outlier tasks critical in practice. These limitations become particularly severe when target tasks exhibit distribution shifts or when optimization budgets are limited in real-world applications. We introduce MetaGameBO, a hierarchical game-theoretic framework that formulates meta-learning as robust optimization through CVaR-based task selection and diversity-aware sample learning. Our approach incorporates uncertainty-aware adaptation via probabilistic embeddings and Thompson sampling for robust generalization to out-of-distribution targets. We establish theoretical guarantees including convergence to game-theoretic equilibria and improved sample complexity, and demonstrate substantial improvements with 95.7% reduction in average loss and 88.6% lower tail risk compared to state-of-the-art methods on challenging tasks and distribution shifts.
Constrained and Robust Policy Synthesis with Satisfiability-Modulo-Probabilistic-Model-Checking
PDF ↗The ability to compute reward-optimal policies for given and known finite Markov decision processes (MDPs) underpins a variety of applications across planning, controller synthesis, and verification. However, we often want policies (1) to be robust, i.e., they perform well on perturbations of the MDP and (2) to satisfy additional structural constraints regarding, e.g., their representation or implementation cost. Computing such robust and constrained policies is indeed computationally more challenging. This paper contributes the first approach to effectively compute robust policies subject to arbitrary structural constraints using a flexible and efficient framework. We achieve flexibility by allowing to express our constraints in a first-order theory over a set of MDPs, while the root for our efficiency lies in the tight integration of satisfiability solvers to handle the combinatorial nature of the problem and probabilistic model checking algorithms to handle the analysis of MDPs. Experiments on a few hundred benchmarks demonstrate the feasibility for constrained and robust policy synthesis and the competitiveness with state-of-the-art methods for various fragments of the problem.
Hierarchical goal networks (HGNs) provide a framework for goal-directed planning by decomposing high-level goals into ordered subgoals. While prior work has examined non-determinism for hierarchical planning (specifically, HTNs), scant work studies how HGNs can help in stochastic settings. We introduce a formalism for probabilistic HGN planning with action-insertion semantics, enabling probabilistic planners to incorporate domain knowledge from goal decomposition methods. We design and evaluate two UCT-based algorithms for solving probabilistic HGN planning problems: an asymptotically optimal approach and a compressed, shared-value approach that optimizes separately for each goal within the goal-subgoal hierarchy. We compare our two UCT-based HGN search algorithms experimentally on modified benchmark domains from the FOND HTN literature. Our results demonstrate that on larger problems, the compressed search converges more quickly and outperforms the asymptotically optimal search. This suggests that HGNs can be effective in probabilistic planning, and compression may yield better performance on large problems in anytime settings with stochastic action outcomes.
Although recent provable methods have been developed to compute preimage bounds for neural networks, their scalability is fundamentally limited by the #P-hardness of the problem. In this work, we adopt a novel probabilistic perspective, aiming to deliver solutions with high-confidence guarantees and bounded error. To this end, we investigate the potential of bootstrap-based and randomized approaches that are capable of capturing complex patterns in high-dimensional spaces, including input regions where a given output property holds. In detail, we introduce Random Forest Property Verifier (RF-ProVe), a method that exploits an ensemble of randomized decision trees to generate candidate input regions satisfying a desired output property and refines them through active resampling. Our theoretical derivations offer formal statistical guarantees on region purity and global coverage, providing a practical, scalable solution for computing compact preimage approximations in cases where exact solvers fail to scale.
Ensuring safety in autonomous systems with vision-based control remains a critical challenge due to the high dimensionality of image inputs and the fact that the relationship between true system state and its visual manifestation is unknown. Existing methods for learning-based control in such settings typically lack formal safety guarantees. To address this challenge, we introduce a novel semi-probabilistic verification framework that integrates reachability analysis with conditional generative networks and distribution-free tail bounds to enable efficient and scalable verification of vision-based neural network controllers. Next, we develop a gradient-based training approach that employs a novel safety loss function, safety-aware data-sampling strategy to efficiently select and store critical training examples, and curriculum learning, to efficiently synthesize safe controllers in the semi-probabilistic framework. Empirical evaluations in X-Plane 11 airplane landing simulation, CARLA-simulated autonomous lane following, F1Tenth vehicle lane following in a physical visually-rich miniature environment, and Airsim-simulated drone navigation and obstacle avoidance demonstrate the effectiveness of our method in achieving formal safety guarantees while maintaining strong nominal performance.
While reinforcement learning with verifiable rewards (RLVR) has advanced LLM reasoning in structured domains like mathematics and programming, its application to general-domain reasoning tasks remains challenging due to the absence of verifiable reward signals. To this end, methods like Reinforcement Learning with Reference Probability Reward (RLPR) have emerged, leveraging the probability of generating the final answer as a reward signal. However, these outcome-focused approaches neglect crucial step-by-step supervision of the reasoning process itself. To address this gap, we introduce Probabilistic Process Supervision (P2S), a novel self-supervision framework that provides fine-grained process rewards without requiring a separate reward model or human-annotated reasoning steps. During reinforcement learning, P2S synthesizes and filters a high-quality reference reasoning chain (gold-CoT). The core of our method is to calculate a Path Faithfulness Reward (PFR) for each reasoning step, which is derived from the conditional probability of generating the gold-CoT's suffix, given the model's current reasoning prefix. Crucially, this PFR can be flexibly integrated with any outcome-based reward, directly tackling the reward sparsity problem by providing dense guidance. Extensive experiments on reading comprehension and medical Question Answering benchmarks show that P2S significantly outperforms strong baselines.
Chain-of-Thought (CoT) reasoning is a critical capability for large language models (LLMs), enabling them to tackle complex multi-step tasks. While base LLMs, pre-trained on general text corpora, often struggle with reasoning due to a lack of specialized training, recent studies reveal their latent reasoning potential tied to hidden states. However, existing hidden state manipulation methods, such as linear activation steering, suffer from limitations due to their rigid and unconstrained nature, often leading to distribution shifts and degraded text quality. In this work, we propose a novel approach for eliciting CoT reasoning from base LLMs through hidden state manipulation grounded in probabilistic conditional generation. By reformulating the challenge as an optimization problem with a balanced likelihood and prior regularization framework, our method guides hidden states toward reasoning-oriented trajectories while preserving linguistic coherence. Extensive evaluations across mathematical, commonsense, and logical reasoning benchmarks demonstrate that our approach consistently outperforms existing steering methods, offering a theoretically principled and effective solution for enhancing reasoning capabilities in base LLMs.
ECD: Evidence-guided Contrastive Decoding in Retrieval-Augmented Generation with Accurate Knowledge Reference Adjustment
PDF ↗Retrieval-Augmented Generation (RAG) enhances the quality of question answering by integrating external knowledge with internal knowledge. A robust RAG system needs to precisely regulate the dependence of the response on the two types of knowledge. The recently proposed context-aware contrastive decoding (CCD) method attempts to achieve this goal by adjusting the knowledge reference weights by comparing the output distribution differences of LLMS when they rely on different knowledge sources. However, these methods are based on probabilistic knowledge reference adjustment strategies (such as the highest probability or entropy), only focus on the relative confidence of the output responses at each decoding step, without considering the absolute confidence of the responses, which may lead to misjudgment of the external knowledge and internal knowledge reference degree in the decoding process. To this end, we propose a novel decoding method, Evidence-guided Contrastive Decoding (ECD), which conducts evidence modeling by constructing the Dirichlet distribution and regards logits as evidence vectors, so as to regulate the reference degree of internal and external knowledge more accurately, and finally improve the quality of generated responses. Extensive evaluations across four public benchmark datasets on three mainstream LLMs have demonstrated the effectiveness and advantages of ECD.
To develop general-purpose collaborative agents, humans need reliable AI systems that can (1) adapt to new domains and (2) transparently reason with uncertainty to allow for verification and correction. Black-box models demonstrate powerful data processing abilities but do not satisfy these criteria due to their opaqueness, domain specificity, and lack of uncertainty awareness. We introduce Bonsai, a compositional and probabilistic reasoning system that generates adaptable inference trees by retrieving relevant grounding evidence and using it to compute likelihoods of sub-claims derived from broader natural language inferences. Bonsai's reasoning power is tunable at test-time via evidence scaling and it demonstrates reliable handling of varied domains including transcripts, photographs, videos, audio, and databases. Question-answering and human alignment experiments demonstrate that Bonsai matches the performance of domain-specific black-box methods while generating interpretable, grounded, and uncertainty-aware reasoning traces.
Latent Self-Consistency for Reliable Majority-Set Selection in Short- and Long-Answer Reasoning
PDF ↗Probabilistic decoding in Large Language Models (LLMs) often yields inconsistent outputs, particularly on complex or long-form questions. Self-Consistency (SC) mitigates this for short-form QA by majority voting over exact strings, whereas Universal Self-Consistency (USC) and Weighted Unigram Consistency Score (WUCS) extend to long-form responses but lose accuracy on short-form benchmarks. We introduce Latent Self-Consistency (LSC), which selects the most semantically consistent response using learnable token embeddings. LSC's lightweight forward processing of summary tokens only introduces negligible runtime overhead (at most 0.9%) on top of standard decoding of the base LLM, and requires no changes to the model architecture. Across 6 short-form and 5 long-form reasoning benchmarks (e.g., MATH, MMLU, TruthfulQA), LSC surpasses SC, USC, and WUCS on both short-form and long-form on average performance, while adding negligible computational overhead on vanilla inference. These results position LSC as a reliable consistency-selection method that works effectively across various answer formats. Additionally, LSC provides well-calibrated confidence estimates, maintaining low expected calibration error across both answer formats.
While large language models (LLMs) demonstrate emerging reasoning capabilities, current inference-time expansion methods incur prohibitive computational costs through exhaustive sampling. Through analyzing decoding trajectories, we observe that most next-token predictions align well with the golden output, except for a few critical tokens that lead to deviations. Inspired by this phenomenon, we propose a novel Hint-Practice Reasoning (HPR) framework that operationalizes this insight through two synergistic components: 1) a hinter (powerful LLM) that provides probabilistic guidance at critical decision points, and 2) a practitioner (efficient smaller model) that executes major reasoning steps. The framework's core innovation lies in Distributional Inconsistency Reduction (DIR), a theoretically-grounded metric that dynamically identifies intervention points by quantifying the divergence between practitioner's reasoning trajectory and hinter's expected distribution in a tree-structured probabilistic space. Through iterative tree updates guided by DIR, HPR reweights promising reasoning paths while deprioritizing low-probability branches. Experiments across arithmetic and commonsense reasoning benchmarks demonstrate HPR's state-of-the-art efficiency-accuracy tradeoffs: it achieves comparable performance to self-consistency and MCTS baselines while decoding only 1/5 tokens, and outperforms existing methods by at most 5.1% absolute accuracy while maintaining similar or lower FLOPs.
Pseudo-Spiking Neurons: A Noise-Based Training Framework for Heterogeneous-Latency Spiking Neural Networks
PDF ↗Spiking Neural Networks (SNNs) promise significant energy efficiency by processing information via sparse, event-driven spikes. However, realizing this potential is hindered by the conventional use of a rigid, uniform timestep, T. This constraint imposes a challenging trade-off between accuracy and latency, while also incurring the prohibitive training costs of Backpropagation Through Time (BPTT). To overcome this limitation, we introduce the Pseudo-Spiking Neuron (PseudoSN), a novel training proxy that conceptualizes latency as an intrinsic, learnable parameter for each neuron. Building on the efficiency of rate-based methods, the PseudoSN models temporal dynamics in a single, BPTT-free pass. It employs a learnable probabilistic noise scheme to emulate the discretization effects of spike generation (e.g., clipping and quantization), making the neuron-specific timestep—and thus latency—directly optimizable via backpropagation. Integrated into a hardware-aware objective, our framework trains heterogeneous-latency SNNs that autonomously learn to optimize the trade-offs among accuracy, latency and energy, establishing a new state-of-the-art on major benchmarks.
Formal verification has emerged as a promising method to ensure the safety and reliability of neural networks. However, many relevant properties, such as fairness or global robustness, pertain to the entire input space. If one applies verification techniques naively, the neural network is checked even on inputs that do not occur in the real world and have no meaning. To tackle this shortcoming, we propose the VeriFlow architecture as a flow-based density model tailored to allow any verification approach to restrict its search to some data distribution of interest. We argue that our architecture is particularly well suited for this purpose because of two major properties. First, we show that the transformation that is defined by our model is piecewise affine. Therefore, the model allows the usage of verifiers based on constraint solving with linear arithmetic. Second, upper density level sets (UDL) of the data distribution are definable via linear constraints in the latent space. As a consequence, representations of UDLs specified by a given probability are effectively computable in the latent space. This property allows for effective verification with a fine-grained, probabilistically interpretable control of how (a-)typical the inputs subject to verification are.
The multi-view clustering methods based on tensor regression can make full use of the potential structural information between views and achieve data-level fusion. However, existing tensor regression-based approaches for anchor graph often overlook the probabilistic nature of anchor graph, focusing solely on sample labels while ignoring the influence of anchor labels on clustering results. To overcome these limitations, we introduce Tensorized Label Learning via Balanced Tensor Regression (TLL-BTR). Our key idea is to exploit the probabilistic nature of the anchor graph by regarding the sample labels as a projection tensor that maps the anchor graph into the label space, thereby producing anchor labels. By enforcing constraints on these anchor labels, we guide the concurrent learning of sample labels and achieve co-label learning between anchors and samples. To prevent trivial solutions, we maximize the nuclear norm to promote an even distribution of samples across clusters. Extensive experiments on benchmark datasets demonstrate that TLL-BTR consistently outperforms state-of-the-art methods.
Most state-of-the-art time series imputation methods can leverage textual information to improve imputation quality, but they often struggle because they fail to effectively filter noisy information from large language model (LLM) derived textual information. Some existing solutions only filter over the entire token set, which can introduce erroneous conditional constraints, extreme token frequency effects and increased computational complexity. To address this, we propose CaT-Diff, a novel cascaded text-enhanced diffusion model for probabilistic imputation of multivariate time series under Missing Not At Random (MNAR) scenarios. To suppress irrelevant semantics and focus on context most predictive of missing values, CaT-Diff introduces an innovative Hierarchical Semantic Filter (HSF) that collaborates with a Mixture-of-Experts (MoE) Network. The MoE projects heterogeneous text embeddings into the time series latent space, and the HSF cascade-filters text embeddings from the segment level to the token level, thereby avoiding the pitfalls of direct token-level filtering and reducing overhead. We also incorporate a lightweight Missing Mechanism Estimator, jointly optimized with the denoising network to explicitly capture MNAR missingness patterns. Extensive tests on nine domains show that CaT-Diff outperforms state-of-the-art baselines. Our work presents a new approach for selectively fusing LLM-derived textual information.
Time series forecasting is an important task that involves analyzing temporal dependencies and underlying patterns (such as trends, cyclicality, and seasonality) in historical data to predict future values or trends. Current deep learning-based forecasting models primarily employ Mean Squared Error (MSE) loss functions for regression modeling. Despite enabling direct value prediction, this method offers no uncertainty estimation and exhibits poor outlier robustness. To address these limitations, we propose OCE-TS, a novel ordinal classification approach for time series forecasting that replaces MSE with Ordinal Cross-Entropy (OCE) loss, preserving prediction order while quantifying uncertainty through probability output. Specifically, OCE-TS begins by discretizing observed values into ordered intervals and deriving their probabilities via a parametric distribution as supervision signals. Using a simple linear model, we then predict probability distributions for each timestep. The OCE loss is computed between the cumulative distributions of predicted and ground-truth probabilities, explicitly preserving ordinal relationships among forecasted values. Through theoretical analysis using influence functions, we establish that cross-entropy (CE) loss exhibits superior stability and outlier robustness compared to MSE loss. Empirically, we compared OCE-TS with five baseline models—Autoformer, DLinear, iTransformer, TimeXer, and TimeBridge—on seven public time series datasets. Using MSE and Mean Absolute Error (MAE) as evaluation metrics, the results demonstrate that OCE-TS consistently outperforms benchmark models.