Real-world systems increasingly require coherent reasoning and generation over diverse data modalities simultaneously. Current generative frameworks rely on complex, multi-stage training, resulting in low efficiency due to iterative inference and high computational cost. They also struggle with unified multimodal representation, failing to balance fine-grained details with global structures and long-term dependencies, which limits generative quality and practical usability. To overcome these limitations, we introduce the Inverse Heat Mean Flow (IHMF), a general-purpose solver that is compatible with a wide range of model backbones. Without requiring pre-training, IHMF directly learns an average velocity field through an inverse heat formul ation. By exploiting the inherent scale-space properties of the inverse heat process, IHMF explicitly decomposes multi-scale complexities, thereby simplifying trajectory learning and enabling adaptive topological alignment. Extensive experiments show that IHMF achieves a competitive performance with state-of-the-art methods, providing a robust and unified mathematical framework for various generative tasks. The code is publicly available at https://github.com/CHBonline/IHMF.
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Bender Decomposition is a well-known solving technique in Operation Research that decomposes a problem into a master and a subproblem, which interact via “cuts". This technique has been extended to Logic-Based Bender Decomposition (LBBD), solving problems specified by logic-based languages and enabling a wider applicability. However, while Bender Decomposition guarantees optimality, LBBD does not: this property is problem-specific and depends on the defined decomposition and cuts. In this paper, we present a theoretical analysis of the conditions under which LBBD, including cuts, can preserve optimality in the context of Answer Set Programming (ASP), a prominent logic-based language in the field of Artificial Intelligence. We also introduce a general-purpose algorithm that employs both minimal unsatisfiable subsets and minimal correction subsets to define cuts in a fully automated, problem-independent way. The algorithm preserves the optimality guarantees of Bender Decomposition. An empirical evaluation on real-world scheduling instances shows that our approach can find significantly more solutions, and more optimal ones, compared to a standard direct ASP encoding, while also consistently reducing the execution time.
In Partial Label Learning (PLL), each instance is associated with a candidate label set, with exactly one label being true. While most studies implicitly assume balanced class distributions, real-world data often exhibit severe class imbalance distributions, leading to the Long-Tailed Partial Label Learning (LT-PLL) problem. In response, prevailing strategies typically manifest the label space to retrieve more tail samples for improved pseudo-label accuracy. However, hard-to-distinguish tail samples can significantly hinder representation learning and, in turn, affect the quality of pseudo-labels. To address this, we propose a novel Distribution-aware Dual-branch Contrastive Learning framework, DEACON, that decouples representation of head and tail labels via a dual-branch mutual-teaching design, enabling disambiguation across different shot-level groups with tailored representations. DEACON comprises two modules: (i)-a instance-balanced branch trained with a vanilla contrastive objective; (ii)-a label-balanced branch trained with a novel reweighted loss that adjusts the contrastive strength through the conditioned von-Mises Fisher density. The two branches mutually teach each other using their pseudo-labels, and we ensemble their predictions to improve overall performance. Extensive experiments on various benchmarks show that our method consistently outperforms state-of-the-art baselines.Code and appendix can be found in https://github.com/YukiNozzzz/DEACON.
Existential rules are a prominent formalism to enrich a database with knowledge from the domain of interest, but make even basic reasoning tasks on the resulting knowledge base undecidable. To circumvent this, several classes of rules offering various useful properties have been identified. One such class, for instance, contains all sets of rules on which the chase algorithm always terminates, which guarantees the existence of a finite universal model. However, these classes are often abstract rather than concrete: it may be undecidable to check whether a given set of rules belongs to them. Given that the most studied classes of existential rules are designed for reasoning on databases, thus ensuring decidable conjunctive query entailment, we ask: Within a class that supports decidable query entailment, do the usual abstract classes become concrete? We answer in the negative for classes based upon the termination of all classical chase variants and for the bts class.
Multimodal Large Language Models (MLLMs) have achieved strong performance on a wide range of vision--language tasks. However, their capabilities remain unclear in relational-diagram (RD) reasoning, where correct answers must satisfy diagram-defined constraints such as directed dependencies, branching conditions, and prerequisite relations. RDs, including hierarchical diagrams, fishbone diagrams, and flowcharts, require models to not only retrieve nodes and relations, but also maintain valid reasoning paths over multi-step dependency chains. In this paper, we introduce RD-Bench, a large-scale benchmark of verified diagram--question pairs covering three diagram categories and four difficulty levels. RD-Bench evaluates hierarchical localization, branch-condition selection, constraint-guided traversal, step counting, and prerequisite identification. Experiments on representative open-source and proprietary MLLMs reveal a consistent limitation: models perform much better on single-step reasoning than on multi-step dependency reasoning, especially for complex flowcharts with branching logic and long-range prerequisites. To reduce this gap, we propose RD-MCTS, a Monte Carlo Tree Search framework that incorporates diagram-derived structural priors, constraint-consistent state transitions, and inference-time step-level process rewards. RD-MCTS guides search toward dependency-relevant nodes and valid next steps, improving constraint-consistent reasoning on high-difficulty questions.
Knowledge concept tagging aims to assign specific concept or topic labels to educational content, which is essential for both educators and learners in traditional and online teaching practices. Recent work has explored large language models (LLMs) for this task, achieving promising performance. However, LLMs still struggle to select the correct concept from a large-scale candidate set due to the high dimensionality of the decision space. In this paper, we propose a novel three-stage Select-Reason-Judge (SRJudge) framework, which empowers LLMs with selective reasoning capability for fine-grained knowledge concept tagging. Specifically, the Selector in Stage 1 first narrows the candidate concepts to a top-K shortlist by fine-tuning a small language model (SLM), e.g., BERT, since the top-K predictions hit the correct concept in most cases, thereby reducing the decision space of correct candidates. Next, the Stage 2 Reasoner employs a lightweight LLM for refined reasoning over the shortlisted candidates. It further integrates an improved reinforcement learning strategy with a dynamic task-specific reward function and a pruning mechanism to better align with human reasoning preferences. Finally, a larger LLM acts as a judger that evaluates the overall rationality of the reasoning process and its explanations to determine the final output. In addition, we construct two high-quality datasets for further validation, i.e., the biology dataset S_Bio and the physics dataset S_Phy. Experimental results demonstrate that our method consistently outperforms state-of-the-art baselines across benchmark datasets, verifying its effectiveness and superiority. Resources are available at: https://github.com/Nicozwy/SRJudge.
Attributed graph clustering has achieved remarkable success by synergistically integrating topological structures and node attributes. While subspace learning has emerged as a dominant paradigm for node partitioning, most existing methods rely on implicit low-rank constraints, which often fail to capture complex nonlinear manifolds and suffer from prohibitive computational overhead on large-scale graphs. In this paper, we propose ELSS (Explicit Low-rank Structured Subspace learning), a scalable and robust framework that transcends implicit formulations. Specifically, ELSS learns an explicit and nonlinear low-rank subspace within a graph-structured embedding space, effectively uncovering latent cluster structures. To effectively mitigate the pervasive oversmoothing issue, we introduce a homophily-aware adaptive graph filter, which dynamically calibrates smoothing intensity to preserve discriminative ego-information. Furthermore, to ensure linear scalability, we develop a PageRank-guided structural sampling strategy for anchor-based approximation, which identifies pivotal landmarks based on their global topological prestige. Theoretical analysis guarantees that ELSS effectively mitigates spectral collapse while maintaining a linear complexity. Extensive experiments on diverse benchmarks demonstrate that ELSS consistently delivers superior clustering accuracy over state-of-the-art methods.
Motor imagery (MI) electroencephalography (EEG) decoding has benefited from deep learning, yet methods operate in Euclidean space and behave as opaque black boxes, neglecting the intrinsic geometry of functional brain connectivity. EEG connectivity descriptors, such as phase synchrony and covariance matrices, naturally reside on the manifold of symmetric positive definite (SPD) matrices, where Euclidean operations are geometrically inconsistent and hinder interpretability. This work proposes the Multi-frequency and Multi-scale Riemannian Network (MFMSRNet), an interpretable end-to-end geometry-aware framework for MI EEG decoding on the SPD manifold. The method constructs kernelized phase-locking value (KPLV) functional connectivity (FC) matrices to capture nonlinear phase synchrony while ensuring positive definiteness. An attention-based Riemannian fusion mechanism adaptively integrates information across multiple frequency bands in the tangent space. Furthermore, a multi-scale Riemannian network extracts global, hemispheric, and local connectivity patterns via manifold-preserving bilinear mappings and smooth eigenvalue rectification. Extensive experiments indicate that MFMSRNet yields more expressive and interpretable representations for robust MI decoding, offering a promising solution for reliable brain–computer interface applications. The code is available at https://github.com/Raeno-Rao/MFMSRNet.
Neural policies have shown promise in solving vehicle routing problems due to their reduced reliance on handcrafted heuristics. However, current training paradigms suffer from a fundamental limitation: they primarily focus on next-node prediction for solution construction, resulting in myopic decision-making that undermines long-horizon planning capacity. To this end, we introduce Multi-node Lookahead Prediction (MnLP), a novel training strategy that extends the supervised learning paradigm to predict multiple future nodes simultaneously. We incorporate causal and discardable MnLP modules that operate exclusively during training, facilitating models to anticipate multi-step decisions while preserving inference-time efficiency. By incorporating multi-depth auxiliary supervision into the loss function, MnLP equips neural policies with the ability of long-range contextual understanding. Experimentally, MnLP outperforms existing training methods, improving the generalization capability of neural policies across various problem sizes, distributions, and real-world benchmarks. Moreover, MnLP can be seamlessly integrated into diverse neural architectures without introducing additional inference overhead.
Mixture-of-Experts (MoE) large language models improve inference efficiency through sparse expert activation, but deployment on resource-constrained devices remains challenging due to the large expert parameter footprint. Expert offloading mitigates this issue by loading experts on demand, yet its effectiveness critically depends on accurate and efficient expert prediction: inaccurate predictions incur redundant expert transfers, while overly expensive predictors negate latency benefits. Existing trajectory-based methods suffer from low accuracy, whereas semantic-based approaches incur prohibitive similarity-matching overhead. We propose DoMoE, a domain-aware MoE inference system that exploits domain locality in inference workloads. DoMoE organizes routing information into domain-specific expert routing tables, restricts semantic matching to domain-relevant tokens and explicitly balances prediction accuracy against prediction overhead. Experiments show that DoMoE achieves a 1.32 X average throughput improvement and a 1.22 X increase in expert hit ratio across multiple MoE models and workloads, enabling efficient and accurate expert routing for practical inference.
Progression, the task of updating a knowledge base to reflect action effects, generally requires second-order logic. Identifying first-order special cases, by restricting either the knowledge base or action effects, has long been a central topic in reasoning about actions. It is known that local-effect, normal, and acyclic actions, three increasingly expressive classes, admit first-order progression. However, a systematic analysis of the size of such progressions, crucial for practical applications, has been missing. In this paper, using the framework of Situation Calculus, we show that under reasonable assumptions, first-order progression for these action classes grows only polynomially. Moreover, we show that when the KB belongs to decidable fragments such as two-variable first-order logic or universal theories with constants, the progression remains within the same fragment, ensuring decidability and practical applicability.
Join ordering is the NP-hard problem of selecting the most efficient order in which to evaluate joins (conjunctive, binary operators) in a database query. Because query execution performance critically depends on this choice, join ordering lies at the core of query optimization. Traditional approaches cast this problem as a discrete combinatorial search over binary trees guided by a cost model, but they have trade-offs between effectiveness and efficiency. We show that when the cost model is differentiable, query plans can be continuously relaxed into a soft adjacency matrix that represents a superposition of plans. This continuous relaxation, combined with differentiable constraints that enforce plan validity, enables a gradient-based search for low-cost plans within this relaxed space. Using a Graph Neural Network as the cost model, we demonstrate that this gradient-based approach can find comparable and even lower-cost plans compared to traditional discrete search methods on two different graph datasets. Furthermore, we empirically show that the runtime of this approach scales better than discrete search algorithms. We believe this first step towards gradient-based join ordering can lead to more effective and efficient query optimizers in the future.
Potential games are a fundamental class of games in which pure Nash equilibria are guaranteed to exist, yet computing such equilibria is computationally intractable for several subclasses. This has led to extensive research on computing approximate pure Nash equilibria. In this paper, we study payoff-maximization potential games. For these games, strong approximation guarantees are known only for restricted subclasses, most notably Pd--Flip games. We show that standard approaches based on unilateral improvement moves can fail to provide any finite approximation guarantee even for simple extensions of Pd--Flip games. To overcome this limitation, we propose an algorithmic framework based on coordinated moves by small groups of players, whose approximation guarantee and number of moves are controlled by two natural game parameters, the stretch and the spread, which are bounded for broad classes of games of interest. In the special case of Pd--Flip games, our framework can be configured to recover the existing algorithm, matching its approximation guarantee and the number of moves performed.
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.
Inductive knowledge graph reasoning (IKGR) requires generalization to entities and relation types not seen during training. We introduce Knowledge Graph Wave Networks (KGWN), an IKGR approach that learns adaptive per-relation wave operators to control relation-dependent propagation, along with velocity normalization ensuring stability at any propagation depth. Experiments demonstrate state-of-the-art results on inductive benchmarks and competitive transductive performance.
Infrared and visible image fusion (IVF) encounters two challenges: 1) image unregistered, where parallax leads to blurred fusion results, and 2) adverse imaging conditions, which introduces outlier data (such as haze) that significantly degrade image registered and fusion performance. Existing IVF methods fail to account for the joint impact of unregistered and haze factor, often neglecting these challenges or addressing them in isolation. However, unregistered and haze are intrinsically coupled in fusion task. For example, haze can obscure structural details, leading to inaccurate registration and ultimately degrading fusion performance. To address the intrinsic coupling between unregistered and haze, we propose a progressive task-cooperative processing pipeline—dehazing, registration, and fusion—to achieve robust fusion of unregistered images under hazy conditions. To mitigate the challenges posed by architectural complexity and excessive parameter overhead in task progressive learning, we propose a lightweight model approximation paradigm through hierarchical knowledge distillation. The framework employs a stage-wise distillation optimization strategy that synergistically integrates: 1) primary task-specific distillation for modality-aware feature extraction, and 2) progressive task-cooperative distillation for fusion-oriented representation learning, which can improve fusion robustness for unregistered multi-modal inputs in hazy conditions. Extensive experiments demonstrate that our method achieves significantly superior performance compared to the State-Of-The-Art (SOTA) methods.
Social Law Synthesis (SLS) in strategic environments is a novel multi-unit mechanism design problem, spanning modeling to computational challenges. We derive a method to specify the problem succinctly, reduce payment determination to allocation determination, and design an integer linear programming (ILP)-based algorithm that further reduces allocation to a polynomial-time ILP formulation. This offloads intractability to powerful ILP solvers, yielding a truthful, individually rational, and profit-optimal mechanism.
Pansharpening aims to fuse a high-resolution panchromatic (PAN) image with a low-resolution multispectral (MS) image to generate a highresolution multispectral output that preserves both fine spatial details and faithful spectral responses. However, enhancing spatial textures without introducing spectral distortion remains challenging due to the inherent spectral–spatial trade-off. To address this issue, we propose a two-stage pansharpening framework that tackles the problem from both modeling and optimization perspectives. In the first stage, we formulate pansharpening as spectral-prior conditioned residual diffusion, where a stable spectral base constrains the generation process and allows the diffusion model to focus on PAN-guided high-frequency details, leading to improved training stability and reduced spectral drift. To better capture the coupled spatial and frequency characteristics of PAN–MS fusion, we adopt a complex-valued denoising network to enhance spectral–spatial interaction modeling. In the second stage, to bridge the gap between distortionoriented training objectives and practical quality preferences, we introduce Group Relative Preference Optimization (GRPO) to fine-tune the diffusion model using multi-objective preference signals, explicitly balancing spectral fidelity, texture sharpness, and perceptual quality. Extensive experiments on standard benchmarks demonstrate that the proposed method achieves a more favorable trade-off between fidelity and perceptual quality compared to competitive end-to-end and diffusionbased approaches.
Graph anomaly detection (GAD) aims to identify nodes that exhibit significant deviations from expected structural or attribute patterns, and has garnered increasing attention in recent years. Recent approaches for GAD have predominantly focused on local inconsistency mining, which refers to the difficulty of establishing high similarity relationships between anomalous nodes and their neighbors. While local inconsistency mining requires the incorporation of topological information, the use of Graph Neural Networks (GNNs) to introduce such information tends to homogenize connected nodes, thereby causing the loss of local anomalous signals. To address this challenge, we propose LTRGAD, a two-stage GAD framework that performs feature selection based on local feature-topological residuals (LTR). By processing features separately, LTRGAD effectively introduces topological information while preserving the original local anomalous patterns, enabling more accurate local anomaly detection. Subsequently, global anomaly detection is conducted on the entire graph by leveraging the results from the local detection phase. Extensive experiments on seven benchmark datasets demonstrate the effectiveness of the proposed LTRGAD framework.
Graph Neural Networks (GNNs) are vulnerable to backdoor attacks, where adversaries implant malicious triggers to manipulate model predictions. Existing trigger generators are often simplistic in structure and overly reliant on specific features, confining them to a single graph learning paradigm, such as graph supervised learning, graph contrastive learning, or graph prompt learning. Such paradigm-specific designs lead to poor transferability across different learning frameworks, limiting attack success rates in general testing scenarios. To bridge this gap, we propose Cross-Paradigm Graph Backdoor Attacks with Promptable Subgraph Triggers (CP-GBA), which employs Graph Prompt Learning (GPL) to synthesize transferable subgraph triggers. Specifically, we first distill a compact yet expressive trigger set into a queryable repository, jointly optimizing for class-awareness, feature richness, and structural fidelity. Furthermore, we pioneer the theoretical exploration of GPL transferability under prompt-based objectives, ensuring robust generalization to diverse and unseen test-time paradigms. Extensive experiments across multiple real-world datasets and defense scenarios show that CP-GBA achieves state-of-the-art attack success rates. Code is available at https://github.com/novdream/CP-GBA.