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We study the fair allocation of indivisible goods with variable groups. In this model, the goal is to partition the agents into groups of given sizes and allocate the goods to the groups in a fair manner. We show that for any number of groups and corresponding sizes, there always exists an envy-free up to one good (EF1) outcome, thereby generalizing an important result from the individual setting. Our result holds for arbitrary monotonic utilities and comes with an efficient algorithm. We also prove that an EF1 outcome is guaranteed to exist even when the goods lie on a path and each group must receive a connected bundle. In addition, we consider a probabilistic model where the utilities are additive and drawn randomly from a distribution. We show that if there are $n$ agents and the number of goods $m$ is divisible by the number of groups $k$, then an envy-free outcome exists with high probability if $m = \omega(\log n)$, and this bound is tight. On the other hand, if $m$ is not divisible by $k$, then an envy-free outcome is unlikely to exist as long as $m = o(\sqrt{n})$.

AAAI 2026

Fair Allocation of Indivisible Goods with Variable Groups

technical paper

We are pleased to announce the Fortieth AAAI Conference on Artificial Intelligence (AAAI-26), which will be held in Singapore EXPO from January 20 to January 27, 2026.

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. AAAI-26 will feature technical paper presentations, special tracks, invited speakers, workshops, tutorials, poster sessions, senior member presentations, competitions, and exhibit programs, and a range of other activities to be announced.<br><br>

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We are pleased to announce the Fortieth AAAI Conference on Artificial Intelligence (AAAI-26), which will be held in Singapore EXPO from January 20 to January 27, 2026.

The increasing scale of graph datasets has significantly improved the performance of graph representation learning methods, but it has also introduced substantial training challenges. Graph dataset condensation techniques have emerged to compress large datasets into smaller yet information-rich datasets, while maintaining similar test performance. However, these methods strictly require downstream applications to match the original dataset and task, which often fails in cross-task and cross-domain scenarios. To address these challenges, we propose a novel causal-invariance-based and transferable graph dataset condensation method, named **TGCC**, providing effective and transferable condensed datasets. Specifically, to preserve domain-invariant knowledge, we first extract domain causal-invariant features from the spatial domain of the graph using causal interventions. Then, to fully capture the structural and feature information of the original graph, we perform enhanced condensation operations. Finally, through spectral-domain Enhanced contrastive learning, we inject the causal-invariant features into the condensed graph, ensuring that the compressed graph retains the causal information of the original graph. Experimental results on five public datasets and our novel **FinReport** dataset demonstrate that TGCC achieves up to a 13.41% improvement in cross-task and cross-domain complex scenarios compared to existing methods, and achieves state-of-the-art performance on 5 out of 6 datasets in the single dataset and task scenario.

Transferable Graph Condensation from the Causal Perspective

Linear programming is a fundamental tool in a wide range of decision systems. However, without privacy protections, sharing the solution to a linear program may reveal information about the underlying data used to formulate it, which may be sensitive. Therefore, in this paper we introduce an approach for protecting sensitive data while formulating and solving a linear program. First, we prove that this method perturbs objectives and constraints in a way that makes them differentially private. Then, we show that (i) privatized problems always have solutions, and (ii) their solutions satisfy the constraints in their corresponding original, non-private problems. The latter result solves an open problem in the literature. Next, we analytically bound the expected sub-optimality of solutions that is induced by privacy. Numerical simulations show that, under a typical privacy setup, the solution produced by our method yields a $65\\%$ reduction in sub-optimality compared to the state of the art.

Differentially Private Linear Programming: Reduced Sub-Optimality and Guaranteed Constraint Satisfaction

RFC (Request for Comments) documents constitute the foundation of network protocol standardization. However, they are expressed in natural language, they tend to be lengthy and ambiguous, forcing protocol implementers to rely on extensive manual parsing and coding—a process that is both labor-intensive and prone to errors. This makes the automated parsing and comprehension of RFC documents a major challenge in network protocol research. 
To address this gap, we introduce large language models (LLMs) into the task of automatic network protocol code generation from RFC documents (RFC2Code) and propose a comprehensive evaluation framework to quantitatively assess LLM performance. We develop an end-to-end automated protocol generation system, APG (Automated Protocol-Generation), which supports implementations of ICMP, IGMP, NTP, and TCP. Compared to prior NLP (Natural language processing) methods, APG achieves a fully automated workflow with approximately 3.17× faster processing, 95\% compile success and behavioral correctness for stateless protocols like ICMP, and 90\% interoperability for complex stateful protocols such as TCP, requiring only minimal manual intervention.

LLMs Unleashed: Generating Protocol Code from RFC Specifications

Knowledge graph reasoning in the fully-inductive setting—where both entities and relations at test time are unseen during training—remains an open challenge. In this work, we introduce \textsc{GraphOracle}, a novel framework that achieves robust fully-inductive reasoning by transforming each knowledge graph into a Relation-Dependency Graph (RDG). The RDG encodes directed precedence links between relations, capturing essential compositional patterns while drastically reducing graph density. Conditioned on a query relation, a multi-head attention mechanism propagates information over the RDG to produce context-aware relation embeddings. These embeddings then guide a second GNN to perform inductive message passing over the original knowledge graph, enabling prediction on entirely new entities and relations. Comprehensive experiments on 60 benchmarks demonstrate that \textsc{GraphOracle} outperforms prior methods by up to 25\% in fully-inductive and 28\% in cross-domain scenarios. Our analysis further confirms that the compact RDG structure and attention-based propagation are key to efficient and accurate generalization

GraphOracle: Efficient Fully-Inductive Knowledge Graph Reasoning via Relation-Dependency Graphs

The Two-Part Allegorical Saying (TPAS) is a Chinese linguistic phenomenon with a riddle-explanation structure, and an important component of Chinese metaphors. Existing research has primarily used TPAS to assist other semantic tasks, but lacks in-depth exploration of its intrinsic mechanisms: semantic rhetoric, logical reasoning, and metaphorical expression. To address this gap, we construct the first Chinese TPAS Reading Comprehension dataset (CTRC), which contains 18,103 TPASs and 75,296 passages. We frame it as a cloze test where the model selects the most suitable TPAS from candidates to fill passage blanks. To tackle the challenges of this CTRC task, we propose a Multi-view TPAS Contrastive Learning Network (MTCLN). Firstly, the joint vector cross-projection module extracts the rhetorical features of TPAS, such as homophonic puns, through vector space mapping to mitigate the semantic deviations caused by rhetoric. Then, the softened contrastive learning module strengthens the modeling of TPAS logical reasoning through feature association. Finally, the multi-view feature fusion module integrates contextual semantics with diverse TPAS features to facilitate the understanding of metaphorical expressions. Experiments on the CTRC dataset demonstrate that MTCLN achieves an average accuracy of 67.47%, outperforming large language models by 25.48%.

Chinese Two-part Allegorical Sayings Reading Comprehension: Exploration from Reasoning to Metaphor

We propose new quantum algorithms for estimating spectral sums of positive semi-definite (PSD) matrices. The spectral sum of an PSD matrix $A$, for a function $f$, is defined as $Tr[f(A)] = \sum_j f(\lambda_j)$, where $\lambda_j$ are the eigenvalues of $A$. 
Typical examples of spectral sums are the von Neumann entropy, the trace of $A^{-1}$, the log-determinant, and the Schatten $p$-norm, where the latter does not require the matrix to be PSD. The current best classical randomized algorithms estimating these quantities have a runtime that is at least linearly in the number of nonzero entries of the matrix and quadratic in the estimation error. Assuming access to a block-encoding of a matrix, our algorithms are sub-linear in the matrix size, and depend at most quadratically on other parameters, like the condition number and the approximation error, and thus can compete with most of the randomized and distributed classical algorithms proposed in the literature, and polynomially improve the runtime of other quantum algorithms proposed for the same problems.
We show how the algorithms and techniques used in this work can be applied to three problems in spectral graph theory: approximating the number of triangles, the effective resistance, and the number of spanning trees in a graph.

Quantum Algorithms for Spectral Sums

In this paper, we present an active exploration framework for high-fidelity 3D reconstruction that incrementally builds a multi-level uncertainty space and selects next-best-views through an uncertainty-driven motion planner. 
We introduce a \emph{hybrid implicit–explicit representation} that fuses neural fields with Gaussian primitives to jointly capture global structural priors and locally observed details. 
Based on this hybrid state, we derive a \emph{hierarchical uncertainty volume} that quantifies both implicit global structure quality and explicit local surface confidence. 
To focus optimization on the most informative regions, we propose an \emph{uncertainty-driven keyframe selection} strategy that anchors high-entropy viewpoints as sparse attention nodes, coupled with a \emph{viewpoint-space sliding window} for uncertainty-aware local refinement. 
The planning module formulates next-best-view selection as an \emph{Expected Hybrid Information Gain} problem and incorporates a risk-sensitive path planner to ensure efficient and safe exploration. 
Extensive experiments on challenging benchmarks demonstrate that our approach consistently achieves state-of-the-art accuracy, completeness, and rendering quality, highlighting its effectiveness for real-world active reconstruction and robotic perception tasks.

Active3D: Active High-Fidelity 3D Reconstruction via Multi-Level Uncertainty Quantification

Training physics-informed neural networks (PINNs) can be viewed as a multi-task optimization problem, where data-driven and physics-driven loss functions must be simultaneously minimized, despite the potential competition between them. Manually tuning the weight coefficients for various loss terms in PINNs is often time-consuming and lacks a systematic approach. To address this challenge, this work proposes an adaptive loss balancing framework for PINNs, using multi-objective optimization (MOO) algorithms to dynamically balance competing loss terms during training. Specifically, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) is integrated into the PINN training process to explore the Pareto front of the multiple objectives. A novel variance-aware relative improvement (VARI) weighting method is proposed to translate Pareto-optimal information into adaptive loss weights. The proposed MOO-VARI method is validated through several examples, where the results show that the MOO-VARI PINN consistently outperforms standard PINN and other state-of-the-art adaptive weighting strategies in terms of convergence speed, predictive accuracy, and parameter estimation performance.

A Multi-Objective Optimization Framework for Adaptive Weighting in Physics-Informed Machine Learning

Explainable AI (XAI) is crucial for building transparent and trustworthy machine learning systems, especially in high-stakes domains. Concept Bottleneck Models (CBMs) have emerged as a promising ante-hoc approach that provides interpretable, concept-level explanations by explicitly modeling human-understandable concepts. However, existing CBMs often suffer from poor locality faithfulness, failing to spatially align concepts with meaningful image regions, which limits their interpretability and reliability. 
In this work, we propose SL-CBM (CBM with Semantic Locality), a novel extension that enforces locality faithfulness by generating spatially coherent saliency maps at both concept and class levels. SL-CBM integrates a $1 \times 1$ convolutional layer with a cross-attention mechanism to enhance alignment between concepts, image regions, and final predictions. Unlike prior methods, SL-CBM produces faithful saliency maps inherently tied to the model’s internal reasoning, facilitating more effective debugging and intervention. Extensive experiments on image datasets demonstrate that SL-CBM substantially improves locality faithfulness, explanation quality, and intervention efficacy while maintaining competitive classification accuracy. Our ablation studies highlight the importance of contrastive and entropy-based regularization for balancing accuracy, sparsity, and faithfulness. Overall, SL-CBM bridges the gap between concept-based reasoning and spatial explainability, setting a new standard for interpretable and trustworthy concept-based models. Our implementation is open-source and can be found at \url{https://github.com/Uzukidd/sl-cbm}.

SL-CBM: Enhancing Concept Bottleneck Models with Semantic Locality for Better Interpretability

The housing market is a classic exchange economy model where each agent on the demand side initially owns an indivisible good (a house) and has a personal preference over all goods. The goal is to find a core-stable allocation that exhausts all mutually beneficial exchanges among subgroups of agents. While this model has been extensively studied in economics and computer science due to its broad applications, little attention has been paid to settings where preferences are unknown and must be learned through repeated interactions.
In this paper, we propose a statistical learning model within the multi-player multi-armed bandit framework, where players (agents) learn their preferences over arms (goods) from stochastic rewards. We introduce the notion of \emph{core regret} for each player as the market objective. We study both centralized and decentralized approaches, proving $\mathcal{O}(\log T / \Delta^2)$ upper bounds on regret, where $T$ is the time horizon and $\Delta$ is the minimum preference gap among players. For the decentralized setting, we also establish a matching lower bound, demonstrating that our algorithm is order-optimal.

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Transferable Graph Condensation from the Causal Perspective

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