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TSP is a classic and extensively studied problem with numerous real-world applications in artificial intelligence and operations research. It is well-known that TSP admits a constant approximation ratio on metric graphs but becomes NP-hard to approximate within any computable function $f(n)$ on general graphs. This disparity highlights a significant gap between the results on metric graphs and general graphs. Recent research has introduced some parameters to measure the ``distance&#39;&#39; of general graphs from being metric and explored FPT approximation algorithms parameterized by these parameters. Two commonly studied parameters are $p$, the number of vertices in triangles violating the triangle inequality, and $q$, the minimum number of vertices whose removal results in a metric graph. In this paper, we present improved FPT approximation algorithms with respect to these two parameters. For $p$, we propose an FPT algorithm with a 1.5-approximation ratio, improving upon the previous ratio of 2.5. For $q$, we significantly enhance the approximation ratio from 11 to 3, advancing the state of the art in both cases.

AAAI 2026

FPT Approximation Algorithms for TSP on Non-Metric Graphs

TSP is a classic and extensively studied problem with numerous real-world applications in artificial intelligence and operations research. It is well-known that TSP admits a constant approximation ratio on metric graphs but becomes NP-hard to approximate within any computable function $f(n)$ on general graphs. This disparity highlights a significant gap between the results on metric graphs and general graphs. Recent research has introduced some parameters to measure the ``distance'' of general graphs from being metric and explored FPT approximation algorithms parameterized by these parameters. Two commonly studied parameters are $p$, the number of vertices in triangles violating the triangle inequality, and $q$, the minimum number of vertices whose removal results in a metric graph. In this paper, we present improved FPT approximation algorithms with respect to these two parameters. For $p$, we propose an FPT algorithm with a 1.5-approximation ratio, improving upon the previous ratio of 2.5. For $q$, we significantly enhance the approximation ratio from 11 to 3, advancing the state of the art in both cases.

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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 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.

Recent advances in LLM-based multi-agent systems have demonstrated remarkable capabilities in complex decision-making scenarios such as financial trading and software engineering. However, evaluating each individual agent’s effectiveness and online optimization of underperforming agents remain open challenges. To address these issues, we present HiveMind, a self-adaptive framework designed to optimize LLM multi-agent collaboration through contribution analysis. At its core, HiveMind introduces Contribution-Guided Online Prompt Optimization (CG-OPO), which autonomously refines agent prompts based on their quantified contributions. We first propose the Shapley value as a grounded metric to quantify each agent's contribution, thereby identifying underperforming agents in a principled manner for automated prompt refinement. To overcome the computational complexity of the classical Shapley value, we present DAG-Shapley, a novel and efficient attribution algorithm that leverages the inherent Directed Acyclic Graph structure of the agent workflow to axiomatically prune non-viable coalitions. By hierarchically reusing intermediate outputs of agents in the DAG, our method further reduces redundant computations, and achieving substantial cost savings without compromising the theoretical guarantees of Shapley values. Evaluated in a multi-agent stock-trading scenario, HiveMind achieves superior performance compared to static baselines. Notably, DAG-Shapley reduces LLM calls by over 80% while maintaining attribution accuracy comparable to full Shapley values, establishing a new standard for efficient credit assignment and enabling scalable, real-world optimization of multi-agent collaboration.

HiveMind: Contribution-Guided Online Prompt Optimization of LLM Multi-Agent Systems

Graph Neural Networks (GNNs) have demonstrated strong performance across various tasks by leveraging the structural information inherent in graph-structured data. To address the challenge of edge heterophily, where connected nodes may have dissimilar labels or features, two main families of GNNs have emerged: Mixture-of-Experts (MoE) based spatial GNNs and frequency filtering based spectral GNNs. While MoE-based spatial GNNs intuitively assign experts to different hops without solid theoretical grounding, spectral GNNs are based on principled insights from graph signal processing but often rely on manually designed filters and global operators, limiting their scalability and adaptability. In this work, we identify an inherent connection between these two families by showing that the eigengraph components in spectral methods can be treated as experts within an MoE framework. Building on this insight, we propose MORGAN, a novel spectral GNN that integrates Mixture-of-Experts into the spectral domain. MORGAN performs eigen-decomposition of the graph Laplacian, partitions the spectrum into multiple frequency bands, and assigns a dedicated expert network to each band. A learnable gating function dynamically combines these experts based on the spectral characteristics of the input. To support scalable and inductive learning, we further develop MORGAN(L), which incorporates subgraph sampling to enable localized spectral filtering without requiring full access to the graph Laplacian. Extensive experiments on 16 real-world benchmark datasets show that MORGAN achieves competitive or superior performance compared to state-of-the-art baselines, particularly in inductive node classification under heterophilic settings.

MORGAN: To Bridge Mixture of Experts and Spectral Graph Neural Network

Traffic simulation is essential for validating the safety and reliability of autonomous driving systems, yet data-driven simulation methods often struggle with distribution shifts, limiting their generalizability across diverse datasets (domains). To address this, we present Causal Driving Pattern Transfer (CDPT), a novel two-stage knowledge distillation framework built upon diffusion model to enhance cross-domain generalizability. In Phase I, we implement hybrid self-distillation within the source domain by integrating feature-, response-, and contrastive-level distillation, which enables the model to decompose complex driving behaviors into their core causal components, including scene-conditioned driven patterns, multi-agent interaction dynamics and casual saliency. In Phase II, we introduce a continual distillation strategy: few-shot samples from the target domain are used to initiate generation of diverse synthetic scenarios, allowing the student model to continually adapt to novel environments without retraining on large-scale data. Extensive experiments demonstrates that CDPT achieves strong generalization in both open-loop and closed-loop simulations, effectively generating realistic, interaction-aware behaviors that are critical for scalable and reliable autonomous driving testing.

Transferring Causal Driving Patterns for Generalizable Traffic Simulation with Diffusion-Based Distillation

Multi-agent path finding (MAPF) is the challenging problem of finding conflict-free paths with minimal costs for multiple agents. While traditional MAPF solvers are centralized using heuristic search, reinforcement learning (RL) is becoming increasingly popular due to its potential to learn decentralized and generalizing policies. RL-based MAPF must cope with spatial coordination, which is often addressed by combining independent training with ad hoc measures like replanning and communication. Such ad hoc measures often complicate the approach and require knowledge beyond the actual accessible information in RL, such as the full map occupation or broadcast communication channels, which limits generalizability, effectiveness, and sample efficiency. In this paper, we propose Partitioned Attention-based Reverse Curricula for Enhanced Learning (PARCEL), considering a bounding region for each agent. PARCEL trains all agents with overlapping regions jointly via self-attention to avoid potential conflicts. By employing a reverse curriculum, where the bounding regions grow as the policies improve, all agents will eventually merge into a single coordinated group. We evaluate PARCEL in two simple coordination tasks and four MAPF benchmark maps. Compared with state-of-the-art RL-based MAPF methods, PARCEL demonstrates better effectiveness and sample efficiency without ad hoc measures.

Spatially Grouped Curriculum Learning for Multi-Agent Path Finding

Rank aggregation is a task of combining the rankings of items from multiple users into a single ranking that best represents the users' rankings. Alabi et al. (AAAI'22) presents differentially-private (DP) polynomial-time approximation schemes (PTASes) and $5$-approximation algorithms with certain additive errors for the Kemeny rank aggregation problem in both central and local models.
In this paper, we present improved DP PTASes with smaller additive error in the central model. Furthermore, we are first to study the footrule rank aggregation problem under DP. We give a near-optimal algorithm for this problem; as a corollary, this leads to 2-approximation algorithms with the same additive error as the $5$-approximation algorithms of Alabi et al. for the Kemeny rank aggregation problem in both central and local models.

Improved Differentially Private Algorithms for Rank Aggregation

Decentralized partially observable Markov decision processes with communication (Dec-POMDP-Com) provide a framework for multiagent decision making under uncertainty, but the NEXP-complete complexity for finite-horizon problems renders solutions intractable in general. While sharing actions and observations can reduce the complexity to PSPACE-complete, we propose an approach that bridges POMDPs and Dec-POMDPs by communicating only suggested joint actions, eliminating the need to share observations while maintaining performance comparable to fully centralized planning and execution. Our algorithm estimates joint beliefs using shared actions to prune infeasible beliefs. Each agent maintains possible belief sets for other agents, pruning them based on suggested actions to form an estimated joint belief usable with any centralized policy. This approach requires solving a POMDP for each agent, reducing computational complexity while preserving performance. We demonstrate its effectiveness on several Dec-POMDP benchmarks, showing performance comparable to centralized methods when shared actions enable effective belief pruning. This action-based communication framework offers a natural avenue for integrating human-agent cooperation, opening new directions for scalable multiagent planning under uncertainty, with applications in both autonomous systems and human-agent teams.

Efficient Multiagent Planning via Shared Action Suggestions

Algorithms for resolving majority cycles in preference aggregation have been studied extensively in computational social choice. Several sophisticated cycle-resolving methods, including Tideman's Ranked Pairs, Schulze's Beat Path, and Heitzig's River, are refinements of the Split Cycle (SC) method that resolves majority cycles by discarding the weakest pairwise majority victories in each cycle. Recently, Holliday and Pacuit proposed a new refinement of Split Cycle, dubbed Stable Voting, and a simplification thereof, called Simple Stable Voting (SSV). They conjectured that SSV is a refinement of SC whenever no two pairwise majority victories are of the same size. In this paper, we prove the conjecture up to 6 alternatives and refute it for more than 6 alternatives. While our proof of the conjecture for up to 5 alternatives uses traditional mathematical reasoning, our 6-alternative proof and 7-alternative counterexample were obtained with the use of SAT solving. The SAT encoding underlying this proof and counterexample is applicable far beyond SC and SSV: it can be used to test properties of any voting method whose choice of winners depends only on the ordering of margins of victory between alternatives by size.

Stable Voting and the Splitting of Cycles

Recent vision-language models (VLMs) show strong reasoning capabilities through training with reinforcement learning from verifiable rewards (RLVR). Despite their impressive capabilities, current VLMs focus on a limited range of reasoning tasks, such as mathematical and logical reasoning, due to the lack of readily available verifiable reward data in broader domains. As a result, these models struggle to generalize their reasoning abilities to the wide variety of challenges encountered in real-world environments. To address this limitation, we collect and assemble a comprehensive RL-ready visual reasoning training dataset encompassing 46 datasets across 13 dimensions of 5 domains, covering a wide range of realistic scenarios such as infographic reasoning, mathematical reasoning, spatial reasoning, and general science reasoning. Based on this dataset, we propose an influence function-based data filtering strategy and a multi-round data curriculum method to iteratively strengthen general visual reasoning abilities. Using this approach, we train a general reasoning VLM, namely Vision-G1. Our 7B model achieves state-of-the-art performance across nine visual reasoning benchmarks, surpassing previous similar-sized VLMs and even GPT-4o and Gemini-1.5 Flash. The code and dataset will be publicly available to facilitate future research.

Vision-G1: Towards General Reasoning Vision-Language Models via Reinforcement Learning

Counterfactual reasoning is widely recognized as one of the most challenging and intricate aspects of causality in artificial intelligence. In this paper, we evaluate the performance of large language models (LLMs) in counterfactual reasoning. In contrast to previous studies that primarily focus on commonsense causal reasoning, where LLMs often rely on prior knowledge for inference, we specifically assess their ability to perform counterfactual inference using a set of formal rules. To support this evaluation, we introduce a new benchmark dataset, \textbf{CounterBench}, comprising 1.2K counterfactual reasoning questions. The dataset is designed with varying levels of difficulty, diverse causal graph structures, distinct types of counterfactual questions, and multiple nonsensical name variants. Our experiments demonstrate that counterfactual reasoning poses a significant challenge for LLMs, with most models performing at levels comparable to random guessing. To enhance LLM's counterfactual reasoning ability, we propose a novel reasoning paradigm, \textbf{CoIn}, which guides LLMs through iterative reasoning and backtracking to systematically explore counterfactual solutions. Experimental results show that our method significantly improves LLM performance on counterfactual reasoning tasks and consistently enhances performance across different LLMs. Our dataset is available at https://huggingface.co/datasets/CounterBench/CounterBench.

CounterBench: Evaluating and Improving Counterfactual Reasoning in Large Language Models

The Profiled Vehicle Routing Problem (PVRP) extends the classical VRP by incorporating vehicle–client-specific preferences and constraints, reflecting real‑world requirements such as zone restrictions and service‑level preferences. While recent reinforcement‑learning solvers have shown promising performance, they require retraining for each new profile distribution, suffer from poor representation ability, and struggle to generalize to out‑of‑distribution instances. In this paper, we address these limitations by introducing **U**nified **S**olver for **P**rofiled **R**outing (USPR), a novel framework that natively handles arbitrary profile types. USPR introduces on three key innovations: (i) Profile Embeddings (PE) to encode any combination of profile types; (ii) Multi‑Head Profiled Attention (MHPA), an attention mechanism that models rich interactions between vehicles and clients; (iii) Profile‑aware Score Reshaping (PSR), which dynamically adjusts decoder logits using profile scores to improve generalization. Empirical results on diverse PVRP benchmarks demonstrate that USPR achieves state‑of‑the‑art results among learning‑based methods while offering significant gains in flexibility and computational efficiency. We make our source code publicly available to foster future research.

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