Random walk neural networks (RWNNs) have emerged as a promising approach for graph representation learning, leveraging recent advances in sequence models to process random walks. However, under realistic sampling constraints, RWNNs often fail to capture global structure even in small graphs due to incomplete node and edge coverage, limiting their expressivity. To address this, we propose \textit{random search neural networks} (RSNNs), which operate on random searches, each of which guarantees full node coverage. Theoretically, we demonstrate that in sparse graphs, only $O(\log |V|)$ searches are needed to achieve full edge coverage, substantially reducing sampling complexity compared to the $O(|V|)$ walks required by RWNNs (assuming walk lengths scale with graph size). Furthermore, when paired with universal sequence models, RSNNs are universal approximators. We lastly show RSNNs are probabilistically invariant to graph isomorphisms, ensuring their expectation is an isomorphism-invariant graph function. Empirically, RSNNs consistently outperform RWNNs on molecular and protein benchmarks, achieving comparable or superior performance with up to 16$\times$ fewer sampled sequences. Our work bridges theoretical and practical advances in random walk based approaches, offering an efficient and expressive framework for learning on sparse graphs.

Motivated by the question of how a principal can maximize its utility in repeated interactions with a learning agent, we study repeated games between an principal and an agent employing a mean-based learning algorithm. Prior work has shown that computing or even approximating the global Stackelberg value in similar settings can require an exponential number of rounds in the size of the agent's action space, making it computationally intractable. In contrast, we shift focus to the computation of local Stackelberg equilibria and introduce an algorithm that, within the smoothed analysis framework, constitutes a Polynomial Time Approximation Scheme (PTAS) for finding an epsilon-approximate local Stackelberg equilibrium. Notably, the algorithm's runtime is polynomial in the size of the agent's action space yet exponential in (1/epsilon) - a dependency we prove to be unavoidable.

Large Vision-Language Models (VLMs) face an inherent contradiction in image captioning: their powerful single-step generation capabilities often lead to a myopic decision-making process. This makes it difficult to maintain global narrative coherence while capturing rich details, a limitation that is particularly pronounced in tasks that require multi-step and complex scene description. To overcome this fundamental challenge, we redefine image captioning as a goal-oriented hierarchical refinement planning problem, and further propose a novel framework, named Top-Down Semantic Refinement (TDSR), which models the generation process as a Markov Decision Process (MDP). However, planning within the vast state space of a VLM presents a significant computational hurdle. Our core contribution, therefore, is the design of a highly efficient Monte Carlo Tree Search (MCTS) algorithm tailored for VLMs. By incorporating a visual-guided parallel expansion and a lightweight value network, our TDSR reduces the call frequency to the expensive VLM by an order of magnitude without sacrificing planning quality. Furthermore, an adaptive early stopping mechanism dynamically matches computational overhead to the image's complexity. Extensive experiments on multiple benchmarks, including DetailCaps, COMPOSITION-CAP, and POPE, demonstrate that our TDSR, as a plug-and-play module, can significantly enhance the performance of existing VLMs (e.g., LLaV A-1.5, Qwen2.5-VL) by achieving state-of-the-art or highly competitive results in fine-grained description, compositional generalization, and hallucination suppression.

Optimization modeling is one of the most crucial but technical parts of operations research (OR). To automate the modeling process, existing works have leveraged large language models (LLMs), prompting them to break down tasks into steps for generating variables, constraints, and objectives. However, due to the highly complex mathematical structures inherent in OR problems, standard fixed-step decomposition often fails to achieve high performance. To address this challenge, we introduce OptiTree, a novel tree search approach designed to enhance modeling capabilities for complex problems through adaptive problem decomposition into simpler subproblems. Specifically, we develop a modeling tree that organizes a wide range of OR problems based on their hierarchical problem taxonomy and complexity, with each node representing a problem category and containing relevant high-level modeling thoughts. Given a problem to model, we recurrently search the tree to identify a series of simpler subproblems and synthesize the global modeling thoughts by adaptively integrating the hierarchical thoughts. Experiments show that OptiTree significantly improves the modeling accuracy compared to the state-of-the-art, achieving over 10\% improvements on the challenging benchmarks. The code is released at https://github.com/MIRALab-USTC/OptiTree/tree/main.

Neural combinatorial optimization (NCO) has achieved remarkable performance, yet its learned model representations and decision rationale remain a black box. This impedes both academic research and practical deployment, since researchers and stakeholders require deeper insights into NCO models. In this paper, we take the first critical step towards interpreting NCO models by investigating their representations through various probing tasks. Moreover, we introduce a novel probing tool named Coefficient Significance Probing (CS-Probing) to enable deeper analysis of NCO representations by examining the coefficients and statistical significance during probing. Extensive experiments and analysis reveal that NCO models encode low-level information essential for solution construction, while capturing high-level knowledge to facilitate better decisions. Using CS-Probing, we find that prevalent NCO models impose varying inductive biases on their learned representations, uncover direct evidence related to model generalization, and identify key embedding dimensions associated with specific knowledge. These insights can be potentially translated into practice, for example, with minor code modifications, we improve the generalization of the analyzed model. Our work represents a first systematic attempt to interpret black-box NCO models, showcasing probing as a promising tool for analyzing their internal mechanisms and revealing insights for the NCO community. The source code is publicly available.

Math word problem (MWP) serves as a fundamental research topic in artificial intelligence (AI) dating back to 1960s. This research aims to advance the reasoning abilities of AI by mirroring the human-like cognitive intelligence. The mainstream technological paradigm has evolved from the early rule-based methods, to deep learning models, and is rapidly advancing towards large language models. However, the field still lacks a systematic taxonomy for the MWP survey along with a discussion of current development trends. Therefore, in this paper, we aim to comprehensively review related research in MWP solving through the lens of human cognition, to demonstrate how recent AI models are advancing in simulating human cognitive abilities. Specifically, we summarize 5 crucial cognitive abilities for MWP solving, including Problem Understanding, Logical Organization, Associative Memory, Critical Thinking, and Knowledge Learning. Focused on these abilities, we review two mainstream MWP models in recent 10 years: neural network solvers, and LLM based solvers, and discuss the core human-like abilities they demonstrated in their intricate problem-solving process. Moreover, we rerun all the representative MWP solvers and supplement their performance on 5 mainstream benchmarks for a unified comparison. To the best of our knowledge, this survey first comprehensively analyzes the influential MWP research of the past decade from the perspective of human reasoning cognition and provides an integrative overall comparison across existing approaches. We hope it can inspire further research in AI reasoning. Our repository is released on https://github.com/Ljyustc/FoI-MWP.

Long-horizon robot manipulation tasks remain challenging for Vision-Language-Action (VLA) policies due to drift and exposure bias, often denoise the entire trajectory with fixed hyperparameters, causing small geometric errors to compound across stages and offering no mechanism to allocate extra test-time compute where clearances are tight. To address these challenges, we introduce FORGE-Tree, a plug-in control layer that couples a stage-aligned Diffusion Forcing (DF) head with test-time Monte Carlo Tree Diffusion (MCTD). With a frozen VLA encoder, DF aligns timesteps to subtask stages; during inference we partially denoise only a target segment while keeping other tokens frozen, turning trajectory refinement into a sequence of local edits. We then apply Monte Carlo Tree Diffusion to select the next segment to refine. A scene graph supplies priors for expansion and geometry relation-aware scoring for rollouts, yielding tree-structured denoising whose performance scales with search budget while preserving the executed prefix. Evaluation on LIBERO, FORGE-Tree improves success rate by 13.4 to 17.2 pp over the native VLA baselines with both OpenVLA and Octo-Base. Gains remain consistent under comparable compute budgets, especially on long-horizon variants. Videos available at: https://taco-group.github.io/FORGE-Tree/

Retrieval-Augmented Generation (RAG) systems have emerged as a pivotal methodology for enhancing Large Language Models (LLMs) through the dynamic integration of external knowledge. To further improve RAG's flexibility, Agentic RAG introduces autonomous agents into the workflow. However, Agentic RAG faces several challenges: (1) the success of each step depends on both high-quality planning and accurate search, (2) the lack of supervision for intermediate reasoning steps, and (3) the exponentially large candidate space for planning and searching. To address these challenges, we propose DecoupleSearch, a novel framework that decouples planning and search processes using dual value models, enabling independent optimization of plan reasoning and search grounding. Our approach constructs a reasoning tree, where each node represents planning and search steps. We leverage Monte Carlo Tree Search to assess the quality of each step. During inference, Hierarchical Beam Search iteratively refines planning and search candidates with dual value models. Extensive experiments across policy models of varying parameter sizes, demonstrate the effectiveness of our method.

In this paper we show that visual diffusion models can serve as effective geometric solvers: they can directly reason about geometric problems by working in pixel space. We first demonstrate this on the Inscribed Square Problem, a long-standing problem in geometry that asks whether every Jordan curve contains four points forming a square. We then extend the approach to two other well-known hard geometric problems: the Steiner Tree Problem and the Simple Polygon Problem. Our method treats each problem instance as an image and trains a standard visual diffusion model that transforms Gaussian noise into an image representing a valid approximate solution that closely matches the exact one. The model learns to transform noisy geometric structures into correct configurations, effectively recasting geometric reasoning as image generation. Unlike prior work that necessitates specialized architectures and domain-specific adaptations when applying diffusion to parametric geometric representations, we employ a standard visual diffusion model that operates on the visual representation of the problem. This simplicity highlights a surprising bridge between generative modeling and geometric problem solving. Beyond the specific problems studied here, our results point toward a broader paradigm: operating in image space provides a general and practical framework for approximating notoriously hard problems, and opens the door to tackling a far wider class of challenging geometric tasks.

Existing neural methods for multi-task vehicle routing problems (VRPs) typically learn unified solvers to handle multiple constraints simultaneously. However, they often underutilize the compositional structure of VRP variants, each derivable from a common set of basis VRP variants. This critical oversight causes unified solvers to miss out the potential benefits of basis solvers, each specialized for a basis VRP variant. To overcome this limitation, we propose a framework that enables unified solvers to perceive the shared-component nature across VRP variants by proactively reusing basis solvers, while mitigating the exponential growth of trained neural solvers. Specifically, we introduce a State-Decomposable MDP (SDMDP) that reformulates VRPs by expressing the state space as the Cartesian product of basis state spaces associated with basis VRP variants. More crucially, this formulation inherently yields the optimal basis policy for each basis VRP variant. Furthermore, a Latent Space-based SDMDP extension is developed by incorporating both the optimal basis policies and a learnable mixture function to enable the policy reuse in the latent space. Under mild assumptions, this extension provably recovers the optimal unified policy of SDMDP through the mixture function that computes the state embedding as a mapping from the basis state embeddings generated by optimal basis policies. For practical implementation, we introduce the Mixture-of-Specialized-Experts Solver (MoSES), which realizes basis policies through specialized Low-Rank Adaptation (LoRA) experts, and implements the mixture function via an adaptive gating mechanism. Extensive experiments conducted across VRP variants showcase the superiority of MoSES over prior methods.