Each header indicates the number of cells that must be marked in a row inside the board to construct a block. If there is more than one number in the same row or column header, at least one empty cell must exist between them. Puzzles of an arbitrary size can be defined as rectangular or square. The cells of a nonogram are defined by two states: filled (| |) and empty (| x |). Figure 1: Examples of different nonogram states: unsolved, partially solved, and solved. The black cells are considered as filled, whereas those with a cross are empty. Figure 1 depicts the three stages of nonogram resolution: unsolved, partially solved, and solved. Note that this type of problem falls into the category of NP completeness [1, 2, 3]; thus, a solution cannot be obtained in polynomial time. Moreover, certain nonograms do not have a single solution, and all solutions that are compatible with the constraints defined by their headers are valid. An example of the situation is illustrated in Figure 2.

Recent advancements in large language models (LLMs) have shown remarkable potential in various complex tasks requiring multi-step reasoning methods like tree search to explore diverse reasoning paths. However, existing methods often suffer from computational inefficiency and redundancy. First, they overlook the diversity of task difficulties, leading to unnecessarily extensive searches even for easy tasks. Second, they neglect the semantics of reasoning paths, resulting in redundant exploration of semantically identical paths. To address these limitations, we propose Semantic Exploration with Adaptive Gating (SEAG), a computationally efficient method. SEAG employs an adaptive gating mechanism that dynamically decides whether to conduct a tree search, based on the confidence level of answers from a preceding simple reasoning method. Furthermore, its tree-based exploration consolidates semantically identical reasoning steps, reducing redundant explorations while maintaining or even improving accuracy. Our extensive experiments demonstrate that SEAG significantly improves accuracy by 4.3% on average while requiring only 31% of computational costs compared to existing tree search-based methods on complex reasoning benchmarks including GSM8K and ARC with diverse language models such as Llama2, Llama3, and Mistral.

Optimization of complex networks is one of the fundamental challenges in computer science research. With the progression of computational resources availability, a great variety of conceptually different algorithms have been presented over the past decades to achieve competitive results in the domain of network optimization. Many approaches, such as Lin-Kernighan-Helsgaun heuristic [1], Genetic Algorithm variations [2,3,4], Ant Colony Optimization [5], k-opt local search [6,7] with sequential improvements have gained acknowledgment from both research community and industry across logistics, telecommunications, and biotechnology verticals. The Traveling Salesman Problem (TSP) [8], first formalized by Karl Menger in 1930, remains a cornerstone problem that has driven network optimization algorithmic innovations for decades. The Vehicle Routing Problem (VRP) [9,10], introduced by Dantzig and Ramser in 1959, extends TSP's complexity by incorporating multiple vehicles and capacity constraints, finding direct applications in logistics and delivery. The Maximum Clique Problem (MCP) [11], important for social network analysis, computational biochemistry and wireless network allocation, focuses on finding the largest complete subgraph within a network.

It has been shown recently that physics-based simulation significantly enhances the disassembly capabilities of real-world assemblies with diverse 3D shapes and stringent motion constraints. However, the efficiency suffers when tackling intricate disassembly tasks that require numerous simulations and increased simulation time. In this work, we propose a State-Based Disassembly Planning (SBDP) approach, prioritizing physics-based simulation with translational motion over rotational motion to facilitate autonomy, reducing dependency on human input, while storing intermediate motion states to improve search scalability. We introduce two novel evaluation functions derived from new Directional Blocking Graphs (DBGs) enriched with state information to scale up the search. Our experiments show that SBDP with new evaluation functions and DBGs constraints outperforms the state-of-the-art in disassembly planning in terms of success rate and computational efficiency over benchmark datasets consisting of thousands of physically valid industrial assemblies.

Retrieval-augmented generation (RAG) is a powerful technique that enhances downstream task execution by retrieving additional information, such as knowledge, skills, and tools from external sources. Graph, by its intrinsic "nodes connected by edges" nature, encodes massive heterogeneous and relational information, making it a golden resource for RAG in tremendous real-world applications. As a result, we have recently witnessed increasing attention on equipping RAG with Graph, i.e., GraphRAG. However, unlike conventional RAG, where the retriever, generator, and external data sources can be uniformly designed in the neural-embedding space, the uniqueness of graph-structured data, such as diverse-formatted and domain-specific relational knowledge, poses unique and significant challenges when designing GraphRAG for different domains. Given the broad applicability, the associated design challenges, and the recent surge in GraphRAG, a systematic and up-to-date survey of its key concepts and techniques is urgently desired. Following this motivation, we present a comprehensive and up-to-date survey on GraphRAG. Our survey first proposes a holistic GraphRAG framework by defining its key components, including query processor, retriever, organizer, generator, and data source. Furthermore, recognizing that graphs in different domains exhibit distinct relational patterns and require dedicated designs, we review GraphRAG techniques uniquely tailored to each domain. Finally, we discuss research challenges and brainstorm directions to inspire cross-disciplinary opportunities.

This paper explores a novel approach aimed at overcoming existing challenges in the realm of local search algorithms. Our aim is to improve the decision process that takes place within a local search algorithm so as to make the best possible transitions in the neighborhood at each iteration. To improve this process, we propose to use a neural network that has the same input information as conventional local search algorithms. In this paper, which is an extension of the work [Goudet et al. 2024] presented at EvoCOP2024, we investigate different ways of representing this information so as to make the algorithm as efficient as possible but also robust to monotonic transformations of the problem objective function. To assess the efficiency of this approach, we develop an experimental setup centered around NK landscape problems, offering the flexibility to adjust problem size and ruggedness. This approach offers a promising avenue for the emergence of new local search algorithms and the improvement of their problem-solving capabilities for black-box problems.

We propose a novel framework, Meta Chain-of-Thought (Meta-CoT), which extends traditional Chain-of-Thought (CoT) by explicitly modeling the underlying reasoning required to arrive at a particular CoT. We present empirical evidence from state-of-the-art models exhibiting behaviors consistent with in-context search, and explore methods for producing Meta-CoT via process supervision, synthetic data generation, and search algorithms. Finally, we outline a concrete pipeline for training a model to produce Meta-CoTs, incorporating instruction tuning with linearized search traces and reinforcement learning post-training. Finally, we discuss open research questions, including scaling laws, verifier roles, and the potential for discovering novel reasoning algorithms. This work provides a theoretical and practical roadmap to enable Meta-CoT in LLMs, paving the way for more powerful and human-like reasoning in artificial intelligence.

The Abstraction and Reasoning Corpus (ARC) challenge [7] is a difficult few-shot benchmark for testing visual reasoning capabilities of machine learning models. The capabilities The Abstraction and Reasoning Corpus (ARC) evaluates of recent general-purpose LLM systems are, as of general reasoning capabilities that are difficult for both now, not good enough to solve ARC at human performance machine learning models and combinatorial search methods. in a reasonably limited amount of time [19, 20, 28]. Arguably We propose a neuro-symbolic approach that combines their pre-training seems to have not imbued them a transformer for proposal generation with combinatorial with enough of the necessary concepts required to solve search using a domain-specific language. The transformer ARC tasks reliably and without an excessive number of narrows the search space by proposing promising search directions, tries. It is unclear whether LLMs lack the correct level of which allows the combinatorial search to find the abstraction and the specific type of high-level visual reasoning actual solution in short time.

The Minimum Weighted Feedback Arc Set (MWFAS) problem is fundamentally connected to the Ranking Problem -- the task of deriving global rankings from pairwise comparisons. Recent work [He et al. ICML2022] has advanced the state-of-the-art for the Ranking Problem using learning-based methods, improving upon multiple previous approaches. However, the connection to MWFAS remains underexplored. This paper investigates this relationship and presents efficient combinatorial algorithms for solving MWFAS, thus addressing the Ranking Problem. Our experimental results demonstrate that these simple, learning-free algorithms not only significantly outperform learning-based methods in terms of speed but also generally achieve superior ranking accuracy.

Bayesian Optimization (BO) is a sample-efficient black-box optimizer commonly used in search spaces where hyperparameters are independent. However, in many practical AutoML scenarios, there will be dependencies among hyperparameters, forming a conditional search space, which can be partitioned into structurally distinct subspaces. The structure and dimensionality of hyperparameter configurations vary across these subspaces, challenging the application of BO. Some previous BO works have proposed solutions to develop multiple Gaussian Process models in these subspaces. However, these approaches tend to be inefficient as they require a substantial number of observations to guarantee each GP's performance and cannot capture relationships between hyperparameters across different subspaces. To address these issues, this paper proposes a novel approach to model the response surfaces of all subspaces in one, which can model the relationships between hyperparameters elegantly via a self-attention mechanism. Concretely, we design a structure-aware hyperparameter embedding to preserve the structural information. Then, we introduce an attention-based deep feature extractor, capable of projecting configurations with different structures from various subspaces into a unified feature space, where the response surfaces can be formulated using a single standard Gaussian Process. The empirical results on a simulation function, various real-world tasks, and HPO-B benchmark demonstrate that our proposed approach improves the efficacy and efficiency of BO within conditional search spaces.