We introduce ZykovColor, a novel SAT-based algorithm to solve the graph coloring problem working on top of an encoding that mimics the Zykov tree. Our method is based on an approach of Hébrard and Katsirelos (2020) that employs a propagator to enforce transitivity constraints, incorporate lower bounds for search tree pruning, and enable inferred propagations. We leverage the recently introduced IPASIR-UP interface for CaDiCaL to implement these techniques with a SAT solver. Furthermore, we propose new features that take advantage of the underlying SAT solver. These include modifying the integrated decision strategy with vertex domination hints and using incremental bottom-up search that allows to reuse learned clauses from previous calls. Additionally, we integrate a more effective clique computation and an algorithm for computing the fractional chromatic number to improve the lower bounds used for pruning during the search. We validate the effectiveness of each new feature through an experimental analysis. ZykovColor outperforms other state-of-the-art graph coloring implementations on the DIMACS benchmark set. Further experiments on random Erdős-Rényi graphs show that our new approach matches or outperforms state-of-the-art SAT-based methods for both very sparse and highly dense graphs. We give an additional configuration of ZykovColor that dominates other SAT-based methods on the Erdős-Rényi graphs.

Algorithms for learning decision trees often include heuristic local-search operations such as (1) adjusting the threshold of a cut or (2) also exchanging the feature of that cut. We study minimizing the number of classification errors by performing a fixed number of a single type of these operations. Although we discover that the corresponding problems are NP-complete in general, we provide a comprehensive parameterized-complexity analysis with the aim of determining those properties of the problems that explain the hardness and those that make the problems tractable. For instance, we show that the problems remain hard for a small number $d$ of features or small domain size $D$ but the combination of both yields fixed-parameter tractability. That is, the problems are solvable in $(D + 1)^{2d} \cdot |I|^{O(1)}$ time, where $|I|$ is the size of the input. We also provide a proof-of-concept implementation of this algorithm and report on empirical results.

Knowledge Hypergraphs (KHs) have recently emerged as a knowledge representation for retrieval-augmented generation (RAG), offering a paradigm to model multi-entity relations into a structured form. However, existing KH-based RAG methods suffer from three major limitations: static retrieval planning, non-adaptive retrieval execution, and superficial use of KH structure and semantics, which constrain their ability to perform effective multi-hop question answering. To overcome these limitations, we propose PRoH, a dynamic Planning and Reasoning over Knowledge Hypergraphs framework. PRoH incorporates three core innovations: (i) a context-aware planning module that sketches the local KH neighborhood to guide structurally grounded reasoning plan generation; (ii) a structured question decomposition process that organizes subquestions as a dynamically evolving Directed Acyclic Graph (DAG) to enable adaptive, multi-trajectory exploration; and (iii) an Entity-Weighted Overlap (EWO)-guided reasoning path retrieval algorithm that prioritizes semantically coherent hyperedge traversals. Experiments across multiple domains demonstrate that PRoH achieves state-of-the-art performance, surpassing the prior SOTA model HyperGraphRAG by an average of 19.73% in F1 and 8.41% in Generation Evaluation (G-E) score, while maintaining strong robustness in long-range multi-hop reasoning tasks.

Translating a general quantum circuit on a specific hardware topology with a reduced set of available gates, also known as transpilation, comes with a substantial increase in the length of the equivalent circuit. Due to decoherence, the quality of the computational outcome can degrade seriously with increasing circuit length. Thus, there is major interest to reduce a quantum circuit to an equivalent circuit which is in its gate count as short as possible. One method to address efficient transpilation is based on approaches known from stochastic optimization, e.g. by using random sampling and token replacement strategies. Here, a core challenge is that these methods can suffer from sampling efficiency, causing long and energy consuming optimization time. As a remedy, we propose in this work 2D neural guided sampling. Thus, given a 2D representation of a quantum circuit, a neural network predicts groups of gates in the quantum circuit, which are likely reducible. Thus, it leads to a sampling prior which can heavily reduce the compute time for quantum circuit reduction. In several experiments, we demonstrate that our method is superior to results obtained from different qiskit or BQSKit optimization levels.

With the increasing capabilities of Large Language Models (LLMs), parallel reasoning has emerged as a new inference paradigm that enhances reasoning robustness by concurrently exploring multiple lines of thought before converging on a final answer. It has become a significant trend to explore parallel reasoning to overcome the fragility of standard sequential methods and improve practical performance. In this paper, we aim to survey and summarize the progress and challenges of parallel reasoning. We first present a formal definition of parallel reasoning and clarify its distinction from related concepts like Chain-of-Thought. Then, we organize and discuss advanced techniques based on a novel taxonomy, including non-interactive reasoning, interactive reasoning, and efficiency-focused decoding strategies. Additionally, we explore various application scenarios, such as solving complex problems and enhancing the reliability of LLM outputs.Finally, we highlight the core challenges of parallel reasoning and suggest potential directions for future research. We hope that our work can provide a useful roadmap for beginners and encourage more research on improving parallel reasoning methods. Related source can be avaliable in https://github.com/PPPP-kaqiu/Awesome-Parallel-Reasoning.

Causal discovery aims to learn causal relationships between variables from targeted data, making it a fundamental task in machine learning. However, causal discovery algorithms often rely on unverifiable causal assumptions, which are usually difficult to satisfy in real-world data, thereby limiting the broad application of causal discovery in practical scenarios. Inspired by these considerations, this work extensively benchmarks the empirical performance of various mainstream causal discovery algorithms, which assume i.i.d. data, under eight model assumption violations. Our experimental results show that differentiable causal discovery methods exhibit robustness under the metrics of Structural Hamming Distance and Structural Intervention Distance of the inferred graphs in commonly used challenging scenarios, except for scale variation. We also provide the theoretical explanations for the performance of differentiable causal discovery methods. Finally, our work aims to comprehensively benchmark the performance of recent differentiable causal discovery methods under model assumption violations, and provide the standard for reasonable evaluation of causal discovery, as well as to further promote its application in real-world scenarios.

Games have long been a microcosm for studying planning and reasoning in both natural and artificial intelligence, especially with a focus on expert-level or even super-human play. But real life also pushes human intelligence along a different frontier, requiring people to flexibly navigate decision-making problems that they have never thought about before. Here, we use novice gameplay to study how people make decisions and form judgments in new problem settings. We show that people are systematic and adaptively rational in how they play a game for the first time, or evaluate a game (e.g., how fair or how fun it is likely to be) before they have played it even once. We explain these capacities via a computational cognitive model that we call the "Intuitive Gamer". The model is based on mechanisms of fast and flat (depth-limited) goal-directed probabilistic simulation--analogous to those used in Monte Carlo tree-search models of expert game-play, but scaled down to use very few stochastic samples, simple goal heuristics for evaluating actions, and no deep search. In a series of large-scale behavioral studies with over 1000 participants and 121 two-player strategic board games (almost all novel to our participants), our model quantitatively captures human judgments and decisions varying the amount and kind of experience people have with a game--from no experience at all ("just thinking"), to a single round of play, to indirect experience watching another person and predicting how they should play--and does so significantly better than much more compute-intensive expert-level models. More broadly, our work offers new insights into how people rapidly evaluate, act, and make suggestions when encountering novel problems, and could inform the design of more flexible and human-like AI systems that can determine not just how to solve new tasks, but whether a task is worth thinking about at all.

The performance gains of LLMs have historically been driven by scaling up model size and training data. However, the rapidly diminishing availability of high-quality training data is introducing a fundamental bottleneck, shifting the focus of research toward inference-time scaling. This paradigm uses additional computation at the time of deployment to substantially improve LLM performance on downstream tasks without costly model re-training. This review systematically surveys the diverse techniques contributing to this new era of inference-time scaling, organizing the rapidly evolving field into two comprehensive perspectives: Output-focused and Input-focused methods. Output-focused techniques encompass complex, multi-step generation strategies, including reasoning (e.g., CoT, ToT, ReAct), various search and decoding methods (e.g., MCTS, beam search), training for long CoT (e.g., RLVR, GRPO), and model ensemble methods. Input-focused techniques are primarily categorized by few-shot and RAG, with RAG as the central focus. The RAG section is further detailed through a structured examination of query expansion, data, retrieval and reranker, LLM generation methods, and multi-modal RAG.

Graph generation is a fundamental problem in graph learning with broad applications across Web-scale systems, knowledge graphs, and scientific domains such as drug and material discovery. Recent approaches leverage diffusion models for step-by-step generation, yet unconditional diffusion offers little control over desired properties, often leading to unstable quality and difficulty in incorporating new objectives. Inference-time guidance methods mitigate these issues by adjusting the sampling process without retraining, but they remain inherently local, heuristic, and limited in controllability. To overcome these limitations, we propose TreeDiff, a Monte Carlo Tree Search (MCTS) guided dual-space diffusion framework for controllable graph generation. TreeDiff is a plug-and-play inference-time method that expands the search space while keeping computation tractable. Specifically, TreeDiff introduces three key designs to make it practical and scalable: (1) a macro-step expansion strategy that groups multiple denoising updates into a single transition, reducing tree depth and enabling long-horizon exploration; (2) a dual-space denoising mechanism that couples efficient latent-space denoising with lightweight discrete correction in graph space, ensuring both scalability and structural fidelity; and (3) a dual-space verifier that predicts long-term rewards from partially denoised graphs, enabling early value estimation and removing the need for full rollouts. Extensive experiments on 2D and 3D molecular generation benchmarks, under both unconditional and conditional settings, demonstrate that TreeDiff achieves state-of-the-art performance. Notably, TreeDiff exhibits favorable inference-time scaling: it continues to improve with additional computation, while existing inference-time methods plateau early under limited resources.

We introduce Aristotle, an AI system that combines formal verification with informal reasoning, achieving gold-medal-equivalent performance on the 2025 International Mathematical Olympiad problems. Aristotle integrates three main components: a Lean proof search system, an informal reasoning system that generates and formalizes lemmas, and a dedicated geometry solver. Our system demonstrates state-of-the-art performance with favorable scaling properties for automated theorem proving.