What is reasoning? This question has driven centuries of philosophical inquiry, from Aristotle's syllogisms to modern computational complexity theory. In the age of large language models achieving superhuman performance on benchmarks like GSM8K (95\% accuracy) and HumanEval (90\% pass@1), we must ask: have these systems learned to \emph{reason}, or have they learned to \emph{pattern-match over reasoning traces}? This paper argues for a specific answer: \textbf{reasoning is iterative operator application in state spaces, converging to fixed points}. This definition is not merely philosophical -- it has concrete architectural implications that explain both the failures of current systems and the path to genuine reasoning capabilities. Our investigation begins with a puzzle (OpenXOR), progresses through theory (OpenOperator), and culminates in a working solution (OpenLM) that achieves 76\% accuracy where state-of-the-art LLMs achieve 0\%. This is not about criticizing existing systems, but about \emph{understanding what reasoning requires} and \emph{building architectures that provide it}.

We present ARCTraj, a dataset and methodological framework for modeling human reasoning through complex visual tasks in the Abstraction and Reasoning Corpus (ARC). While ARC has inspired extensive research on abstract reasoning, most existing approaches rely on static input--output supervision, which limits insight into how reasoning unfolds over time. ARCTraj addresses this gap by recording temporally ordered, object-level actions that capture how humans iteratively transform inputs into outputs, revealing intermediate reasoning steps that conventional datasets overlook. Collected via the O2ARC web interface, it contains around 10,000 trajectories annotated with task identifiers, timestamps, and success labels across 400 training tasks from the ARC-AGI-1 benchmark. It further defines a unified reasoning pipeline encompassing data collection, action abstraction, Markov decision process (MDP) formulation, and downstream learning, enabling integration with reinforcement learning, generative modeling, and sequence modeling methods such as PPO, World Models, GFlowNets, Diffusion agents, and Decision Transformers. Analyses of spatial selection, color attribution, and strategic convergence highlight the structure and diversity of human reasoning. Together, these contributions position ARCTraj as a structured and interpretable foundation for studying human-like reasoning, advancing explainability, alignment, and generalizable intelligence.

A world model enables an intelligent agent to imagine, predict, and reason about how the world evolves in response to its actions, and accordingly to plan and strategize. While recent video generation models produce realistic visual sequences, they typically operate in the prompt-to-full-video manner without causal control, interactivity, or long-horizon consistency required for purposeful reasoning. Existing world modeling efforts, on the other hand, often focus on restricted domains (e.g., physical, game, or 3D-scene dynamics) with limited depth and controllability, and struggle to generalize across diverse environments and interaction formats. In this work, we introduce PAN, a general, interactable, and long-horizon world model that predicts future world states through high-quality video simulation conditioned on history and natural language actions. PAN employs the Generative Latent Prediction (GLP) architecture that combines an autoregressive latent dynamics backbone based on a large language model (LLM), which grounds simulation in extensive text-based knowledge and enables conditioning on language-specified actions, with a video diffusion decoder that reconstructs perceptually detailed and temporally coherent visual observations, to achieve a unification between latent space reasoning (imagination) and realizable world dynamics (reality). Trained on large-scale video-action pairs spanning diverse domains, PAN supports open-domain, action-conditioned simulation with coherent, long-term dynamics. Extensive experiments show that PAN achieves strong performance in action-conditioned world simulation, long-horizon forecasting, and simulative reasoning compared to other video generators and world models, taking a step towards general world models that enable predictive simulation of future world states for reasoning and acting.

We introduce VeriStruct, a novel framework that extends AI-assisted automated verification from single functions to more complex data structure modules in Verus. VeriStruct employs a planner module to orchestrate the systematic generation of abstractions, type invariants, specifications, and proof code. To address the challenge that LLMs often misunderstand Verus' annotation syntax and verification-specific semantics, VeriStruct embeds syntax guidance within prompts and includes a repair stage to automatically correct annotation errors. In an evaluation on eleven Rust data structure modules, VeriStruct succeeds on ten of the eleven, successfully verifying 128 out of 129 functions (99.2%) in total. These results represent an important step toward the goal of automatic AI-assisted formal verification.

Semantic occupancy has emerged as a powerful representation in world models for its ability to capture rich spatial semantics. However, most existing occupancy world models rely on static and fixed embeddings or grids, which inherently limit the flexibility of perception. Moreover, their ``in-place classification" over grids exhibits a potential misalignment with the dynamic and continuous nature of real scenarios. In this paper, we propose SparseWorld, a novel 4D occupancy world model that is flexible, adaptive, and efficient, powered by sparse and dynamic queries. We propose a Range-Adaptive Perception module, in which learnable queries are modulated by the ego vehicle states and enriched with temporal-spatial associations to enable extended-range perception. To effectively capture the dynamics of the scene, we design a State-Conditioned Forecasting module, which replaces classification-based forecasting with regression-guided formulation, precisely aligning the dynamic queries with the continuity of the 4D environment. In addition, We specifically devise a Temporal-Aware Self-Scheduling training strategy to enable smooth and efficient training. Extensive experiments demonstrate that SparseWorld achieves state-of-the-art performance across perception, forecasting, and planning tasks. Comprehensive visualizations and ablation studies further validate the advantages of SparseWorld in terms of flexibility, adaptability, and efficiency.

CAPTCHA, originally designed to distinguish humans from robots, has evolved into a real-world benchmark for assessing the spatial reasoning capabilities of vision-language models. In this work, we first show that step-by-step reasoning is crucial for vision-language models (VLMs) to solve CAPTCHAs, which represent high-difficulty spatial reasoning tasks, and that current commercial vision-language models still struggle with such reasoning. In particular, we observe that most commercial VLMs (e.g., Gemini, Claude, GPT, etc.) fail to effectively solve CAPTCHAs and thus achieve low accuracy (around 21.9 percent). However, our findings indicate that requiring the model to perform step-by-step reasoning before generating the final coordinates can significantly enhance its solving accuracy, underscoring the severity of the gap. To systematically study this issue, we introduce CAPTCHA-X, the first real-world CAPTCHA benchmark with reasoning, covering seven categories of CAPTCHAs (such as Gobang, hCaptcha, etc.) with step-by-step action solutions and grounding annotations. We further define five reasoning-oriented metrics that enable a comprehensive evaluation of models reasoning capabilities. To validate the effectiveness of reasoning, we also propose a general agentic VLM-based framework that incorporates the models inherent reasoning abilities. Our method achieves state-of-the-art performance across five high-difficulty CAPTCHA types, with an average solving accuracy of 83.9 percent, substantially surpassing existing baselines. These results reveal the limitations of current models and highlight the importance of reasoning in advancing visual-spatial challenges in the future.

Recent Large Reasoning Language Models (LRLMs) employ long chain-of-thought reasoning with complex reflection behaviors, typically signaled by specific trigger words (e.g., "Wait" and "Alternatively") to enhance performance. However, these reflection behaviors can lead to the overthinking problem where the generation of redundant reasoning steps that unnecessarily increase token usage, raise inference costs, and reduce practical utility. In this paper, we propose Certainty-Guided Reflection Suppression (CGRS), a novel method that mitigates overthinking in LRLMs while maintaining reasoning accuracy. CGRS operates by dynamically suppressing the model's generation of reflection triggers when it exhibits high confidence in its current response, thereby preventing redundant reflection cycles without compromising output quality. Our approach is model-agnostic, requires no retraining or architectural modifications, and can be integrated seamlessly with existing autoregressive generation pipelines. Extensive experiments across four reasoning benchmarks (i.e., AIME24, AMC23, MATH500, and GPQA-D) demonstrate CGRS's effectiveness: it reduces token usage by an average of 18.5% to 41.9% while preserving accuracy. It also achieves the optimal balance between length reduction and performance compared to state-of-the-art baselines. These results hold consistently across model architectures (e.g., DeepSeek-R1-Distill series, QwQ-32B, and Qwen3 family) and scales (4B to 32B parameters), highlighting CGRS's practical value for efficient reasoning.

Long-term action anticipation from egocentric video is critical for applications such as human-computer interaction and assistive technologies, where anticipating user intent enables proactive and context-aware AI assistance. However, existing approaches suffer from three key limitations: 1) un-derutilization of fine-grained visual cues from hand-object interactions, 2) neglect of semantic dependencies between verbs and nouns, and 3) lack of explicit cognitive reasoning, limiting generalization and long-term forecasting ability. To overcome these challenges, we propose INSIGHT, a unified two-stage framework for egocentric action anticipation. In the first stage, INSIGHT focuses on extracting semantically rich features from hand-object interaction regions and enhances action representations using a verb-noun co-occurrence matrix. In the second stage, it introduces a reinforcement learning-based module that simulates explicit cognitive reasoning through a structured process: visual perception (think) intention inference (reason) action anticipation (answer). Extensive experiments on Ego4D, EPIC-Kitchens-55, and EGTEA Gaze+ benchmarks show that INSIGHT achieves state-of-the-art performance, demonstrating its effectiveness and strong generalization capability. Introduction In real-world applications such as human-computer interaction (Azam and Desai 2024; Plizzari et al. 2024), augmented reality (Abreu et al. 2024; Xu et al. 2024), and assistive systems for visually impaired individuals (Lee et al. 2024; Xiao et al. 2025), AI agents must accurately interpret user intent and demonstrate effective long-term planning capabilities within egocentric vision scenarios.

We introduce a novel paradigm of emergent local memory. It is a continuous-learning completely-parallel content-addressable memory encoding global order. It demonstrates how local constraints on uncoordinated learning can produce topologically protected memories realizing emergent symbolic order. It is therefore a neuro-symbolic bridge. It further has the ability to produce human language without data, by exploiting its own self-organizing dynamics. It teaches us that words arise as a side-effect of emergent symbolic order, and that human language patterns at all structural levels reflect a universal mechanism of word formation (which is subregular). This work answers essential questions about the existence \& origin of all the human language data.

Table-based question answering requires complex reasoning capabilities that current LLMs struggle to achieve with single-pass inference. Existing approaches, such as Chain-of-Thought reasoning and question decomposition, lack error detection mechanisms and discard problem-solving experiences, contrasting sharply with how humans tackle such problems. In this paper, we propose MAPLE (Multi-agent Adaptive Planning with Long-term mEmory), a novel framework that mimics human problem-solving through specialized cognitive agents working in a feedback-driven loop. MAPLE integrates 4 key components: (1) a Solver using the ReAct paradigm for reasoning, (2) a Checker for answer verification, (3) a Reflector for error diagnosis and strategy correction, and (4) an Archiver managing long-term memory for experience reuse and evolution. Experiments on WiKiTQ and TabFact demonstrate significant improvements over existing methods, achieving state-of-the-art performance across multiple LLM backbones.