Obtaining large-scale, high-quality reasoning data is crucial for improving the geometric reasoning capabilities of multi-modal large language models (MLLMs). However, existing data generation methods, whether based on predefined tem plates or constrained symbolic provers, inevitably face diversity and numerical generalization limitations. To address these limitations, we propose NeSyGeo, a novel neuro-symbolic framework for generating geometric reasoning data. First, we propose a domain-specific language grounded in the entity-attributes-relations paradigm to comprehensively represent all components of plane geometry, along with generative actions defined within this symbolic space. We then design a symbolic-visual-text pipeline that synthesizes symbolic sequences, maps them to visual and textual representations and generates reasoning path with reverse search and forward validation. Based on this framework, we construct NeSyGeo CoT and NeSyGeo-Caption datasets, containing 100k samples, and release a new benchmark NeSyGeo-Test for evaluating geometric reasoning abilities in MLLMs. Experiments demonstrate that the proposal significantly and consistently improves the performance of multiple MLLMs under both reinforcement and supervised fine-tuning. With only 4k samples and two epochs of reinforcement fine-tuning, base models achieve improvements of up to +15.8% on MathVision, +8.4% on MathVerse, and +7.3% on GeoQA. Notably, a 4B model can be improved to outperform an 8B model from the same series on geometric reasoning tasks.s

Analogical reasoning lies at the core of human cognition and remains a fundamental challenge for artificial intelligence. Raven's Progressive Matrices (RPM) serve as a widely used benchmark to assess abstract reasoning by requiring the inference of underlying structural rules. While many vision-based and language-based models have achieved success on RPM tasks, it remains unclear whether their performance reflects genuine reasoning ability or reliance on statistical shortcuts. This study investigates the generalization capacity of modern AI systems under conditions of incomplete training by deliberately omitting several structural rules during training. Both sequence-to-sequence transformer models and vision-based architectures such as CoPINet and the Dual-Contrast Network are evaluated on the Impartial-RAVEN (I-RAVEN) dataset. Experiments reveal that although transformers demonstrate strong performance on familiar rules, their accuracy declines sharply when faced with novel or omitted rules. Moreover, the gap between token-level accuracy and complete answer accuracy highlights fundamental limitations in current approaches. These findings provide new insights into the reasoning mechanisms underlying deep learning models and underscore the need for architectures that move beyond pattern recognition toward robust abstract reasoning.

Associative Memories like the famous Hopfield Networks are elegant models for describing fully recurrent neural networks whose fundamental job is to store and retrieve information. In the past few years they experienced a surge of interest due to novel theoretical results pertaining to their information storage capabilities, and their relationship with SOTA AI architectures, such as Transformers and Diffusion Models. These connections open up possibilities for interpreting the computation of traditional AI networks through the theoretical lens of Associative Memories. Additionally, novel Lagrangian formulations of these networks make it possible to design powerful distributed models that learn useful representations and inform the design of novel architectures. This tutorial provides an approachable introduction to Associative Memories, emphasizing the modern language and methods used in this area of research, with practical hands-on mathematical derivations and coding notebooks.

Multi-Hop Question Answering (MHQA) tasks permeate real-world applications, posing challenges in orchestrating multi-step reasoning across diverse knowledge domains. While existing approaches have been improved with iterative retrieval, they still struggle to identify and organize dynamic knowledge. To address this, we propose DualRAG, a synergistic dual-process framework that seamlessly integrates reasoning and retrieval. DualRAG operates through two tightly coupled processes: Reasoning-augmented Querying (RaQ) and progressive Knowledge Aggregation (pKA). They work in concert: as RaQ navigates the reasoning path and generates targeted queries, pKA ensures that newly acquired knowledge is systematically integrated to support coherent reasoning. This creates a virtuous cycle of knowledge enrichment and reasoning refinement. Through targeted fine-tuning, DualRAG preserves its sophisticated reasoning and retrieval capabilities even in smaller-scale models, demonstrating its versatility and core advantages across different scales. Extensive experiments demonstrate that this dual-process approach substantially improves answer accuracy and coherence, approaching, and in some cases surpassing, the performance achieved with oracle knowledge access. These results establish DualRAG as a robust and efficient solution for complex multi-hop reasoning tasks.

Recent advancements in large language models (LLMs) have significantly improved their reasoning abilities, particularly through techniques involving search and backtracking. Backtracking naturally scales test-time compute by enabling sequential, linearized exploration via long chain-of-thought (CoT) generation. However, this is not the only strategy for scaling test time-compute: parallel sampling with best-of-N selection provides an alternative that generates diverse solutions simultaneously. Despite the growing adoption of sequential search, its advantages over parallel sampling-especially under a fixed compute budget-remain poorly understood. In this paper, we systematically compare these two approaches on two challenging reasoning tasks: CountDown and Sudoku. Surprisingly, we find that sequential search underperforms parallel sampling on CountDown but outperforms it on Sudoku, suggesting that backtracking is not universally beneficial. We identify two factors that can cause backtracking to degrade performance: (1) training on fixed search traces can lock models intro suboptimal strategies, and (2) explicit CoT supervision can discourage implicit (non verbalized) reasoning. Extending our analysis to reinforcement learning (RL), we show that models with backtracking capabilities benefit significantly from RL fine-tuning, while models without backtracking see limited, mixed gains. Together, these findings challenge the assumption that backtracking universally enhances LLM reasoning, instead revealing a complex interaction between task structure, training data, model scale, and learning paradigm.

We are interested in solving the problem of imitation learning with a limited amount of real-world expert data. Existing offline imitation methods often struggle with poor data coverage and severe performance degradation. We propose a solution that leverages robot simulators to achieve online imitation learning. Our sim-to-real framework is based on world models and combines online imitation pretraining with offline finetuning. By leveraging online interactions, our approach alleviates the data coverage limitations of offline methods, leading to improved robustness and reduced performance degradation during finetuning. It also enhances generalization during domain transfer. Our empirical results demonstrate its effectiveness, improving success rates by at least 31.7% in sim-to-sim transfer and 23.3% in sim-to-real transfer over existing offline imitation learning baselines.

Cinematography understanding refers to the ability to recognize not only the visual content of a scene but also the cinematic techniques that shape narrative meaning. This capability is attracting increasing attention, as it enhances mul-timodal understanding in real-world applications and underpins coherent content creation in film and media. However, our analysis reveals that ambiguous option design in ShotBench and ShotVL's shortcomings in reasoning consistency and instruction adherence undermine evaluation reliability, limiting fair comparison and hindering future progress. To overcome these issues, we systematically refine ShotBench through consistent option restructuring, conduct the first critical analysis of ShotVL's reasoning behavior, and introduce an extended evaluation protocol that jointly assesses task accuracy and core model competencies. These efforts lead to RefineShot, a refined and expanded benchmark that enables more reliable assessment and fosters future advances in cinematography understanding. We first analyze and refine the options in ShotBench to address their inconsistencies, then examine state-of-the-art models and reveal their reliability defects. Based on these findings, we propose a new evaluation protocol and demonstrate its effectiveness through comprehensive experiments.

Let q N and Π be a closed set of strictly positive distributions over [q ] . Let CH (Π) denote the convex hull of Π .

We thank all reviewers for their careful reviews and many positive comments. We feel that the typos and minor issues are easily addressable and will be corrected. We will incorporate this analysis into a revision of the paper. We thank R1 for bringing this highly related work to our attention. That work focuses on environments for which mice have previously developed spatial maps.

Perception and reasoning are two representative abilities of intelligence that are integrated seamlessly during human problem-solving processes.