Daily Papers

Test-Time Scaling (TTS) refers to approaches that improve reasoning performance by allocating extra computation during inference, without altering the model's parameters. While existing TTS methods operate in a discrete token space by generating more intermediate steps, recent studies in Coconut and SoftCoT have demonstrated that thinking in the continuous latent space can further enhance the reasoning performance. Such latent thoughts encode informative thinking without the information loss associated with autoregressive token generation, sparking increased interest in continuous-space reasoning. Unlike discrete decoding, where repeated sampling enables exploring diverse reasoning paths, latent representations in continuous space are fixed for a given input, which limits diverse exploration, as all decoded paths originate from the same latent thought. To overcome this limitation, we introduce SoftCoT++ to extend SoftCoT to the Test-Time Scaling paradigm by enabling diverse exploration of thinking paths. Specifically, we perturb latent thoughts via multiple specialized initial tokens and apply contrastive learning to promote diversity among soft thought representations. Experiments across five reasoning benchmarks and two distinct LLM architectures demonstrate that SoftCoT++ significantly boosts SoftCoT and also outperforms SoftCoT with self-consistency scaling. Moreover, it shows strong compatibility with conventional scaling techniques such as self-consistency. Source code is available at https://github.com/xuyige/SoftCoT.

Chain-of-Thought (CoT) reasoning enables Large Language Models (LLMs) to solve complex reasoning tasks by generating intermediate reasoning steps. However, most existing approaches focus on hard token decoding, which constrains reasoning within the discrete vocabulary space and may not always be optimal. While recent efforts explore continuous-space reasoning, they often suffer from catastrophic forgetting, limiting their applicability to state-of-the-art LLMs that already perform well in zero-shot settings with a proper instruction. To address this challenge, we propose a novel approach for continuous-space reasoning that does not require modifying the underlying LLM. Specifically, we employ a lightweight assistant model to generate instance-specific soft thought tokens speculatively as the initial chain of thoughts, which are then mapped into the LLM's representation space via a projection module. Experimental results on five reasoning benchmarks demonstrate that our method enhances LLM reasoning performance through supervised, parameter-efficient fine-tuning.

We introduce iterative reasoning through energy diffusion (IRED), a novel framework for learning to reason for a variety of tasks by formulating reasoning and decision-making problems with energy-based optimization. IRED learns energy functions to represent the constraints between input conditions and desired outputs. After training, IRED adapts the number of optimization steps during inference based on problem difficulty, enabling it to solve problems outside its training distribution -- such as more complex Sudoku puzzles, matrix completion with large value magnitudes, and pathfinding in larger graphs. Key to our method's success is two novel techniques: learning a sequence of annealed energy landscapes for easier inference and a combination of score function and energy landscape supervision for faster and more stable training. Our experiments show that IRED outperforms existing methods in continuous-space reasoning, discrete-space reasoning, and planning tasks, particularly in more challenging scenarios. Code and visualizations at https://energy-based-model.github.io/ired/

Many reasoning techniques for large multimodal models adapt language model approaches, such as Chain-of-Thought (CoT) prompting, which express reasoning as word sequences. While effective for text, these methods are suboptimal for multimodal contexts, struggling to align audio, visual, and textual information dynamically. To explore an alternative paradigm, we propose the Multimodal Chain of Continuous Thought (MCOUT), which enables reasoning directly in a joint latent space rather than in natural language. In MCOUT, the reasoning state is represented as a continuous hidden vector, iteratively refined and aligned with visual and textual embeddings, inspired by human reflective cognition. We develop two variants: MCOUT-Base, which reuses the language model`s last hidden state as the continuous thought for iterative reasoning, and MCOUT-Multi, which integrates multimodal latent attention to strengthen cross-modal alignment between visual and textual features. Experiments on benchmarks including MMMU, ScienceQA, and MMStar show that MCOUT consistently improves multimodal reasoning, yielding up to 8.23% accuracy gains over strong baselines and improving BLEU scores up to 8.27% across multiple-choice and open-ended tasks. These findings highlight latent continuous reasoning as a promising direction for advancing LMMs beyond language-bound CoT, offering a scalable framework for human-like reflective multimodal inference. Code is available at https://github.com/Hanhpt23/OmniMod.

In human cognition, there exist numerous thought processes that are tacit and beyond verbal expression, enabling us to understand and interact with the world in multiple ways. However, contemporary Vision-Language Models (VLMs) remain constrained to reasoning within the discrete and rigid space of linguistic tokens, thereby bottlenecking the rich, high-dimensional nature of visual perception. To bridge this gap, we propose CoCoVa (Chain of Continuous Vision-Language Thought), a novel framework for vision-language model that leverages continuous cross-modal reasoning for diverse vision-language tasks. The core of CoCoVa is an iterative reasoning cycle, where a novel Latent Q-Former (LQ-Former) acts as a dynamic reasoning engine, iteratively refining a chain of latent thought vectors through cross-modal fusion. To focus this process, a token selection mechanism dynamically identifies salient visual regions, mimicking attentional focus. To ensure these latent thoughts remain grounded, we train the model with a multi-task objective that combines contrastive learning and diffusion-based reconstruction, enforcing alignment between latent representations and both visual and textual modalities. Evaluations show CoCoVa improves accuracy and token efficiency over strong baselines. With a 1.5B backbone, it competes with or surpasses larger 7B-9B models on almost all benchmarks. When scaled to 7B LLM backbones, it remains competitive with state-of-the-art models. Qualitative analysis validates that learned latent space captures interpretable and structured reasoning patterns, highlighting the potential of CoCoVa to bridge the representational gap between discrete language processing and the continuous nature of visual understanding.

Chain-of-Thought (CoT) enhances Large Language Models (LLMs) by enabling step-by-step reasoning in natural language. However, the language space may be suboptimal for reasoning. While implicit CoT methods attempt to enable reasoning without explicit CoT tokens, they have consistently lagged behind explicit CoT method in task performance. We propose CODI (Continuous Chain-of-Thought via Self-Distillation), a novel framework that distills CoT into a continuous space, where a shared model acts as both teacher and student, jointly learning explicit and implicit CoT while aligning their hidden activation on the token generating the final answer. CODI is the first implicit CoT method to match explicit CoT's performance on GSM8k while achieving 3.1x compression, surpassing the previous state-of-the-art by 28.2% in accuracy. Furthermore, CODI demonstrates scalability, robustness, and generalizability to more complex CoT datasets. Additionally, CODI retains interpretability by decoding its continuous thoughts, making its reasoning process transparent. Our findings establish implicit CoT as not only a more efficient but a powerful alternative to explicit CoT.

Parallel test-time scaling (TTS) is a pivotal approach for enhancing large language models (LLMs), typically by sampling multiple token-based chains-of-thought in parallel and aggregating outcomes through voting or search. Recent advances in latent reasoning, where intermediate reasoning unfolds in continuous vector spaces, offer a more efficient alternative to explicit Chain-of-Thought, yet whether such latent models can similarly benefit from parallel TTS remains open, mainly due to the absence of sampling mechanisms in continuous space, and the lack of probabilistic signals for advanced trajectory aggregation. \ This work enables parallel TTS for latent reasoning models by addressing the above issues. For sampling, we introduce two uncertainty-inspired stochastic strategies: Monte Carlo Dropout and Additive Gaussian Noise. For aggregation, we design a Latent Reward Model (LatentRM) trained with step-wise contrastive objective to score and guide latent reasoning. Extensive experiments and visualization analyses show that both sampling strategies scale effectively with compute and exhibit distinct exploration dynamics, while LatentRM enables effective trajectory selection. Together, our explorations open a new direction for scalable inference in continuous spaces. Code released at https://github.com/YRYangang/LatentTTS.

Human cognition typically involves thinking through abstract, fluid concepts rather than strictly using discrete linguistic tokens. Current reasoning models, however, are constrained to reasoning within the boundaries of human language, processing discrete token embeddings that represent fixed points in the semantic space. This discrete constraint restricts the expressive power and upper potential of such reasoning models, often causing incomplete exploration of reasoning paths, as standard Chain-of-Thought (CoT) methods rely on sampling one token per step. In this work, we introduce Soft Thinking, a training-free method that emulates human-like "soft" reasoning by generating soft, abstract concept tokens in a continuous concept space. These concept tokens are created by the probability-weighted mixture of token embeddings, which form the continuous concept space, enabling smooth transitions and richer representations that transcend traditional discrete boundaries. In essence, each generated concept token encapsulates multiple meanings from related discrete tokens, implicitly exploring various reasoning paths to converge effectively toward the correct answer. Empirical evaluations on diverse mathematical and coding benchmarks consistently demonstrate the effectiveness and efficiency of Soft Thinking, improving pass@1 accuracy by up to 2.48 points while simultaneously reducing token usage by up to 22.4% compared to standard CoT. Qualitative analysis further reveals that Soft Thinking outputs remain highly interpretable and readable, highlighting the potential of Soft Thinking to break the inherent bottleneck of discrete language-based reasoning. Code is available at https://github.com/eric-ai-lab/Soft-Thinking.

Large language models (LLMs) are restricted to reason in the "language space", where they typically express the reasoning process with a chain-of-thought (CoT) to solve a complex reasoning problem. However, we argue that language space may not always be optimal for reasoning. For example, most word tokens are primarily for textual coherence and not essential for reasoning, while some critical tokens require complex planning and pose huge challenges to LLMs. To explore the potential of LLM reasoning in an unrestricted latent space instead of using natural language, we introduce a new paradigm Coconut (Chain of Continuous Thought). We utilize the last hidden state of the LLM as a representation of the reasoning state (termed "continuous thought"). Rather than decoding this into a word token, we feed it back to the LLM as the subsequent input embedding directly in the continuous space. Experiments show that Coconut can effectively augment the LLM on several reasoning tasks. This novel latent reasoning paradigm leads to emergent advanced reasoning patterns: the continuous thought can encode multiple alternative next reasoning steps, allowing the model to perform a breadth-first search (BFS) to solve the problem, rather than prematurely committing to a single deterministic path like CoT. Coconut outperforms CoT in certain logical reasoning tasks that require substantial backtracking during planning, with fewer thinking tokens during inference. These findings demonstrate the promise of latent reasoning and offer valuable insights for future research.

Reinforcement Learning (RL) has become a pivotal approach for enhancing the reasoning capabilities of Large Language Models (LLMs). However, a significant theoretical gap persists, as traditional token-level RL frameworks fail to align with the reasoning-level nature of complex, multi-step thought processes like Chain-of-Thought (CoT). To address this challenge, we introduce CoT-Space, a novel theoretical framework that recasts LLM reasoning from a discrete token-prediction task to an optimization process within a continuous, reasoning-level semantic space. By analyzing this process from both a noise perspective and a risk perspective, we demonstrate that the convergence to an optimal CoT length is a natural consequence of the fundamental trade-off between underfitting and overfitting. Furthermore, extensive experiments provide strong empirical validation for our theoretical findings. Our framework not only provides a coherent explanation for empirical phenomena such as overthinking but also offers a solid theoretical foundation to guide the future development of more effective and generalizable reasoning agents.

Chain-of-thought (CoT) reasoning enables large language models (LLMs) to move beyond fast System-1 responses and engage in deliberative System-2 reasoning. However, this comes at the cost of significant inefficiency due to verbose intermediate output. Recent latent-space reasoning methods improve efficiency by operating on hidden states without decoding into language, yet they treat all steps uniformly, failing to distinguish critical deductions from auxiliary steps and resulting in suboptimal use of computational resources. In this paper, we propose System-1.5 Reasoning, an adaptive reasoning framework that dynamically allocates computation across reasoning steps through shortcut paths in latent space. Specifically, System-1.5 Reasoning introduces two types of dynamic shortcuts. The model depth shortcut (DS) adaptively reasons along the vertical depth by early exiting non-critical tokens through lightweight adapter branches, while allowing critical tokens to continue through deeper Transformer layers. The step shortcut (SS) reuses hidden states across the decoding steps to skip trivial steps and reason horizontally in latent space. Training System-1.5 Reasoning involves a two-stage self-distillation process: first distilling natural language CoT into latent-space continuous thought, and then distilling full-path System-2 latent reasoning into adaptive shortcut paths (System-1.5 Reasoning). Experiments on reasoning tasks demonstrate the superior performance of our method. For example, on GSM8K, System-1.5 Reasoning achieves reasoning performance comparable to traditional CoT fine-tuning methods while accelerating inference by over 20x and reducing token generation by 92.31% on average.

Complex Reasoning in Large Language Models can be dynamically optimized using Test-Time Scaling (TTS) to mitigate Overthinking. Methods such as Coconut, SoftCoT and its variant are effective in continuous latent space inference, the core bottleneck still lies in the efficient generation and utilization of high-quality Latent Thought. Drawing from the theory of SoftCoT++ that a larger variance in the generated Latent Thought distribution more closely approximates the golden truth distribution, we propose a Latent Thought-Augmented Training Framework--LTA-Thinker, which improves distributional variance and enhances reasoning performance from two perspectives. First, LTA-Thinker constructs a Latent Thought generation architecture based on a learnable prior. This architecture aims to increase the variance distribution of generated Latent Thought Vectors in order to simplify the overall structure and raise the performance ceiling. Second, LTA-Thinker introduces a distribution-based directional optimization paradigm that jointly constrains both distribution locality and distribution scale. This mechanism improves information efficiency and computational cost through a multi-objective co-training strategy, which combines standard Supervised Fine-Tuning (SFT) loss with two novel losses: Semantic Alignment Loss, which utilizes KL divergence to ensure that the Latent Thought is highly relevant to the semantics of the question; Reasoning Focus Loss, which utilizes a contrastive learning mechanism to guide the model to focus on the most critical reasoning steps. Experiments show that LTA-thinker achieves state-of-the-art (SOTA) performance among various baselines and demonstrates a higher performance ceiling and better scaling effects.

Aligning pretrained audio encoders and Large Language Models (LLMs) offers a promising, parameter-efficient path to building powerful multimodal agents. However, existing methods often require costly full-model finetuning or rely on static adapters that may lack expressive power. Drawing inspiration from the Platonic Representation Hypothesis, we introduce SteerMoE, a novel and modular framework for audio-language alignment. SteerMoE freezes both the audio encoder and the LLM decoder, training only a lightweight steering module integrated within the encoder's layers. This module uses a Mixture-of-Experts (MoE) router to dynamically select and apply learned steering vectors, progressively transforming continuous audio representations into a space comprehensible to the LLM. By operating entirely in the continuous embedding space, our approach requires no modifications to the LLM's vocabulary and preserves its advanced reasoning and agentic capabilities. We demonstrate through experiments on ASR, audio understanding, and a qualitative function-calling task that SteerMoE achieves strong performance while remaining highly modular and computationally efficient, offering a robust new paradigm for developing sophisticated audio-language systems.

"Thinking with images" has emerged as an effective paradigm for advancing visual reasoning, extending beyond text-only chains of thought by injecting visual evidence into intermediate reasoning steps. However, existing methods fall short of human-like abstract visual thinking, as their flexibility is fundamentally limited by external tools. In this work, we introduce Monet, a training framework that enables multimodal large language models (MLLMs) to reason directly within the latent visual space by generating continuous embeddings that function as intermediate visual thoughts. We identify two core challenges in training MLLMs for latent visual reasoning: high computational cost in latent-vision alignment and insufficient supervision over latent embeddings, and address them with a three-stage distillation-based supervised fine-tuning (SFT) pipeline. We further reveal a limitation of applying GRPO to latent reasoning: it primarily enhances text-based reasoning rather than latent reasoning. To overcome this, we propose VLPO (Visual-latent Policy Optimization), a reinforcement learning method that explicitly incorporates latent embeddings into policy gradient updates. To support SFT, we construct Monet-SFT-125K, a high-quality text-image interleaved CoT dataset containing 125K real-world, chart, OCR, and geometry CoTs. Our model, Monet-7B, shows consistent gains across real-world perception and reasoning benchmarks and exhibits strong out-of-distribution generalization on challenging abstract visual reasoning tasks. We also empirically analyze the role of each training component and discuss our early unsuccessful attempts, providing insights for future developments in visual latent reasoning. Our model, data, and code are available at https://github.com/NOVAglow646/Monet.

Traditional multimodal learning approaches require expensive alignment pre-training to bridge vision and language modalities, typically projecting visual features into discrete text token spaces. We challenge both fundamental assumptions underlying this paradigm by proposing Inverse-LLaVA, a novel approach that eliminates alignment pre-training entirely while inverting the conventional mapping direction. Rather than projecting visual features to text space, our method maps text embeddings into continuous visual representation space and performs fusion within transformer intermediate layers. Through selective additive components in attention mechanisms, we enable dynamic integration of visual and textual representations without requiring massive image-text alignment datasets. Comprehensive experiments across nine multimodal benchmarks demonstrate nuanced performance trade-offs: Inverse-LLaVA achieves notable improvements on reasoning-intensive and cognitive tasks (MM-VET: +0.2%, VizWiz: +1.8%, ScienceQA: +0.2%, cognitive reasoning: +27.2%), while showing expected decreases in perception tasks requiring memorized visual-text associations (celebrity recognition: -49.5%, OCR: -21.3%). These results provide the first empirical evidence that alignment pre-training is not necessary for effective multimodal learning, particularly for complex reasoning tasks. Our work establishes the feasibility of a new paradigm that reduces computational requirements by 45%, challenges conventional wisdom about modality fusion, and opens new research directions for efficient multimodal architectures that preserve modality-specific characteristics. Our project website with code and additional resources is available at https://inverse-llava.github.io.

Reasoning from sequences of raw sensory data is a ubiquitous problem across fields ranging from medical devices to robotics. These problems often involve using long sequences of raw sensor data (e.g. magnetometers, piezoresistors) to predict sequences of desirable physical quantities (e.g. force, inertial measurements). While classical approaches are powerful for locally-linear prediction problems, they often fall short when using real-world sensors. These sensors are typically non-linear, are affected by extraneous variables (e.g. vibration), and exhibit data-dependent drift. For many problems, the prediction task is exacerbated by small labeled datasets since obtaining ground-truth labels requires expensive equipment. In this work, we present Hierarchical State-Space Models (HiSS), a conceptually simple, new technique for continuous sequential prediction. HiSS stacks structured state-space models on top of each other to create a temporal hierarchy. Across six real-world sensor datasets, from tactile-based state prediction to accelerometer-based inertial measurement, HiSS outperforms state-of-the-art sequence models such as causal Transformers, LSTMs, S4, and Mamba by at least 23% on MSE. Our experiments further indicate that HiSS demonstrates efficient scaling to smaller datasets and is compatible with existing data-filtering techniques. Code, datasets and videos can be found on https://hiss-csp.github.io.

Vision-Language Models (VLMs) excel at reasoning in linguistic space but struggle with perceptual understanding that requires dense visual perception, e.g., spatial reasoning and geometric awareness. This limitation stems from the fact that current VLMs have limited mechanisms to capture dense visual information across spatial dimensions. We introduce Chain-of-Visual-Thought (COVT), a framework that enables VLMs to reason not only in words but also through continuous visual tokens-compact latent representations that encode rich perceptual cues. Within a small budget of roughly 20 tokens, COVT distills knowledge from lightweight vision experts, capturing complementary properties such as 2D appearance, 3D geometry, spatial layout, and edge structure. During training, the VLM with COVT autoregressively predicts these visual tokens to reconstruct dense supervision signals (e.g., depth, segmentation, edges, and DINO features). At inference, the model reasons directly in the continuous visual token space, preserving efficiency while optionally decoding dense predictions for interpretability. Evaluated across more than ten diverse perception benchmarks, including CV-Bench, MMVP, RealWorldQA, MMStar, WorldMedQA, and HRBench, integrating COVT into strong VLMs such as Qwen2.5-VL and LLaVA consistently improves performance by 3% to 16% and demonstrates that compact continuous visual thinking enables more precise, grounded, and interpretable multimodal intelligence.

Retrieval-augmented generation (RAG) enhances large language models (LLMs) with external knowledge but still suffers from long contexts and disjoint retrieval-generation optimization. In this work, we propose CLaRa (Continuous Latent Reasoning), a unified framework that performs embedding-based compression and joint optimization in a shared continuous space. To obtain semantically rich and retrievable compressed vectors, we introduce SCP, a key-preserving data synthesis framework using QA and paraphrase supervision. CLaRa then trains the reranker and generator end-to-end via a single language modeling loss, with gradients flowing through both modules using a differentiable top-k estimator. Theoretically, this unified optimization aligns retrieval relevance with answer quality. Experiments across multiple QA benchmarks show that CLaRa achieves state-of-the-art compression and reranking performance, often surpassing text-based fine-tuned baselines.

Multi-agent systems (MAS) extend large language models (LLMs) from independent single-model reasoning to coordinative system-level intelligence. While existing LLM agents depend on text-based mediation for reasoning and communication, we take a step forward by enabling models to collaborate directly within the continuous latent space. We introduce LatentMAS, an end-to-end training-free framework that enables pure latent collaboration among LLM agents. In LatentMAS, each agent first performs auto-regressive latent thoughts generation through last-layer hidden embeddings. A shared latent working memory then preserves and transfers each agent's internal representations, ensuring lossless information exchange. We provide theoretical analyses establishing that LatentMAS attains higher expressiveness and lossless information preservation with substantially lower complexity than vanilla text-based MAS. In addition, empirical evaluations across 9 comprehensive benchmarks spanning math and science reasoning, commonsense understanding, and code generation show that LatentMAS consistently outperforms strong single-model and text-based MAS baselines, achieving up to 14.6% higher accuracy, reducing output token usage by 70.8%-83.7%, and providing 4x-4.3x faster end-to-end inference. These results demonstrate that our new latent collaboration framework enhances system-level reasoning quality while offering substantial efficiency gains without any additional training. Code and data are fully open-sourced at https://github.com/Gen-Verse/LatentMAS.

Human cognition naturally engages with abstract and fluid concepts, whereas existing reasoning models often rely on generating discrete tokens, potentially constraining their expressive capabilities. Recent advancements aim to address this limitation by enabling large language models (LLMs) to generate soft, abstract tokens, thus facilitating reasoning within a continuous concept space. This paper explores the `Soft Thinking' capabilities of various LLMs by examining the models' internal behavior using a suite of probing techniques. Contrary to the common belief that Soft Thinking enables the simultaneous exploration of diverse reasoning paths, our findings reveal that LLMs predominantly rely on the most influential component of the soft inputs during subsequent decoding steps. This reliance hinders the exploration of different reasoning paths and reduces vanilla Soft Thinking to a form of greedy decoding, obscuring the advantage of transmitting more information through Soft Tokens. To tackle this issue, we explore sampling strategies to introduce randomness, employing methods such as Dirichlet resampling and the Gumbel-Softmax trick. Our experiments demonstrate that incorporating randomness can alleviate the limitations of vanilla approaches and unleash the potential of Soft Thinking. Notably, the Gumbel-Softmax trick provides adequate randomness with controlled smoothness, resulting in superior performance across eight reasoning benchmarks.

Chain-of-thought reasoning has significantly improved the performance of Large Language Models (LLMs) across various domains. However, this reasoning process has been confined exclusively to textual space, limiting its effectiveness in visually intensive tasks. To address this limitation, we introduce the concept of reasoning in the pixel-space. Within this novel framework, Vision-Language Models (VLMs) are equipped with a suite of visual reasoning operations, such as zoom-in and select-frame. These operations enable VLMs to directly inspect, interrogate, and infer from visual evidences, thereby enhancing reasoning fidelity for visual tasks. Cultivating such pixel-space reasoning capabilities in VLMs presents notable challenges, including the model's initially imbalanced competence and its reluctance to adopt the newly introduced pixel-space operations. We address these challenges through a two-phase training approach. The first phase employs instruction tuning on synthesized reasoning traces to familiarize the model with the novel visual operations. Following this, a reinforcement learning (RL) phase leverages a curiosity-driven reward scheme to balance exploration between pixel-space reasoning and textual reasoning. With these visual operations, VLMs can interact with complex visual inputs, such as information-rich images or videos to proactively gather necessary information. We demonstrate that this approach significantly improves VLM performance across diverse visual reasoning benchmarks. Our 7B model, \model, achieves 84\% on V* bench, 74\% on TallyQA-Complex, and 84\% on InfographicsVQA, marking the highest accuracy achieved by any open-source model to date. These results highlight the importance of pixel-space reasoning and the effectiveness of our framework.

Self-improving systems require environmental interaction for continuous adaptation. We introduce SPICE (Self-Play In Corpus Environments), a reinforcement learning framework where a single model acts in two roles: a Challenger that mines documents from a large corpus to generate diverse reasoning tasks, and a Reasoner that solves them. Through adversarial dynamics, the Challenger creates an automatic curriculum at the frontier of the Reasoner's capability, while corpus grounding provides the rich, near-inexhaustible external signal necessary for sustained improvement. Unlike existing ungrounded self-play methods that offer more limited benefits, SPICE achieves consistent gains across mathematical (+8.9%) and general reasoning (+9.8%) benchmarks on multiple model families. Our analysis reveals how document grounding is a key ingredient in SPICE to continuously generate its own increasingly challenging goals and achieve them, enabling sustained self-improvement.

Large multimodal models exhibit remarkable intelligence, yet their embodied cognitive abilities during motion in open-ended urban 3D space remain to be explored. We introduce a benchmark to evaluate whether video-large language models (Video-LLMs) can naturally process continuous first-person visual observations like humans, enabling recall, perception, reasoning, and navigation. We have manually control drones to collect 3D embodied motion video data from real-world cities and simulated environments, resulting in 1.5k video clips. Then we design a pipeline to generate 5.2k multiple-choice questions. Evaluations of 17 widely-used Video-LLMs reveal current limitations in urban embodied cognition. Correlation analysis provides insight into the relationships between different tasks, showing that causal reasoning has a strong correlation with recall, perception, and navigation, while the abilities for counterfactual and associative reasoning exhibit lower correlation with other tasks. We also validate the potential for Sim-to-Real transfer in urban embodiment through fine-tuning.

Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of probability theory. Programs may use both higher-order functions and continuous distributions, or even define a probability distribution on functions. But standard probability theory does not handle higher-order functions well: the category of measurable spaces is not cartesian closed. Here we introduce quasi-Borel spaces. We show that these spaces: form a new formalization of probability theory replacing measurable spaces; form a cartesian closed category and so support higher-order functions; form a well-pointed category and so support good proof principles for equational reasoning; and support continuous probability distributions. We demonstrate the use of quasi-Borel spaces for higher-order functions and probability by: showing that a well-known construction of probability theory involving random functions gains a cleaner expression; and generalizing de Finetti's theorem, that is a crucial theorem in probability theory, to quasi-Borel spaces.

Humans possess spatial reasoning abilities that enable them to understand spaces through multimodal observations, such as vision and sound. Large multimodal reasoning models extend these abilities by learning to perceive and reason, showing promising performance across diverse spatial tasks. However, systematic reviews and publicly available benchmarks for these models remain limited. In this survey, we provide a comprehensive review of multimodal spatial reasoning tasks with large models, categorizing recent progress in multimodal large language models (MLLMs) and introducing open benchmarks for evaluation. We begin by outlining general spatial reasoning, focusing on post-training techniques, explainability, and architecture. Beyond classical 2D tasks, we examine spatial relationship reasoning, scene and layout understanding, as well as visual question answering and grounding in 3D space. We also review advances in embodied AI, including vision-language navigation and action models. Additionally, we consider emerging modalities such as audio and egocentric video, which contribute to novel spatial understanding through new sensors. We believe this survey establishes a solid foundation and offers insights into the growing field of multimodal spatial reasoning. Updated information about this survey, codes and implementation of the open benchmarks can be found at https://github.com/zhengxuJosh/Awesome-Spatial-Reasoning.

We study how large language models (LLMs) ``think'' through their representation space. We propose a novel geometric framework that models an LLM's reasoning as flows -- embedding trajectories evolving where logic goes. We disentangle logical structure from semantics by employing the same natural deduction propositions with varied semantic carriers, allowing us to test whether LLMs internalize logic beyond surface form. This perspective connects reasoning with geometric quantities such as position, velocity, and curvature, enabling formal analysis in representation and concept spaces. Our theory establishes: (1) LLM reasoning corresponds to smooth flows in representation space, and (2) logical statements act as local controllers of these flows' velocities. Using learned representation proxies, we design controlled experiments to visualize and quantify reasoning flows, providing empirical validation of our theoretical framework. Our work serves as both a conceptual foundation and practical tools for studying reasoning phenomenon, offering a new lens for interpretability and formal analysis of LLMs' behavior.

Exploiting large language models (LLMs) to tackle deductive reasoning has garnered growing attention. It still remains highly challenging to achieve satisfactory results in complex deductive problems, characterized by plenty of premises (i.e., facts or rules) entailing intricate relationships among entities and requiring multi-hop reasoning. One intuitive solution is to decompose the original task into smaller sub-tasks, and then chain the multiple casual reasoning steps together in a forward (e.g., Selection-Inference) or backward (e.g., LAMBADA) direction. However, these techniques inevitably necessitate a large number of overall stages, leading to computationally expensive operations and a higher possibility of making misleading steps. In addition to stage-by-stage decomposition, we draw inspiration from another aspect of human problem-solving. Humans tend to distill the most relevant information and organize their thoughts systematically (e.g., creating mind maps), which assists them in answering questions or drawing conclusions precisely and quickly. In light of this, we propose a novel reasoning approach named Concise and Organized Perception (COP). COP carefully analyzes the given statements to efficiently identify the most pertinent information while eliminating redundancy. It then prompts the LLMs in a more organized form that adapts to the model's inference process. By perceiving concise and organized proofs, the deductive reasoning abilities of LLMs can be better elicited, and the risk of acquiring errors caused by excessive reasoning stages is mitigated. Furthermore, our approach can be combined with the aforementioned ones to further boost their performance. Extensive experimental results on three popular deductive benchmarks (i.e., ProofWriter, PrOntoQA and PrOntoQA-OOD) show that COP significantly outperforms previous state-of-the-art methods.

With the current surge in spatial reasoning explorations, researchers have made significant progress in understanding indoor scenes, but still struggle with diverse applications such as robotics and autonomous driving. This paper aims to advance all-scale spatial reasoning across diverse scenarios by tackling two key challenges: 1) the heavy reliance on indoor 3D scans and labor-intensive manual annotations for dataset curation; 2) the absence of effective all-scale scene modeling, which often leads to overfitting to individual scenes. In this paper, we introduce a holistic solution that integrates a structured spatial reasoning knowledge system, scale-aware modeling, and a progressive training paradigm, as the first attempt to broaden the all-scale spatial intelligence of MLLMs to the best of our knowledge. Using a task-specific, specialist-driven automated pipeline, we curate over 38K video scenes across 5 spatial scales to create SpaceVista-1M, a dataset comprising approximately 1M spatial QA pairs spanning 19 diverse task types. While specialist models can inject useful domain knowledge, they are not reliable for evaluation. We then build an all-scale benchmark with precise annotations by manually recording, retrieving, and assembling video-based data. However, naive training with SpaceVista-1M often yields suboptimal results due to the potential knowledge conflict. Accordingly, we introduce SpaceVista-7B, a spatial reasoning model that accepts dense inputs beyond semantics and uses scale as an anchor for scale-aware experts and progressive rewards. Finally, extensive evaluations across 5 benchmarks, including our SpaceVista-Bench, demonstrate competitive performance, showcasing strong generalization across all scales and scenarios. Our dataset, model, and benchmark will be released on https://peiwensun2000.github.io/mm2km .

Visual reasoning is challenging, requiring both precise object grounding and understanding complex spatial relationships. Existing methods fall into two camps: language-only chain-of-thought approaches, which demand large-scale (image, query, answer) supervision, and program-synthesis approaches which use pre-trained models and avoid training, but suffer from flawed logic and erroneous grounding. We propose an annotation-free training framework that improves both reasoning and grounding. Our framework uses AI-powered verifiers: an LLM verifier refines LLM reasoning via reinforcement learning, while a VLM verifier strengthens visual grounding through automated hard-negative mining, eliminating the need for ground truth labels. This design combines the strengths of modern AI systems: advanced language-only reasoning models for decomposing spatial queries into simpler subtasks, and strong vision specialist models improved via performant VLM critics. We evaluate our approach across diverse spatial reasoning tasks, and show that our method improves visual reasoning and surpasses open-source and proprietary models, while with our improved visual grounding model we further outperform recent text-only visual reasoning methods. Project webpage: https://glab-caltech.github.io/valor/

The use of continuous instead of discrete tokens during the Chain-of-Thought (CoT) phase of reasoning LLMs has garnered attention recently, based on the intuition that a continuous mixture of discrete tokens could simulate a superposition of several reasoning paths simultaneously. Theoretical results have formally proven that continuous tokens have much greater expressivity and can solve specific problems more efficiently. However, practical use of continuous tokens has been limited by strong training difficulties: previous works either just use continuous tokens at inference time on a pre-trained discrete-token model, or must distill the continuous CoT from ground-truth discrete CoTs and face computational costs that limit the CoT to very few tokens. This is the first work introducing a scalable method to learn continuous CoTs via reinforcement learning (RL), without distilling from reference discrete CoTs. We use "soft" tokens: mixtures of tokens together with noise on the input embedding to provide RL exploration. Computational overhead is minimal, enabling us to learn continuous CoTs with hundreds of tokens. On math reasoning benchmarks with Llama and Qwen models up to 8B, training with continuous CoTs match discrete-token CoTs for pass@1 and surpass them for pass@32, showing greater CoT diversity. In systematic comparisons, the best-performing scenario is to train with continuous CoT tokens then use discrete tokens for inference, meaning the "soft" models can be deployed in a standard way. Finally, we show continuous CoT RL training better preserves the predictions of the base model on out-of-domain tasks, thus providing a softer touch to the base model.

Reasoning about motion and space is a fundamental cognitive capability that is required by multiple real-world applications. While many studies highlight that large multimodal language models (MLMs) struggle to reason about space, they only focus on static spatial relationships, and not dynamic awareness of motion and space, i.e., reasoning about the effect of egocentric and object motions on spatial relationships. Manually annotating such object and camera movements is expensive. Hence, we introduce SAT, a simulated spatial aptitude training dataset comprising both static and dynamic spatial reasoning across 175K question-answer (QA) pairs and 20K scenes. Complementing this, we also construct a small (150 image-QAs) yet challenging dynamic spatial test set using real-world images. Leveraging our SAT datasets and 6 existing static spatial benchmarks, we systematically investigate what improves both static and dynamic spatial awareness. Our results reveal that simulations are surprisingly effective at imparting spatial aptitude to MLMs that translate to real images. We show that perfect annotations in simulation are more effective than existing approaches of pseudo-annotating real images. For instance, SAT training improves a LLaVA-13B model by an average 11% and a LLaVA-Video-7B model by an average 8% on multiple spatial benchmarks, including our real-image dynamic test set and spatial reasoning on long videos -- even outperforming some large proprietary models. While reasoning over static relationships improves with synthetic training data, there is still considerable room for improvement for dynamic reasoning questions.

Reasoning requires going beyond pattern matching or memorization of solutions to identify and implement "algorithmic procedures" that can be used to deduce answers to hard problems. Doing so requires realizing the most relevant primitives, intermediate results, or shared procedures, and building upon them. While RL post-training on long chains of thought ultimately aims to uncover this kind of algorithmic behavior, most reasoning traces learned by large models fail to consistently capture or reuse procedures, instead drifting into verbose and degenerate exploration. To address more effective reasoning, we introduce reasoning abstractions: concise natural language descriptions of procedural and factual knowledge that guide the model toward learning successful reasoning. We train models to be capable of proposing multiple abstractions given a problem, followed by RL that incentivizes building a solution while using the information provided by these abstractions. This results in a two-player RL training paradigm, abbreviated as RLAD, that jointly trains an abstraction generator and a solution generator. This setup effectively enables structured exploration, decouples learning signals of abstraction proposal and solution generation, and improves generalization to harder problems. We also show that allocating more test-time compute to generating abstractions is more beneficial for performance than generating more solutions at large test budgets, illustrating the role of abstractions in guiding meaningful exploration.

Large language models have shown impressive results for multi-hop mathematical reasoning when the input question is only textual. Many mathematical reasoning problems, however, contain both text and image. With the ever-increasing adoption of vision language models (VLMs), understanding their reasoning abilities for such problems is crucial. In this paper, we evaluate the reasoning capabilities of VLMs along various axes through the lens of geometry problems. We procedurally create a synthetic dataset of geometry questions with controllable difficulty levels along multiple axes, thus enabling a systematic evaluation. The empirical results obtained using our benchmark for state-of-the-art VLMs indicate that these models are not as capable in subjects like geometry (and, by generalization, other topics requiring similar reasoning) as suggested by previous benchmarks. This is made especially clear by the construction of our benchmark at various depth levels, since solving higher-depth problems requires long chains of reasoning rather than additional memorized knowledge. We release the dataset for further research in this area.

Spatial reasoning plays a vital role in both human cognition and machine intelligence, prompting new research into language models' (LMs) capabilities in this regard. However, existing benchmarks reveal shortcomings in evaluating qualitative spatial reasoning (QSR). These benchmarks typically present oversimplified scenarios or unclear natural language descriptions, hindering effective evaluation. We present a novel benchmark for assessing QSR in LMs, which is grounded in realistic 3D simulation data, offering a series of diverse room layouts with various objects and their spatial relationships. This approach provides a more detailed and context-rich narrative for spatial reasoning evaluation, diverging from traditional, toy-task-oriented scenarios. Our benchmark encompasses a broad spectrum of qualitative spatial relationships, including topological, directional, and distance relations. These are presented with different viewing points, varied granularities, and density of relation constraints to mimic real-world complexities. A key contribution is our logic-based consistency-checking tool, which enables the assessment of multiple plausible solutions, aligning with real-world scenarios where spatial relationships are often open to interpretation. Our benchmark evaluation of advanced LMs reveals their strengths and limitations in spatial reasoning. They face difficulties with multi-hop spatial reasoning and interpreting a mix of different view descriptions, pointing to areas for future improvement.

Reasoning models have demonstrated remarkable progress in solving complex and logic-intensive tasks by generating extended Chain-of-Thoughts (CoTs) prior to arriving at a final answer. Yet, the emergence of this "slow-thinking" paradigm, with numerous tokens generated in sequence, inevitably introduces substantial computational overhead. To this end, it highlights an urgent need for effective acceleration. This survey aims to provide a comprehensive overview of recent advances in efficient reasoning. It categorizes existing works into three key directions: (1) shorter - compressing lengthy CoTs into concise yet effective reasoning chains; (2) smaller - developing compact language models with strong reasoning capabilities through techniques such as knowledge distillation, other model compression techniques, and reinforcement learning; and (3) faster - designing efficient decoding strategies to accelerate inference. A curated collection of papers discussed in this survey is available in our GitHub repository.

Vision Language Models (VLMs) exhibit a fundamental semantic-to-geometric gap in spatial reasoning: they excel at qualitative semantic inference but their reasoning operates within a lossy semantic space, misaligned with high-fidelity geometry. Current paradigms fail to bridge this gap. Training-based methods suffer from an ``oracle paradox,'' learning flawed spatial logic from imperfect oracles. Tool-integrated methods constrain the final computation but critically leave the VLM's planning process unconstrained, resulting in geometrically flawed plans. In this work, we propose Geometrically-Constrained Agent (GCA), a training-free agentic paradigm that resolves this gap by introducing a formal task constraint. Specifically, we strategically decouples the VLM's role into two stages. First, acting as a semantic analyst, the VLM translates the user's ambiguous query into the formal, verifiable task constraint, which defines the reference frame and objective. Second, acting as a task solver, the VLM generates and executes tool calls strictly within the deterministic bounds defined by the constraint. This geometrically-constrained reasoning strategy successfully resolve the semantic-to-geometric gap, yielding a robust and verifiable reasoning pathway for spatial reasoning. Comprehensive experiments demonstrate that GCA achieves SOTA performance on multiple spatial reasoning benchmarks, surpassing existing training-based and tool-integrated methods by ~27%. Please see our homepage at https://gca-spatial-reasoning.github.io.

Spatial reasoning is a critical capability for intelligent robots, yet current vision-language models (VLMs) still fall short of human-level performance in video-based spatial reasoning. This gap mainly stems from two challenges: a semantic-geometric misalignment that prevents consistent 3D understanding, and the absence of persistent memory to retain 3D representation and understanding over time. To address these limitations, we present VLM^2, a Vision-Language Model with persistent Memory for spatial reasoning with a view-consistent, 3D-aware representation purely from 2D video. Specifically, to enhance long-horizon reasoning, we incorporate a dual-memory module, consisting of a working memory that operates as a sliding window to focus on immediate context, and an episodic memory that consolidates and stores critical long-term information. This design enables efficient and long-horizon spatial reasoning with a fixed computational cost. Extensive experiments on multiple benchmarks show that VLM^2 achieves state-of-the-art performance among video-only models, significantly advancing the frontier of visual-spatial intelligence.

As textual reasoning with large language models (LLMs) has advanced significantly, there has been growing interest in enhancing the multimodal reasoning capabilities of large vision-language models (LVLMs). However, existing methods primarily approach multimodal reasoning in a straightforward, text-centric manner, where both reasoning and answer derivation are conducted purely through text, with the only difference being the presence of multimodal input. As a result, these methods often encounter fundamental limitations in spatial reasoning tasks that demand precise geometric understanding and continuous spatial tracking-capabilities that humans achieve through mental visualization and manipulation. To address the limitations, we propose drawing to reason in space, a novel paradigm that enables LVLMs to reason through elementary drawing operations in the visual space. By equipping models with basic drawing operations, including annotating bounding boxes and drawing auxiliary lines, we empower them to express and analyze spatial relationships through direct visual manipulation, meanwhile avoiding the performance ceiling imposed by specialized perception tools in previous tool-integrated reasoning approaches. To cultivate this capability, we develop a three-stage training framework: cold-start training with synthetic data to establish basic drawing abilities, reflective rejection sampling to enhance self-reflection behaviors, and reinforcement learning to directly optimize for target rewards. Extensive experiments demonstrate that our model, named VILASR, consistently outperforms existing methods across diverse spatial reasoning benchmarks, involving maze navigation, static spatial reasoning, video-based reasoning, and multi-view-based reasoning tasks, with an average improvement of 18.4%.

Recently, slow-thinking reasoning systems, such as o1, have demonstrated remarkable capabilities in solving complex reasoning tasks. These systems typically engage in an extended thinking process before responding to a query, allowing them to generate more thorough, accurate, and well-reasoned solutions. These systems are primarily developed and maintained by industry, with their core techniques not publicly disclosed. In response, an increasing number of studies from the research community aim to explore the technical foundations underlying these powerful reasoning systems. Building on these prior efforts, this paper presents a reproduction report on implementing o1-like reasoning systems. We introduce an "imitate, explore, and self-improve" framework as our primary technical approach to train the reasoning model. In the initial phase, we use distilled long-form thought data to fine-tune the reasoning model, enabling it to invoke a slow-thinking mode. The model is then encouraged to explore challenging problems by generating multiple rollouts, which can result in increasingly more high-quality trajectories that lead to correct answers. Furthermore, the model undergoes self-improvement by iteratively refining its training dataset. To verify the effectiveness of this approach, we conduct extensive experiments on three challenging benchmarks. The experimental results demonstrate that our approach achieves competitive performance compared to industry-level reasoning systems on these benchmarks.

Deep iterative chain-of-thought (CoT) reasoning enables LLMs to tackle complex tasks by progressively activating relevant pre-trained knowledge. However, it faces challenges in ensuring continual improvement and determining a stopping criterion. In this paper, we investigate whether the relevant knowledge that contributes directly to solving the given question can be activated from the initial reasoning path, thus circumventing the need for iterative refinement. Our experiments reveal that increasing the diversity of initial reasoning paths can achieve comparable or superior performance, a concept we term breadth reasoning. However, existing breadth reasoning approaches, such as self-consistency, offer limited diversity. To address this limitation, we propose a simple yet effective method that enhances reasoning breadth by integrating contextual exploration with reduced sampling randomness. Extensive experiments demonstrate that our approach significantly outperforms deep iterative reasoning. Our code is provided in https://github.com/zongqianwu/breadth.

Remarkable progress has been made on automated reasoning with natural text, by using Language Models (LMs) and methods such as Chain-of-Thought and Selection-Inference. These techniques search for proofs in the forward direction from axioms to the conclusion, which suffers from a combinatorial explosion of the search space, and thus high failure rates for problems requiring longer chains of reasoning. The classical automated reasoning literature has shown that reasoning in the backward direction (i.e. from the intended conclusion to supporting axioms) is significantly more efficient at proof-finding. Importing this intuition into the LM setting, we develop a Backward Chaining algorithm, called LAMBADA, that decomposes reasoning into four sub-modules. These sub-modules are simply implemented by few-shot prompted LM inference. We show that LAMBADA achieves sizable accuracy boosts over state-of-the-art forward reasoning methods on challenging logical reasoning datasets, particularly when deep and accurate proof chains are required.

Spatial reasoning is a key aspect of cognitive psychology and remains a major bottleneck for current vision-language models (VLMs). While extensive research has aimed to evaluate or improve VLMs' understanding of basic spatial relations, such as distinguishing left from right, near from far, and object counting, these tasks represent only the most fundamental level of spatial reasoning. In this work, we introduce OmniSpatial, a comprehensive and challenging benchmark for spatial reasoning, grounded in cognitive psychology. OmniSpatial covers four major categories: dynamic reasoning, complex spatial logic, spatial interaction, and perspective-taking, with 50 fine-grained subcategories. Through Internet data crawling and careful manual annotation, we construct over 1.5K question-answer pairs. Extensive experiments show that both open- and closed-source VLMs, as well as existing reasoning and spatial understanding models, exhibit significant limitations in comprehensive spatial understanding. We further analyze failure cases and propose potential directions for future research.

This paper presents a novel framework for enhancing reasoning capabilities in large language models (LLMs) by leveraging iterative reasoning and feedback-driven methodologies. Building on the limitations identified in the SimpleBench benchmark, a dataset designed to evaluate logical coherence and real-world reasoning, we propose a multi-step prompting strategy coupled with global consistency checks to improve model accuracy and robustness. Through comparative analysis of state-of-the-art models, including Claude 3 Opus, Claude 3.5, GPT- 4o, and o1-preview, we demonstrate that iterative reasoning significantly enhances model performance, with improvements observed in both standard accuracy metrics (AVG@5) and a newly introduced metric, Extreme Averaging (EAG@5). Our results reveal model-specific strengths: Claude excels in maintaining logical consistency, while GPT-4o exhibits exploratory creativity but struggles with ambiguous prompts. By analyzing case studies and identifying gaps in spatial and temporal reasoning, we highlight areas for further refinement. The findings underscore the potential of structured reasoning frameworks to address inherent model limitations, irrespective of pretraining methodologies. This study lays the groundwork for integrating dynamic feedback mechanisms, adaptive restart strategies, and diverse evaluation metrics to advance LLM reasoning capabilities across complex and multi-domain problem spaces.

In this paper, we claim that 3D visual grounding is the cornerstone of spatial reasoning and introduce the Grounded-Spatial Reasoner (GS-Reasoner) to explore the effective spatial representations that bridge the gap between them. Existing 3D LLMs suffer from the absence of a unified 3D representation capable of jointly capturing semantic and geometric information. This deficiency is manifested either in poor performance on grounding or in an excessive reliance on external modules, ultimately hindering the seamless integration of grounding and spatial reasoning. To address this, we propose a simple yet effective dual-path pooling mechanism that tightly aligns geometric features with both semantic and positional cues, constructing a unified image patch-based 3D representation that encapsulates all essential information without increasing the number of input tokens. Leveraging this holistic representation, GS-Reasoner is the first 3D LLM that achieves autoregressive grounding entirely without external modules while delivering performance comparable to state-of-the-art models, establishing a unified and self-contained framework for 3D spatial reasoning. To further bridge grounding and spatial reasoning, we introduce the Grounded Chain-of-Thought (GCoT) dataset. This dataset is meticulously curated to include both 3D bounding box annotations for objects referenced in reasoning questions and step-by-step reasoning paths that integrate grounding as a core component of the problem-solving process. Extensive experiments demonstrate that GS-Reasoner achieves impressive results on 3D visual grounding, which in turn significantly enhances its spatial reasoning capabilities, leading to state-of-the-art performance.

We present a model inspired by the Global Workspace Theory that integrates specialized modules to perform a sequential reasoning task. A controller selectively routes information between modules through the workspace using a gating mechanism. This approach allows the model to chain operations by iteratively broadcasting information between specialized domains, mimicking System-2 reasoning. We evaluate the model's performance on a simple addition task, where two addends must be summed. The task can be solved by routing information sequentially through an Input module, an Increment module (multiple times), and finally an Output module. We consider two implementations of this system with increasing complexity. First, using hand-designed modules operating on one-hot digit representations, the controller (a LSTM recurrent network) learns to select the appropriate modules (input, increment, output) in the appropriate sequence. Second, we replace the hand-designed modules with learned representation modules for MNIST images and an increment module trained on the task objectives; here again, the controller learns the appropriate sequential module selection to solve the task. Finally, we show that the Global Workspace model, while having fewer parameters, outperforms LSTMs and Transformers when tested on unseen addition operations (both interpolations and extrapolations of addition operations seen during training). Our results highlight the potential of architectures inspired by the Global Workspace Theory to enhance deep learning's reasoning capabilities.

Large Language Reasoning Models have demonstrated remarkable success on static tasks, yet their application to multi-round agentic planning in interactive environments faces two fundamental challenges. First, the intractable credit assignment problem renders conventional reinforcement learning ineffective in sparse-reward settings. Second, the computational overhead of verbose, step-by-step reasoning histories is prohibitive. To address these challenges, we propose BPO, a three-stage framework (bootstrapping, extrapolation, and refinement) that establishes a self-improving data flywheel to develop robust reasoning models for long-horizon, sparse-reward environments. Our framework first bootstraps efficient reasoning using the proposed planning quaternions with long-short chain-of-thought fusion. It then extrapolates to out-of-distribution tasks through complexity-stratified curriculum learning. Finally, the model iteratively refines itself by learning exclusively on experiences selected via reward-gated rejection sampling. Experiments on ALFWorld, ScienceWorld, and WebShop demonstrate that our approach achieves state-of-the-art with significant token efficiency, providing a new recipe for reasoning models in agentic planning.

Recent advancements in Multimodal Large Language Models (MLLMs), particularly through Reinforcement Learning with Verifiable Rewards (RLVR), have significantly enhanced their reasoning abilities. However, a critical gap persists: these models struggle with dynamic spatial interactions, a capability essential for real-world applications. To bridge this gap, we introduce M2-Reasoning-7B, a model designed to excel in both general and spatial reasoning. Our approach integrates two key innovations: (1) a novel data pipeline that generates 294.2K high-quality data samples (168K for cold-start fine-tuning and 126.2K for RLVR), which feature logically coherent reasoning trajectories and have undergone comprehensive assessment; and (2) a dynamic multi-task training strategy with step-wise optimization to mitigate conflicts between data, and task-specific rewards for delivering tailored incentive signals. This combination of curated data and advanced training allows M2-Reasoning-7B to set a new state-of-the-art (SOTA) across 8 benchmarks, showcasing superior performance in both general and spatial reasoning domains.

While Chain-of-Thought (CoT) prompting enables sophisticated symbolic reasoning in LLMs, it remains confined to discrete text and cannot simulate the continuous, physics-governed dynamics of the real world. Recent video generation models have emerged as potential world simulators through Chain-of-Frames (CoF) reasoning -- materializing thought as frame-by-frame visual sequences, with each frame representing a physically-grounded reasoning step. Despite compelling demonstrations, a challenge persists: existing benchmarks, focusing on fidelity or alignment, do not assess CoF reasoning and thus cannot measure core cognitive abilities in multi-step planning, algorithmic logic, or abstract pattern extrapolation. This evaluation void prevents systematic understanding of model capabilities and principled guidance for improvement. We introduce Gen-ViRe (Generative Visual Reasoning Benchmark), a framework grounded in cognitive science and real-world AI applications, which decomposes CoF reasoning into six cognitive dimensions -- from perceptual logic to abstract planning -- and 24 subtasks. Through multi-source data curation, minimal prompting protocols, and hybrid VLM-assisted evaluation with detailed criteria, Gen-ViRe delivers the first quantitative assessment of video models as reasoners. Our experiments on SOTA systems reveal substantial discrepancies between impressive visual quality and actual reasoning depth, establishing baselines and diagnostic tools to advance genuine world simulators.

This paper proposes a question-answering (QA) benchmark for spatial reasoning on natural language text which contains more realistic spatial phenomena not covered by prior work and is challenging for state-of-the-art language models (LM). We propose a distant supervision method to improve on this task. Specifically, we design grammar and reasoning rules to automatically generate a spatial description of visual scenes and corresponding QA pairs. Experiments show that further pretraining LMs on these automatically generated data significantly improves LMs' capability on spatial understanding, which in turn helps to better solve two external datasets, bAbI, and boolQ. We hope that this work can foster investigations into more sophisticated models for spatial reasoning over text.

Spatial reasoning is a crucial component of both biological and artificial intelligence. In this work, we present a comprehensive study of the capability of current state-of-the-art large language models (LLMs) on spatial reasoning. To support our study, we created and contribute a novel Spatial Reasoning Characterization (SpaRC) framework and Spatial Reasoning Paths (SpaRP) datasets, to enable an in-depth understanding of the spatial relations and compositions as well as the usefulness of spatial reasoning chains. We found that all the state-of-the-art LLMs do not perform well on the datasets -- their performances are consistently low across different setups. The spatial reasoning capability improves substantially as model sizes scale up. Finetuning both large language models (e.g., Llama-2-70B) and smaller ones (e.g., Llama-2-13B) can significantly improve their F1-scores by 7--32 absolute points. We also found that the top proprietary LLMs still significantly outperform their open-source counterparts in topological spatial understanding and reasoning.

Large Language Models (LLMs) have achieved impressive performance on complex reasoning tasks with Chain-of-Thought (CoT) prompting. However, conventional CoT relies on reasoning steps explicitly verbalized in natural language, introducing inefficiencies and limiting its applicability to abstract reasoning. To address this, there has been growing research interest in latent CoT reasoning, where inference occurs within latent spaces. By decoupling reasoning from language, latent reasoning promises richer cognitive representations and more flexible, faster inference. Researchers have explored various directions in this promising field, including training methodologies, structural innovations, and internal reasoning mechanisms. This paper presents a comprehensive overview and analysis of this reasoning paradigm. We begin by proposing a unified taxonomy from four perspectives: token-wise strategies, internal mechanisms, analysis, and applications. We then provide in-depth discussions and comparative analyses of representative methods, highlighting their design patterns, strengths, and open challenges. We aim to provide a structured foundation for advancing this emerging direction in LLM reasoning. The relevant papers will be regularly updated at https://github.com/EIT-NLP/Awesome-Latent-CoT.

Spatial reasoning is a core aspect of human intelligence that allows perception, inference and planning in 3D environments. However, current vision-language models (VLMs) struggle to maintain geometric coherence and cross-view consistency for spatial reasoning in multi-view settings. We attribute this gap to the lack of fine-grained benchmarks that isolate multi-view reasoning from single-view perception and temporal factors. To address this, we present ReMindView-Bench, a cognitively grounded benchmark for evaluating how VLMs construct, align and maintain spatial mental models across complementary viewpoints. ReMindView-Bench systematically varies viewpoint spatial pattern and query type to probe key factors of spatial cognition. Evaluations of 15 current VLMs reveals consistent failures in cross-view alignment and perspective-taking in multi-view spatial reasoning, motivating deeper analysis on the reasoning process. Explicit phase-wise analysis using LLM-as-a-judge and self-consistency prompting shows that VLMs perform well on in-frame perception but degrade sharply when integrating information across views. Implicit analysis, including linear probing and entropy dynamics, further show progressive loss of task-relevant information and uncertainty separation between correct and incorrect trajectories. These results provide a cognitively grounded diagnosis of VLM spatial reasoning and reveal how multi-view spatial mental models are formed, degraded and destabilized across reasoning phases. The ReMindView-Bench benchmark is available at https://huggingface.co/datasets/Xue0823/ReMindView-Bench, and the source codes of benchmark construction and VLM reasoning analysis are available at https://github.com/pittisl/ReMindView-Bench.

Recent advances in Large Reasoning Models (LRMs) trained with Long Chain-of-Thought (Long CoT) reasoning have demonstrated remarkable cross-domain generalization capabilities. However, the underlying mechanisms supporting such transfer remain poorly understood. We hypothesize that cross-domain generalization arises from shared abstract reasoning prototypes -- fundamental reasoning patterns that capture the essence of problems across domains. These prototypes minimize the nuances of the representation, revealing that seemingly diverse tasks are grounded in shared reasoning structures.Based on this hypothesis, we propose ProtoReasoning, a framework that enhances the reasoning ability of LLMs by leveraging scalable and verifiable prototypical representations (Prolog for logical reasoning, PDDL for planning).ProtoReasoning features: (1) an automated prototype construction pipeline that transforms problems into corresponding prototype representations; (2) a comprehensive verification system providing reliable feedback through Prolog/PDDL interpreters; (3) the scalability to synthesize problems arbitrarily within prototype space while ensuring correctness. Extensive experiments show that ProtoReasoning achieves 4.7% improvement over baseline models on logical reasoning (Enigmata-Eval), 6.3% improvement on planning tasks, 4.0% improvement on general reasoning (MMLU) and 1.0% on mathematics (AIME24). Significantly, our ablation studies confirm that learning in prototype space also demonstrates enhanced generalization to structurally similar problems compared to training solely on natural language representations, validating our hypothesis that reasoning prototypes serve as the foundation for generalizable reasoning in large language models.

Recent reinforcement-learning frameworks for visual perception policy have begun to incorporate intermediate reasoning chains expressed in natural language. Empirical observations indicate that such purely linguistic intermediate reasoning often reduces performance on perception tasks. We argue that the core issue lies not in reasoning per se but in the form of reasoning: while these chains perform semantic reasoning in an unstructured linguistic space, visual perception requires reasoning in a spatial and object-centric space. In response, we introduce Artemis, a perception-policy learning framework that performs structured proposal-based reasoning, where each intermediate step is represented as a (label, bounding-box) pair capturing a verifiable visual state. This design enables explicit tracking of intermediate states, direct supervision for proposal quality, and avoids ambiguity introduced by language-based reasoning. Artemis is built on Qwen2.5-VL-3B, achieves strong performance on grounding and detection task and exhibits substantial generalization to counting and geometric-perception tasks. The consistent improvements across these diverse settings confirm that aligning reasoning with spatial representations enhances perception-policy learning. Owing to its strengthened visual reasoning, Artemis also achieves competitive performance on general MLLM benchmarks, illustrating that spatially grounded reasoning provides a principled route toward scalable and general perception policies.

Given the intractably large size of the space of proofs, any model that is capable of general deductive reasoning must generalize to proofs of greater complexity. Recent studies have shown that large language models (LLMs) possess some abstract deductive reasoning ability given chain-of-thought prompts. However, they have primarily been tested on proofs using modus ponens or of a specific size, and from the same distribution as the in-context examples. To measure the general deductive reasoning ability of LLMs, we test on a broad set of deduction rules and measure their ability to generalize to more complex proofs from simpler demonstrations from multiple angles: depth-, width-, and compositional generalization. To facilitate systematic exploration, we construct a new synthetic and programmable reasoning dataset that enables control over deduction rules and proof complexity. Our experiments on four LLMs of various sizes and training objectives show that they are able to generalize to longer and compositional proofs. However, they require explicit demonstrations to produce hypothetical subproofs, specifically in proof by cases and proof by contradiction.

Spatial reasoning remains a critical yet underdeveloped capability in existing vision-language models (VLMs), especially for Spatial Visual Question Answering (Spatial VQA) tasks that require understanding relative positions, distances, and object configurations. Inspired by the R1 paradigm introduced in DeepSeek-R1, which enhances reasoning in language models through rule-based reinforcement learning (RL), we propose SVQA-R1, the first framework to extend R1-style training to spatial VQA. In particular, we introduce Spatial-GRPO, a novel group-wise RL strategy that constructs view-consistent rewards by perturbing spatial relations between objects, e.g., mirror flipping, thereby encouraging the model to develop a consistent and grounded understanding of space. Our model, SVQA-R1, not only achieves dramatically improved accuracy on spatial VQA benchmarks but also exhibits interpretable reasoning paths even without using supervised fine-tuning (SFT) data. Extensive experiments and visualization demonstrate the effectiveness of SVQA-R1 across multiple spatial reasoning benchmarks.

Time series reasoning treats time as a first-class axis and incorporates intermediate evidence directly into the answer. This survey defines the problem and organizes the literature by reasoning topology with three families: direct reasoning in one step, linear chain reasoning with explicit intermediates, and branch-structured reasoning that explores, revises, and aggregates. The topology is crossed with the main objectives of the field, including traditional time series analysis, explanation and understanding, causal inference and decision making, and time series generation, while a compact tag set spans these axes and captures decomposition and verification, ensembling, tool use, knowledge access, multimodality, agent loops, and LLM alignment regimes. Methods and systems are reviewed across domains, showing what each topology enables and where it breaks down in faithfulness or robustness, along with curated datasets, benchmarks, and resources that support study and deployment (https://github.com/blacksnail789521/Time-Series-Reasoning-Survey). Evaluation practices that keep evidence visible and temporally aligned are highlighted, and guidance is distilled on matching topology to uncertainty, grounding with observable artifacts, planning for shift and streaming, and treating cost and latency as design budgets. We emphasize that reasoning structures must balance capacity for grounding and self-correction against computational cost and reproducibility, while future progress will likely depend on benchmarks that tie reasoning quality to utility and on closed-loop testbeds that trade off cost and risk under shift-aware, streaming, and long-horizon settings. Taken together, these directions mark a shift from narrow accuracy toward reliability at scale, enabling systems that not only analyze but also understand, explain, and act on dynamic worlds with traceable evidence and credible outcomes.

Reasoning models such as OpenAI o3 and DeepSeek-R1 have demonstrated strong performance on reasoning-intensive tasks through extended Chain-of-Thought (CoT) prompting. While longer reasoning traces can facilitate a more thorough exploration of solution paths for complex problems, researchers have observed that these models often "overthink", leading to inefficient inference. In this paper, we introduce ShorterBetter, a simple yet effective reinforcement learning methed that enables reasoning language models to discover their own optimal CoT lengths without human intervention. By sampling multiple outputs per problem and defining the Sample Optimal Length (SOL) as the shortest correct response among all the outputs, our method dynamically guides the model toward optimal inference lengths. Applied to the DeepSeek-Distill-Qwen-1.5B model, ShorterBetter achieves up to an 80% reduction in output length on both in-domain and out-of-domain reasoning tasks while maintaining accuracy. Our analysis shows that overly long reasoning traces often reflect loss of reasoning direction, and thus suggests that the extended CoT produced by reasoning models is highly compressible.

Advanced reasoning in large language models has achieved remarkable performance on challenging tasks, but the prevailing long-context reasoning paradigm faces critical limitations: quadratic computational scaling with sequence length, reasoning constrained by maximum context boundaries, and performance degradation beyond pre-training context windows. Existing approaches primarily compress reasoning chains without addressing the fundamental scaling problem. To overcome these challenges, we introduce InftyThink, a paradigm that transforms monolithic reasoning into an iterative process with intermediate summarization. By interleaving short reasoning segments with concise progress summaries, our approach enables unbounded reasoning depth while maintaining bounded computational costs. This creates a characteristic sawtooth memory pattern that significantly reduces computational complexity compared to traditional approaches. Furthermore, we develop a methodology for reconstructing long-context reasoning datasets into our iterative format, transforming OpenR1-Math into 333K training instances. Experiments across multiple model architectures demonstrate that our approach reduces computational costs while improving performance, with Qwen2.5-Math-7B showing 3-13% improvements across MATH500, AIME24, and GPQA_diamond benchmarks. Our work challenges the assumed trade-off between reasoning depth and computational efficiency, providing a more scalable approach to complex reasoning without architectural modifications.

Mixture-of-Experts (MoE) architectures within Large Reasoning Models (LRMs) have achieved impressive reasoning capabilities by selectively activating experts to facilitate structured cognitive processes. Despite notable advances, existing reasoning models often suffer from cognitive inefficiencies like overthinking and underthinking. To address these limitations, we introduce a novel inference-time steering methodology called Reinforcing Cognitive Experts (RICE), designed to improve reasoning performance without additional training or complex heuristics. Leveraging normalized Pointwise Mutual Information (nPMI), we systematically identify specialized experts, termed ''cognitive experts'' that orchestrate meta-level reasoning operations characterized by tokens like ''<think>''. Empirical evaluations with leading MoE-based LRMs (DeepSeek-R1 and Qwen3-235B) on rigorous quantitative and scientific reasoning benchmarks demonstrate noticeable and consistent improvements in reasoning accuracy, cognitive efficiency, and cross-domain generalization. Crucially, our lightweight approach substantially outperforms prevalent reasoning-steering techniques, such as prompt design and decoding constraints, while preserving the model's general instruction-following skills. These results highlight reinforcing cognitive experts as a promising, practical, and interpretable direction to enhance cognitive efficiency within advanced reasoning models.

Large Language Models (LLMs) have demonstrated impressive reasoning abilities through test-time computation (TTC) techniques such as chain-of-thought prompting and tree-based reasoning. However, we argue that current reasoning LLMs (RLLMs) lack the ability to systematically explore the solution space. This paper formalizes what constitutes systematic problem solving and identifies common failure modes that reveal reasoning LLMs to be wanderers rather than systematic explorers. Through qualitative and quantitative analysis across multiple state-of-the-art LLMs, we uncover persistent issues: invalid reasoning steps, redundant explorations, hallucinated or unfaithful conclusions, and so on. Our findings suggest that current models' performance can appear to be competent on simple tasks yet degrade sharply as complexity increases. Based on the findings, we advocate for new metrics and tools that evaluate not just final outputs but the structure of the reasoning process itself.

Large vision language models exhibit notable limitations on Geometry Problem Solving (GPS) because of their unreliable diagram interpretation and pure natural-language reasoning. A recent line of work mitigates this by using symbolic solvers: the model directly generates a formal program that a geometry solver can execute. However, this direct program generation lacks intermediate reasoning, making the decision process opaque and prone to errors. In this work, we explore a new approach that integrates Chain-of-Thought (CoT) with formal language. The model interleaves natural language reasoning with incremental emission of solver-executable code, producing a hybrid reasoning trace in which critical derivations are expressed in formal language. To teach this behavior at scale, we combine (1) supervised fine-tuning on an 11K newly developed synthetic dataset with interleaved natural language reasoning and automatic formalization, and (2) solver-in-the-loop reinforcement learning that jointly optimizes both the CoT narrative and the resulting program through outcome-based rewards. Built on Qwen2.5-VL-7B, our new model, named GF-Reasoner, achieves up to 15% accuracy improvements on standard GPS benchmarks, surpassing both 7B-scale peers and the much larger model Qwen2.5-VL-72B. By exploiting high-order geometric knowledge and offloading symbolic computation to the solver, the generated reasoning traces are noticeably shorter and cleaner. Furthermore, we present a comprehensive analysis of method design choices (e.g., reasoning paradigms, data synthesis, training epochs, etc.), providing actionable insights for future research.

With the emergence of advanced reasoning models like OpenAI o3 and DeepSeek-R1, large language models (LLMs) have demonstrated remarkable reasoning capabilities. However, their ability to perform rigorous logical reasoning remains an open question. This survey synthesizes recent advancements in logical reasoning within LLMs, a critical area of AI research. It outlines the scope of logical reasoning in LLMs, its theoretical foundations, and the benchmarks used to evaluate reasoning proficiency. We analyze existing capabilities across different reasoning paradigms - deductive, inductive, abductive, and analogical - and assess strategies to enhance reasoning performance, including data-centric tuning, reinforcement learning, decoding strategies, and neuro-symbolic approaches. The review concludes with future directions, emphasizing the need for further exploration to strengthen logical reasoning in AI systems.

Inspired by recent advancements in LLM reasoning, the field of multimodal reasoning has seen remarkable progress, achieving significant performance gains on intricate tasks such as mathematical problem-solving. Despite this progress, current multimodal large reasoning models exhibit two key limitations. They tend to employ computationally expensive reasoning even for simple queries, leading to inefficiency. Furthermore, this focus on specialized reasoning often impairs their broader, more general understanding capabilities. In this paper, we propose Metis-HOME: a Hybrid Optimized Mixture-of-Experts framework designed to address this trade-off. Metis-HOME enables a ''Hybrid Thinking'' paradigm by structuring the original dense model into two distinct expert branches: a thinking branch tailored for complex, multi-step reasoning, and a non-thinking branch optimized for rapid, direct inference on tasks like general VQA and OCR. A lightweight, trainable router dynamically allocates queries to the most suitable expert. We instantiate Metis-HOME by adapting the Qwen2.5-VL-7B into an MoE architecture. Comprehensive evaluations reveal that our approach not only substantially enhances complex reasoning abilities but also improves the model's general capabilities, reversing the degradation trend observed in other reasoning-specialized models. Our work establishes a new paradigm for building powerful and versatile MLLMs, effectively resolving the prevalent reasoning-vs-generalization dilemma.

Recent advancements in reasoning with large language models (RLLMs), such as OpenAI-O1 and DeepSeek-R1, have demonstrated their impressive capabilities in complex domains like mathematics and coding. A central factor in their success lies in the application of long chain-of-thought (Long CoT) characteristics, which enhance reasoning abilities and enable the solution of intricate problems. However, despite these developments, a comprehensive survey on Long CoT is still lacking, limiting our understanding of its distinctions from traditional short chain-of-thought (Short CoT) and complicating ongoing debates on issues like "overthinking" and "test-time scaling." This survey seeks to fill this gap by offering a unified perspective on Long CoT. (1) We first distinguish Long CoT from Short CoT and introduce a novel taxonomy to categorize current reasoning paradigms. (2) Next, we explore the key characteristics of Long CoT: deep reasoning, extensive exploration, and feasible reflection, which enable models to handle more complex tasks and produce more efficient, coherent outcomes compared to the shallower Short CoT. (3) We then investigate key phenomena such as the emergence of Long CoT with these characteristics, including overthinking, and test-time scaling, offering insights into how these processes manifest in practice. (4) Finally, we identify significant research gaps and highlight promising future directions, including the integration of multi-modal reasoning, efficiency improvements, and enhanced knowledge frameworks. By providing a structured overview, this survey aims to inspire future research and further the development of logical reasoning in artificial intelligence.

Spatial reasoning remains a fundamental challenge for Vision-Language Models (VLMs), with current approaches struggling to achieve robust performance despite recent advances. We identify that this limitation stems from a critical gap: existing methods attempt to learn spatial reasoning directly without establishing the hierarchical foundations of perception and understanding. To address this challenge, we present a comprehensive methodology for building spatial intelligence progressively. We introduce SpatialLadder-26k, a multimodal dataset containing 26,610 samples spanning object localization, single image, multi-view, and video spatial reasoning tasks, constructed through a standardized pipeline that ensures systematic coverage across modalities. Building on this dataset, we design a three-stage progressive training framework that (1) establishes spatial perception through object localization, (2) develops spatial understanding through multi-dimensional spatial tasks, and (3) strengthens complex reasoning via reinforcement learning with verifiable rewards. This approach yields SpatialLadder, a 3B-parameter model that achieves state-of-the-art performance on spatial reasoning benchmarks, with 23.4% average improvement over the base model, surpassing GPT-4o by 20.8% and Gemini-2.0-Flash by 10.1%. Notably, SpatialLadder maintains strong generalization with 7.2% improvement on out-of-domain benchmarks, demonstrating that progressive training from perception to reasoning is essential for robust spatial intelligence.

Spatial reasoning is an essential problem in embodied AI research. Efforts to enhance spatial reasoning abilities through supplementary spatial data and fine-tuning have proven limited and ineffective when addressing complex embodied tasks, largely due to their dependence on language-based outputs. While some approaches have introduced a point-based action space to mitigate this issue, they fall short in managing more intricate tasks within complex environments. This deficiency arises from their failure to fully exploit the inherent thinking and reasoning capabilities that are fundamental strengths of Vision-Language Models (VLMs). To address these limitations, we propose a novel approach named SpatialCoT, specifically designed to bolster the spatial reasoning capabilities of VLMs. Our approach comprises two stages: spatial coordinate bi-directional alignment, which aligns vision-language inputs with spatial coordinates, and chain-of-thought spatial grounding, which harnesses the reasoning capabilities of language models for advanced spatial reasoning. We evaluate SpatialCoT on challenging navigation and manipulation tasks, both in simulation and real-world settings. Experimental results demonstrate that our method significantly outperforms previous state-of-the-art approaches in both tasks.

Recent advances in visual reasoning (VR), particularly with the aid of Large Vision-Language Models (VLMs), show promise but require access to large-scale datasets and face challenges such as high computational costs and limited generalization capabilities. Compositional visual reasoning approaches have emerged as effective strategies; however, they heavily rely on the commonsense knowledge encoded in Large Language Models (LLMs) to perform planning, reasoning, or both, without considering the effect of their decisions on the visual reasoning process, which can lead to errors or failed procedures. To address these challenges, we introduce HYDRA, a multi-stage dynamic compositional visual reasoning framework designed for reliable and incrementally progressive general reasoning. HYDRA integrates three essential modules: a planner, a Reinforcement Learning (RL) agent serving as a cognitive controller, and a reasoner. The planner and reasoner modules utilize an LLM to generate instruction samples and executable code from the selected instruction, respectively, while the RL agent dynamically interacts with these modules, making high-level decisions on selection of the best instruction sample given information from the historical state stored through a feedback loop. This adaptable design enables HYDRA to adjust its actions based on previous feedback received during the reasoning process, leading to more reliable reasoning outputs and ultimately enhancing its overall effectiveness. Our framework demonstrates state-of-the-art performance in various VR tasks on four different widely-used datasets.

Vision language models (VLMs) have demonstrated impressive performance across a wide range of downstream tasks. However, their proficiency in spatial reasoning remains limited, despite its crucial role in tasks involving navigation and interaction with physical environments. Specifically, most of these tasks rely on the core spatial reasoning capabilities in two-dimensional (2D) environments, and our evaluation reveals that state-of-the-art VLMs frequently generate implausible and incorrect responses to composite spatial reasoning problems, including simple pathfinding tasks that humans can solve effortlessly at a glance. To address this, we explore an effective approach to enhance 2D spatial reasoning within VLMs by training the model solely on basic spatial capabilities. We begin by disentangling the key components of 2D spatial reasoning: direction comprehension, distance estimation, and localization. Our central hypothesis is that mastering these basic spatial capabilities can significantly enhance a model's performance on composite spatial tasks requiring advanced spatial understanding and combinatorial problem-solving, with generalized improvements in visual-spatial tasks. To investigate this hypothesis, we introduce Sparkle, a framework that fine-tunes VLMs on these three basic spatial capabilities by synthetic data generation and targeted supervision to form an instruction dataset for each capability. Our experiments demonstrate that VLMs fine-tuned with Sparkle achieve significant performance gains, not only in the basic tasks themselves but also in generalizing to composite and out-of-distribution spatial reasoning tasks. These findings underscore the effectiveness of mastering basic spatial capabilities in enhancing composite spatial problem-solving, offering insights into systematic strategies for improving VLMs' spatial reasoning capabilities.

Although contemporary large language models (LMs) demonstrate impressive question-answering capabilities, their answers are typically the product of a single call to the model. This entails an unwelcome degree of opacity and compromises performance, especially on problems that are inherently multi-step. To address these limitations, we show how LMs can be made to perform faithful multi-step reasoning via a process whose causal structure mirrors the underlying logical structure of the problem. Our approach works by chaining together reasoning steps, where each step results from calls to two fine-tuned LMs, one for selection and one for inference, to produce a valid reasoning trace. Our method carries out a beam search through the space of reasoning traces to improve reasoning quality. We demonstrate the effectiveness of our model on multi-step logical deduction and scientific question-answering, showing that it outperforms baselines on final answer accuracy, and generates humanly interpretable reasoning traces whose validity can be checked by the user.

This study investigates the spatial reasoning capabilities of vision-language models (VLMs) through Chain-of-Thought (CoT) prompting and reinforcement learning. We begin by evaluating the impact of different prompting strategies and find that simple CoT formats, where the model generates a reasoning step before the answer, not only fail to help, but can even harm the model's original performance. In contrast, structured multi-stage prompting based on scene graphs (SceneGraph CoT) significantly improves spatial reasoning accuracy. Furthermore, to improve spatial reasoning ability, we fine-tune models using Group Relative Policy Optimization (GRPO) on the SAT dataset and evaluate their performance on CVBench. Compared to supervised fine-tuning (SFT), GRPO achieves higher accuracy on Pass@1 evaluations and demonstrates superior robustness under out-of-distribution (OOD) conditions. In particular, we find that SFT overfits to surface-level linguistic patterns and may degrade performance when test-time phrasing changes (e.g., from "closer to" to "farther from"). GRPO, on the other hand, generalizes more reliably and maintains stable performance under such shifts. Our findings provide insights into how reinforcement learning and structured prompting improve the spatial reasoning capabilities and generalization behavior of modern VLMs. All code is open source at: https://github.com/Yvonne511/spatial-vlm-investigator

Visual reasoning is dominated by end-to-end neural networks scaled to billions of model parameters and training examples. However, even the largest models struggle with compositional reasoning, generalization, fine-grained spatial and temporal reasoning, and counting. Visual reasoning with large language models (LLMs) as controllers can, in principle, address these limitations by decomposing the task and solving subtasks by orchestrating a set of (visual) tools. Recently, these models achieved great performance on tasks such as compositional visual question answering, visual grounding, and video temporal reasoning. Nevertheless, in their current form, these models heavily rely on human engineering of in-context examples in the prompt, which are often dataset- and task-specific and require significant labor by highly skilled programmers. In this work, we present a framework that mitigates these issues by introducing spatially and temporally abstract routines and by leveraging a small number of labeled examples to automatically generate in-context examples, thereby avoiding human-created in-context examples. On a number of visual reasoning tasks, we show that our framework leads to consistent gains in performance, makes LLMs as controllers setup more robust, and removes the need for human engineering of in-context examples.

We endow Large Language Models (LLMs) with fine-grained self-evaluation to refine multi-step reasoning inference. We propose an effective prompting approach that integrates self-evaluation guidance through stochastic beam search. Our approach explores the reasoning search space using a well-calibrated automatic criterion. This enables an efficient search to produce higher-quality final predictions. With the self-evaluation guided stochastic beam search, we also balance the quality-diversity trade-off in the generation of reasoning chains. This allows our approach to adapt well with majority voting and surpass the corresponding Codex-backboned baselines by 6.34%, 9.56%, and 5.46% on the GSM8K, AQuA, and StrategyQA benchmarks, respectively, in few-shot accuracy. Analysis of our decompositional reasoning finds it pinpoints logic failures and leads to higher consistency and robustness. Our code is publicly available at https://github.com/YuxiXie/SelfEval-Guided-Decoding.

Human processes video reasoning in a sequential spatio-temporal reasoning logic, we first identify the relevant frames ("when") and then analyse the spatial relationships ("where") between key objects, and finally leverage these relationships to draw inferences ("what"). However, can Video Large Language Models (Video-LLMs) also "reason through a sequential spatio-temporal logic" in videos? Existing Video-LLM benchmarks primarily focus on assessing object presence, neglecting relational reasoning. Consequently, it is difficult to measure whether a model truly comprehends object interactions (actions/events) in videos or merely relies on pre-trained "memory" of co-occurrences as biases in generating answers. In this work, we introduce a Video Spatio-Temporal Reasoning (V-STaR) benchmark to address these shortcomings. The key idea is to decompose video understanding into a Reverse Spatio-Temporal Reasoning (RSTR) task that simultaneously evaluates what objects are present, when events occur, and where they are located while capturing the underlying Chain-of-thought (CoT) logic. To support this evaluation, we construct a dataset to elicit the spatial-temporal reasoning process of Video-LLMs. It contains coarse-to-fine CoT questions generated by a semi-automated GPT-4-powered pipeline, embedding explicit reasoning chains to mimic human cognition. Experiments from 14 Video-LLMs on our V-STaR reveal significant gaps between current Video-LLMs and the needs for robust and consistent spatio-temporal reasoning.

We present Hermes 4, a family of hybrid reasoning models that combine structured, multi-turn reasoning with broad instruction-following ability. We describe the challenges encountered during data curation, synthesis, training, and evaluation, and outline the solutions employed to address these challenges at scale. We comprehensively evaluate across mathematical reasoning, coding, knowledge, comprehension, and alignment benchmarks, and we report both quantitative performance and qualitative behavioral analysis. To support open research, all model weights are published publicly at https://huggingface.co/collections/NousResearch/hermes-4-collection-68a731bfd452e20816725728

This paper presents AlphaSpace, a novel methodology designed to enhance the spatial reasoning capabilities of large language models (LLMs) for 3D Cartesian space navigation. AlphaSpace employs a semantics-based tokenization strategy, encoding height information through specialized semantic tokens, and integrates primarily symbolic synthetic reasoning data. This approach enables LLMs to accurately manipulate objects by positioning them at specific [x, y, z] coordinates. Experimental results demonstrate that AlphaSpace significantly outperforms existing models on manipulation subtasks, achieving a total accuracy of 66.67%, compared to 37.5% for GPT-4o and 29.17% for Claude 3.5 Sonnet.

Recent advances in large language models (LLMs), particularly those enhanced through reinforced post-training, have demonstrated impressive reasoning capabilities, as exemplified by models such as OpenAI o1 and DeepSeek-R1. However, these capabilities are predominantly benchmarked on domains like mathematical problem solving and code generation -- leaving open the question of whether such reasoning skills generalize to complex, real-world scenarios. In this paper, we introduce LocationReasoner, a benchmark designed to evaluate LLMs' reasoning abilities in the context of real-world site selection, where models must identify feasible locations by reasoning over diverse and complicated spatial, environmental, and logistical constraints. The benchmark comprises over 300 carefully crafted queries of varying difficulty levels, supported by a sandbox environment with in-house tools for constraint-based location search. Extensive evaluations reveal that state-of-the-art reasoning models offer limited improvement over their non-reasoning predecessors in real-world contexts, with even the latest OpenAI o4 model failing on 30% of site selection tasks. Moreover, agentic strategies such as ReAct and Reflexion often suffer from over-reasoning, leading to worse outcomes than direct code-generation prompting. With key limitations of LLMs in holistic and non-linear reasoning highlighted, we release LocationReasoner to foster the development of LLMs and agents capable of robust, grounded reasoning in real-world decision-making tasks. Codes and data for our benchmark are available at https://github.com/miho-koda/LocationReasoner.

To achieve faithful reasoning that aligns with human expectations, large language models (LLMs) need to ground their reasoning to real-world knowledge (e.g., web facts, math and physical rules). Tools help LLMs access this external knowledge, but there remains challenges for fine-tuning LLM agents (e.g., Toolformer) to invoke tools in multi-step reasoning problems, where inter-connected tool calls require holistic and efficient tool usage planning. In this work, we propose a new method for LLMs to better leverage tools in multi-step reasoning. Our method, Chain-of-Abstraction (CoA), trains LLMs to first decode reasoning chains with abstract placeholders, and then call domain tools to reify each reasoning chain by filling in specific knowledge. This planning with abstract chains enables LLMs to learn more general reasoning strategies, which are robust to shifts of domain knowledge (e.g., math results) relevant to different reasoning questions. It also allows LLMs to perform decoding and calling of external tools in parallel, which avoids the inference delay caused by waiting for tool responses. In mathematical reasoning and Wiki QA domains, we show that our method consistently outperforms previous chain-of-thought and tool-augmented baselines on both in-distribution and out-of-distribution test sets, with an average ~6% absolute QA accuracy improvement. LLM agents trained with our method also show more efficient tool use, with inference speed being on average ~1.4x faster than baseline tool-augmented LLMs.

Visual reasoning, particularly spatial reasoning, is a challenging cognitive task that requires understanding object relationships and their interactions within complex environments, especially in robotics domain. Existing vision_language models (VLMs) excel at perception tasks but struggle with fine-grained spatial reasoning due to their implicit, correlation-driven reasoning and reliance solely on images. We propose a novel neuro_symbolic framework that integrates both panoramic-image and 3D point cloud information, combining neural perception with symbolic reasoning to explicitly model spatial and logical relationships. Our framework consists of a perception module for detecting entities and extracting attributes, and a reasoning module that constructs a structured scene graph to support precise, interpretable queries. Evaluated on the JRDB-Reasoning dataset, our approach demonstrates superior performance and reliability in crowded, human_built environments while maintaining a lightweight design suitable for robotics and embodied AI applications.

Human reasoning relies on constructing and manipulating mental models-simplified internal representations of situations that we use to understand and solve problems. Conceptual diagrams (for example, sketches drawn by humans to aid reasoning) externalize these mental models, abstracting irrelevant details to efficiently capture relational and spatial information. In contrast, Large Language Models (LLMs) and Large Multimodal Models (LMMs) predominantly reason through textual representations, limiting their effectiveness in complex multi-step combinatorial and planning tasks. In this paper, we propose a zero-shot fully automatic framework that enables LMMs to reason through multiple chains of self-generated intermediate conceptual diagrams, significantly enhancing their combinatorial planning capabilities. Our approach does not require any human initialization beyond a natural language description of the task. It integrates both textual and diagrammatic reasoning within an optimized graph-of-thought inference framework, enhanced by beam search and depth-wise backtracking. Evaluated on multiple challenging PDDL planning domains, our method substantially improves GPT-4o's performance (for example, from 35.5% to 90.2% in Blocksworld). On more difficult planning domains with solution depths up to 40, our approach outperforms even the o1-preview reasoning model (for example, over 13% improvement in Parking). These results highlight the value of conceptual diagrams as a complementary reasoning medium in LMMs.

Current multimodal benchmarks often conflate reasoning with domain-specific knowledge, making it difficult to isolate and evaluate general reasoning abilities in non-expert settings. To address this, we introduce VisualPuzzles, a benchmark that targets visual reasoning while deliberately minimizing reliance on specialized knowledge. VisualPuzzles consists of diverse questions spanning five categories: algorithmic, analogical, deductive, inductive, and spatial reasoning. One major source of our questions is manually translated logical reasoning questions from the Chinese Civil Service Examination. Experiments show that VisualPuzzles requires significantly less intensive domain-specific knowledge and more complex reasoning compared to benchmarks like MMMU, enabling us to better evaluate genuine multimodal reasoning. Evaluations show that state-of-the-art multimodal large language models consistently lag behind human performance on VisualPuzzles, and that strong performance on knowledge-intensive benchmarks does not necessarily translate to success on reasoning-focused, knowledge-light tasks. Additionally, reasoning enhancements such as scaling up inference compute (with "thinking" modes) yield inconsistent gains across models and task types, and we observe no clear correlation between model size and performance. We also found that models exhibit different reasoning and answering patterns on VisualPuzzles compared to benchmarks with heavier emphasis on knowledge. VisualPuzzles offers a clearer lens through which to evaluate reasoning capabilities beyond factual recall and domain knowledge.

Spatial reasoning ability is crucial for Vision Language Models (VLMs) to support real-world applications in diverse domains including robotics, augmented reality, and autonomous navigation. Unfortunately, existing benchmarks are inadequate in assessing spatial reasoning ability, especially the intrinsic-dynamic spatial reasoning which is a fundamental aspect of human spatial cognition. In this paper, we propose a unified benchmark, Spatial-DISE, based on a cognitively grounded taxonomy that categorizes tasks into four fundamental quadrants: Intrinsic-Static, Intrinsic-Dynamic, Extrinsic-Static, and Extrinsic-Dynamic spatial reasoning. Moreover, to address the issue of data scarcity, we develop a scalable and automated pipeline to generate diverse and verifiable spatial reasoning questions, resulting in a new Spatial-DISE dataset that includes Spatial-DISE Bench (559 evaluation VQA pairs) and Spatial-DISE-12K (12K+ training VQA pairs). Our comprehensive evaluation across 28 state-of-the-art VLMs reveals that, current VLMs have a large and consistent gap to human competence, especially on multi-step multi-view spatial reasoning. Spatial-DISE offers a robust framework, valuable dataset, and clear direction for future research toward human-like spatial intelligence. Benchmark, dataset, and code will be publicly released.

As Vision-Language Models (VLMs) grow in sophistication, their ability to perform reasoning is coming under increasing supervision. While they excel at many tasks, their grasp of fundamental scientific principles, such as physics, remains an underexplored frontier. To reflect the advancements in these capabilities, we introduce a novel and accessible framework designed to rigorously evaluate VLMs on their understanding of 2D physics. Our framework features a pragmatic scenario generator that creates a diverse testbed of over 400 problems across four core domains: Projectile Motion, Collision Dynamics, Mechanics, and Fluid Dynamics. Through comprehensive evaluation of four state-of-the-art VLMs, we demonstrate a strong correlation between model scale and reasoning ability, with our top-performing model, Qwen2.5-VL-7B, achieving an overall score of 0.815. We find that while models excel at formulaic problems, they struggle significantly with domains requiring abstract spatial reasoning. By designing this framework, we aim to democratize the study of scientific reasoning in VLMs and foster deeper insights into their capabilities and limitations.

We envision a continuous collaborative learning system where groups of LLM agents work together to solve reasoning problems, drawing on memory they collectively build to improve performance as they gain experience. This work establishes the foundations for such a system by studying the interoperability of chain-of-thought reasoning styles, multi-agent collaboration, and memory banks. Extending beyond the identical agents of self-consistency, we introduce varied-context agents with diverse exemplars and a summarizer agent in place of voting. We generate frozen and continuously learned memory banks of exemplars and pair them with fixed, random, and similarity-based retrieval mechanisms. Our systematic study reveals where various methods contribute to reasoning performance of two LLMs on three grounded reasoning tasks, showing that random exemplar selection can often beat more principled approaches, and in some tasks, inclusion of any exemplars serves only to distract both weak and strong models.

Mathematical reasoning has long represented one of the most fundamental and challenging frontiers in artificial intelligence research. In recent years, large language models (LLMs) have achieved significant advances in this area. This survey examines the development of mathematical reasoning abilities in LLMs through two high-level cognitive phases: comprehension, where models gain mathematical understanding via diverse pretraining strategies, and answer generation, which has progressed from direct prediction to step-by-step Chain-of-Thought (CoT) reasoning. We review methods for enhancing mathematical reasoning, ranging from training-free prompting to fine-tuning approaches such as supervised fine-tuning and reinforcement learning, and discuss recent work on extended CoT and "test-time scaling". Despite notable progress, fundamental challenges remain in terms of capacity, efficiency, and generalization. To address these issues, we highlight promising research directions, including advanced pretraining and knowledge augmentation techniques, formal reasoning frameworks, and meta-generalization through principled learning paradigms. This survey tries to provide some insights for researchers interested in enhancing reasoning capabilities of LLMs and for those seeking to apply these techniques to other domains.

Large Language Models (LLMs) increasingly rely on prolonged reasoning chains to solve complex tasks. However, this trial-and-error approach often leads to high computational overhead and error propagation, where early mistakes can derail subsequent steps. To address these issues, we introduce Meta-Reasoner, a framework that dynamically optimizes inference-time reasoning by enabling LLMs to "think about how to think." Drawing inspiration from human meta-cognition and dual-process theory, Meta-Reasoner operates as a strategic advisor, decoupling high-level guidance from step-by-step generation. It employs "contextual multi-armed bandits" to iteratively evaluate reasoning progress, and select optimal strategies (e.g., backtrack, clarify ambiguity, restart from scratch, or propose alternative approaches), and reallocates computational resources toward the most promising paths. Our evaluations on mathematical reasoning and puzzles highlight the potential of dynamic reasoning chains to overcome inherent challenges in the LLM reasoning process and also show promise in broader applications, offering a scalable and adaptable solution for reasoning-intensive tasks.

Chart understanding presents a critical test to the reasoning capabilities of Vision-Language Models (VLMs). Prior approaches face critical limitations: some rely on external tools, making them brittle and constrained by a predefined toolkit, while others fine-tune specialist models that often adopt a single reasoning strategy, such as text-based chain-of-thought (CoT). The intermediate steps of text-based reasoning are difficult to verify, which complicates the use of reinforcement-learning signals that reward factual accuracy. To address this, we propose a Code-as-Thought (CaT) approach to represent the visual information of a chart in a verifiable, symbolic format. Our key insight is that this strategy must be adaptive: a fixed, code-only implementation consistently fails on complex charts where symbolic representation is unsuitable. This finding leads us to introduce Visual Programmability: a learnable property that determines if a chart-question pair is better solved with code or direct visual analysis. We implement this concept in an adaptive framework where a VLM learns to choose between the CaT pathway and a direct visual reasoning pathway. The selection policy of the model is trained with reinforcement learning using a novel dual-reward system. This system combines a data-accuracy reward to ground the model in facts and prevent numerical hallucination, with a decision reward that teaches the model when to use each strategy, preventing it from defaulting to a single reasoning mode. Experiments demonstrate strong and robust performance across diverse chart-understanding benchmarks. Our work shows that VLMs can be taught not only to reason but also how to reason, dynamically selecting the optimal reasoning pathway for each task.

Physical AI systems need to perceive, understand, and perform complex actions in the physical world. In this paper, we present the Cosmos-Reason1 models that can understand the physical world and generate appropriate embodied decisions (e.g., next step action) in natural language through long chain-of-thought reasoning processes. We begin by defining key capabilities for Physical AI reasoning, with a focus on physical common sense and embodied reasoning. To represent physical common sense, we use a hierarchical ontology that captures fundamental knowledge about space, time, and physics. For embodied reasoning, we rely on a two-dimensional ontology that generalizes across different physical embodiments. Building on these capabilities, we develop two multimodal large language models, Cosmos-Reason1-8B and Cosmos-Reason1-56B. We curate data and train our models in four stages: vision pre-training, general supervised fine-tuning (SFT), Physical AI SFT, and Physical AI reinforcement learning (RL) as the post-training. To evaluate our models, we build comprehensive benchmarks for physical common sense and embodied reasoning according to our ontologies. Evaluation results show that Physical AI SFT and reinforcement learning bring significant improvements. To facilitate the development of Physical AI, we will make our code and pre-trained models available under the NVIDIA Open Model License at https://github.com/nvidia-cosmos/cosmos-reason1.

Recently, long-thought reasoning models achieve strong performance on complex reasoning tasks, but often incur substantial inference overhead, making efficiency a critical concern. Our empirical analysis reveals that the benefit of using Long-CoT varies across problems: while some problems require elaborate reasoning, others show no improvement, or even degraded accuracy. This motivates adaptive reasoning strategies that tailor reasoning depth to the input. However, prior work primarily reduces redundancy within long reasoning paths, limiting exploration of more efficient strategies beyond the Long-CoT paradigm. To address this, we propose a novel two-stage framework for adaptive and efficient reasoning. First, we construct a hybrid reasoning model by merging long and short CoT models to enable diverse reasoning styles. Second, we apply bi-level preference training to guide the model to select suitable reasoning styles (group-level), and prefer concise and correct reasoning within each style group (instance-level). Experiments demonstrate that our method significantly reduces inference costs compared to other baseline approaches, while maintaining performance. Notably, on five mathematical datasets, the average length of reasoning is reduced by more than 50%, highlighting the potential of adaptive strategies to optimize reasoning efficiency in large language models. Our code is coming soon at https://github.com/StarDewXXX/AdaR1

Reasoning is central to human intelligence, enabling structured problem-solving across diverse tasks. Recent advances in large language models (LLMs) have greatly enhanced their reasoning abilities in arithmetic, commonsense, and symbolic domains. However, effectively extending these capabilities into multimodal contexts-where models must integrate both visual and textual inputs-continues to be a significant challenge. Multimodal reasoning introduces complexities, such as handling conflicting information across modalities, which require models to adopt advanced interpretative strategies. Addressing these challenges involves not only sophisticated algorithms but also robust methodologies for evaluating reasoning accuracy and coherence. This paper offers a concise yet insightful overview of reasoning techniques in both textual and multimodal LLMs. Through a thorough and up-to-date comparison, we clearly formulate core reasoning challenges and opportunities, highlighting practical methods for post-training optimization and test-time inference. Our work provides valuable insights and guidance, bridging theoretical frameworks and practical implementations, and sets clear directions for future research.

Although great progress has been made in 3D visual grounding, current models still rely on explicit textual descriptions for grounding and lack the ability to reason human intentions from implicit instructions. We propose a new task called 3D reasoning grounding and introduce a new benchmark ScanReason which provides over 10K question-answer-location pairs from five reasoning types that require the synerization of reasoning and grounding. We further design our approach, ReGround3D, composed of the visual-centric reasoning module empowered by Multi-modal Large Language Model (MLLM) and the 3D grounding module to obtain accurate object locations by looking back to the enhanced geometry and fine-grained details from the 3D scenes. A chain-of-grounding mechanism is proposed to further boost the performance with interleaved reasoning and grounding steps during inference. Extensive experiments on the proposed benchmark validate the effectiveness of our proposed approach.

Current vision-language models may incorporate single-dimensional spatial cues, such as depth, object boundary, and basic spatial directions (e.g. left, right, front, back), yet often lack the multi-dimensional spatial reasoning necessary for human-like understanding and real-world applications. To address this gap, we develop SPHERE (Spatial Perception and Hierarchical Evaluation of REasoning), a hierarchical evaluation framework with a new human-annotated dataset to pinpoint model strengths and weaknesses, advancing from single-skill tasks to multi-skill tasks, and ultimately to complex reasoning tasks that require the integration of multiple spatial and visual cues with logical reasoning. Benchmark evaluation of state-of-the-art open-source models reveal significant shortcomings, especially in the abilities to understand distance and proximity, to reason from both allocentric and egocentric viewpoints, and to perform complex reasoning in a physical context. This work underscores the need for more advanced approaches to spatial understanding and reasoning, paving the way for improvements in vision-language models and their alignment with human-like spatial capabilities. The dataset will be open-sourced upon publication.

Chain-of-Thought (CoT) prompting has been shown to improve Large Language Model (LLM) performance on various tasks. With this approach, LLMs appear to produce human-like reasoning steps before providing answers (a.k.a., CoT reasoning), which often leads to the perception that they engage in deliberate inferential processes. However, some initial findings suggest that CoT reasoning may be more superficial than it appears, motivating us to explore further. In this paper, we study CoT reasoning via a data distribution lens and investigate if CoT reasoning reflects a structured inductive bias learned from in-distribution data, allowing the model to conditionally generate reasoning paths that approximate those seen during training. Thus, its effectiveness is fundamentally bounded by the degree of distribution discrepancy between the training data and the test queries. With this lens, we dissect CoT reasoning via three dimensions: task, length, and format. To investigate each dimension, we design DataAlchemy, an isolated and controlled environment to train LLMs from scratch and systematically probe them under various distribution conditions. Our results reveal that CoT reasoning is a brittle mirage that vanishes when it is pushed beyond training distributions. This work offers a deeper understanding of why and when CoT reasoning fails, emphasizing the ongoing challenge of achieving genuine and generalizable reasoning.

Spatial reasoning is a core component of human cognition, enabling individuals to perceive, comprehend, and interact with the physical world. It relies on a nuanced understanding of spatial structures and inter-object relationships, serving as the foundation for complex reasoning and decision-making. To investigate whether current vision-language models (VLMs) exhibit similar capability, we introduce Jigsaw-Puzzles, a novel benchmark consisting of 1,100 carefully curated real-world images with high spatial complexity. Based on this dataset, we design five tasks to rigorously evaluate VLMs' spatial perception, structural understanding, and reasoning capabilities, while deliberately minimizing reliance on domain-specific knowledge to better isolate and assess the general spatial reasoning capability. We conduct a comprehensive evaluation across 24 state-of-the-art VLMs. The results show that even the strongest model, Gemini-2.5-Pro, achieves only 77.14% overall accuracy and performs particularly poorly on the Order Generation task, with only 30.00% accuracy, far below the performance exceeding 90% achieved by human participants. This persistent gap underscores the need for continued progress, positioning Jigsaw-Puzzles as a challenging and diagnostic benchmark for advancing spatial reasoning research in VLMs.

We study how different Chain-of-Thought (CoT) designs affect the acquisition of the generalizable visual reasoning ability in vision-language models (VLMs). While CoT data, especially long or visual CoT such as "think with image", has been widely used to supervise intermediate reasoning, it remains unclear why specific CoT designs help and which ones truly support generalizable reasoning. To systematically evaluate this, we focus on a controlled maze-solving benchmark where reasoning rules are fully visual, difficulty can be tuned by grid size, and all the intermediate steps can be automatically generated. Using Qwen2.5-VL-7B under a standard SFT-then-RL pipeline, we compare three representative CoT formats: Language CoT, Grounding CoT (with spatial coordinate trajectories), and Visual CoT (with image manipulations). Our experiments reveal that visual and longer CoT mainly accelerate convergence but do not lift the final performance ceiling; concise CoT containing only essential grounding steps outperforms longer traces; and, strikingly, CoT retaining only the minimal grounding results generalizes best across different maze sizes. We further validate these insights on other vision-centric tasks. These findings highlight a "short is long" effect and provide practical guidance for constructing more generalizable SFT datasets for visual reasoning.

Chain-of-thought reasoning, while powerful, can produce unnecessarily verbose output for simpler problems. We present a framework for difficulty-aware reasoning that teaches models to dynamically adjust reasoning depth based on problem complexity. Remarkably, we show that models can be endowed with such dynamic inference pathways without any architectural modifications; we simply post-train on data that is carefully curated to include chain-of-thought traces that are proportional in length to problem difficulty. Our analysis reveals that post-training via supervised fine-tuning (SFT) primarily captures patterns like reasoning length and format, while direct preference optimization (DPO) preserves reasoning accuracy, with their combination reducing length and maintaining or improving performance. Both quantitative metrics and qualitative assessments confirm that models can learn to "think proportionally", reasoning minimally on simple problems while maintaining depth for complex ones.

While many natural language inference (NLI) datasets target certain semantic phenomena, e.g., negation, tense & aspect, monotonicity, and presupposition, to the best of our knowledge, there is no NLI dataset that involves diverse types of spatial expressions and reasoning. We fill this gap by semi-automatically creating an NLI dataset for spatial reasoning, called SpaceNLI. The data samples are automatically generated from a curated set of reasoning patterns, where the patterns are annotated with inference labels by experts. We test several SOTA NLI systems on SpaceNLI to gauge the complexity of the dataset and the system's capacity for spatial reasoning. Moreover, we introduce a Pattern Accuracy and argue that it is a more reliable and stricter measure than the accuracy for evaluating a system's performance on pattern-based generated data samples. Based on the evaluation results we find that the systems obtain moderate results on the spatial NLI problems but lack consistency per inference pattern. The results also reveal that non-projective spatial inferences (especially due to the "between" preposition) are the most challenging ones.

Visual reasoning -- the ability to interpret the visual world -- is crucial for embodied agents that operate within three-dimensional scenes. Progress in AI has led to vision and language models capable of answering questions from images. However, their performance declines when tasked with 3D spatial reasoning. To tackle the complexity of such reasoning problems, we introduce an agentic program synthesis approach where LLM agents collaboratively generate a Pythonic API with new functions to solve common subproblems. Our method overcomes limitations of prior approaches that rely on a static, human-defined API, allowing it to handle a wider range of queries. To assess AI capabilities for 3D understanding, we introduce a new benchmark of queries involving multiple steps of grounding and inference. We show that our method outperforms prior zero-shot models for visual reasoning in 3D and empirically validate the effectiveness of our agentic framework for 3D spatial reasoning tasks. Project website: https://glab-caltech.github.io/vadar/

Reasoning is a fundamental capability of Large Language Models. While prior research predominantly focuses on enhancing narrow skills like math or code generation, improving performance on many other reasoning tasks remains challenging due to sparse and fragmented training data. To address this issue, we propose CodeI/O, a novel approach that systematically condenses diverse reasoning patterns inherently embedded in contextually-grounded codes, through transforming the original code into a code input-output prediction format. By training models to predict inputs/outputs given code and test cases entirely in natural language as Chain-of-Thought (CoT) rationales, we expose them to universal reasoning primitives -- like logic flow planning, state-space searching, decision tree traversal, and modular decomposition -- while decoupling structured reasoning from code-specific syntax and preserving procedural rigor. Experimental results demonstrate CodeI/O leads to consistent improvements across symbolic, scientific, logic, math & numerical, and commonsense reasoning tasks. By matching the existing ground-truth outputs or re-executing the code with predicted inputs, we can verify each prediction and further enhance the CoTs through multi-turn revision, resulting in CodeI/O++ and achieving higher performance. Our data and models are available at https://github.com/hkust-nlp/CodeIO.

Vision-Language Navigation (VLN) is a critical task for developing embodied agents that can follow natural language instructions to navigate in complex real-world environments. Recent advances in VLN by large pretrained models have significantly improved generalization and instruction grounding compared to traditional approaches. However, the role of reasoning strategies in navigation-an action-centric, long-horizon task-remains underexplored, despite Chain-of-Thought (CoT) reasoning's demonstrated success in static tasks like visual question answering. To address this gap, we conduct the first systematic evaluation of reasoning strategies for VLN, including No-Think (direct action prediction), Pre-Think (reason before action), and Post-Think (reason after action). Surprisingly, our findings reveal the Inference-time Reasoning Collapse issue, where inference-time reasoning degrades navigation accuracy, highlighting the challenges of integrating reasoning into VLN. Based on this insight, we propose Aux-Think, a framework that trains models to internalize structured reasoning patterns through CoT supervision, while inferring action directly without reasoning in online prediction. To support this framework, we release R2R-CoT-320k, the first Chain-of-Thought annotated dataset for VLN. Extensive experiments show that Aux-Think reduces training effort greatly and achieves the best performance under the same data scale.

A recent approach to neurosymbolic reasoning is to explicitly combine the strengths of large language models (LLMs) and symbolic solvers to tackle complex reasoning tasks. However, current approaches face significant limitations, including poor generalizability due to task-specific prompts, inefficiencies caused by the lack of separation between knowledge and queries, and restricted inferential capabilities. These shortcomings hinder their scalability and applicability across diverse domains. In this paper, we introduce VERUS-LM, a novel framework designed to address these challenges. VERUS-LM employs a generic prompting mechanism, clearly separates domain knowledge from queries, and supports a wide range of different logical reasoning tasks. This framework enhances adaptability, reduces computational cost, and allows for richer forms of reasoning, such as optimization and constraint satisfaction. We show that our approach succeeds in diverse reasoning on a novel dataset, markedly outperforming LLMs. Additionally, our system achieves competitive results on common reasoning benchmarks when compared to other state-of-the-art approaches, and significantly surpasses them on the difficult AR-LSAT dataset. By pushing the boundaries of hybrid reasoning, VERUS-LM represents a significant step towards more versatile neurosymbolic AI systems

Video Models have achieved remarkable success in high-fidelity video generation with coherent motion dynamics. Analogous to the development from text generation to text-based reasoning in language modeling, the development of video models motivates us to ask: Can video models reason via video generation? Compared with the discrete text corpus, video grounds reasoning in explicit spatial layouts and temporal continuity, which serves as an ideal substrate for spatial reasoning. In this work, we explore the reasoning via video paradigm and introduce VR-Bench -- a comprehensive benchmark designed to systematically evaluate video models' reasoning capabilities. Grounded in maze-solving tasks that inherently require spatial planning and multi-step reasoning, VR-Bench contains 7,920 procedurally generated videos across five maze types and diverse visual styles. Our empirical analysis demonstrates that SFT can efficiently elicit the reasoning ability of video model. Video models exhibit stronger spatial perception during reasoning, outperforming leading VLMs and generalizing well across diverse scenarios, tasks, and levels of complexity. We further discover a test-time scaling effect, where diverse sampling during inference improves reasoning reliability by 10--20%. These findings highlight the unique potential and scalability of reasoning via video for spatial reasoning tasks.

Despite recent advances on multi-modal models, 3D spatial reasoning remains a challenging task for state-of-the-art open-source and proprietary models. Recent studies explore data-driven approaches and achieve enhanced spatial reasoning performance by fine-tuning models on 3D-related visual question-answering data. However, these methods typically perform spatial reasoning in an implicit manner and often fail on questions that are trivial to humans, even with long chain-of-thought reasoning. In this work, we introduce SpatialReasoner, a novel large vision-language model (LVLM) that addresses 3D spatial reasoning with explicit 3D representations shared between multiple stages--3D perception, computation, and reasoning. Explicit 3D representations provide a coherent interface that supports advanced 3D spatial reasoning and improves the generalization ability to novel question types. Furthermore, by analyzing the explicit 3D representations in multi-step reasoning traces of SpatialReasoner, we study the factual errors and identify key shortcomings of current LVLMs. Results show that our SpatialReasoner achieves improved performance on a variety of spatial reasoning benchmarks, outperforming Gemini 2.0 by 9.2% on 3DSRBench, and generalizes better when evaluating on novel 3D spatial reasoning questions. Our study bridges the 3D parsing capabilities of prior visual foundation models with the powerful reasoning abilities of large language models, opening new directions for 3D spatial reasoning.

Large Reasoning Models (LRMs) achieve strong performance in mathematics, code generation, and task planning, but their reliance on long chains of verbose "thinking" tokens leads to high latency, redundancy, and incoherent reasoning paths. Inspired by the Language of Thought Hypothesis, which posits that human reasoning operates over a symbolic, compositional mental language called Mentalese, we introduce a framework that trains models to reason in a similarly compact style. Mentalese encodes abstract reasoning as ultra-compressed, structured tokens, enabling models to solve complex problems with far fewer steps. To improve both efficiency and accuracy, we propose SHORTER LENGTH PREFERENCE OPTIMIZATION (SLPO), a reinforcement learning method that rewards concise solutions that stay correct, while still allowing longer reasoning when needed. Applied to Mentalese-aligned models, SLPO yields significantly higher compression rates by enabling concise reasoning that preserves the benefits of detailed thinking without the computational overhead. Across benchmarks including AIME 2024 and 2025, MinervaMath, OlympiadBench, Math500, and AMC, our ORION models produce reasoning traces with 4-16x fewer tokens, achieve up to 5x lower inference latency, and reduce training costs by 7-9x relative to the DeepSeek R1 Distilled model, while maintaining 90-98% of its accuracy. ORION also surpasses Claude and ChatGPT-4o by up to 5% in accuracy while maintaining 2x compression. These results show that Mentalese-style compressed reasoning offers a step toward human-like cognitive efficiency, enabling real-time, cost-effective reasoning without sacrificing accuracy.

Understanding and reasoning about spatial relationships is a fundamental capability for Visual Question Answering (VQA) and robotics. While Vision Language Models (VLM) have demonstrated remarkable performance in certain VQA benchmarks, they still lack capabilities in 3D spatial reasoning, such as recognizing quantitative relationships of physical objects like distances or size differences. We hypothesize that VLMs' limited spatial reasoning capability is due to the lack of 3D spatial knowledge in training data and aim to solve this problem by training VLMs with Internet-scale spatial reasoning data. To this end, we present a system to facilitate this approach. We first develop an automatic 3D spatial VQA data generation framework that scales up to 2 billion VQA examples on 10 million real-world images. We then investigate various factors in the training recipe, including data quality, training pipeline, and VLM architecture. Our work features the first internet-scale 3D spatial reasoning dataset in metric space. By training a VLM on such data, we significantly enhance its ability on both qualitative and quantitative spatial VQA. Finally, we demonstrate that this VLM unlocks novel downstream applications in chain-of-thought spatial reasoning and robotics due to its quantitative estimation capability. Project website: https://spatial-vlm.github.io/

Pre-trained language models (PLMs) have shown impressive performance in various language tasks. However, they are prone to spurious correlations, and often generate illusory information. In real-world applications, PLMs should justify decisions with formalized, coherent reasoning chains, but this challenge remains under-explored. Cognitive psychology theorizes that humans are capable of utilizing fast and intuitive heuristic thinking to make decisions based on past experience, then rationalizing the decisions through slower and deliberative analytic reasoning. We incorporate these interlinked dual processes in fine-tuning and in-context learning with PLMs, applying them to two language understanding tasks that require coherent physical commonsense reasoning. We show that our proposed Heuristic-Analytic Reasoning (HAR) strategies drastically improve the coherence of rationalizations for model decisions, yielding state-of-the-art results on Tiered Reasoning for Intuitive Physics (TRIP). We also find that this improved coherence is a direct result of more faithful attention to relevant language context in each step of reasoning. Our findings suggest that human-like reasoning strategies can effectively improve the coherence and reliability of PLM reasoning.

This paper introduces an innovative approach to analyzing and improving multi-hop reasoning in AI systems by drawing inspiration from Hamiltonian mechanics. We propose a novel framework that maps reasoning chains in embedding spaces to Hamiltonian systems, allowing us to leverage powerful analytical tools from classical physics. Our method defines a Hamiltonian function that balances the progression of reasoning (kinetic energy) against the relevance to the question at hand (potential energy). Using this framework, we analyze a large dataset of reasoning chains from a multi-hop question-answering task, revealing intriguing patterns that distinguish valid from invalid reasoning. We show that valid reasoning chains have lower Hamiltonian energy and move in ways that make the best trade-off between getting more information and answering the right question. Furthermore, we demonstrate the application of this framework to steer the creation of more efficient reasoning algorithms within AI systems. Our results not only provide new insights into the nature of valid reasoning but also open up exciting possibilities for physics-inspired approaches to understanding and improving artificial intelligence.

Visual Spatial Reasoning (VSR) is a core human cognitive ability and a critical requirement for advancing embodied intelligence and autonomous systems. Despite recent progress in Vision-Language Models (VLMs), achieving human-level VSR remains highly challenging due to the complexity of representing and reasoning over three-dimensional space. In this paper, we present a systematic investigation of VSR in VLMs, encompassing a review of existing methodologies across input modalities, model architectures, training strategies, and reasoning mechanisms. Furthermore, we categorize spatial intelligence into three levels of capability, ie, basic perception, spatial understanding, spatial planning, and curate SIBench, a spatial intelligence benchmark encompassing nearly 20 open-source datasets across 23 task settings. Experiments with state-of-the-art VLMs reveal a pronounced gap between perception and reasoning, as models show competence in basic perceptual tasks but consistently underperform in understanding and planning tasks, particularly in numerical estimation, multi-view reasoning, temporal dynamics, and spatial imagination. These findings underscore the substantial challenges that remain in achieving spatial intelligence, while providing both a systematic roadmap and a comprehensive benchmark to drive future research in the field. The related resources of this study are accessible at https://sibench.github.io/Awesome-Visual-Spatial-Reasoning/.

Significant advancements in the reasoning capabilities of Large Language Models (LLMs) are now driven by test-time scaling laws, particularly those leveraging extended Chain-of-Thought (CoT) reasoning. Inspired by these breakthroughs, researchers have extended these paradigms to Large Multimodal Models (LMMs). However, a critical limitation emerges: as their reasoning chains extend, LMMs increasingly rely on textual logic, progressively losing grounding in the underlying visual information. This leads to reasoning paths that diverge from the image content, culminating in erroneous conclusions. To address this, we introduce a strikingly simple yet effective training-free visual-reasoning pipeline. The core concept is to decouple the reasoning and perception processes. A powerful LLM orchestrates the high-level reasoning, strategically interrogating a LMM to extract specific visual information required for its logical chain. The LMM, in turn, functions exclusively as a visual question-answering engine, supplying the necessary perceptual details on demand. This lightweight, plug-and-play approach requires no additional training or architectural changes. Comprehensive evaluations validate that our framework effectively governs the visual reasoning process, leading to a significant reduction in visually-unfounded reasoning steps and a substantial improvement in reasoning fidelity.

We introduce Phi-4-reasoning, a 14-billion parameter reasoning model that achieves strong performance on complex reasoning tasks. Trained via supervised fine-tuning of Phi-4 on carefully curated set of "teachable" prompts-selected for the right level of complexity and diversity-and reasoning demonstrations generated using o3-mini, Phi-4-reasoning generates detailed reasoning chains that effectively leverage inference-time compute. We further develop Phi-4-reasoning-plus, a variant enhanced through a short phase of outcome-based reinforcement learning that offers higher performance by generating longer reasoning traces. Across a wide range of reasoning tasks, both models outperform significantly larger open-weight models such as DeepSeek-R1-Distill-Llama-70B model and approach the performance levels of full DeepSeek-R1 model. Our comprehensive evaluations span benchmarks in math and scientific reasoning, coding, algorithmic problem solving, planning, and spatial understanding. Interestingly, we observe a non-trivial transfer of improvements to general-purpose benchmarks as well. In this report, we provide insights into our training data, our training methodologies, and our evaluations. We show that the benefit of careful data curation for supervised fine-tuning (SFT) extends to reasoning language models, and can be further amplified by reinforcement learning (RL). Finally, our evaluation points to opportunities for improving how we assess the performance and robustness of reasoning models.

Multimodal Large Language Models (MLLMs) have powered Graphical User Interface (GUI) Agents, showing promise in automating tasks on computing devices. Recent works have begun exploring reasoning in GUI tasks with encouraging results. However, many current approaches rely on manually designed reasoning templates, which may result in reasoning that is not sufficiently robust and adaptive for complex GUI environments. Meanwhile, some existing agents continue to operate as Reactive Actors, relying primarily on implicit reasoning that may lack sufficient depth for GUI tasks demanding planning and error recovery. We argue that advancing these agents requires a shift from reactive acting towards acting based on deliberate reasoning. To facilitate this transformation, we introduce InfiGUI-R1, an MLLM-based GUI agent developed through our Actor2Reasoner framework, a reasoning-centric, two-stage training approach designed to progressively evolve agents from Reactive Actors to Deliberative Reasoners. The first stage, Reasoning Injection, focuses on establishing a basic reasoner. We employ Spatial Reasoning Distillation to transfer cross-modal spatial reasoning capabilities from teacher models to MLLMs through trajectories with explicit reasoning steps, enabling models to integrate GUI visual-spatial information with logical reasoning before action generation. The second stage, Deliberation Enhancement, refines the basic reasoner into a deliberative one using Reinforcement Learning. This stage introduces two approaches: Sub-goal Guidance, which rewards models for generating accurate intermediate sub-goals, and Error Recovery Scenario Construction, which creates failure-and-recovery training scenarios from identified prone-to-error steps. Experimental results show InfiGUI-R1 achieves strong performance in GUI grounding and trajectory tasks. Resources at https://github.com/Reallm-Labs/InfiGUI-R1.

Recent video generation models can produce high-fidelity, temporally coherent videos, indicating that they may encode substantial world knowledge. Beyond realistic synthesis, they also exhibit emerging behaviors indicative of visual perception, modeling, and manipulation. Yet, an important question still remains: Are video models ready to serve as zero-shot reasoners in challenging visual reasoning scenarios? In this work, we conduct an empirical study to comprehensively investigate this question, focusing on the leading and popular Veo-3. We evaluate its reasoning behavior across 12 dimensions, including spatial, geometric, physical, temporal, and embodied logic, systematically characterizing both its strengths and failure modes. To standardize this study, we curate the evaluation data into MME-CoF, a compact benchmark that enables in-depth and thorough assessment of Chain-of-Frame (CoF) reasoning. Our findings reveal that while current video models demonstrate promising reasoning patterns on short-horizon spatial coherence, fine-grained grounding, and locally consistent dynamics, they remain limited in long-horizon causal reasoning, strict geometric constraints, and abstract logic. Overall, they are not yet reliable as standalone zero-shot reasoners, but exhibit encouraging signs as complementary visual engines alongside dedicated reasoning models. Project page: https://video-cof.github.io

The chain-of-though (CoT) prompting methods were successful in various natural language processing (NLP) tasks thanks to their ability to unveil the underlying complex reasoning processes. Such reasoning processes typically exhibit implicitly structured steps. Recent efforts also started investigating methods to encourage more explicitly structured reasoning procedures to be captured. In this work, we propose Tab-CoT, a novel tabular-format CoT prompting method, which allows the complex reasoning process to be explicitly modelled in a highly structured manner. Despite its simplicity, we show that our approach is capable of performing reasoning across multiple dimensions (i.e., both rows and columns). We demonstrate our approach's strong zero-shot and few-shot capabilities through extensive experiments on a range of reasoning tasks.

Reasoning over knowledge graphs (KGs) is a challenging task that requires a deep understanding of the complex relationships between entities and the underlying logic of their relations. Current approaches rely on learning geometries to embed entities in vector space for logical query operations, but they suffer from subpar performance on complex queries and dataset-specific representations. In this paper, we propose a novel decoupled approach, Language-guided Abstract Reasoning over Knowledge graphs (LARK), that formulates complex KG reasoning as a combination of contextual KG search and logical query reasoning, to leverage the strengths of graph extraction algorithms and large language models (LLM), respectively. Our experiments demonstrate that the proposed approach outperforms state-of-the-art KG reasoning methods on standard benchmark datasets across several logical query constructs, with significant performance gain for queries of higher complexity. Furthermore, we show that the performance of our approach improves proportionally to the increase in size of the underlying LLM, enabling the integration of the latest advancements in LLMs for logical reasoning over KGs. Our work presents a new direction for addressing the challenges of complex KG reasoning and paves the way for future research in this area.

With the release of R1, a publicly available large reasoning model (LRM), researchers commonly train new LRMs by training language models on R1's long chain-of-thought (CoT) inferences. While prior works show that LRMs' capabilities can be reproduced through direct distillation, the continued reliance on the existing models (e.g., R1) remains a critical limitation in advancing the field. As a first step toward independent LRM development, this paper explores the possibility of constructing a long CoT dataset with LLMs that are not trained for inference-time scaling. To this end, we present the Long CoT Collection, a dataset of 100K CoT rationales annotated using existing short CoT LLMs. We develop a pipeline that induces o1's novel reasoning strategies into short CoT LLMs, enabling them to think longer and introducing controllability over the thought budget to better manage the overthinking problem. Our extensive analyses validate that our dataset achieves quality comparable to--or slightly below--R1. Furthermore, our experiments demonstrate that training on our dataset not only strengthens general reasoning skills, but also provides a strong foundation for reinforcement learning--models initialized on our data achieve 2-3x larger gains with RLVR.

Leveraging the autonomous decision-making capabilities of large language models (LLMs) demonstrates superior performance in reasoning tasks. Despite the successes of iterative or recursive retrieval-augmented generation (RAG), they often are trapped in a single solution space when confronted with complex tasks. In this paper, we propose a novel thinking pattern in RAG which integrates system analysis with efficient reasoning actions, significantly activating intrinsic reasoning capabilities and expanding the solution space of specific tasks via Monte Carlo Tree Search (MCTS), dubbed AirRAG. Specifically, our approach designs five fundamental reasoning actions that are expanded to a wide tree-based reasoning spaces using MCTS. The extension also uses self-consistency verification to explore potential reasoning paths and implement inference scaling. In addition, computationally optimal strategies are used to apply more inference computation to key actions to achieve further performance improvements. Experimental results demonstrate the effectiveness of AirRAG through considerable performance gains over complex QA datasets. Furthermore, AirRAG is flexible and lightweight, making it easy to integrate with other advanced technologies.

Large Language Models (LLMs) have revolutionized natural language processing and hold immense potential for advancing Artificial Intelligence. However, the core architecture of most mainstream LLMs -- the Transformer -- has inherent limitations in computational depth, rendering them theoretically incapable of solving many reasoning tasks that demand increasingly deep computations. Chain of Thought (CoT) prompting has emerged as a technique to address these architectural limitations, as evidenced by several theoretical studies. It offers a promising approach to solving complex reasoning tasks that were previously beyond the capabilities of these models. Despite its successes, CoT and its variants (such as Tree of Thought, Graph of Thought, etc.) rely on a "one-prompt-for-all" approach, using a single prompt structure (e.g., "think step by step") for a wide range of tasks -- from counting and sorting to solving mathematical and algorithmic problems. This approach poses significant challenges for models to generate the correct reasoning steps, as the model must navigate through a vast prompt template space to find the appropriate template for each task. In this work, we build upon previous theoretical analyses of CoT to demonstrate how the one-prompt-for-all approach can negatively affect the computability of LLMs. We partition the solution search space into two: the prompt space and the answer space. Our findings show that task-specific supervision is essential for navigating the prompt space accurately and achieving optimal performance. Through experiments with state-of-the-art LLMs, we reveal a gap in reasoning performance when supervision is applied versus when it is not.

Reasoning is a fundamental cognitive process that enables logical inference, problem-solving, and decision-making. With the rapid advancement of large language models (LLMs), reasoning has emerged as a key capability that distinguishes advanced AI systems from conventional models that empower chatbots. In this survey, we categorize existing methods along two orthogonal dimensions: (1) Regimes, which define the stage at which reasoning is achieved (either at inference time or through dedicated training); and (2) Architectures, which determine the components involved in the reasoning process, distinguishing between standalone LLMs and agentic compound systems that incorporate external tools, and multi-agent collaborations. Within each dimension, we analyze two key perspectives: (1) Input level, which focuses on techniques that construct high-quality prompts that the LLM condition on; and (2) Output level, which methods that refine multiple sampled candidates to enhance reasoning quality. This categorization provides a systematic understanding of the evolving landscape of LLM reasoning, highlighting emerging trends such as the shift from inference-scaling to learning-to-reason (e.g., DeepSeek-R1), and the transition to agentic workflows (e.g., OpenAI Deep Research, Manus Agent). Additionally, we cover a broad spectrum of learning algorithms, from supervised fine-tuning to reinforcement learning such as PPO and GRPO, and the training of reasoners and verifiers. We also examine key designs of agentic workflows, from established patterns like generator-evaluator and LLM debate to recent innovations. ...

Large Language Models (LLMs) have succeeded remarkably in various natural language processing (NLP) tasks, yet their reasoning capabilities remain a fundamental challenge. While LLMs exhibit impressive fluency and factual recall, their ability to perform complex reasoning-spanning logical deduction, mathematical problem-solving, commonsense inference, and multi-step reasoning-often falls short of human expectations. This survey provides a comprehensive review of emerging techniques enhancing reasoning in LLMs. We categorize existing methods into key approaches, including prompting strategies (e.g., Chain-of-Thought reasoning, Self-Consistency, and Tree-of-Thought reasoning), architectural innovations (e.g., retrieval-augmented models, modular reasoning networks, and neuro-symbolic integration), and learning paradigms (e.g., fine-tuning with reasoning-specific datasets, reinforcement learning, and self-supervised reasoning objectives). Additionally, we explore evaluation frameworks used to assess reasoning in LLMs and highlight open challenges, such as hallucinations, robustness, and reasoning generalization across diverse tasks. By synthesizing recent advancements, this survey aims to provide insights into promising directions for future research and practical applications of reasoning-augmented LLMs.

We present SpinBench, a cognitively grounded diagnostic benchmark for evaluating spatial reasoning in vision language models (VLMs). SpinBench is designed around the core challenge of spatial reasoning: perspective taking, the ability to reason about how scenes and object relations change under viewpoint transformation. Since perspective taking requires multiple cognitive capabilities, such as recognizing objects across views, relative positions grounding, and mentally simulating transformations, SpinBench introduces a set of fine-grained diagnostic categories. Our categories target translation, rotation, object relative pose, and viewpoint change, and are progressively structured so that single-object simpler tasks scaffold toward the most demanding multi-object perspective-taking setting. We evaluate 37 state-of-the-art VLMs, both proprietary and open source. Results reveal systematic weaknesses: strong egocentric bias, poor rotational understanding, and inconsistencies under symmetrical and syntactic reformulations. Scaling analysis shows both smooth improvements and emergent capabilities. While human subjects achieve high accuracy (91.2\%), task difficulty as measured by human response time shows strong correlation with VLM accuracy, indicating that SpinBench captures spatial reasoning challenges shared across humans and VLMs. We believe SpinBench provides critical insights into spatial reasoning in VLMs and highlights key gaps in their ability to reason about physical space. Our website can be found at https://spinbench25.github.io/.