Daily Papers

Learning-rate steps are usually treated as hyperparameters. This paper isolates a local beliefspace calculation: when an update is modeled as a projected forward step on the probability simplex, admissibility means contractivity in the natural KL/Bregman geometry. Under this model, the upper bound of an admissible step is not a tuning slogan but a formula.

Beliefs serve as the foundation for human cognition and decision-making. They guide individuals in deriving meaning from their lives, shaping their behaviors, and forming social connections. Therefore, a model that encapsulates beliefs and their interrelationships is crucial for quantitatively studying the influence of beliefs on our actions. Despite its importance, research on the interplay between human beliefs has often been limited to a small set of beliefs pertaining to specific issues, with a heavy reliance on surveys or experiments. Here, we propose a method for extracting nuanced relations between thousands of beliefs by leveraging large-scale user participation data from an online debate platform and mapping these beliefs to an embedding space using a fine-tuned large language model (LLM). This belief embedding space effectively encapsulates the interconnectedness of diverse beliefs as well as polarization across various social issues. We discover that the positions within this belief space predict new beliefs of individuals. Furthermore, we find that the relative distance between one's existing beliefs and new beliefs can serve as a quantitative estimate of cognitive dissonance, allowing us to predict new beliefs. Our study highlights how modern LLMs, when combined with collective online records of human beliefs, can offer insights into the fundamental principles that govern human belief formation and decision-making processes.

Standard methods for detecting discontinuities in conditional means are not applicable to outcomes that are complex, non-Euclidean objects like distributions, networks, or covariance matrices. This article develops a nonparametric test for jumps in conditional means when outcomes lie in a non-Euclidean metric space. Using local Fr\'echet regressionx2014which generalizes standard regression to metric-space valued datax2014the method estimates a mean path on either side of a candidate cutoff, extending existing k-sample tests to a flexible regression setting. Key theoretical contributions include a central limit theorem for the local estimator of the conditional Fr\'echet variance and the asymptotic validity and consistency of the proposed test. Simulations confirm nominal size control and robust power in finite samples. Two applications demonstrate the method's value by revealing effects invisible to scalar-based tests. First, I detect a sharp change in work-from-home compositions at Washington State's income threshold for non-compete enforceability during COVID-19, highlighting remote work's role as a bargaining margin. Second, I find that countries restructure their input-output networks after losing preferential US trade access. These findings underscore that analyzing regression functions within their native metric spaces can reveal structural discontinuities that scalar summaries would miss.

Spatial embodied intelligence requires agents to act to acquire information under partial observability. While multimodal foundation models excel at passive perception, their capacity for active, self-directed exploration remains understudied. We propose Theory of Space, defined as an agent's ability to actively acquire information through self-directed, active exploration and to construct, revise, and exploit a spatial belief from sequential, partial observations. We evaluate this through a benchmark where the goal is curiosity-driven exploration to build an accurate cognitive map. A key innovation is spatial belief probing, which prompts models to reveal their internal spatial representations at each step. Our evaluation of state-of-the-art models reveals several critical bottlenecks. First, we identify an Active-Passive Gap, where performance drops significantly when agents must autonomously gather information. Second, we find high inefficiency, as models explore unsystematically compared to program-based proxies. Through belief probing, we diagnose that while perception is an initial bottleneck, global beliefs suffer from instability that causes spatial knowledge to degrade over time. Finally, using a false belief paradigm, we uncover Belief Inertia, where agents fail to update obsolete priors with new evidence. This issue is present in text-based agents but is particularly severe in vision-based models. Our findings suggest that current foundation models struggle to maintain coherent, revisable spatial beliefs during active exploration.

Understanding the internal mechanisms of large language models (LLMs) remains a challenging and complex endeavor. Even fundamental questions, such as how fine-tuning affects model behavior, often require extensive empirical evaluation. In this paper, we introduce a novel perspective based on the geometric properties of contextual latent embeddings to study the effects of training and fine-tuning. To that end, we measure the local dimensions of a contextual language model's latent space and analyze their shifts during training and fine-tuning. We show that the local dimensions provide insights into the model's training dynamics and generalization ability. Specifically, the mean of the local dimensions predicts when the model's training capabilities are exhausted, as exemplified in a dialogue state tracking task, overfitting, as demonstrated in an emotion recognition task, and grokking, as illustrated with an arithmetic task. Furthermore, our experiments suggest a practical heuristic: reductions in the mean local dimension tend to accompany and predict subsequent performance gains. Through this exploration, we aim to provide practitioners with a deeper understanding of the implications of fine-tuning on embedding spaces, facilitating informed decisions when configuring models for specific applications. The results of this work contribute to the ongoing discourse on the interpretability, adaptability, and generalizability of LLMs by bridging the gap between intrinsic model mechanisms and geometric properties in the respective embeddings.

As Large Language Models (LLMs) are increasingly deployed in real-world settings, correctness alone is insufficient. Reliable deployment requires maintaining truthful beliefs under contextual perturbations. Existing evaluations largely rely on point-wise confidence like Self-Consistency, which can mask brittle belief. We show that even facts answered with perfect self-consistency can rapidly collapse under mild contextual interference. To address this gap, we propose Neighbor-Consistency Belief (NCB), a structural measure of belief robustness that evaluates response coherence across a conceptual neighborhood. To validate the efficiency of NCB, we introduce a new cognitive stress-testing protocol that probes outputs stability under contextual interference. Experiments across multiple LLMs show that the performance of high-NCB data is relatively more resistant to interference. Finally, we present Structure-Aware Training (SAT), which optimizes context-invariant belief structure and reduces long-tail knowledge brittleness by approximately 30%. Code will be available at https://github.com/zjunlp/belief.

LLM agents that operate over long context depend on external memory to accumulate knowledge over time. However, existing methods typically store each observation as a single deterministic conclusion (e.g., inferring "API~X failed" from temporary errors), even though such observations are inherently partial and potentially ambiguous. By committing to one conclusion and discarding uncertainty, these methods introduce self-reinforcing error: the agent acts on the stored conclusion, never revisits alternatives, and reinforces the conclusion over time. To address this issue, we propose BeliefMem, which shifts the memory paradigm from committing to a single conclusion per observation to retaining multiple candidate conclusions with their probabilities. Concretely, BeliefMem stores the candidate conclusions as separate memory entries, each carrying a probability that is updated via Noisy-OR rules as new observations arrive. At retrieval, all candidates surface together with their probabilities, keeping alternatives visible to the agent. Since each conclusion in memory retains its probability, BeliefMem preserves the uncertainty that the deterministic paradigm discards, enabling the agent to act with high confidence on well-evidenced knowledge while retaining the capacity to update its confidence when new evidence arrives. Empirical evaluations on LoCoMo and ALFWorld benchmarks show that, even with limited data, BeliefMem achieves the best average performance, remarkably outperforming well-known baselines. More broadly, such probabilistic memory produces substantial gains and explores a new direction for agent memory in partially observable environments.

Why do we need another AI to help the AI? We argue you don't. Stateless LLM sessions impose re-orientation costs on iterative, session-heavy workflows. Prior work addresses cross-session memory through retrieval-augmented approaches: store history, embed it, retrieve by semantic similarity. Cross-session memory is a state management problem, not a search problem. Similarity search fails for named entity resolution within bounded vocabulary contexts because beliefs about a shared technical domain are semantically proximate by construction. A single user is the simplest bounded vocabulary context; engineering teams converge on the same property through shared codebases and terminology. We present Tenure, a local-first proxy that maintains a typed belief store with epistemic status, versioned supersession, and scope isolation, injecting curated context into every LLM session through precision-first retrieval. Hard scope isolation provides a structural guarantee: the right beliefs surface, and only within the boundaries the user has authorized. Tenure's typed schema converts extracted facts into imperative instructions via a why it matters field, making injected beliefs directly actionable rather than raw material for the model to re-derive. A controlled evaluation on 72 retrieval cases demonstrates the gap. Cosine similarity over dense embeddings achieves mean precision of 0.12. Alias-weighted BM25 maintains mean precision of 1.0, passing 72/72 cases versus 8/72 for cosine similarity on the same corpus. Hybrid retrieval typically solves vocabulary mismatch between disparate authors; Tenure eliminates this structurally: query and belief authors are the same person, and an alias enrichment flywheel continuously indexes their specific vocabulary. Under multi-turn topic drift this worsens: the vector backend produces drift scores of 0.43--0.50 on noise-critical turns where BM25 maintains 0.

Chain-of-Thought (CoT) reasoning typically utilizes the discrete language space for thinking, which is inherently inefficient, as many generated tokens only enforce linguistic rules that are not required for reasoning. To bypass this, latent-space thinking allows models to think using the continuous embedding space. While existing methods for training those models show domain-specific gains, they fail to maintain performance in complex tasks, such as mathematical reasoning. We experimentally demonstrate that the Coconut approach, a form of supervised fine-tuning for latent-space thinking, is highly sensitive to design choices and exhibits several inherent limitations. To address these issues, we investigate reinforcement learning (RL) techniques -- an underexplored direction in latent-space thinking -- including GRPO and design a novel Latent RL method for directly optimizing the latent thinking steps. Our experimental results reveal that these RL-trained models still lag behind traditional language-space CoT models in the mathematical reasoning domain. We make our codebase publicly available.

Reliable application of machine learning is of primary importance to the practical deployment of deep learning methods. A fundamental challenge is that models are often unreliable due to overconfidence. In this paper, we estimate a model's reliability by measuring the agreement between its latent space, and the latent space of a foundation model. However, it is challenging to measure the agreement between two different latent spaces due to their incoherence, \eg, arbitrary rotations and different dimensionality. To overcome this incoherence issue, we design a neighborhood agreement measure between latent spaces and find that this agreement is surprisingly well-correlated with the reliability of a model's predictions. Further, we show that fusing neighborhood agreement into a model's predictive confidence in a post-hoc way significantly improves its reliability. Theoretical analysis and extensive experiments on failure detection across various datasets verify the effectiveness of our method on both in-distribution and out-of-distribution settings.

Diffusion large language models (dLLMs) represent a significant advancement in text generation, offering parallel token decoding capabilities. However, existing open-source implementations suffer from quality-speed trade-offs that impede their practical deployment. Conservative sampling strategies typically decode only the most confident token per step to ensure quality (i.e., greedy decoding), at the cost of inference efficiency due to repeated redundant refinement iterations--a phenomenon we term delayed decoding. Through systematic analysis of dLLM decoding dynamics, we characterize this delayed decoding behavior and propose a training-free adaptive parallel decoding strategy, named LocalLeap, to address these inefficiencies. LocalLeap is built on two fundamental empirical principles: local determinism propagation centered on high-confidence anchors and progressive spatial consistency decay. By applying these principles, LocalLeap identifies anchors and performs localized relaxed parallel decoding within bounded neighborhoods, achieving substantial inference step reduction through early commitment of already-determined tokens without compromising output quality. Comprehensive evaluation on various benchmarks demonstrates that LocalLeap achieves 6.94times throughput improvements and reduces decoding steps to just 14.2\% of the original requirement, achieving these gains with negligible performance impact. The source codes are available at: https://github.com/friedrichor/LocalLeap.

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 .

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.

LLMs are increasingly used as long-running conversational agents, yet every major benchmark evaluating their memory treats user information as static facts to be stored and retrieved. That's the wrong model. People change their minds, and over extended interactions, phenomena like opinion drift, over-alignment, and confirmation bias start to matter a lot. BeliefShift introduces a longitudinal benchmark designed specifically to evaluate belief dynamics in multi-session LLM interactions. It covers three tracks: Temporal Belief Consistency, Contradiction Detection, and Evidence-Driven Revision. The dataset includes 2,400 human-annotated multi-session interaction trajectories spanning health, politics, personal values, and product preferences. We evaluate seven models including GPT-4o, Claude 3.5 Sonnet, Gemini 1.5 Pro, LLaMA-3, and Mistral-Large under zero-shot and retrieval-augmented generation (RAG) settings. Results reveal a clear trade-off: models that personalize aggressively resist drift poorly, while factually grounded models miss legitimate belief updates. We further introduce four novel evaluation metrics: Belief Revision Accuracy (BRA), Drift Coherence Score (DCS), Contradiction Resolution Rate (CRR), and Evidence Sensitivity Index (ESI).

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.

Knowledge editing techniques promise to implant new factual knowledge into large language models (LLMs). But do LLMs really believe these facts? We develop a framework to measure belief depth and use it to evaluate the success of knowledge editing techniques. We operationalize belief depth as the extent to which implanted knowledge 1) generalizes to related contexts (e.g. Fermi estimates several logical steps removed), 2) is robust to self-scrutiny and direct challenge, and 3) is represented similarly to genuine knowledge (as measured by linear probes). Our evaluations show that simple prompting and mechanistic editing techniques fail to implant knowledge deeply. In contrast, Synthetic Document Finetuning (SDF) - where models are trained on LLM-generated documents consistent with a fact - often succeeds at implanting beliefs that behave similarly to genuine knowledge. However, SDF's success is not universal, as implanted beliefs that contradict basic world knowledge are brittle and representationally distinct from genuine knowledge. Overall, our work introduces measurable criteria for belief depth and enables the rigorous evaluation necessary for deploying knowledge editing in real-world applications.

Strategic dialogue requires agents to execute distinct dialogue acts, for which belief estimation is essential. While prior work often estimates beliefs accurately, it lacks a principled mechanism to use those beliefs during generation. We bridge this gap by first formalizing two core acts Adversarial and Alignment, and by operationalizing them via probabilistic constraints on what an agent may generate. We instantiate this idea in BEDA, a framework that consists of the world set, the belief estimator for belief estimation, and the conditional generator that selects acts and realizes utterances consistent with the inferred beliefs. Across three settings, Conditional Keeper Burglar (CKBG, adversarial), Mutual Friends (MF, cooperative), and CaSiNo (negotiation), BEDA consistently outperforms strong baselines: on CKBG it improves success rate by at least 5.0 points across backbones and by 20.6 points with GPT-4.1-nano; on Mutual Friends it achieves an average improvement of 9.3 points; and on CaSiNo it achieves the optimal deal relative to all baselines. These results indicate that casting belief estimation as constraints provides a simple, general mechanism for reliable strategic dialogue.

Humans have a powerful and mysterious capacity to reason. By working through a series of purely mental steps, we can make inferences we would not be capable of making directly -- despite the fact that we get no additional data from the world. Similarly, when large language models generate a series of intermediate steps (a chain of thought) before answering a question, they often produce better answers than they otherwise would. We investigate why and how chain-of-thought reasoning is useful in language models, testing the hypothesis that reasoning is effective when training data consists of local clusters of variables that influence each other strongly. These training conditions enable the chaining of accurate local inferences in order to estimate relationships between variables that were not seen together in training. We prove that there will exist a "reasoning gap", where reasoning through intermediate variables improves inference, for the simple case of an autoregressive density estimator trained on local samples from a chain-structured probabilistic model. We then test our hypothesis empirically in more complex models, training an autoregressive language model on samples from Bayes nets but only including a subset of variables in each sample. We test language models' ability to match conditional probabilities with and without intermediate reasoning steps, finding that intermediate steps are only helpful when the training data is locally structured with respect to dependencies between variables and that the combination of locally-structured observations and reasoning is much more data-efficient than training on all variables. Our results illustrate how the effectiveness of reasoning step by step is rooted in the local statistical structure of the training data.

Rapid advancements in large language models (LLMs) have sparked the question whether these models possess some form of consciousness. To tackle this challenge, Butlin et al. (2023) introduced a list of indicators for consciousness in artificial systems based on neuroscientific theories. In this work, we evaluate a key indicator from this list, called HOT-3, which tests for agency guided by a general belief-formation and action selection system that updates beliefs based on meta-cognitive monitoring. We view beliefs as representations in the model's latent space that emerge in response to a given input, and introduce a metric to quantify their dominance during generation. Analyzing the dynamics between competing beliefs across models and tasks reveals three key findings: (1) external manipulations systematically modulate internal belief formation, (2) belief formation causally drives the model's action selection, and (3) models can monitor and report their own belief states. Together, these results provide empirical support for the existence of belief-guided agency and meta-cognitive monitoring in LLMs. More broadly, our work lays methodological groundwork for investigating the emergence of agency, beliefs, and meta-cognition in LLMs.

Recent advances in large reasoning models (LRMs) have enabled agentic search systems to perform complex multi-step reasoning across multiple sources. However, most studies focus on general information retrieval and rarely explores vertical domains with unique challenges. In this work, we focus on local life services and introduce LocalSearchBench, which encompass diverse and complex business scenarios. Real-world queries in this domain are often ambiguous and require multi-hop reasoning across merchants and products, remaining challenging and not fully addressed. As the first comprehensive benchmark for agentic search in local life services, LocalSearchBench includes over 150,000 high-quality entries from various cities and business types. We construct 300 multi-hop QA tasks based on real user queries, challenging agents to understand questions and retrieve information in multiple steps. We also developed LocalPlayground, a unified environment integrating multiple tools for agent interaction. Experiments show that even state-of-the-art LRMs struggle on LocalSearchBench: the best model (DeepSeek-V3.1) achieves only 34.34% correctness, and most models have issues with completeness (average 77.33%) and faithfulness (average 61.99%). This highlights the need for specialized benchmarks and domain-specific agent training in local life services. Code, Benchmark, and Leaderboard are available at localsearchbench.github.io.

AI agents deployed as persistent assistants must maintain correct beliefs as their information environment evolves. In practice, evidence is scattered across heterogeneous sources that often contradict one another, new information can invalidate earlier conclusions, and user preferences surface through corrections rather than explicit instructions. Existing benchmarks largely assume static, single-authority settings and do not evaluate whether agents can keep up with this complexity. We introduce ClawArena, a benchmark for evaluating AI agents in evolving information environments. Each scenario maintains a complete hidden ground truth while exposing the agent only to noisy, partial, and sometimes contradictory traces across multi-channel sessions, workspace files, and staged updates. Evaluation is organized around three coupled challenges: multi-source conflict reasoning, dynamic belief revision, and implicit personalization, whose interactions yield a 14-category question taxonomy. Two question formats, multi-choice (set-selection) and shell-based executable checks, test both reasoning and workspace grounding. The current release contains 64 scenarios across 8 professional domains, totaling 1{,}879 evaluation rounds and 365 dynamic updates. Experiments on five agent frameworks and five language models show that both model capability (15.4% range) and framework design (9.2%) substantially affect performance, that self-evolving skill frameworks can partially close model-capability gaps, and that belief revision difficulty is determined by update design strategy rather than the mere presence of updates. Code is available at https://github.com/aiming-lab/ClawArena.

Understanding geometric properties of natural language processing models' latent spaces allows the manipulation of these properties for improved performance on downstream tasks. One such property is the amount of data spread in a model's latent space, or how fully the available latent space is being used. In this work, we define data spread and demonstrate that the commonly used measures of data spread, Average Cosine Similarity and a partition function min/max ratio I(V), do not provide reliable metrics to compare the use of latent space across models. We propose and examine eight alternative measures of data spread, all but one of which improve over these current metrics when applied to seven synthetic data distributions. Of our proposed measures, we recommend one principal component-based measure and one entropy-based measure that provide reliable, relative measures of spread and can be used to compare models of different sizes and dimensionalities.

In the field of algorithmic fairness, significant attention has been put on group fairness criteria, such as Demographic Parity and Equalized Odds. Nevertheless, these objectives, measured as global averages, have raised concerns about persistent local disparities between sensitive groups. In this work, we address the problem of local fairness, which ensures that the predictor is unbiased not only in terms of expectations over the whole population, but also within any subregion of the feature space, unknown at training time. To enforce this objective, we introduce ROAD, a novel approach that leverages the Distributionally Robust Optimization (DRO) framework within a fair adversarial learning objective, where an adversary tries to infer the sensitive attribute from the predictions. Using an instance-level re-weighting strategy, ROAD is designed to prioritize inputs that are likely to be locally unfair, i.e. where the adversary faces the least difficulty in reconstructing the sensitive attribute. Numerical experiments demonstrate the effectiveness of our method: it achieves Pareto dominance with respect to local fairness and accuracy for a given global fairness level across three standard datasets, and also enhances fairness generalization under distribution shift.

Large language models (LLMs) are increasingly deployed on long-horizon tasks in partially observable environments, where they must act while inferring and tracking a complex environment state over many steps. This leads to two challenges: partial observability requires maintaining uncertainty over unobserved world attributes, and long interaction history causes context to grow without bound, diluting task-relevant information. A principled solution to both challenges is a belief state: a posterior distribution over environment states given past observations and actions, which compactly encodes history for decision making regardless of episode length. In LLM agents, however, the open-ended nature of text makes it unclear how to represent such a distribution. Therefore, we introduce Agent-BRACE: Agent Belief state Representation via Abstraction and Confidence Estimation, a method that decouples an LLM agent into a belief state model and a policy model, jointly optimized via reinforcement learning. The belief state model produces a structured approximation of the belief distribution: a set of atomic natural language claims about the environment, each annotated with an ordinal verbalized certainty label ranging from certain to unknown. The policy model conditions on this compact, structured approximate belief rather than the full history, learning to select actions under explicit uncertainty. Across long-horizon, partially observable embodied language environments, Agent-BRACE achieves an average absolute improvement of +14.5% (Qwen2.5-3B-Instruct) and +5.3% (Qwen3-4B-Instruct), outperforming strong RL baselines while maintaining a near-constant context window independent of episode length. Further analysis shows that the learned belief becomes increasingly calibrated over the course of an episode as evidence accumulates.

Large language model (LLM) queries are predominantly processed by frontier models in centralized cloud infrastructure. Rapidly growing demand strains this paradigm, and cloud providers struggle to scale infrastructure at pace. Two advances enable us to rethink this paradigm: small LMs (<=20B active parameters) now achieve competitive performance to frontier models on many tasks, and local accelerators (e.g., Apple M4 Max) run these models at interactive latencies. This raises the question: can local inference viably redistribute demand from centralized infrastructure? Answering this requires measuring whether local LMs can accurately answer real-world queries and whether they can do so efficiently enough to be practical on power-constrained devices (i.e., laptops). We propose intelligence per watt (IPW), task accuracy divided by unit of power, as a metric for assessing capability and efficiency of local inference across model-accelerator pairs. We conduct a large-scale empirical study across 20+ state-of-the-art local LMs, 8 accelerators, and a representative subset of LLM traffic: 1M real-world single-turn chat and reasoning queries. For each query, we measure accuracy, energy, latency, and power. Our analysis reveals 3 findings. First, local LMs can accurately answer 88.7% of single-turn chat and reasoning queries with accuracy varying by domain. Second, from 2023-2025, IPW improved 5.3x and local query coverage rose from 23.2% to 71.3%. Third, local accelerators achieve at least 1.4x lower IPW than cloud accelerators running identical models, revealing significant headroom for optimization. These findings demonstrate that local inference can meaningfully redistribute demand from centralized infrastructure, with IPW serving as the critical metric for tracking this transition. We release our IPW profiling harness for systematic intelligence-per-watt benchmarking.

Large language models (LLMs) can exhibit advanced reasoning yet still generate incorrect answers. We hypothesize that such errors frequently stem from spurious beliefs, propositions the model internally considers true but are incorrect. To address this, we propose a method to rectify the belief space by suppressing these spurious beliefs while simultaneously enhancing true ones, thereby enabling more reliable inferences. Our approach first identifies the beliefs that lead to incorrect or correct answers by prompting the model to generate textual explanations, using our Forward-Backward Beam Search (FBBS). We then apply unlearning to suppress the identified spurious beliefs and enhance the true ones, effectively rectifying the model's belief space. Empirical results on multiple QA datasets and LLMs show that our method corrects previously misanswered questions without harming overall model performance. Furthermore, our approach yields improved generalization on unseen data, suggesting that rectifying a model's belief space is a promising direction for mitigating errors and enhancing overall reliability.

The discovery of the disentanglement properties of the latent space in GANs motivated a lot of research to find the semantically meaningful directions on it. In this paper, we suggest that the disentanglement property is closely related to the geometry of the latent space. In this regard, we propose an unsupervised method for finding the semantic-factorizing directions on the intermediate latent space of GANs based on the local geometry. Intuitively, our proposed method, called Local Basis, finds the principal variation of the latent space in the neighborhood of the base latent variable. Experimental results show that the local principal variation corresponds to the semantic factorization and traversing along it provides strong robustness to image traversal. Moreover, we suggest an explanation for the limited success in finding the global traversal directions in the latent space, especially W-space of StyleGAN2. We show that W-space is warped globally by comparing the local geometry, discovered from Local Basis, through the metric on Grassmannian Manifold. The global warpage implies that the latent space is not well-aligned globally and therefore the global traversal directions are bound to show limited success on it.

Making statements about the performance of trained models on tasks involving new data is one of the primary goals of machine learning, i.e., to understand the generalization power of a model. Various capacity measures try to capture this ability, but usually fall short in explaining important characteristics of models that we observe in practice. In this study, we propose the local effective dimension as a capacity measure which seems to correlate well with generalization error on standard data sets. Importantly, we prove that the local effective dimension bounds the generalization error and discuss the aptness of this capacity measure for machine learning models.

We propose a new localized inference algorithm for answering marginalization queries in large graphical models with the correlation decay property. Given a query variable and a large graphical model, we define a much smaller model in a local region around the query variable in the target model so that the marginal distribution of the query variable can be accurately approximated. We introduce two approximation error bounds based on the Dobrushin's comparison theorem and apply our bounds to derive a greedy expansion algorithm that efficiently guides the selection of neighbor nodes for localized inference. We verify our theoretical bounds on various datasets and demonstrate that our localized inference algorithm can provide fast and accurate approximation for large graphical models.

Retrieval-Augmented Generation (RAG) mitigates hallucinations in Large Language Models (LLMs) by integrating external knowledge. However, conflicts between parametric knowledge and retrieved context pose challenges, particularly when retrieved information is unreliable or the model's internal knowledge is outdated. In such cases, LLMs struggle to determine whether to rely more on their own parameters or the conflicted context. To address this, we propose **CK-PLUG**, a plug-and-play method for controlling LLMs' reliance on parametric and contextual knowledge. We introduce a novel knowledge consistency metric, Confidence Gain, which detects knowledge conflicts by measuring entropy shifts in token probability distributions after context insertion. CK-PLUG then enables fine-grained control over knowledge preference by adjusting the probability distribution of tokens with negative confidence gain through a single tuning parameter. Experiments demonstrate CK-PLUG's ability to significantly regulate knowledge reliance in counterfactual RAG scenarios while maintaining generation fluency and knowledge accuracy. For instance, on Llama3-8B, memory recall (MR) of RAG response can be adjusted within a broad range (9.9%-71.9%), compared to the baseline of 42.1%. Moreover, CK-PLUG supports adaptive control based on the model's confidence in both internal and external knowledge, achieving consistent performance improvements across various general RAG tasks. Our code is available at: https://github.com/byronBBL/CK-PLUG{this https URL}.

Large language models (LLMs) face issues in handling factual knowledge, making it vital to evaluate their true ability to understand facts. In this study, we introduce knowledge probing frameworks, BELIEF(-ICL), to evaluate the knowledge understanding ability of not only encoder-based PLMs but also decoder-based PLMs from diverse perspectives. BELIEFs utilize a multi-prompt dataset to evaluate PLM's accuracy, consistency, and reliability in factual knowledge understanding. To provide a more reliable evaluation with BELIEFs, we semi-automatically create MyriadLAMA, which has more diverse prompts than existing datasets. We validate the effectiveness of BELIEFs in correctly and comprehensively evaluating PLM's factual understanding ability through extensive evaluations. We further investigate key factors in learning facts in LLMs, and reveal the limitation of the prompt-based knowledge probing. The dataset is anonymously publicized.

Recent work explores latent reasoning to improve reasoning efficiency by replacing explicit reasoning trajectories with continuous representations in a latent space, yet its effectiveness varies across settings. Analysis of model confidence dynamics under latent reasoning reveals that thinking trajectories ending in incorrect answers contain fewer low-confidence steps than those ending in correct answers. Meanwhile, we suggest that soft embeddings aggregated by multiple low-confidence thinking alternatives may introduce and propagate noise, leading to high confidence in unreliable reasoning trajectories. Motivated by these observations, ThinkRouter, an inference-time confidence-aware routing mechanism is proposed to avoid high confidence and noise for efficient reasoning. ThinkRouter routes thinking to the discrete token space when model confidence is low, and to the latent space otherwise. Extensive experiments on STEM reasoning and coding benchmarks across diverse large reasoning models demonstrate that ThinkRouter outperforms explicit CoT, random routing, and latent reasoning baselines in terms of accuracy, achieving an average improvement of 19.70 points in Pass@1, while reducing generation length by up to 15.55%. Further comprehensive analysis reveals that ThinkRouter can calibrate errors arising from explicit CoT and latent reasoning, and accelerates end-of-thinking token generation by globally lowering model confidence.

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.

We address the neural network robustness problem by adding Similarity (i.e., correctly predicted depth-matches into training)-awareness and Distance-to-training-distribution-awareness to the existing output Magnitude (i.e., decision-boundary)-awareness of the softmax function. The resulting SDM activation function provides strong signals of the relative epistemic (reducible) predictive uncertainty. We use this novel behavior to further address the complementary HCI problem of mapping the output to human-interpretable summary statistics over relevant partitions of a held-out calibration set. Estimates of prediction-conditional uncertainty are obtained via a parsimonious learned transform over the class-conditional empirical CDFs of the output of a final-layer SDM activation function. For decision-making and as an intrinsic model check, estimates of class-conditional accuracy are obtained by further partitioning the high-probability regions of this calibrated output into class-conditional, region-specific CDFs. The uncertainty estimates from SDM calibration are remarkably robust to test-time distribution shifts and out-of-distribution inputs; incorporate awareness of the effective sample size; provide estimates of uncertainty from the learning and data splitting processes; and are well-suited for selective classification and conditional branching for additional test-time compute based on the predictive uncertainty, as for selective LLM generation, routing, and composition over multiple models and retrieval. Finally, we construct SDM networks, LLMs with uncertainty-aware verification and interpretability-by-exemplar as intrinsic properties. We provide open-source software implementing these results.

Long-horizon interactions require language models to manage accumulating information: when to update their state, when to preserve their state, and what to ignore. We study this challenge as Contextual Belief Management (CBM): maintaining a predicted belief state aligned with formal evidence while isolating task-irrelevant noise. To make CBM measurable, we introduce BeliefTrack, a closed-world benchmark spanning Rule Discovery and Circuit Diagnosis, where a finite belief space and symbolic verifiers enable exact turn-level evaluation. BeliefTrack diagnoses three failures: Failed Stay, Failed Update, and Failed Isolation. Across multiple LLMs, vanilla models exhibit severe CBM failures, while explicit belief-tracking prompts provide limited gains. In contrast, reinforcement learning with belief-state rewards reduces failure rates by 70.9\% on average. Further probing reveals latent belief-state dynamics behind these failures, and representation-level steering reduces failure rates by 46.1\% across two tasks\footnote{Code is coming soon at https://github.com/zjunlp/CBM.

We study how to characterize and predict the truthfulness of texts generated from large language models (LLMs), which serves as a crucial step in building trust between humans and LLMs. Although several approaches based on entropy or verbalized uncertainty have been proposed to calibrate model predictions, these methods are often intractable, sensitive to hyperparameters, and less reliable when applied in generative tasks with LLMs. In this paper, we suggest investigating internal activations and quantifying LLM's truthfulness using the local intrinsic dimension (LID) of model activations. Through experiments on four question answering (QA) datasets, we demonstrate the effectiveness ohttps://info.arxiv.org/help/prep#abstractsf our proposed method. Additionally, we study intrinsic dimensions in LLMs and their relations with model layers, autoregressive language modeling, and the training of LLMs, revealing that intrinsic dimensions can be a powerful approach to understanding LLMs.

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.

Latent space is rapidly emerging as a native substrate for language-based models. While modern systems are still commonly understood through explicit token-level generation, an increasing body of work shows that many critical internal processes are more naturally carried out in continuous latent space than in human-readable verbal traces. This shift is driven by the structural limitations of explicit-space computation, including linguistic redundancy, discretization bottlenecks, sequential inefficiency, and semantic loss. This survey aims to provide a unified and up-to-date landscape of latent space in language-based models. We organize the survey into five sequential perspectives: Foundation, Evolution, Mechanism, Ability, and Outlook. We begin by delineating the scope of latent space, distinguishing it from explicit or verbal space and from the latent spaces commonly studied in generative visual models. We then trace the field's evolution from early exploratory efforts to the current large-scale expansion. To organize the technical landscape, we examine existing work through the complementary lenses of mechanism and ability. From the perspective of Mechanism, we identify four major lines of development: Architecture, Representation, Computation, and Optimization. From the perspective of Ability, we show how latent space supports a broad capability spectrum spanning Reasoning, Planning, Modeling, Perception, Memory, Collaboration, and Embodiment. Beyond consolidation, we discuss the key open challenges, and outline promising directions for future research. We hope this survey serves not only as a reference for existing work, but also as a foundation for understanding latent space as a general computational and systems paradigm for next-generation intelligence.

Concept Bottleneck Models (CBMs) predict through human-interpretable concepts, but they typically output point concept probabilities that conflate epistemic uncertainty (reducible model underspecification) with aleatoric uncertainty (irreducible input ambiguity). This makes concept-level uncertainty hard to interpret and, more importantly, hard to act upon. We introduce CREDENCE (Credal Ensemble Concept Estimation), a CBM framework that decomposes concept uncertainty by construction. CREDENCE represents each concept as a credal prediction (a probability interval), derives epistemic uncertainty from disagreement across diverse concept heads, and estimates aleatoric uncertainty via a dedicated ambiguity output trained to match annotator disagreement when available. The resulting signals support prescriptive decisions: automate low-uncertainty cases, prioritize data collection for high-epistemic cases, route high-aleatoric cases to human review, and abstain when both are high. Across several tasks, we show that epistemic uncertainty is positively associated with prediction errors, whereas aleatoric uncertainty closely tracks annotator disagreement, providing guidance beyond error correlation. Our implementation is available at the following link: https://github.com/Tankiit/Credal_Sets/tree/ensemble-credal-cbm

Can LLMs accurately adjust their confidence when facing opposition? Building on previous studies measuring calibration on static fact-based question-answering tasks, we evaluate Large Language Models (LLMs) in a dynamic, adversarial debate setting, uniquely combining two realistic factors: (a) a multi-turn format requiring models to update beliefs as new information emerges, and (b) a zero-sum structure to control for task-related uncertainty, since mutual high-confidence claims imply systematic overconfidence. We organized 60 three-round policy debates among ten state-of-the-art LLMs, with models privately rating their confidence (0-100) in winning after each round. We observed five concerning patterns: (1) Systematic overconfidence: models began debates with average initial confidence of 72.9% vs. a rational 50% baseline. (2) Confidence escalation: rather than reducing confidence as debates progressed, debaters increased their win probabilities, averaging 83% by the final round. (3) Mutual overestimation: in 61.7% of debates, both sides simultaneously claimed >=75% probability of victory, a logical impossibility. (4) Persistent self-debate bias: models debating identical copies increased confidence from 64.1% to 75.2%; even when explicitly informed their chance of winning was exactly 50%, confidence still rose (from 50.0% to 57.1%). (5) Misaligned private reasoning: models' private scratchpad thoughts sometimes differed from their public confidence ratings, raising concerns about faithfulness of chain-of-thought reasoning. These results suggest LLMs lack the ability to accurately self-assess or update their beliefs in dynamic, multi-turn tasks; a major concern as LLMs are now increasingly deployed without careful review in assistant and agentic roles. Code for our experiments is available at https://github.com/pradyuprasad/llms_overconfidence

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.

Spatial confounding poses a significant challenge in scientific studies involving spatial data, where unobserved spatial variables can influence both treatment and outcome, possibly leading to spurious associations. To address this problem, we introduce SpaCE: The Spatial Confounding Environment, the first toolkit to provide realistic benchmark datasets and tools for systematically evaluating causal inference methods designed to alleviate spatial confounding. Each dataset includes training data, true counterfactuals, a spatial graph with coordinates, and smoothness and confounding scores characterizing the effect of a missing spatial confounder. It also includes realistic semi-synthetic outcomes and counterfactuals, generated using state-of-the-art machine learning ensembles, following best practices for causal inference benchmarks. The datasets cover real treatment and covariates from diverse domains, including climate, health and social sciences. SpaCE facilitates an automated end-to-end pipeline, simplifying data loading, experimental setup, and evaluating machine learning and causal inference models. The SpaCE project provides several dozens of datasets of diverse sizes and spatial complexity. It is publicly available as a Python package, encouraging community feedback and contributions.

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.

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.

Forecasting from partial observations is central to world modeling. Many recent methods represent the world through images, and reduce forecasting to stochastic video generation. Although such methods excel at realism and visual fidelity, predicting pixels is computationally intensive and not directly useful in many applications, as it requires translating RGB into signals useful for decision making. An alternative approach uses features from vision foundation models (VFMs) as world representations, performing deterministic regression to predict future world states. These features can be directly translated into actionable signals such as semantic segmentation and depth, while remaining computationally efficient. However, deterministic regression averages over multiple plausible futures, undermining forecast accuracy by failing to capture uncertainty. To address this crucial limitation, we introduce a generative forecaster that performs autoregressive flow matching in VFM feature space. Our key insight is that generative modeling in this space requires encoding VFM features into a compact latent space suitable for diffusion. We show that this latent space preserves information more effectively than previously used PCA-based alternatives, both for forecasting and other applications, such as image generation. Our latent predictions can be easily decoded into multiple useful and interpretable output modalities: semantic segmentation, depth, surface normals, and even RGB. With matched architecture and compute, our method produces sharper and more accurate predictions than regression across all modalities. Our results suggest that stochastic conditional generation of VFM features offers a promising and scalable foundation for future world models.

Numerous applications of large language models (LLMs) rely on their ability to perform step-by-step reasoning. However, the reasoning behavior of LLMs remains poorly understood, posing challenges to research, development, and safety. To address this gap, we introduce landscape of thoughts-the first visualization tool for users to inspect the reasoning paths of chain-of-thought and its derivatives on any multi-choice dataset. Specifically, we represent the states in a reasoning path as feature vectors that quantify their distances to all answer choices. These features are then visualized in two-dimensional plots using t-SNE. Qualitative and quantitative analysis with the landscape of thoughts effectively distinguishes between strong and weak models, correct and incorrect answers, as well as different reasoning tasks. It also uncovers undesirable reasoning patterns, such as low consistency and high uncertainty. Additionally, users can adapt our tool to a model that predicts the property they observe. We showcase this advantage by adapting our tool to a lightweight verifier that evaluates the correctness of reasoning paths. The code is publicly available at: https://github.com/tmlr-group/landscape-of-thoughts.

Large language models (LLMs) have shown impressive performance in various reasoning benchmarks with the emergence of Chain-of-Thought (CoT) and its derivative methods, particularly in tasks involving multi-choice questions (MCQs). However, current works all process data uniformly without considering the problem-solving difficulty, which means an excessive focus on simple questions while insufficient to intricate ones. To address this challenge, we inspired by humans using heuristic strategies to categorize tasks and handle them individually, propose to apply the Divide and Conquer to LLMs reasoning. First, we divide questions into different subsets based on the statistical confidence score (CS), then fix nearly resolved sets and conquer demanding nuanced process ones with elaborately designed methods, including Prior Knowledge based Reasoning (PKR) and Filter Choices based Reasoning (FCR), as well as their integration variants. Our experiments demonstrate that this proposed strategy significantly boosts the models' reasoning abilities across nine datasets involving arithmetic, commonsense, and logic tasks. For instance, compared to baseline, we make a striking improvement on low confidence subsets of 8.72\% for AQuA, 15.07\% for ARC Challenge and 7.71\% for RiddleSense. In addition, through extensive analysis on length of rationale and number of options, we verify that longer reasoning paths in PKR could prevent models from referring infer-harmful shortcuts, and also find that removing irrelevant choices in FCR would substantially avoid models' confusion. The code is at https://github.com/AiMijie/Divide-and-Conquer

Recent large language models (LLMs) can generate long Chain-of-Thought (CoT) at test time, enabling them to solve complex tasks. These reasoning steps in CoT are often assumed as a faithful reflection of the model's internal thinking process, and used to monitor unsafe intentions. However, we find many reasoning steps don't truly contribute to LLMs' prediction. We measure the step-wise causal influence of each reasoning step on the model's final prediction with a proposed True Thinking Score (TTS). We reveal that LLMs often interleave between true-thinking steps (which are genuinely used to produce the final output) and decorative-thinking steps (which only give the appearance of reasoning but have minimal causal impact). Notably, only a small subset of the total reasoning steps have a high TTS that causally drive the model's prediction: e.g., for the AIME dataset, only an average of 2.3% of reasoning steps in CoT have a TTS >= 0.7 (range: 0-1) under the Qwen-2.5 model. Furthermore, we identify a TrueThinking direction in the latent space of LLMs. By steering along or against this direction, we can force the model to perform or disregard certain CoT steps when computing the final result. Finally, we highlight that self-verification steps in CoT (i.e., aha moments) can also be decorative, where LLMs do not truly verify their solution. Steering along the TrueThinking direction can force internal reasoning over these steps, resulting in a change in the final results. Overall, our work reveals that LLMs often verbalize reasoning steps without actually performing them internally, which undermines both the efficiency of LLM reasoning and the trustworthiness of CoT.

Activation decomposition methods in language models are tightly coupled to geometric assumptions on how concepts are realized in activation space. Existing approaches search for individual global directions, implicitly assuming linear separability, which overlooks concepts with nonlinear or multi-dimensional structure. In this work, we leverage Mixture of Factor Analyzers (MFA) as a scalable, unsupervised alternative that models the activation space as a collection of Gaussian regions with their local covariance structure. MFA decomposes activations into two compositional geometric objects: the region's centroid in activation space, and the local variation from the centroid. We train large-scale MFAs for Llama-3.1-8B and Gemma-2-2B, and show they capture complex, nonlinear structures in activation space. Moreover, evaluations on localization and steering benchmarks show that MFA outperforms unsupervised baselines, is competitive with supervised localization methods, and often achieves stronger steering performance than sparse autoencoders. Together, our findings position local geometry, expressed through subspaces, as a promising unit of analysis for scalable concept discovery and model control, accounting for complex structures that isolated directions fail to capture.

It is important for Large Language Models to be aware of the boundary of their knowledge, the mechanism of identifying known and unknown queries. This type of awareness can help models perform adaptive inference, such as invoking RAG, engaging in slow and deep thinking, or adopting the abstention mechanism, which is beneficial to the development of efficient and trustworthy AI. In this work, we propose a method to detect knowledge boundaries via Query-Level Uncertainty, which aims to determine if the model is able to address a given query without generating any tokens. To this end, we introduce a novel and training-free method called Internal Confidence, which leverages self-evaluations across layers and tokens. Empirical results on both factual QA and mathematical reasoning tasks demonstrate that our internal confidence can outperform several baselines. Furthermore, we showcase that our proposed method can be used for efficient RAG and model cascading, which is able to reduce inference costs while maintaining performance.

Forecasting has become a natural benchmark for reasoning under uncertainty. Yet existing evaluations of large language models remain limited to judgmental tasks in simple formats, such as binary or multiple-choice questions. In practice, however, forecasting spans a far broader scope. Across domains such as economics, public health, and social demographics, decisions hinge on numerical estimates over continuous quantities, a capability that current benchmarks do not capture. Evaluating such estimates requires a format that makes uncertainty explicit and testable. We propose prediction intervals as a natural and rigorous interface for this purpose. They demand scale awareness, internal consistency across confidence levels, and calibration over a continuum of outcomes, making them a more suitable evaluation format than point estimates for numerical forecasting. To assess this capability, we introduce a new benchmark QuantSightBench, and evaluate frontier models under multiple settings, assessing both empirical coverage and interval sharpness. Our results show that none of the 11 evaluated frontier and open-weight models achieves the 90\% coverage target, with the top performers Gemini 3.1 Pro (79.1\%), Grok 4 (76.4\%), and GPT-5.4 (75.3\%) all falling at least 10 percentage points short. Calibration degrades sharply at extreme magnitudes, revealing systematic overconfidence across all evaluated models.

While Vision-Language-Action (VLA) models have revolutionized autonomous driving by unifying perception and planning, their reliance on explicit textual Chain-of-Thought (CoT) leads to semantic-perceptual decoupling and perceptual-symbolic conflicts. Recent shifts toward latent reasoning attempt to bypass these bottlenecks by thinking in continuous hidden space. However, without explicit intermediate constraints, standard latent CoT often operates as a physics-agnostic representation. To address this, we propose the Latent Spatio-Temporal VLA (LaST-VLA), a framework shifting the reasoning paradigm from discrete symbolic processing into a physically grounded Latent Spatio-Temporal CoT. By implementing a dual-feature alignment mechanism, we distill geometric constraints from 3D foundation models and dynamic foresight from world models directly into the latent space. Coupled with a progressive SFT training strategy that transitions from feature alignment to trajectory generation, and refined via Reinforcement Learning with Group Relative Policy Optimization (GRPO) to ensure safety and rule compliance. \method~setting a new record on NAVSIM v1 (91.3 PDMS) and NAVSIM v2 (87.1 EPDMS), while excelling in spatial-temporal reasoning on SURDS and NuDynamics benchmarks.

Large language models (LLMs) can perform reasoning computations both internally within their latent space and externally by generating explicit token sequences like chains of thought. Significant progress in enhancing reasoning abilities has been made by scaling test-time compute. However, understanding and quantifying model-internal reasoning abilities - the inferential "leaps" models make between individual token predictions - remains crucial. This study introduces a benchmark (n = 4,000 items) designed to quantify model-internal reasoning in different domains. We achieve this by having LLMs indicate the correct solution to reasoning problems not through descriptive text, but by selecting a specific language of their initial response token that is different from English, the benchmark language. This not only requires models to reason beyond their context window, but also to overrise their default tendency to respond in the same language as the prompt, thereby posing an additional cognitive strain. We evaluate a set of 18 LLMs, showing significant performance variations, with GPT-4.5 achieving the highest accuracy (74.7%), outperforming models like Grok-2 (67.2%), and Llama 3.1 405B (65.6%). Control experiments and difficulty scaling analyses suggest that while LLMs engage in internal reasoning, we cannot rule out heuristic exploitations under certain conditions, marking an area for future investigation. Our experiments demonstrate that LLMs can "think" via latent-space computations, revealing model-internal inference strategies that need further understanding, especially regarding safety-related concerns such as covert planning, goal-seeking, or deception emerging without explicit token traces.

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.

While confidence estimation is a promising direction for mitigating hallucinations in Large Language Models (LLMs), current research dominantly focuses on single-turn settings. The dynamics of model confidence in multi-turn conversations, where context accumulates and ambiguity is progressively resolved, remain largely unexplored. Reliable confidence estimation in multi-turn settings is critical for many downstream applications, such as autonomous agents and human-in-the-loop systems. This work presents the first systematic study of confidence estimation in multi-turn interactions, establishing a formal evaluation framework grounded in two key desiderata: per-turn calibration and monotonicity of confidence as more information becomes available. To facilitate this, we introduce novel metrics, including a length-normalized Expected Calibration Error (InfoECE), and a new "Hinter-Guesser" paradigm for generating controlled evaluation datasets. Our experiments reveal that widely-used confidence techniques struggle with calibration and monotonicity in multi-turn dialogues. We propose P(Sufficient), a logit-based probe that achieves comparatively better performance, although the task remains far from solved. Our work provides a foundational methodology for developing more reliable and trustworthy conversational agents.

We introduce Minary, a computational framework designed as a candidate for the first formally provable autopoietic primitive. Minary represents interacting probabilistic events as multi-dimensional vectors and combines them via linear superposition rather than multiplicative scalar operations, thereby preserving uncertainty and enabling constructive and destructive interference in the range [-1,1]. A fixed set of ``perspectives'' evaluates ``semantic dimensions'' according to hidden competencies, and their interactions drive two discrete-time stochastic processes. We model this system as an iterated random affine map and use the theory of iterated random functions to prove that it converges in distribution to a unique stationary law; we moreover obtain an explicit closed form for the limiting expectation in terms of row, column, and global averages of the competency matrix. We then derive exact formulas for the mean and variance of the normalized consensus conditioned on the activation of a given semantic dimension, revealing how consensus depends on competency structure rather than raw input signals. Finally, we argue that Minary is organizationally closed yet operationally open in the sense of Maturana and Varela, and we discuss implications for building self-maintaining, distributed, and parallelizable computational systems that house a uniquely subjective notion of identity.

Recent advancements in large language models (LLMs) often rely on generating intermediate reasoning steps to enhance accuracy. However, little work has examined how reasoning utility contributes to the final answer's correctness. Due to the stochastic nature of autoregressive generation, generating more context does not guarantee increased confidence in the answer. If we could predict, during generation, whether a reasoning step will be useful, we could stop early or prune ineffective steps, avoiding distractions in the final decision. We present an oracle study on MATH dataset, using Qwen2.5-32B and GPT-4o to generate reasoning chains, and then employing a separate model (Qwen3-8B) to quantify the utility of these chains for final accuracy. Specifically, we measure the model's uncertainty on the answer span Y at each reasoning step using conditional entropy (expected negative log-likelihood over the vocabulary) with context expanding step by step. Our results show a clear pattern: conditional entropy that decreases over steps is strongly associated with correct answers, whereas flat or increasing entropy often results in wrong answers. We also corroborate that incorrect reasoning paths tend to be longer than correct ones, suggesting that longer reasoning does not necessarily yield better outcomes. These findings serve as a foundation to inspire future work on designing efficient reasoning pipelines that detect and avoid unproductive reasoning early.

Large vision-language models (LVLMs) have recently achieved rapid progress, exhibiting great perception and reasoning abilities concerning visual information. However, when faced with prompts in different sizes of solution spaces, LVLMs fail to always give consistent answers regarding the same knowledge point. This inconsistency of answers between different solution spaces is prevalent in LVLMs and erodes trust. To this end, we provide a multi-modal benchmark ConBench, to intuitively analyze how LVLMs perform when the solution space of a prompt revolves around a knowledge point. Based on the ConBench tool, we are the first to reveal the tapestry and get the following findings: (1) In the discriminate realm, the larger the solution space of the prompt, the lower the accuracy of the answers. (2) Establish the relationship between the discriminative and generative realms: the accuracy of the discriminative question type exhibits a strong positive correlation with its Consistency with the caption. (3) Compared to open-source models, closed-source models exhibit a pronounced bias advantage in terms of Consistency. Eventually, we ameliorate the consistency of LVLMs by trigger-based diagnostic refinement, indirectly improving the performance of their caption. We hope this paper will accelerate the research community in better evaluating their models and encourage future advancements in the consistency domain. The project is available at https://github.com/foundation-multimodal-models/ConBench.

Large reasoning models, such as OpenAI o1 and DeepSeek-R1, tend to become increasingly verbose as their reasoning capabilities improve. These inflated Chain-of-Thought (CoT) trajectories often exceed what the underlying problems require, wasting compute, latency, and context budgets. While introducing length-based efficiency rewards during reinforcement learning offers a natural remedy, existing methods struggle with two fundamental challenges: the optimal balance between correctness and efficiency is non-stationary throughout training, and intrinsic reasoning budgets vary drastically across problems. Relying on static reward weights and global length constraints inevitably forces a compromise between degraded accuracy and unrealized compression. To overcome these limitations, we propose LEAD (Length-Efficient Adaptive and Dynamic reasoning), a method that replaces static heuristics with online, self-adaptive mechanisms. LEAD dynamically calibrates the correctness-efficiency trade-off at each step using a Potential-Scaled Instability, directing optimization capacity to the most informative learning signal. Furthermore, it estimates an adaptive per-problem target length online based on the model's own correct rollouts, applying a symmetric efficiency reward that penalizes both overthinking and over-compression. Evaluated on five mathematical reasoning benchmarks, LEAD achieves the highest accuracy and Accuracy-Efficiency Score among RL-trained efficient-reasoning methods while producing substantially shorter outputs than the base model.

Hallucination in large language models (LLMs) can be detected by assessing the uncertainty of model outputs, typically measured using entropy. Semantic entropy (SE) enhances traditional entropy estimation by quantifying uncertainty at the semantic cluster level. However, as modern LLMs generate longer one-sentence responses, SE becomes less effective because it overlooks two crucial factors: intra-cluster similarity (the spread within a cluster) and inter-cluster similarity (the distance between clusters). To address these limitations, we propose a simple black-box uncertainty quantification method inspired by nearest neighbor estimates of entropy. Our approach can also be easily extended to white-box settings by incorporating token probabilities. Additionally, we provide theoretical results showing that our method generalizes semantic entropy. Extensive empirical results demonstrate its effectiveness compared to semantic entropy across two recent LLMs (Phi3 and Llama3) and three common text generation tasks: question answering, text summarization, and machine translation. Our code is available at https://github.com/BigML-CS-UCLA/SNNE.

Large Reasoning Models have demonstrated remarkable performance with the advancement of test-time scaling techniques, which enhances prediction accuracy by generating multiple candidate responses and selecting the most reliable answer. While prior work has analyzed that internal model signals like confidence scores can partly indicate response correctness and exhibit a distributional correlation with accuracy, such distributional information has not been fully utilized to guide answer selection. Motivated by this, we propose DistriVoting, which incorporates distributional priors as another signal alongside confidence during voting. Specifically, our method (1) first decomposes the mixed confidence distribution into positive and negative components using Gaussian Mixture Models, (2) then applies a reject filter based on positive/negative samples from them to mitigate overlap between the two distributions. Besides, to further alleviate the overlap from the perspective of distribution itself, we propose SelfStepConf, which uses step-level confidence to dynamically adjust inference process, increasing the separation between the two distributions to improve the reliability of confidences in voting. Experiments across 16 models and 5 benchmarks demonstrate that our method significantly outperforms state-of-the-art approaches.

Humans build shared spatial understanding by communicating partial, viewpoint-dependent observations. We ask whether Multimodal Large Language Models (MLLMs) can do the same, aligning distinct egocentric views through dialogue to form a coherent, allocentric mental model of a shared environment. To study this systematically, we introduce COSMIC, a benchmark for Collaborative Spatial Communication. In this setting, two static MLLM agents observe a 3D indoor environment from different viewpoints and exchange natural-language messages to solve spatial queries. COSMIC contains 899 diverse scenes and 1250 question-answer pairs spanning five tasks. We find a consistent capability hierarchy, MLLMs are most reliable at identifying shared anchor objects across views, perform worse on relational reasoning, and largely fail at building globally consistent maps, performing near chance, even for the frontier models. Moreover, we find thinking capability yields consistent gains in anchor grounding, but is insufficient for higher-level spatial communication. To contextualize model behavior, we additionally collect 250 human-human dialogues. Humans achieve 95% aggregate accuracy, leaving significant room for improvement for even the best performing model Gemini-3-Pro-Thinking which achieves 72% aggregate accuracy. Moreover, human conversations become increasingly specific as partners converge on a shared mental model, whereas model dialogues continue to explore new possibilities rather than converging, consistent with a limited ability to build and maintain a robust shared mental model. Our code and data is available at https://github.com/ankursikarwar/Cosmic

Multimodal reasoning models (MRMs) trained with reinforcement learning with verifiable rewards (RLVR) show improved accuracy on visual reasoning benchmarks. However, we observe that accuracy gains often come at the cost of reasoning quality: generated Chain-of-Thought (CoT) traces are frequently inconsistent with the final answer and poorly grounded in the visual evidence. We systematically study this phenomenon across seven challenging real-world spatial reasoning benchmarks and find that it affects contemporary MRMs such as ViGoRL-Spatial, TreeVGR as well as our own models trained with standard Group Relative Policy Optimization (GRPO). We characterize CoT reasoning quality along two complementary axes: "logical consistency" (does the CoT entail the final answer?) and "visual grounding" (does each reasoning step accurately describe objects, attributes, and spatial relationships in the image?). To address this, we propose Faithful GRPO (FGRPO), a variant of GRPO that enforces consistency and grounding as constraints via Lagrangian dual ascent. FGRPO incorporates batch-level consistency and grounding constraints into the advantage computation within a group, adaptively adjusting the relative importance of constraints during optimization. We evaluate FGRPO on Qwen2.5-VL-7B and 3B backbones across seven spatial datasets. Our results show that FGRPO substantially improves reasoning quality, reducing the inconsistency rate from 24.5% to 1.7% and improving visual grounding scores by +13%. It also improves final answer accuracy over simple GRPO, demonstrating that faithful reasoning enables better answers.

Large language models (LLMs) have demonstrated remarkable performance across diverse tasks by encoding vast amounts of factual knowledge. However, they are still prone to hallucinations, generating incorrect or misleading information, often accompanied by high uncertainty. Existing methods for hallucination detection primarily focus on quantifying internal uncertainty, which arises from missing or conflicting knowledge within the model. However, hallucinations can also stem from external uncertainty, where ambiguous user queries lead to multiple possible interpretations. In this work, we introduce Semantic Volume, a novel mathematical measure for quantifying both external and internal uncertainty in LLMs. Our approach perturbs queries and responses, embeds them in a semantic space, and computes the determinant of the Gram matrix of the embedding vectors, capturing their dispersion as a measure of uncertainty. Our framework provides a generalizable and unsupervised uncertainty detection method without requiring white-box access to LLMs. We conduct extensive experiments on both external and internal uncertainty detection, demonstrating that our Semantic Volume method consistently outperforms existing baselines in both tasks. Additionally, we provide theoretical insights linking our measure to differential entropy, unifying and extending previous sampling-based uncertainty measures such as the semantic entropy. Semantic Volume is shown to be a robust and interpretable approach to improving the reliability of LLMs by systematically detecting uncertainty in both user queries and model responses.

GUI grounding, which localizes interface elements from screenshots given natural language queries, remains challenging for small icons and dense layouts. Test-time zoom-in methods improve localization by cropping and re-running inference at higher resolution, but apply cropping uniformly across all instances with fixed crop sizes, ignoring whether the model is actually uncertain on each case. We propose UI-Zoomer, a training-free adaptive zoom-in framework that treats both the trigger and scale of zoom-in as a prediction uncertainty quantification problem. A confidence-aware gate fuses spatial consensus among stochastic candidates with token-level generation confidence to selectively trigger zoom-in only when localization is uncertain. When triggered, an uncertainty-driven crop sizing module decomposes prediction variance into inter-sample positional spread and intra-sample box extent, deriving a per-instance crop radius via the law of total variance. Extensive experiments on ScreenSpot-Pro, UI-Vision, and ScreenSpot-v2 demonstrate consistent improvements over strong baselines across multiple model architectures, achieving gains of up to +13.4\%, +10.3\%, and +4.2\% respectively, with no additional training required.

Long chain-of-thought (CoT) traces are widely used as supervision for reasoning-oriented LLM SFT, yet answer-correct traces can still lead to markedly different fine-tuning outcomes. We study post-conclusion continuation in answer-correct long-CoT data: a continuation where the answer appears sufficiently supported, but the trace continues with additional reasoning that remains in the supervised target. To test its training effect, we use a delete-only editor to construct answer-preserving suffix removal and compare CoT-based SFT on the original and processed traces. We observe improved SFT outcomes after removing the editor-identified post-conclusion continuation, suggesting that this continuation is harmful to training in our setting. We therefore refer to this empirically supported phenomenon as harmful continuation. Beyond this intervention, we further characterize the removed post-conclusion continuation through uncertainty and hidden-state progress. We observe persistent local uncertainty together with weakened terminal-directional progress, forming an uncertainty--geometry mismatch. Finally, we instantiate Harmful Continuation Cut (HCC), a lightweight boundary proxy that approximates the editor-identified post-conclusion continuation boundary.

Multi-view visual reasoning is essential for intelligent systems that must understand complex environments from sparse and discrete viewpoints, yet existing research has largely focused on single-image or temporally dense video settings. In real-world scenarios, reasoning across views requires integrating partial observations without explicit guidance, while collecting large-scale multi-view data with accurate geometric and semantic annotations remains challenging. To address this gap, we leverage physically grounded simulation to construct diverse, high-fidelity 3D scenes with precise per-view metadata, enabling scalable data generation that remains transferable to real-world settings. Based on this engine, we introduce VIEW2SPACE, a multi-dimensional benchmark for sparse multi-view reasoning, together with a scalable, disjoint training split supporting millions of grounded question-answer pairs. Using this benchmark, a comprehensive evaluation of state-of-the-art vision-language and spatial models reveals that multi-view reasoning remains largely unsolved, with most models performing only marginally above random guessing. We further investigate whether training can bridge this gap. Our proposed Grounded Chain-of-Thought with Visual Evidence substantially improves performance under moderate difficulty, and generalizes to real-world data, outperforming existing approaches in cross-dataset evaluation. We further conduct difficulty-aware scaling analyses across model size, data scale, reasoning depth, and visibility constraints, indicating that while geometric perception can benefit from scaling under sufficient visibility, deep compositional reasoning across sparse views remains a fundamental challenge.

Partition logics -- non-Boolean event structures obtained by pasting Boolean algebras -- provide a natural language for situations in which a system has a definite latent state but can be accessed and resolved only through mutually incompatible coarse-grained modes of observation. We show that this structure arises in a range of social-science settings by constructing six explicit examples from personnel assessment, survey framing, clinical diagnosis, espionage coordination, legal pluralism, and organizational auditing. For each case we identify the latent state space, the observational contexts as partitions, and the shared atoms that intertwine contexts, yielding instances of the L_{12} bowtie, triangle, pentagon, and automaton partition logics. These examples make precise a notion of social complementarity: different modes of inquiry can be incompatible even though the underlying system remains fully value-definite. Complementarity in this sense does not entail contextuality or ontic indeterminacy. We further compare the classical probabilities generated by convex mixtures of dispersion-free states with the quantum-like Born probabilities available when the same exclusivity graph admits a faithful orthogonal representation. The framework thus separates logical structure from probabilistic realization and suggests empirically testable benchmarks for quantum-cognition models.

This paper presents the first empirical demonstration of controllable locality in transformer language models, a novel architectural framework that enables continuous control over the degree of representation localization through a tunable locality dial parameter. Unlike traditional language models that rely exclusively on distributed representations, our approach allows dynamic interpolation between highly interpretable localist encodings and efficient distributed representations without requiring model retraining. We conducted experiments on the WikiText corpus using a two-layer transformer architecture, systematically varying the locality parameter λ across the full spectrum from 1.0 (fully localist) to 0.0 (fully distributed). Our results demonstrate that localist configurations achieve dramatically lower attention entropy, with λ = 1.0 yielding 5.36 bits compared to 7.18 bits at λ = 0.0, while maintaining substantially higher pointer fidelity scores reflecting stronger alignment with rule-specified targets. Prediction experiments reveal that intermediate locality values optimize the tradeoff between interpretability and performance, with λ = 0.6 achieving test perplexity of 4.65 and accuracy of 84.7%. These findings establish that localist language models provide a practical framework for applications in regulated domains requiring both transparency and capability, offering precise mathematical control over the interpretability-performance spectrum through explicit penalty thresholds and information-theoretic design principles.

Genuine spatial reasoning relies on the capacity to construct and manipulate coherent internal spatial representations, often conceptualized as mental models, rather than merely processing surface linguistic associations. While large language models exhibit advanced capabilities across various domains, existing benchmarks fail to isolate this intrinsic spatial cognition from statistical language heuristics. Furthermore, multimodal evaluations frequently conflate genuine spatial reasoning with visual perception. To systematically investigate whether models construct flexible spatial mental models, we introduce SpatialText, a theory-driven diagnostic framework. Rather than functioning simply as a dataset, SpatialText isolates text-based spatial reasoning through a dual-source methodology. It integrates human-annotated descriptions of real 3D indoor environments, which capture natural ambiguities, perspective shifts, and functional relations, with code-generated, logically precise scenes designed to probe formal spatial deduction and epistemic boundaries. Systematic evaluation across state-of-the-art models reveals fundamental representational limitations. Although models demonstrate proficiency in retrieving explicit spatial facts and operating within global, allocentric coordinate systems, they exhibit critical failures in egocentric perspective transformation and local reference frame reasoning. These systematic errors provide strong evidence that current models rely heavily on linguistic co-occurrence heuristics rather than constructing coherent, verifiable internal spatial representations. SpatialText thus serves as a rigorous instrument for diagnosing the cognitive boundaries of artificial spatial intelligence.

Reinforcement learning (RL) has made a lot of advances for solving a single problem in a given environment; but learning policies that generalize to unseen variations of a problem remains challenging. To improve sample efficiency for learning on such instances of a problem domain, we present Self-Paced Context Evaluation (SPaCE). Based on self-paced learning, \spc automatically generates \task curricula online with little computational overhead. To this end, SPaCE leverages information contained in state values during training to accelerate and improve training performance as well as generalization capabilities to new instances from the same problem domain. Nevertheless, SPaCE is independent of the problem domain at hand and can be applied on top of any RL agent with state-value function approximation. We demonstrate SPaCE's ability to speed up learning of different value-based RL agents on two environments, showing better generalization capabilities and up to 10x faster learning compared to naive approaches such as round robin or SPDRL, as the closest state-of-the-art approach.

With the widespread application of Large Language Models (LLMs) to various domains, concerns regarding the trustworthiness of LLMs in safety-critical scenarios have been raised, due to their unpredictable tendency to hallucinate and generate misinformation. Existing LLMs do not have an inherent functionality to provide the users with an uncertainty/confidence metric for each response it generates, making it difficult to evaluate trustworthiness. Although several studies aim to develop uncertainty quantification methods for LLMs, they have fundamental limitations, such as being restricted to classification tasks, requiring additional training and data, considering only lexical instead of semantic information, and being prompt-wise but not response-wise. A new framework is proposed in this paper to address these issues. Semantic density extracts uncertainty/confidence information for each response from a probability distribution perspective in semantic space. It has no restriction on task types and is "off-the-shelf" for new models and tasks. Experiments on seven state-of-the-art LLMs, including the latest Llama 3 and Mixtral-8x22B models, on four free-form question-answering benchmarks demonstrate the superior performance and robustness of semantic density compared to prior approaches.

Most existing spatial reasoning benchmarks focus on static or globally observable environments, failing to capture the challenges of long-horizon reasoning and memory utilization under partial observability and dynamic changes. We introduce two dynamic spatial benchmarks, locally observable maze navigation and match-2 elimination that systematically evaluate models' abilities in spatial understanding and adaptive planning when local perception, environment feedback, and global objectives are tightly coupled. Each action triggers structural changes in the environment, requiring continuous update of cognition and strategy. We further propose a subjective experience-based memory mechanism for cross-task experience transfer and validation. Experiments show that our benchmarks reveal key limitations of mainstream models in dynamic spatial reasoning and long-term memory, providing a comprehensive platform for future methodological advances. Our code and data are available at https://anonymous.4open.science/r/EvoEmpirBench-143C/.

Humans possess the visual-spatial intelligence to remember spaces from sequential visual observations. However, can Multimodal Large Language Models (MLLMs) trained on million-scale video datasets also ``think in space'' from videos? We present a novel video-based visual-spatial intelligence benchmark (VSI-Bench) of over 5,000 question-answer pairs, and find that MLLMs exhibit competitive - though subhuman - visual-spatial intelligence. We probe models to express how they think in space both linguistically and visually and find that while spatial reasoning capabilities remain the primary bottleneck for MLLMs to reach higher benchmark performance, local world models and spatial awareness do emerge within these models. Notably, prevailing linguistic reasoning techniques (e.g., chain-of-thought, self-consistency, tree-of-thoughts) fail to improve performance, whereas explicitly generating cognitive maps during question-answering enhances MLLMs' spatial distance ability.

Language model (LM) assistants are increasingly used in applications such as brainstorming and research. Improvements in memory and context size have allowed these models to become more autonomous, which has also resulted in more text accumulation in their context windows without explicit user intervention. This comes with a latent risk: the belief profiles of models -- their understanding of the world as manifested in their responses or actions -- may silently change as context accumulates. This can lead to subtly inconsistent user experiences, or shifts in behavior that deviate from the original alignment of the models. In this paper, we explore how accumulating context by engaging in interactions and processing text -- talking and reading -- can change the beliefs of language models, as manifested in their responses and behaviors. Our results reveal that models' belief profiles are highly malleable: GPT-5 exhibits a 54.7% shift in its stated beliefs after 10 rounds of discussion about moral dilemmas and queries about safety, while Grok 4 shows a 27.2% shift on political issues after reading texts from the opposing position. We also examine models' behavioral changes by designing tasks that require tool use, where each tool selection corresponds to an implicit belief. We find that these changes align with stated belief shifts, suggesting that belief shifts will be reflected in actual behavior in agentic systems. Our analysis exposes the hidden risk of belief shift as models undergo extended sessions of talking or reading, rendering their opinions and actions unreliable.

We introduce the Probabilistic Worldbuilding Model (PWM), a new fully-symbolic Bayesian model of semantic parsing and reasoning, as a first step in a research program toward more domain- and task-general NLU and AI. Humans create internal mental models of their observations which greatly aid in their ability to understand and reason about a large variety of problems. In PWM, the meanings of sentences, acquired facts about the world, and intermediate steps in reasoning are all expressed in a human-readable formal language, with the design goal of interpretability. PWM is Bayesian, designed specifically to be able to generalize to new domains and new tasks. We derive and implement an inference algorithm that reads sentences by parsing and abducing updates to its latent world model that capture the semantics of those sentences, and evaluate it on two out-of-domain question-answering datasets: (1) ProofWriter and (2) a new dataset we call FictionalGeoQA, designed to be more representative of real language but still simple enough to focus on evaluating reasoning ability, while being robust against heuristics. Our method outperforms baselines on both, thereby demonstrating its value as a proof-of-concept.

We explore uncertainty quantification in large language models (LLMs), with the goal to identify when uncertainty in responses given a query is large. We simultaneously consider both epistemic and aleatoric uncertainties, where the former comes from the lack of knowledge about the ground truth (such as about facts or the language), and the latter comes from irreducible randomness (such as multiple possible answers). In particular, we derive an information-theoretic metric that allows to reliably detect when only epistemic uncertainty is large, in which case the output of the model is unreliable. This condition can be computed based solely on the output of the model obtained simply by some special iterative prompting based on the previous responses. Such quantification, for instance, allows to detect hallucinations (cases when epistemic uncertainty is high) in both single- and multi-answer responses. This is in contrast to many standard uncertainty quantification strategies (such as thresholding the log-likelihood of a response) where hallucinations in the multi-answer case cannot be detected. We conduct a series of experiments which demonstrate the advantage of our formulation. Further, our investigations shed some light on how the probabilities assigned to a given output by an LLM can be amplified by iterative prompting, which might be of independent interest.

Theory-of-Mind (ToM) tasks pose a unique challenge for small language models (SLMs) with limited scale, which often lack the capacity to perform deep social reasoning. In this work, we propose DEL-ToM, a framework that improves ToM reasoning through inference-time scaling rather than architectural changes. Our approach decomposes ToM tasks into a sequence of belief updates grounded in Dynamic Epistemic Logic (DEL), enabling structured and transparent reasoning. We train a verifier, called the Process Belief Model (PBM), to score each belief update step using labels generated automatically via a DEL simulator. During inference, candidate belief traces generated by a language model are evaluated by the PBM, and the highest-scoring trace is selected. This allows SLMs to emulate more deliberate reasoning by allocating additional compute at test time. Experiments across multiple model scales and benchmarks show that DEL-ToM consistently improves performance, demonstrating that verifiable belief supervision can significantly enhance ToM abilities of SLMs without retraining.

Large Language Models and multi-agent systems have shown promise in decomposing complex tasks, yet they struggle with long-horizon reasoning tasks and escalating computation cost. This work introduces a hierarchical multi-agent architecture that distributes reasoning across a 64*64 grid of lightweight agents, supported by a selective oracle. A spatial curriculum progressively expands the operational region of the grid, ensuring that agents master easier central tasks before tackling harder peripheral ones. To improve reliability, the system integrates Negative Log-Likelihood as a measure of confidence, allowing the curriculum to prioritize regions where agents are both accurate and well calibrated. A Thompson Sampling curriculum manager adaptively chooses training zones based on competence and NLL-driven reward signals. We evaluate the approach on a spatially grounded Tower of Hanoi benchmark, which mirrors the long-horizon structure of many robotic manipulation and planning tasks. Results demonstrate improved stability, reduced oracle usage, and stronger long-range reasoning from distributed agent cooperation.

Large language models (LLMs) have majorly advanced NLP and AI, and next to their ability to perform a wide range of procedural tasks, a major success factor is their internalized factual knowledge. Since Petroni et al. (2019), analyzing this knowledge has gained attention. However, most approaches investigate one question at a time via modest-sized pre-defined samples, introducing an ``availability bias'' (Tversky&Kahnemann, 1973) that prevents the analysis of knowledge (or beliefs) of LLMs beyond the experimenter's predisposition. To address this challenge, we propose a novel methodology to comprehensively materialize an LLM's factual knowledge through recursive querying and result consolidation. Our approach is a milestone for LLM research, for the first time providing constructive insights into the scope and structure of LLM knowledge (or beliefs). As a prototype, we build GPTKB, a knowledge base (KB) comprising 101 million relational triples for over 2.9 million entities from GPT-4o-mini. We use GPTKB to exemplarily analyze GPT-4o-mini's factual knowledge in terms of scale, accuracy, bias, cutoff and consistency, at the same time. GPTKB is accessible at https://gptkb.org

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.

One of the key challenges in deploying RL to real-world applications is to adapt to variations of unknown environment contexts, such as changing terrains in robotic tasks and fluctuated bandwidth in congestion control. Existing works on adaptation to unknown environment contexts either assume the contexts are the same for the whole episode or assume the context variables are Markovian. However, in many real-world applications, the environment context usually stays stable for a stochastic period and then changes in an abrupt and unpredictable manner within an episode, resulting in a segment structure, which existing works fail to address. To leverage the segment structure of piecewise stable context in real-world applications, in this paper, we propose a \textbf{Segmented Context Belief Augmented Deep~(SeCBAD)} RL method. Our method can jointly infer the belief distribution over latent context with the posterior over segment length and perform more accurate belief context inference with observed data within the current context segment. The inferred belief context can be leveraged to augment the state, leading to a policy that can adapt to abrupt variations in context. We demonstrate empirically that SeCBAD can infer context segment length accurately and outperform existing methods on a toy grid world environment and Mujuco tasks with piecewise-stable context.

Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or whether a patient has died or not), because the ground-truth probabilities of the events of interest are typically unknown. The problem is therefore analogous to binary classification, with the difference that the objective is to estimate probabilities rather than predicting the specific outcome. This work investigates probability estimation from high-dimensional data using deep neural networks. There exist several methods to improve the probabilities generated by these models but they mostly focus on model (epistemic) uncertainty. For problems with inherent uncertainty, it is challenging to evaluate performance without access to ground-truth probabilities. To address this, we build a synthetic dataset to study and compare different computable metrics. We evaluate existing methods on the synthetic data as well as on three real-world probability estimation tasks, all of which involve inherent uncertainty: precipitation forecasting from radar images, predicting cancer patient survival from histopathology images, and predicting car crashes from dashcam videos. We also give a theoretical analysis of a model for high-dimensional probability estimation which reproduces several of the phenomena evinced in our experiments. Finally, we propose a new method for probability estimation using neural networks, which modifies the training process to promote output probabilities that are consistent with empirical probabilities computed from the data. The method outperforms existing approaches on most metrics on the simulated as well as real-world data.

Hallucination and factuality deficits remain key obstacles to the reliability of large language models (LLMs) in long-form generation. Existing reinforcement learning from human feedback (RLHF) frameworks primarily rely on preference rewards, yet they often overlook the model's internal knowledge boundaries, exacerbating the so-called "hallucination tax". To address this challenge, we propose Knowledge-Level Consistency Reinforcement Learning Framework (KLCF), a novel framework that focuses on the knowledge consistency between the policy model's expressed knowledge and the base model's parametric knowledge, and introduces a Dual-Fact Alignment mechanism to jointly optimize factual recall and precision. Specifically, KLCF leverages pretrained knowledge boundaries to construct fact checklist, guiding online reinforcement learning to improve factual coverage and recall; simultaneously, it trains a self-assessment module based on the base model's internal knowledge to enhance factual precision during generation. Unlike prior methods that rely on external retrieval or heavy verification, our reward design is fully external-knowledge-free and lightweight, making KLCF efficient and easily scalable to large-scale training. Experimental results demonstrate that KLCF substantially improves factuality metrics across multiple long-form benchmarks and effectively alleviates model hallucinations.

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/

Multi-agent LLM systems improve reasoning by combining outputs from multiple agents, but interaction-heavy methods can introduce error propagation and high communication overhead. When agents exchange raw responses or reasoning traces, incorrect intermediate reasoning may be adopted and amplified, leading to confident but wrong consensus; multi-round communication also increases token consumption, latency, and inference cost. In this paper, we propose a controlled-communication coordination framework named DarkForest. DarkForest first keeps agents independent, so each agent produces an answer without seeing the others' outputs. It then parses the raw responses into structured candidate records, groups semantically equivalent candidates into clusters, and estimates a calibrated belief distribution over these clusters using agent reliability, confidence, parse quality, support-pattern reliability, and independence corrections. A coordinator receives only policy-permitted evidence from this belief state with controlled communication. Experiments on six reasoning benchmarks show that DarkForest achieves leading overall quality, improves the strongest baseline by up to 30.7\% on benchmark metrics, and reduces token consumption by up to 6.5times compared with communication-heavy baselines.

Current work on human-machine alignment aims at understanding machine-learned latent spaces and their correspondence to human representations. G{\"a}rdenfors' conceptual spaces is a prominent framework for understanding human representations. Convexity of object regions in conceptual spaces is argued to promote generalizability, few-shot learning, and interpersonal alignment. Based on these insights, we investigate the notion of convexity of concept regions in machine-learned latent spaces. We develop a set of tools for measuring convexity in sampled data and evaluate emergent convexity in layered representations of state-of-the-art deep networks. We show that convexity is robust to basic re-parametrization and, hence, meaningful as a quality of machine-learned latent spaces. We find that approximate convexity is pervasive in neural representations in multiple application domains, including models of images, audio, human activity, text, and medical images. Generally, we observe that fine-tuning increases the convexity of label regions. We find evidence that pretraining convexity of class label regions predicts subsequent fine-tuning performance.

Health Indicators (HIs) are essential for predicting system failures in predictive maintenance. While methods like RaPP (Reconstruction along Projected Pathways) improve traditional HI approaches by leveraging autoencoder latent spaces, their performance can be hindered by both aleatoric and epistemic uncertainties. In this paper, we propose a novel framework that integrates uncertainty quantification into autoencoder-based latent spaces, enhancing RaPP-generated HIs. We demonstrate that separating aleatoric uncertainty from epistemic uncertainty and cross combining HI information is the driver of accuracy improvements in Remaining Useful Life (RUL) prediction. Our method employs both standard and variational autoencoders to construct these HIs, which are then used to train a machine learning model for RUL prediction. Benchmarked on the NASA C-MAPSS turbofan dataset, our approach outperforms traditional HI-based methods and end-to-end RUL prediction models and is competitive with RUL estimation methods. These results underscore the importance of uncertainty quantification in health assessment and showcase its significant impact on predictive performance when incorporated into the HI construction process.

The common approach to communicate a large language model's (LLM) uncertainty is to add a percentage number or a hedging word to its response. But is this all we can do? Instead of generating a single answer and then hedging it, an LLM that is fully transparent to the user needs to be able to reflect on its internal belief distribution and output a summary of all options it deems possible, and how likely they are. To test whether LLMs possess this capability, we develop the SelfReflect metric, an information-theoretic distance between a given summary and a distribution over answers. In interventional and human studies, we find that SelfReflect indicates even slight deviations, yielding a fine measure of faithfulness between a summary string and an LLM's actual internal distribution over answers. With SelfReflect, we make a resounding negative observation: modern LLMs are, across the board, incapable of revealing what they are uncertain about, neither through reasoning, nor chains-of-thoughts, nor explicit finetuning. However, we do find that LLMs are able to generate faithful summaries of their uncertainties if we help them by sampling multiple outputs and feeding them back into the context. This simple approach shines a light at the universal way of communicating LLM uncertainties whose future development the SelfReflect score enables.

Reasoning training incentivizes LLMs to produce long chains of thought (long CoT), which among other things, allows them to explore solution strategies with self-checking. This results in higher accuracy, but inflates context length, token/compute cost, and answer latency. We ask: Can current models leverage their metacognition to provide other combinations on this Pareto frontier, e.g., better accuracy with lower context length and/or latency? Abstractly, we view the model as an improvement operator on its own "thoughts" with a continuum of possible strategies. We identify an interesting inference family Parallel-Distill-Refine (PDR), which performs the following: (i) generate diverse drafts in parallel; (ii) distill them into a bounded, textual workspace; and (iii) refine conditioned on this workspace, producing an output that seeds the next round. Importantly, context length (hence compute cost) is controllable via degree of parallelism, and is no longer conflated with the total number of generated tokens. We report PDR instantiations of current models that give better accuracy than long CoT while incurring lower latency. Setting degree of parallelism to 1 yields an interesting subcase, Sequential Refinement (SR) (iteratively improve a single candidate answer) which provides performance superior to long CoT. Success of such model orchestrations raises the question whether further training could shift the Pareto frontier. To this end, we train an 8B thinking model with Reinforcement Learning (RL) to make it consistent with PDR as the inference method. On math tasks with verifiable answers, iterative pipelines surpass single-pass baselines at matched sequential budgets, with PDR delivering the largest gains (e.g., +11% on AIME 2024 and +9% on AIME 2025).

Commonsense is defined as the knowledge that is shared by everyone. However, certain types of commonsense knowledge are correlated with culture and geographic locations and they are only shared locally. For example, the scenarios of wedding ceremonies vary across regions due to different customs influenced by historical and religious factors. Such regional characteristics, however, are generally omitted in prior work. In this paper, we construct a Geo-Diverse Visual Commonsense Reasoning dataset (GD-VCR) to test vision-and-language models' ability to understand cultural and geo-location-specific commonsense. In particular, we study two state-of-the-art Vision-and-Language models, VisualBERT and ViLBERT trained on VCR, a standard multimodal commonsense benchmark with images primarily from Western regions. We then evaluate how well the trained models can generalize to answering the questions in GD-VCR. We find that the performance of both models for non-Western regions including East Asia, South Asia, and Africa is significantly lower than that for Western region. We analyze the reasons behind the performance disparity and find that the performance gap is larger on QA pairs that: 1) are concerned with culture-related scenarios, e.g., weddings, religious activities, and festivals; 2) require high-level geo-diverse commonsense reasoning rather than low-order perception and recognition. Dataset and code are released at https://github.com/WadeYin9712/GD-VCR.

Every act of language generation compresses a rich internal state into a single token sequence. We call this process intention collapse: a many-to-one projection from a high dimensional intention space I into an external language space L. We formalize intention collapse for contemporary language models, define three simple, model agnostic intention metrics (intention entropy Hint, effective dimensionality dimeff, and latent knowledge recoverability Recov), and propose an empirical agenda for studying how inference time computation shapes internal intentions before they are verbalized. We also report a first small scale experiment. Using a 4 bit Mistral 7B model on 200 GSM8K problems, we compare a direct answer baseline, a chain of thought (CoT) regime, and a babble control. CoT raises accuracy from 5.5 percent to 53 percent, sharply reduces pre collapse intention entropy (from 1.42 to 0.37 bits), and shows higher global effective dimensionality than the other regimes despite producing fewer tokens than babble. At the same time, Hint has little item level predictive power, and a linear probe on I achieves AUROC 0.65 in the CoT regime but only about chance in the baseline regime, where it collapses to the majority class. These preliminary results indicate that intention level metrics can distinguish inference regimes and expose latent information that is partly lost during collapse, while also revealing important limitations of our current proxies

This work presents a framework for assessing whether large language models (LLMs) encode more factual knowledge in their parameters than what they express in their outputs. While a few studies hint at this possibility, none has clearly defined or demonstrated this phenomenon. We first propose a formal definition of knowledge, quantifying it for a given question as the fraction of correct-incorrect answer pairs where the correct one is ranked higher. This gives rise to external and internal knowledge, depending on the information used to score individual answer candidates: either the model's observable token-level probabilities or its intermediate computations. Hidden knowledge arises when internal knowledge exceeds external knowledge. We then present a case study, applying this framework to three popular open-weights LLMs in a closed-book QA setup. Our results indicate that: (1) LLMs consistently encode more factual knowledge internally than what they express externally, with an average gap of 40%. (2) Surprisingly, some knowledge is so deeply hidden that a model can internally know an answer perfectly, yet fail to generate it even once, despite large-scale repeated sampling of 1,000 answers. This reveals fundamental limitations in the generation capabilities of LLMs, which (3) puts a practical constraint on scaling test-time compute via repeated answer sampling in closed-book QA: significant performance improvements remain inaccessible because some answers are practically never sampled, yet if they were, we would be guaranteed to rank them first.

Large Language Models (LLMs) demonstrate an impressive capacity to recall a vast range of factual knowledge. However, understanding their underlying reasoning and internal mechanisms in exploiting this knowledge remains a key research area. This work unveils the factual information an LLM represents internally for sentence-level claim verification. We propose an end-to-end framework to decode factual knowledge embedded in token representations from a vector space to a set of ground predicates, showing its layer-wise evolution using a dynamic knowledge graph. Our framework employs activation patching, a vector-level technique that alters a token representation during inference, to extract encoded knowledge. Accordingly, we neither rely on training nor external models. Using factual and common-sense claims from two claim verification datasets, we showcase interpretability analyses at local and global levels. The local analysis highlights entity centrality in LLM reasoning, from claim-related information and multi-hop reasoning to representation errors causing erroneous evaluation. On the other hand, the global reveals trends in the underlying evolution, such as word-based knowledge evolving into claim-related facts. By interpreting semantics from LLM latent representations and enabling graph-related analyses, this work enhances the understanding of the factual knowledge resolution process.

Linguistic cues such as "I believe" and "probably" offer an intuitive interface for communicating confidence, yet a generalisable, principled calibration framework for linguistic confidence expressions remains underexplored. In particular, co-occurring linguistic cues, contextual variation, and subjective audience interpretation pose unique challenges. We therefore model linguistic confidence as a distribution over plausible perceived probability values that a statement is correct, capturing interpretation variability that scalar representations discard. Within this distributional framework, we introduce faithfulness as a complementary evaluation dimension and present Faithfulness Divergence (FD), an information-theoretic metric quantifying the surprise induced in audience beliefs upon truth revelation. Building on these foundations, we present Retrieval-Augmented Linguistic Calibration (RALC), a lightweight post-hoc pipeline that propagates calibrated confidence signals back into natural language via retrieval-augmented rewriting. Across three QA benchmarks and five LLM families, RALC improves in-domain faithfulness and calibration up to 66% and 58%, respectively, outperforming black-box and grey-box calibration baselines.

Latent or continuous chain-of-thought methods replace explicit textual rationales with a number of internal latent steps, but these intermediate computations are difficult to evaluate beyond correlation-based probes. In this paper, we view latent chain-of-thought as a manipulable causal process in representation space by modeling latent steps as variables in a structural causal model (SCM) and analyzing their effects through step-wise do-interventions. We study two representative paradigms (i.e., Coconut and CODI) on both mathematical and general reasoning tasks to investigate three key questions: (1) which steps are causally necessary for correctness and when answers become decidable early; (2) how does influence propagate across steps, and how does this structure compare to explicit CoT; and (3) do intermediate trajectories retain competing answer modes, and how does output-level commitment differ from representational commitment across steps. We find that latent-step budgets behave less like homogeneous extra depth and more like staged functionality with non-local routing, and we identify a persistent gap between early output bias and late representational commitment. These results motivate mode-conditional and stability-aware analyses -- and corresponding training/decoding objectives -- as more reliable tools for interpreting and improving latent reasoning systems. Code is available at https://github.com/J1mL1/causal-latent-cot.

Test-time reinforcement learning mitigates the reliance on annotated data by using majority voting results as pseudo-labels, emerging as a complementary direction to reinforcement learning with verifiable rewards (RLVR) for improving reasoning ability of large language models (LLMs). However, this voting strategy often induces confirmation bias and suffers from sparse rewards, limiting the overall performance. In this work, we propose subgroup-specific step-wise confidence-weighted pseudo-label estimation (SCOPE), a framework integrating model confidence and dynamic subgroup partitioning to address these issues. Specifically, SCOPE integrates the proposed step-wise confidence into pseudo label deduction, prioritizing high-quality reasoning paths over simple frequency count. Furthermore, it dynamically partitions the candidate outputs pool into independent subgroups by balancing reasoning quality against exploration diversity. By deriving local consensus via repeat sampling for each sub group, SCOPE provides diverse supervision targets to encourage broader exploration. We conduct experiments across various models and benchmarks, experimental results show that SCOPE consistently outperforms recent baselines. Notably, SCOPE achieving relative improvements of 13.1% on challenging AIME 2025 and 8.1% on AMC. The code is released at https://github.com/szu-tera/SCOPE.

Reasoning ability, a core component of human intelligence, continues to pose a significant challenge for Large Language Models (LLMs) in the pursuit of AGI. Although model performance has improved under the training scaling law, significant challenges remain, particularly with respect to training algorithms, such as catastrophic forgetting, and the limited availability of novel training data. As an alternative, test-time scaling enhances reasoning performance by increasing test-time computation without parameter updating. Unlike prior methods in this paradigm focused on token space, we propose leveraging latent space for more effective reasoning and better adherence to the test-time scaling law. We introduce LatentSeek, a novel framework that enhances LLM reasoning through Test-Time Instance-level Adaptation (TTIA) within the model's latent space. Specifically, LatentSeek leverages policy gradient to iteratively update latent representations, guided by self-generated reward signals. LatentSeek is evaluated on a range of reasoning benchmarks, including GSM8K, MATH-500, and AIME2024, across multiple LLM architectures. Results show that LatentSeek consistently outperforms strong baselines, such as Chain-of-Thought prompting and fine-tuning-based methods. Furthermore, our analysis demonstrates that LatentSeek is highly efficient, typically converging within a few iterations for problems of average complexity, while also benefiting from additional iterations, thereby highlighting the potential of test-time scaling in the latent space. These findings position LatentSeek as a lightweight, scalable, and effective solution for enhancing the reasoning capabilities of LLMs.

The hallucination of non-existent facts by LLMs is an important problem given its widespread adoption across various applications. Previous research addresses this problem by analyzing the internal parameterized knowledge boundaries to estimate confidence. However, these studies focus on the single-problem setting and have not explored the more challenging multi-problem setting, which requires accurately answering multiple questions simultaneously. We introduce a novel method for the multi-problem setting, Multiple Answers and Confidence Stepwise Tuning (MAC-Tuning), that separates the learning of answer prediction and confidence estimation during fine-tuning on instruction data. Extensive experiments demonstrate that our method outperforms baselines by up to 25\% in average precision.

Scientific reasoning relies not only on logical inference but also on activating prior knowledge and experiential structures. Memory can efficiently reuse knowledge and enhance reasoning consistency and stability. However, existing benchmarks mainly evaluate final answers or step-by-step coherence, overlooking the memory-driven mechanisms that underlie human reasoning, which involves activating anchors and attractors, then integrating them into multi-step inference. To address this gap, we propose A^3-Bench~ https://a3-bench.github.io, a benchmark designed to evaluate scientific reasoning through dual-scale memory-driven activation, grounded in Anchor and Attractor Activation. First, we annotate 2,198 science reasoning problems across domains using the SAPM process(subject, anchor & attractor, problem, and memory developing). Second, we introduce a dual-scale memory evaluation framework utilizing anchors and attractors, along with the AAUI(Anchor--Attractor Utilization Index) metric to measure memory activation rates. Finally, through experiments with various base models and paradigms, we validate A^3-Bench and analyze how memory activation impacts reasoning performance, providing insights into memory-driven scientific reasoning.

We present a novel framework for training large language models with continuously adjustable internal representations that span the full spectrum from localist (interpretable, rule-based) to distributed (generalizable, efficient) encodings. The key innovation is a locality dial, a tunable parameter that dynamically controls the degree of localization during both training and inference without requiring model retraining. This is achieved through group sparsity penalties on attention mechanisms, information-theoretic anchor design, and dynamic rule injection. We provide rigorous mathematical proofs establishing explicit threshold conditions under which attention provably concentrates on semantically relevant blocks, with exponential bounds on attention entropy and pointer fidelity. Specifically, we prove that when group sparsity penalties exceed certain threshold values, the model's attention mechanisms concentrate on semantically relevant blocks, achieving low entropy and high fidelity with negligible error. This framework enables practitioners to continuously interpolate between interpretable and high-performance modes, supporting applications in regulated domains requiring both transparency and capability.

We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higher-order functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higher-order functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasi-Borel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasi-Borel counterpart to the Metropolis-Hastings-Green theorem.

Current benchmarks for AI clinician systems, often based on multiple-choice exams or manual rubrics, fail to capture the depth, robustness, and safety required for real-world clinical practice. To address this, we introduce the GAPS framework, a multidimensional paradigm for evaluating Grounding (cognitive depth), Adequacy (answer completeness), Perturbation (robustness), and Safety. Critically, we developed a fully automated, guideline-anchored pipeline to construct a GAPS-aligned benchmark end-to-end, overcoming the scalability and subjectivity limitations of prior work. Our pipeline assembles an evidence neighborhood, creates dual graph and tree representations, and automatically generates questions across G-levels. Rubrics are synthesized by a DeepResearch agent that mimics GRADE-consistent, PICO-driven evidence review in a ReAct loop. Scoring is performed by an ensemble of large language model (LLM) judges. Validation confirmed our automated questions are high-quality and align with clinician judgment. Evaluating state-of-the-art models on the benchmark revealed key failure modes: performance degrades sharply with increased reasoning depth (G-axis), models struggle with answer completeness (A-axis), and they are highly vulnerable to adversarial perturbations (P-axis) as well as certain safety issues (S-axis). This automated, clinically-grounded approach provides a reproducible and scalable method for rigorously evaluating AI clinician systems and guiding their development toward safer, more reliable clinical practice.

While Large Language Models (LLMs) have emerged with remarkable capabilities in complex tasks through Chain-of-Thought reasoning, practical resource constraints have sparked interest in transferring these abilities to smaller models. However, achieving both domain performance and cross-domain generalization remains challenging. Existing approaches typically restrict students to following a single golden rationale and treat different reasoning paths independently. Due to distinct inductive biases and intrinsic preferences, alongside the student's evolving capacity and reasoning preferences during training, a teacher's "optimal" rationale could act as out-of-distribution noise. This misalignment leads to a degeneration of the student's latent reasoning distribution, causing suboptimal performance. To bridge this gap, we propose MIND, a capability-adaptive framework that transitions distillation from passive mimicry to active cognitive construction. We synthesize diverse teacher perspectives through a novel "Teaching Assistant" network. By employing a Feedback-Driven Inertia Calibration mechanism, this network utilizes inertia-filtered training loss to align supervision with the student's current adaptability, effectively enhancing performance while mitigating catastrophic forgetting. Extensive experiments demonstrate that MIND achieves state-of-the-art performance on both in-distribution and out-of-distribution benchmarks, and our sophisticated latent space analysis further confirms the mechanism of reasoning ability internalization.

A new prior is proposed for learning representations of high-level concepts of the kind we manipulate with language. This prior can be combined with other priors in order to help disentangling abstract factors from each other. It is inspired by cognitive neuroscience theories of consciousness, seen as a bottleneck through which just a few elements, after having been selected by attention from a broader pool, are then broadcast and condition further processing, both in perception and decision-making. The set of recently selected elements one becomes aware of is seen as forming a low-dimensional conscious state. This conscious state is combining the few concepts constituting a conscious thought, i.e., what one is immediately conscious of at a particular moment. We claim that this architectural and information-processing constraint corresponds to assumptions about the joint distribution between high-level concepts. To the extent that these assumptions are generally true (and the form of natural language seems consistent with them), they can form a useful prior for representation learning. A low-dimensional thought or conscious state is analogous to a sentence: it involves only a few variables and yet can make a statement with very high probability of being true. This is consistent with a joint distribution (over high-level concepts) which has the form of a sparse factor graph, i.e., where the dependencies captured by each factor of the factor graph involve only very few variables while creating a strong dip in the overall energy function. The consciousness prior also makes it natural to map conscious states to natural language utterances or to express classical AI knowledge in a form similar to facts and rules, albeit capturing uncertainty as well as efficient search mechanisms implemented by attention mechanisms.

When faced with novel situations, people are able to marshal relevant considerations from a wide range of background knowledge and put these to use in inferences and predictions. What permits us to draw in globally relevant information and reason over it coherently? Here, we explore the hypothesis that people use a combination of distributed and symbolic representations to construct bespoke mental models tailored to novel situations. We propose a computational implementation of this idea -- a ``Model Synthesis Architecture'' (MSA) -- using language models to implement global relevance-based retrieval and model synthesis and probabilistic programs to implement bespoke, coherent world models. We evaluate our MSA as a model of human judgments on a novel reasoning dataset. The dataset -- built around a `Model Olympics` domain of sports vignettes -- tests models' capacity for human-like, open-ended reasoning by requiring (i) judgments about novel causal structures described in language; (ii) drawing on large bodies of background knowledge; and (iii) doing both in light of observations that introduce arbitrary novel variables. Our MSA approach captures human judgments better than language model-only baselines, under both direct and chain-of-thought generations from the LM that supports model synthesis. These results suggest that MSAs can be implemented in a way that mirrors people's ability to deliver locally coherent reasoning over globally relevant variables, offering a path to understanding and replicating human reasoning in open-ended domains.

Multi-Agent Debate~(MAD) has emerged as a promising paradigm for improving the performance of large language models through collaborative reasoning. Despite recent advances, the key factors driving MAD's effectiveness remain unclear. In this work, we disentangle MAD into two key components--Majority Voting and inter-agent Debate--and assess their respective contributions. Through extensive experiments across seven NLP benchmarks, we find that Majority Voting alone accounts for most of the performance gains typically attributed to MAD. To explain this, we propose a theoretical framework that models debate as a stochastic process. We prove that it induces a martingale over agents' belief trajectories, implying that debate alone does not improve expected correctness. Guided by these insights, we demonstrate that targeted interventions, by biasing the belief update toward correction, can meaningfully enhance debate effectiveness. Overall, our findings suggest that while MAD has potential, simple ensembling methods remain strong and more reliable alternatives in many practical settings. Code is released in https://github.com/deeplearning-wisc/debate-or-vote.

RL post-training with verifiable rewards (RLVR) has become a practical route to eliciting chain-of-thought reasoning in vision--language models (VLMs), but scaling it in the visual domain remains challenging due to costly or noisy supervision and reliance on external verifiers. Puzzle-based RLVR is a promising alternative, yet existing approaches often treat puzzle rewards as flat or sparse, which weakens group-relative learning signal. Existing curriculum strategies are overly restrictive: they rely mainly on reward statistics and do not account for exploration in the solution space, which can lead to collapsed rollout dynamics. Further, RL post-training can induce reasoning--answer inconsistency as training progresses. To address these shortcomings, we present PuzzleCraft, a supervision-free framework that scales vision-centric RLVR using a set of lightweight puzzle environments with built-in verification. PuzzleCraft instantiates three puzzles inspired by classic visual pretext tasks: PatchFit, Rotation, and Jigsaw. We introduce a curriculum that combines difficulty with an exploration signal derived from solution-space dispersion, and use it to downweight collapsed prompt groups. In addition, we introduce a new post-training metric, Reasoning-Answer Consistency (RAC), to measure the degree that the chain-of-though supports the answer, and show our exploration-aware curriculum improves RAC and downstream performance. Across a broad suite of vision-centric benchmarks, PuzzleCraft improves robustness and reasoning consistency, yielding consistent downstream gains on both Qwen2.5-VL and Qwen3-VL backbones. Overall, our results suggest that scalable puzzle-based RLVR benefits from curricula that account for both difficulty and solution-space collapse, together with explicit consistency-enhancing schemes.

Large language models (LLMs) now exhibit strong multi-step reasoning abilities, but existing inference-time scaling methods remain computationally expensive, often relying on extensive sampling or external evaluators. We propose a principled strategy that frames reasoning as uncertainty minimisation and operates at the level of individual thoughts rather than tokens. Our method selects, at each reasoning step, the continuation that maximizes the model's self-certainty, a metric computed from its internal predictive distribution. This approach achieves significant improvement with a small number of samples, relies exclusively on model-internal signals, and applies to open-ended questions as opposed to methods like majority voting. Experiments on MATH500 and GSM8K across multiple model sizes demonstrate that thought-level self-certainty maximization consistently outperforms greedy decoding and matches or exceeds self-consistency under comparable token budgets. Cross-linguistic evaluations further indicate that the method transfers robustly beyond high-resource languages. Furthermore, analysis of self-certainty dynamics reveals that correct reasoning trajectories converge early to stable paths, suggesting that early decisions, likely associated with the planning of the reasoning process, are predictive of final accuracy. Building on this result, we show that self-certainty maximisation applied to the early steps can explain most of the performance gain and provide a simple yet efficient inference-time scaling method.

As language models (LMs) become integral to fields like healthcare, law, and journalism, their ability to differentiate between fact, belief, and knowledge is essential for reliable decision-making. Failure to grasp these distinctions can lead to significant consequences in areas such as medical diagnosis, legal judgments, and dissemination of fake news. Despite this, current literature has largely focused on more complex issues such as theory of mind, overlooking more fundamental epistemic challenges. This study systematically evaluates the epistemic reasoning capabilities of modern LMs, including GPT-4, Claude-3, and Llama-3, using a new dataset, KaBLE, consisting of 13,000 questions across 13 tasks. Our results reveal key limitations. First, while LMs achieve 86% accuracy on factual scenarios, their performance drops significantly with false scenarios, particularly in belief-related tasks. Second, LMs struggle with recognizing and affirming personal beliefs, especially when those beliefs contradict factual data, which raises concerns for applications in healthcare and counseling, where engaging with a person's beliefs is critical. Third, we identify a salient bias in how LMs process first-person versus third-person beliefs, performing better on third-person tasks (80.7%) compared to first-person tasks (54.4%). Fourth, LMs lack a robust understanding of the factive nature of knowledge, namely, that knowledge inherently requires truth. Fifth, LMs rely on linguistic cues for fact-checking and sometimes bypass the deeper reasoning. These findings highlight significant concerns about current LMs' ability to reason about truth, belief, and knowledge while emphasizing the need for advancements in these areas before broad deployment in critical sectors.

Despite significant strides in factual reliability, errors -- often termed hallucinations -- remain a major concern for generative AI, especially as LLMs are increasingly expected to be helpful in more complex or nuanced setups. Yet even in the simplest setting -- factoid question-answering with clear ground truth-frontier models without external tools continue to hallucinate. We argue that most factuality gains in this domain have come from expanding the model's knowledge boundary (encoding more facts) rather than improving awareness of that boundary (distinguishing known from unknown). We conjecture that the latter is inherently difficult: models may lack the discriminative power to perfectly separate truths from errors, creating an unavoidable tradeoff between eliminating hallucinations and preserving utility. This tradeoff dissolves under a different framing. If we understand hallucinations as confident errors -- incorrect information delivered without appropriate qualification -- a third path emerges beyond the answer-or-abstain dichotomy: expressing uncertainty. We propose faithful uncertainty: aligning linguistic uncertainty with intrinsic uncertainty. This is one facet of metacognition -- the ability to be aware of one's own uncertainty and to act on it. For direct interaction, acting on uncertainty means communicating it honestly; for agentic systems, it becomes the control layer governing when to search and what to trust. Metacognition is thus essential for LLMs to be both trustworthy and capable; we conclude by highlighting open problems for progress towards this objective.

Model-based reinforcement learning (MBRL) improves sample efficiency by optimizing policies inside imagined rollouts, but long-horizon planning degrades when model errors compound and imagined trajectories drift off the training manifold. We introduce GIRL (Generative Imagination Reinforcement Learning), a latent world-model framework that addresses this failure mode with two key components. First, a cross-modal grounding signal derived from a frozen foundation model (DINOv2) anchors the latent transition prior to a semantically consistent embedding space, penalizing inconsistent or implausible predictions. Second, an uncertainty-adaptive trust-region bottleneck interprets the KL regularizer as the Lagrange multiplier of a constrained optimization problem, restricting imagination drift within a learned region calibrated by Expected Information Gain and a Relative Performance Loss signal. We re-derive a value-gap bound using the Performance Difference Lemma and Integral Probability Metrics, yielding a bound that remains informative as the discount factor approaches one and connects the objective to real-environment regret. Experiments across three benchmark suites, including DeepMind Control, Adroit Hand Manipulation, and Meta-World with visual distractors, show that GIRL reduces latent rollout drift by 38 to 61 percent across tasks relative to DreamerV3, improves asymptotic return, and requires fewer environment interactions on long-horizon tasks. GIRL also outperforms TD-MPC2 on sparse-reward and high-contact settings under standard evaluation metrics. A distilled-prior variant reduces inference overhead and improves computational efficiency relative to the full model.

Large language models (LLMs) are becoming deeply embedded in human communication and decision-making, yet they inherit the ambiguity, bias, and lack of direct access to truth inherent in language itself. While their outputs are fluent, emotionally resonant, and coherent, they are generated through statistical prediction rather than grounded reasoning. This creates the risk of hallucination, responses that sound convincing but lack factual validity. Building on Geoffrey Hinton's observation that AI mirrors human intuition rather than reasoning, this paper argues that LLMs operationalize System 1 cognition at scale: fast, associative, and persuasive, but without reflection or falsification. To address this, we introduce the Rose-Frame, a three-dimensional framework for diagnosing cognitive and epistemic drift in human-AI interaction. The three axes are: (i) Map vs. Territory, which distinguishes representations of reality (epistemology) from reality itself (ontology); (ii) Intuition vs. Reason, drawing on dual-process theory to separate fast, emotional judgments from slow, reflective thinking; and (iii) Conflict vs. Confirmation, which examines whether ideas are critically tested through disagreement or simply reinforced through mutual validation. Each dimension captures a distinct failure mode, and their combination amplifies misalignment. Rose-Frame does not attempt to fix LLMs with more data or rules. Instead, it offers a reflective tool that makes both the model's limitations and the user's assumptions visible, enabling more transparent and critically aware AI deployment. It reframes alignment as cognitive governance: intuition, whether human or artificial, must remain governed by human reason. Only by embedding reflective, falsifiable oversight can we align machine fluency with human understanding.

Spatial reasoning is a fundamental aspect of human cognition, yet it remains a major challenge for contemporary vision-language models (VLMs). Prior work largely relied on synthetic or LLM-generated environments with limited task designs and puzzle-like setups, failing to capture the real-world complexity, visual noise, and diverse spatial relationships that VLMs encounter. To address this, we introduce SpatiaLab, a comprehensive benchmark for evaluating VLMs' spatial reasoning in realistic, unconstrained contexts. SpatiaLab comprises 1,400 visual question-answer pairs across six major categories: Relative Positioning, Depth & Occlusion, Orientation, Size & Scale, Spatial Navigation, and 3D Geometry, each with five subcategories, yielding 30 distinct task types. Each subcategory contains at least 25 questions, and each main category includes at least 200 questions, supporting both multiple-choice and open-ended evaluation. Experiments across diverse state-of-the-art VLMs, including open- and closed-source models, reasoning-focused, and specialized spatial reasoning models, reveal a substantial gap in spatial reasoning capabilities compared with humans. In the multiple-choice setup, InternVL3.5-72B achieves 54.93% accuracy versus 87.57% for humans. In the open-ended setting, all models show a performance drop of around 10-25%, with GPT-5-mini scoring highest at 40.93% versus 64.93% for humans. These results highlight key limitations in handling complex spatial relationships, depth perception, navigation, and 3D geometry. By providing a diverse, real-world evaluation framework, SpatiaLab exposes critical challenges and opportunities for advancing VLMs' spatial reasoning, offering a benchmark to guide future research toward robust, human-aligned spatial understanding. SpatiaLab is available at: https://spatialab-reasoning.github.io/.

This work presents an information-theoretic perspective to group fairness trade-offs in federated learning (FL) with respect to sensitive attributes, such as gender, race, etc. Existing works often focus on either global fairness (overall disparity of the model across all clients) or local fairness (disparity of the model at each client), without always considering their trade-offs. There is a lack of understanding regarding the interplay between global and local fairness in FL, particularly under data heterogeneity, and if and when one implies the other. To address this gap, we leverage a body of work in information theory called partial information decomposition (PID), which first identifies three sources of unfairness in FL, namely, Unique Disparity, Redundant Disparity, and Masked Disparity. We demonstrate how these three disparities contribute to global and local fairness using canonical examples. This decomposition helps us derive fundamental limits on the trade-off between global and local fairness, highlighting where they agree or disagree. We introduce the Accuracy and Global-Local Fairness Optimality Problem (AGLFOP), a convex optimization that defines the theoretical limits of accuracy and fairness trade-offs, identifying the best possible performance any FL strategy can attain given a dataset and client distribution. We also present experimental results on synthetic datasets and the ADULT dataset to support our theoretical findings.

Spatial reasoning is a fundamental capability for vision-language models (VLMs) deployed in real-world environments. However, visual observations are inherently limited representations of a 3D world: occlusion can render objects invisible, and perspective can make geometric properties misleading. Despite this, existing spatial reasoning benchmarks typically assume that observations are sufficient and reliable, focusing on whether models produce correct answers rather than whether they recognize when a question cannot be answered and what additional observations would be needed. In this work, we challenge this assumption by constructing a controlled evaluation framework, SpatialUncertain, and introducing two types of observation challenges: (1) occlusion, which hides target information, and (2) perspective ambiguity, which produces misleading visual cues. For each configuration, we design spatial questions that are answerable under clean observations but require abstention under the introduced challenges. We further evaluate whether models can identify which additional viewpoints would resolve perspective ambiguity. Our results across a diverse set of frontier open- and closed-source VLMs reveal two consistent failure modes. First, models are prone to overconfident answering, attempting to solve spatial reasoning tasks even when visual evidence is incomplete or misleading, with average accuracy around 30\% under occlusion and below 10\% under perspective ambiguity. Second, even when additional views are available, some models perform near random chance in identifying which would provide reliable evidence. Together, our findings call for moving beyond answer correctness toward evaluating whether models know when to abstain and how to seek reliable evidence.

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.

Spatial intelligence is a critical frontier for Multimodal Large Language Models (MLLMs), empowering them to comprehend the physical world. Drawing inspiration from human perception mechanisms, existing studies attempt to construct a coherent spatial understanding via grid-based cognitive maps from multi-frame visual inputs. However, current grid-based map methods rely on discretized raster representations, which limit the model's ability in fine-grained spatial reasoning. To overcome this limitation, we propose Video2Layout, a framework for reconstructing metric-grounded spatial layouts from video. The framework employs continuous object boundary coordinates to quantify inter-object physical distances and object size. This empowers the model with quantitative spatial computation capabilities, effectively alleviating the inherent ambiguity when describing spatial relationships in natural language. Specifically, our method comprises two core stages. First, in supervised fine-tuning stage, we construct a high-quality dataset from the AI2THOR simulator, which enables the model to learn the mapping from visual inputs to precise boundary coordinates. Subsequently, a reinforcement fine-tuning stage further enhances the model's real-world generalization capabilities. To systematically evaluate the correlation between cognitive map accuracy and image quantity, as well as how the quantity of image inputs affects spatial reasoning accuracy, we introduce QVS-Bench, a diagnostic benchmark designed to analyze the relevant mechanisms. Evaluated on QVS-Bench and mainstream spatial reasoning benchmarks, our model, V2LO-7B achieves an average improvement of 4.92% over the model trained on grid maps, validating the superiority of our method. Our code is available at https://github.com/ybrrraway/Video2Layout.

As LLMs grow more powerful, their most profound achievement may be recognising when to say "I don't know". Existing studies on LLM self-knowledge have been largely constrained by human-defined notions of feasibility, often neglecting the reasons behind unanswerability by LLMs and failing to study deficient types of self-knowledge. This study aims to obtain intrinsic insights into different types of LLM self-knowledge with a novel methodology: allowing them the flexibility to set their own feasibility boundaries and then analysing the consistency of these limits. We find that even frontier models like GPT-4o and Mistral Large are not sure of their own capabilities more than 80% of the time, highlighting a significant lack of trustworthiness in responses. Our analysis of confidence balance in LLMs indicates that models swing between overconfidence and conservatism in feasibility boundaries depending on task categories and that the most significant self-knowledge weaknesses lie in temporal awareness and contextual understanding. These difficulties in contextual comprehension additionally lead models to question their operational boundaries, resulting in considerable confusion within the self-knowledge of LLMs. We make our code and results available publicly at https://github.com/knowledge-verse-ai/LLM-Self_Knowledge_Eval

Internal world models (WMs) enable agents to understand the world's state and predict transitions, serving as the basis for advanced deliberative reasoning. Recent large Vision-Language Models (VLMs), such as OpenAI o3, GPT-4o and Gemini, exhibit potential as general-purpose WMs. While the latest studies have evaluated and shown limitations in specific capabilities such as visual understanding, a systematic evaluation of VLMs' fundamental WM abilities remains absent. Drawing on comparative psychology and cognitive science, we propose a two-stage framework that assesses Perception (visual, spatial, temporal, quantitative, and motion) and Prediction (mechanistic simulation, transitive inference, compositional inference) to provide an atomic evaluation of VLMs as WMs. Guided by this framework, we introduce WM-ABench, a large-scale benchmark comprising 23 fine-grained evaluation dimensions across 6 diverse simulated environments with controlled counterfactual simulations. Through 660 experiments on 15 latest commercial and open-source VLMs, we find that these models exhibit striking limitations in basic world modeling abilities. For instance, almost all models perform at near-random accuracy when distinguishing motion trajectories. Additionally, they lack disentangled understanding -- e.g., some models tend to believe blue objects move faster than green ones. More rich results and analyses reveal significant gaps between VLMs and human-level world modeling.