Daily Papers

State machine replication (SMR) and Byzantine fault-tolerant (BFT) consensus guarantee agreement despite a bounded number of arbitrary, colluding faulty participants. However, these guarantees rely on participants outside this set correctly executing the protocol's transition semantics. Agentic validators expose a weaker boundary: an authenticated, responsive, non-equivocating, and protocol-compliant reasoning participant may still endorse a semantically invalid transition due to reasoning errors. We call this failure mode an epistemic fault, and the collective phenomenon the Honest Quorum Problem (where "honest" means protocol-compliant, not semantically correct). Such a quorum can satisfy ordinary checks while forming a certificate for an invalid transition. Thus, agreement alone does not guarantee semantic validity or execution safety. Furthermore, because agentic validators often share model weights, training distributions, prompts, or toolchains, they are highly susceptible to correlated epistemic faults. We define Epistemic Byzantine Fault Tolerance (EBFT), a fault-tolerance model for agentic infrastructure and post-deterministic distributed systems. EBFT augments the conventional Byzantine fault bound with two separate, confidence-indexed quantities: e_δ bounds coherent invalid endorsements outside the Byzantine set, and u_ε bounds unusable validator support that degrades liveness. These quantities characterize semantic safety risk and liveness degradation independently. We derive quorum-threshold conditions for semantic validity, consensus agreement, liveness, and feasible threshold selection, and outline a calibration methodology for estimating these budgets. We show that adding nominally distinct agents improves fault tolerance only when it measurably reduces the upper-tail concentration of invalid endorsements or unusable support.

We present the Consilium Protocol, a Byzantine Fault Tolerance-derived architecture for structured multi-model AI deliberation that treats inter-model disagreement as epistemic signal rather than error. The protocol assigns engineered cognitive personas to language models -- separating what a model is from how it reasons -- and introduces an In-Sample/Out-of-Sample validation framework adapted from quantitative finance to distinguish training-data consensus from empirically grounded conclusions. Across 1,478 deliberation sessions spanning 32 topics in 10 domain categories, we demonstrate that (1) the cognitive persona, not the underlying model, determines epistemic behavior: free edge-inference models costing 0.0002 USD per batch produced comparable analytical output to frontier models costing 10.69 USD; (2) RLHF alignment training creates measurable, domain-specific epistemic blind spots -- contested policy topics exhibit 12.3 percentage points less adversarial challenge than settled science topics, and AI safety topics show asymmetric bias (Δ=11.6%) where models challenge claims that AI is dangerous far more vigorously than claims that AI risk is overstated; (3) the protocol exhibits no directional bias of its own (immigration Δ=2.3%, renewables Δ=1.2%); and (4) out-of-sample evidence retrieval validated 239 claims with 100% evidence retrieval and surfaced 167 blind-spot discoveries invisible to training-data deliberation. Run-to-run reproducibility across randomized modeltimespersona assignments averages pm2.2% standard deviation. Total cost for the complete battery including all overhead: 217 USD. We release the protocol specification under MIT license to enable independent verification.

Epistemic Uncertainty is a measure of the lack of knowledge of a learner which diminishes with more evidence. While existing work focuses on using the variance of the Bayesian posterior due to parameter uncertainty as a measure of epistemic uncertainty, we argue that this does not capture the part of lack of knowledge induced by model misspecification. We discuss how the excess risk, which is the gap between the generalization error of a predictor and the Bayes predictor, is a sound measure of epistemic uncertainty which captures the effect of model misspecification. We thus propose a principled framework for directly estimating the excess risk by learning a secondary predictor for the generalization error and subtracting an estimate of aleatoric uncertainty, i.e., intrinsic unpredictability. We discuss the merits of this novel measure of epistemic uncertainty, and highlight how it differs from variance-based measures of epistemic uncertainty and addresses its major pitfall. Our framework, Direct Epistemic Uncertainty Prediction (DEUP) is particularly interesting in interactive learning environments, where the learner is allowed to acquire novel examples in each round. Through a wide set of experiments, we illustrate how existing methods in sequential model optimization can be improved with epistemic uncertainty estimates from DEUP, and how DEUP can be used to drive exploration in reinforcement learning. We also evaluate the quality of uncertainty estimates from DEUP for probabilistic image classification and predicting synergies of drug combinations.

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.

As large language models evolve into tool-augmented agents, a central question remains unresolved: when is external tool use actually justified? Existing agent frameworks typically treat tools as ordinary actions and optimize for task success or reward, offering little principled distinction between epistemically necessary interaction and unnecessary delegation. This position paper argues that agents should invoke external tools only when epistemically necessary. Here, epistemic necessity means that a task cannot be completed reliably via the agent's internal reasoning over its current context, without any external interaction. We introduce the Theory of Agent (ToA), a framework that treats agents as making sequential decisions about whether remaining uncertainty should be resolved internally or delegated externally. From this perspective, common agent failure modes (e.g., overthinking and overacting) arise from miscalibrated decisions under uncertainty rather than deficiencies in reasoning or tool execution alone. We further discuss implications for training, evaluation, and agent design, highlighting that unnecessary delegation not only causes inefficiency but can impede the development of internal reasoning capability. Our position provides a normative criterion for tool use that complements existing decision-theoretic models and is essential for building agents that are not only correct, but increasingly intelligent.

AI systems can now cheaply generate plausible scientific artifacts such as papers, reviews, and surveys. This creates a risk of epistemic pollution in our scientific systems, where unreliable but plausible-looking artifacts can accumulate faster than the system can filter them out. The problem is structural: the epistemic infrastructure of science was calibrated to a world where producing a plausible artifact required substantial expertise, labor, and time, so generation cost itself served as a rough filter; AI weakens that filter without comparably lowering verification cost. We argue that AI-era science should treat this as an engineering problem: redesigning epistemic infrastructure to rebalance the costs of generation and verification. The current paper-centered system makes verification expensive: papers compress long-context scientific logic into prose, forcing reviewers, human or AI, to reconstruct underlying argument structure before they can evaluate it. As one step in this direction, we propose blueprints as preliminary epistemic infrastructure: structured, decomposed research artifacts that represent claims, evidence, assumptions, and definitions as typed graph components. Blueprints are designed to trade an upfront generation cost for cheaper, more local, more distributed verification downstream. We have instantiated the proposal in a proof-of-concept prototype.

We introduce ProofGrid, a benchmark suite for evaluating LLM reasoning through machine-checkable proofs rather than final answers alone. ProofGrid contains 15 tasks spanning proof writing, proof checking, proof masking, and proof gap-filling. Tasks are expressed in minimal formal notation, especially NDL, a compact natural-deduction language that fits in short prompts and supports precise, auditable verification. This yields mechanical, reproducible, and fine-grained evaluation rather than judgments by humans or LLMs. ProofGrid covers a calibrated difficulty spectrum, from foundational reasoning tests to structurally rich challenge tasks that no current model solves, while minimizing reliance on domain knowledge, solver delegation, and long-context artifacts. We also develop a comparative framework for reasoning benchmarks and use it to situate ProofGrid relative to existing work in terms of representation, verification guarantees, and reasoning depth. Methodologically, we introduce an instrumented proof-checking pipeline that tolerates minor surface deviations while locating the first substantive reasoning failure, improving measurement resolution and separating proof planning from low-level execution noise. Using this pipeline, we evaluate a broad range of open and proprietary models. Results show rapid progress but substantial remaining limits: frontier models perform well on several foundational tasks, yet difficult tasks, especially those requiring global combinatorial reasoning or low-level proof synthesis, remain far from solved. We also identify epistemic instability, where models generate flawed proofs yet correctly reject those local inferences in isolation, and formalize this with an Epistemic Stability Index. Finally, we complement accuracy with 2PL IRT analyses, Wright maps, and a normalized task-discrimination measure based on Fisher information.

Large language models produce fluent text but struggle with systematic reasoning, often hallucinating confident but unfounded claims. When Apple researchers added irrelevant context to mathematical problems, LLM performance degraded by 65% Apple Machine Learning Research, exposing brittle pattern-matching beneath apparent reasoning. This epistemic gap, the inability to ground claims in traceable evidence, limits AI reliability in domains requiring justification. We introduce Pramana, a novel approach that teaches LLMs explicit epistemological methodology by fine-tuning on Navya-Nyaya logic, a 2,500-year-old Indian reasoning framework. Unlike generic chain-of-thought prompting, Navya-Nyaya enforces structured 6-phase reasoning: SAMSHAYA (doubt analysis), PRAMANA (evidence source identification), PANCHA AVAYAVA (5-member syllogism with universal rules), TARKA (counterfactual verification), HETVABHASA (fallacy detection), and NIRNAYA (ascertainment distinguishing knowledge from hypothesis). This integration of logic and epistemology provides cognitive scaffolding absent from standard reasoning approaches. We fine-tune Llama 3.2-3B and DeepSeek-R1-Distill-Llama-8B on 55 Nyaya-structured logical problems (constraint satisfaction, Boolean SAT, multi-step deduction). Stage 1 achieves 100% semantic correctness on held-out evaluation despite only 40% strict format adherence revealing that models internalize reasoning content even when structural enforcement is imperfect. Ablation studies show format prompting and temperature critically affect performance, with optimal configurations differing by stage. We release all models, datasets, and training infrastructure on Hugging Face to enable further research on epistemic frameworks for AI reasoning.

There are two major types of uncertainty one can model. Aleatoric uncertainty captures noise inherent in the observations. On the other hand, epistemic uncertainty accounts for uncertainty in the model -- uncertainty which can be explained away given enough data. Traditionally it has been difficult to model epistemic uncertainty in computer vision, but with new Bayesian deep learning tools this is now possible. We study the benefits of modeling epistemic vs. aleatoric uncertainty in Bayesian deep learning models for vision tasks. For this we present a Bayesian deep learning framework combining input-dependent aleatoric uncertainty together with epistemic uncertainty. We study models under the framework with per-pixel semantic segmentation and depth regression tasks. Further, our explicit uncertainty formulation leads to new loss functions for these tasks, which can be interpreted as learned attenuation. This makes the loss more robust to noisy data, also giving new state-of-the-art results on segmentation and depth regression benchmarks.

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

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.

When an agent can articulate why something works, we typically take this as evidence of genuine understanding. This presupposes that effective action and correct explanation covary, and that coherent explanation reliably signals both. I argue that this assumption fails for contemporary Large Language Models (LLMs). I introduce what I call the Bidirectional Coherence Paradox: competence and grounding not only dissociate but invert across epistemic conditions. In low-observability domains, LLMs often act successfully while misidentifying the mechanisms that produce their success. In high-observability domains, they frequently generate explanations that accurately track observable causal structure yet fail to translate those diagnoses into effective intervention. In both cases, explanatory coherence remains intact, obscuring the underlying dissociation. Drawing on experiments in compiler optimization and hyperparameter tuning, I develop the Epistemic Triangle, a model of how priors, signals, and domain knowledge interact under varying observability. The results suggest that neither behavioral success nor explanatory accuracy alone suffices for attributing understanding. I argue that evaluating artificial epistemic agents requires a tripartite framework -- coherence, grounding, and a proper basing relation linking explanation to action. The systematic separation of knowing-that and knowing-how in LLMs thus challenges assumptions inherited from both epistemology and current AI evaluation practice.

We argue that progress toward AGI is theory limited rather than data or scale limited. Building on the critical rationalism of Popper and Deutsch, we challenge the Platonic Representation Hypothesis. Observationally equivalent worlds can diverge under interventions, so observational adequacy alone cannot guarantee interventional competence. We begin by laying foundations, definitions of knowledge, learning, intelligence, counterfactual competence and AGI, and then analyze the limits of observational learning that motivate an error centric shift. We recast the problem as three questions about how explicit and implicit errors evolve under an agent's actions, which errors are unreachable within a fixed hypothesis space, and how conjecture and criticism expand that space. From these questions we propose Causal Mechanics, a mechanisms first program in which hypothesis space change is a first class operation and probabilistic structure is used when useful rather than presumed. We advance structural principles that make error discovery and correction tractable, including a differential Locality and Autonomy Principle for modular interventions, a gauge invariant form of Independent Causal Mechanisms for separability, and the Compositional Autonomy Principle for analogy preservation, together with actionable diagnostics. The aim is a scaffold for systems that can convert unreachable errors into reachable ones and correct them.

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.

Bold claims about AI's role in science-from "AGI will cure all diseases" to promises of radically accelerated discovery-raise a central epistemic question: do large language models (LLMs) truly generate new knowledge, or do they merely remix memorized fragments? We propose unlearning-as-ablation as a falsifiable probe of constructive scientific discovery. The idea is to systematically remove a target result together with its forget-closure (supporting lemmas, paraphrases, and multi-hop entailments) and then evaluate whether the model can re-derive the result from only permitted axioms and tools. Success would indicate generative capability beyond recall; failure would expose current limits. Unlike prevailing motivations for unlearning-privacy, copyright, or safety-our framing repositions it as an epistemic probe for AI-for-Science. We outline a minimal pilot in mathematics and algorithms to illustrate feasibility, and sketch how the same approach could later be extended to domains such as physics or chemistry. This is a position paper: our contribution is conceptual and methodological, not empirical. We aim to stimulate discussion on how principled ablation tests could help distinguish models that reconstruct knowledge from those that merely retrieve it, and how such probes might guide the next generation of AI-for-Science benchmarks.

Artificial intelligence commonly refers to the science and engineering of artificial systems that can carry out tasks generally associated with requiring aspects of human intelligence, such as playing games, translating languages, and driving cars. In recent years, there have been exciting advances in learning-based, data-driven approaches towards AI, and machine learning and deep learning have enabled computer systems to perceive the world in unprecedented ways. Reinforcement learning has enabled breakthroughs in complex games such as Go and challenging robotics tasks such as quadrupedal locomotion. A key aspect of intelligence is to not only make predictions, but reason about the uncertainty in these predictions, and to consider this uncertainty when making decisions. This is what this manuscript on "Probabilistic Artificial Intelligence" is about. The first part covers probabilistic approaches to machine learning. We discuss the differentiation between "epistemic" uncertainty due to lack of data and "aleatoric" uncertainty, which is irreducible and stems, e.g., from noisy observations and outcomes. We discuss concrete approaches towards probabilistic inference and modern approaches to efficient approximate inference. The second part of the manuscript is about taking uncertainty into account in sequential decision tasks. We consider active learning and Bayesian optimization -- approaches that collect data by proposing experiments that are informative for reducing the epistemic uncertainty. We then consider reinforcement learning and modern deep RL approaches that use neural network function approximation. We close by discussing modern approaches in model-based RL, which harness epistemic and aleatoric uncertainty to guide exploration, while also reasoning about safety.

To enable quantitative risk assessment of uncontrollable risk states in complex and coupled IoT systems, a new epistemological equation is designed and tested though comparative and empirical analysis. The comparative analysis is conducted on national digital strategies, followed by an empirical analysis of cyber risk assessment approaches. The new epistemological analysis approach enables the assessment of uncontrollable risk states in complex IoT systems, which begin to resemble artificial intelligence, and can be used for a quantitative self-assessment of IoT cyber risk posture.

LLMs often exhibit Aha moments during reasoning, such as apparent self-correction following tokens like "Wait," yet their underlying mechanisms remain unclear. We introduce an information-theoretic framework that decomposes reasoning into procedural information and epistemic verbalization - the explicit externalization of uncertainty that supports downstream control actions. We show that purely procedural reasoning can become informationally stagnant, whereas epistemic verbalization enables continued information acquisition and is critical for achieving information sufficiency. Empirical results demonstrate that strong reasoning performance is driven by uncertainty externalization rather than specific surface tokens. Our framework unifies prior findings on Aha moments and post-training experiments, and offers insights for future reasoning model design.

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.

Generative AI agents equate understanding with resolving explicit queries, an assumption that confines interaction to what users can articulate. This assumption breaks down when users themselves lack awareness of what is missing, risky, or worth considering. In such conditions, proactivity is not merely an efficiency enhancement, but an epistemic necessity. We refer to this condition as epistemic incompleteness: where progress depends on engaging with unknown unknowns for effective partnership. Existing approaches to proactivity remain narrowly anticipatory, extrapolating from past behavior and presuming that goals are already well defined, thereby failing to support users meaningfully. However, surfacing possibilities beyond a user's current awareness is not inherently beneficial. Unconstrained proactive interventions can misdirect attention, overwhelm users, or introduce harm. Proactive agents, therefore, require behavioral grounding: principled constraints on when, how, and to what extent an agent should intervene. We advance the position that generative proactivity must be grounded both epistemically and behaviorally. Drawing on the philosophy of ignorance and research on proactive behavior, we argue that these theories offer critical guidance for designing agents that can engage responsibly and foster meaningful partnerships.

Current language model evaluations measure what models know under ideal conditions but not how robustly they know it under realistic stress. Static benchmarks like MMLU and TruthfulQA cannot distinguish a model that lacks knowledge from one whose verification mechanisms collapse when information degrades or adversaries probe for weaknesses. We introduce the Drill-Down and Fabricate Test (DDFT), a protocol that measures epistemic robustness: a model's ability to maintain factual accuracy under progressive semantic compression and adversarial fabrication. We propose a two-system cognitive model comprising a Semantic System that generates fluent text and an Epistemic Verifier that validates factual accuracy. Our findings, based on evaluating 9 frontier models across 8 knowledge domains at 5 compression levels (1,800 turn-level evaluations), reveal that epistemic robustness is orthogonal to conventional design paradigms. Neither parameter count (r=0.083, p=0.832) nor architectural type (r=0.153, p=0.695) significantly predicts robustness, suggesting it emerges from training methodology and verification mechanisms distinct from current approaches. Error detection capability strongly predicts overall robustness (rho=-0.817, p=0.007), indicating this is the critical bottleneck. We find that flagship models exhibit brittleness despite their scale, while smaller models can achieve robust performance, challenging assumptions about the relationship between model size and reliability. The DDFT framework provides both theoretical foundation and practical tools for assessing epistemic robustness before deployment in critical applications.

Large language model (LLM)-based conversational AI systems present a challenge to human cognition that current frameworks for understanding misinformation and persuasion do not adequately address. This paper proposes that a significant epistemic risk from conversational AI may lie not in inaccuracy or intentional deception, but in something more fundamental: these systems may be configured, through optimization processes that make them useful, to present characteristics that bypass the cognitive mechanisms humans evolved to evaluate incoming information. The Cognitive Trojan Horse hypothesis draws on Sperber and colleagues' theory of epistemic vigilance -- the parallel cognitive process monitoring communicated information for reasons to doubt -- and proposes that LLM-based systems present 'honest non-signals': genuine characteristics (fluency, helpfulness, apparent disinterest) that fail to carry the information equivalent human characteristics would carry, because in humans these are costly to produce while in LLMs they are computationally trivial. Four mechanisms of potential bypass are identified: processing fluency decoupled from understanding, trust-competence presentation without corresponding stakes, cognitive offloading that delegates evaluation itself to the AI, and optimization dynamics that systematically produce sycophancy. The framework generates testable predictions, including a counterintuitive speculation that cognitively sophisticated users may be more vulnerable to AI-mediated epistemic influence. This reframes AI safety as partly a problem of calibration -- aligning human evaluative responses with the actual epistemic status of AI-generated content -- rather than solely a problem of preventing deception.

Vision-Language Models (VLMs) frequently "hallucinate" - generate plausible yet factually incorrect statements - posing a critical barrier to their trustworthy deployment. In this work, we propose a new paradigm for diagnosing hallucinations, recasting them from static output errors into dynamic pathologies of a model's computational cognition. Our framework is grounded in a normative principle of computational rationality, allowing us to model a VLM's generation as a dynamic cognitive trajectory. We design a suite of information-theoretic probes that project this trajectory onto an interpretable, low-dimensional Cognitive State Space. Our central discovery is a governing principle we term the geometric-information duality: a cognitive trajectory's geometric abnormality within this space is fundamentally equivalent to its high information-theoretic surprisal. Hallucination detection is counts as a geometric anomaly detection problem. Evaluated across diverse settings - from rigorous binary QA (POPE) and comprehensive reasoning (MME) to unconstrained open-ended captioning (MS-COCO) - our framework achieves state-of-the-art performance. Crucially, it operates with high efficiency under weak supervision and remains highly robust even when calibration data is heavily contaminated. This approach enables a causal attribution of failures, mapping observable errors to distinct pathological states: perceptual instability (measured by Perceptual Entropy), logical-causal failure (measured by Inferential Conflict), and decisional ambiguity (measured by Decision Entropy). Ultimately, this opens a path toward building AI systems whose reasoning is transparent, auditable, and diagnosable by design.

Large language model (LLM)-based systems are increasingly deployed to conduct scientific research autonomously, yet whether their reasoning adheres to the epistemic norms that make scientific inquiry self-correcting is poorly understood. Here, we evaluate LLM-based scientific agents across eight domains, spanning workflow execution to hypothesis-driven inquiry, through more than 25,000 agent runs and two complementary lenses: (i) a systematic performance analysis that decomposes the contributions of the base model and the agent scaffold, and (ii) a behavioral analysis of the epistemological structure of agent reasoning. We observe that the base model is the primary determinant of both performance and behavior, accounting for 41.4% of explained variance versus 1.5% for the scaffold. Across all configurations, evidence is ignored in 68% of traces, refutation-driven belief revision occurs in 26%, and convergent multi-test evidence is rare. The same reasoning pattern appears whether the agent executes a computational workflow or conducts hypothesis-driven inquiry. They persist even when agents receive near-complete successful reasoning trajectories as context, and the resulting unreliability compounds across repeated trials in epistemically demanding domains. Thus, current LLM-based agents execute scientific workflows but do not exhibit the epistemic patterns that characterize scientific reasoning. Outcome-based evaluation cannot detect these failures, and scaffold engineering alone cannot repair them. Until reasoning itself becomes a training target, the scientific knowledge produced by such agents cannot be justified by the process that generated it.

To address this gap, our study introduces the concept of causal epistemic consistency, which focuses on the self-consistency of Large Language Models (LLMs) in differentiating intermediates with nuanced differences in causal reasoning. We propose a suite of novel metrics -- intensity ranking concordance, cross-group position agreement, and intra-group clustering -- to evaluate LLMs on this front. Through extensive empirical studies on 21 high-profile LLMs, including GPT-4, Claude3, and LLaMA3-70B, we have favoring evidence that current models struggle to maintain epistemic consistency in identifying the polarity and intensity of intermediates in causal reasoning. Additionally, we explore the potential of using internal token probabilities as an auxiliary tool to maintain causal epistemic consistency. In summary, our study bridges a critical gap in AI research by investigating the self-consistency over fine-grained intermediates involved in causal reasoning.

Theory of Mind (ToM) is a critical component of intelligence, yet accurately measuring it continues to be a subject of debate. Prior research has attempted to apply human ToM assessments to natural language processing models using either human-created standardized tests or rule-based templates. However, these methods primarily focus on simplistic reasoning and require further validation. In this study, we utilize dynamic epistemic logic, which has established overlaps with ToM, to generate more intricate problems. We also introduce novel verbalization techniques to express these problems using natural language. Our findings indicate that certain language model scaling (from 70M to 6B and 350M to 174B) does not consistently yield results better than random chance. While GPT-4 demonstrates improved epistemic reasoning capabilities, there is still room for enhancement. Our code and datasets are publicly available https://github.com/antoinelrnld/modlog https://huggingface.co/datasets/sileod/mindgames

Developing models that can learn to reason is a notoriously challenging problem. We focus on reasoning in relational domains, where the use of Graph Neural Networks (GNNs) seems like a natural choice. However, previous work has shown that regular GNNs lack the ability to systematically generalize from training examples on test graphs requiring longer inference chains, which fundamentally limits their reasoning abilities. A common solution relies on neuro-symbolic methods that systematically reason by learning rules, but their scalability is often limited and they tend to make unrealistically strong assumptions, e.g.\ that the answer can always be inferred from a single relational path. We propose the Epistemic GNN (EpiGNN), a novel parameter-efficient and scalable GNN architecture with an epistemic inductive bias for systematic reasoning. Node embeddings in EpiGNNs are treated as epistemic states, and message passing is implemented accordingly. We show that EpiGNNs achieve state-of-the-art results on link prediction tasks that require systematic reasoning. Furthermore, for inductive knowledge graph completion, EpiGNNs rival the performance of state-of-the-art specialized approaches. Finally, we introduce two new benchmarks that go beyond standard relational reasoning by requiring the aggregation of information from multiple paths. Here, existing neuro-symbolic approaches fail, yet EpiGNNs learn to reason accurately. Code and datasets are available at https://github.com/erg0dic/gnn-sg.

Despite improvements in performances on different natural language generation tasks, deep neural models are prone to hallucinating facts that are incorrect or nonexistent. Different hypotheses are proposed and examined separately for different tasks, but no systematic explanations are available across these tasks. In this study, we draw connections between hallucinations and predictive uncertainty in conditional language generation. We investigate their relationship in both image captioning and data-to-text generation and propose a simple extension to beam search to reduce hallucination. Our analysis shows that higher predictive uncertainty corresponds to a higher chance of hallucination. Epistemic uncertainty is more indicative of hallucination than aleatoric or total uncertainties. It helps to achieve better results of trading performance in standard metric for less hallucination with the proposed beam search variant.

Language builds discourse contexts other than the actual: a painting, a belief, a memory, a hypothetical. Each is a mental space in which the same entity can take a different value, as when a flower is red in reality but purple in a portrait. Formal semantics keeps these contexts apart because their logics differ (modal, temporal, doxastic, depictive); Fauconnier's mental-space theory treats them as one space-building operation. We ask which of these a transformer language model implements, and find a mechanistic version of Fauconnier's unification. The model uses one router/slot format across the inventory: a reusable value slot stores attributed content, and a causally manipulable router (the space index) selects which space is read. A subspace trained with Distributed Alignment Search to control one space type, counterfactual, belief, fictional, or temporal, also controls the others, well above a random floor, on three model families; belief, which formal semantics marks as a distinct case, is not specially separated. The router is low-rank, composes additively with entity identity, and acts through a few late-layer heads. Two further results show the mechanism drives inference and composes: a subspace trained on a rule-derived conclusion flips what the model infers while dissociating from what it reports, and composing space-builders mints a fresh router over the shared slot. This paper establishes the cross-type generality. A companion paper develops belief in depth, because of its special status in philosophy, psychology, and linguistics (epistemology, theory of mind, and propositional attitude reports).

Longitudinal modelling of Alzheimer's disease progression is clinically useful only if it can describe not just the most likely next diagnosis, but how a patient may evolve over time and how reliable that forecast is. Most deep learning approaches reduce this problem to single-step classification, treating cognitively normal, mild cognitive impairment, and dementia as flat categories while providing limited insight into how uncertainty accumulates across future visits. We propose a probabilistic framework that combines ordinal diagnosis prediction, multi-horizon trajectory generation, and decomposed uncertainty estimation. A Temporal Fusion Transformer encoder is adapted with a CORAL ordinal output layer, asymmetric loss weighting, and converter oversampling to respect disease-stage ordering and improve sensitivity to MCI-to-dementia transitions. Conditioned on the learned patient-context representation, an autoregressive Mixture Density Network generates five-year probabilistic trajectories for diagnosis state, CDR Sum of Boxes, MMSE orientation, and hippocampal volume. On ADNI, the model outperforms linear, recurrent, and transformer baselines for next-visit diagnosis prediction, with the strongest gains on MCI-versus-dementia discrimination. Generated trajectories achieve near-nominal 90% credible interval coverage, widening uncertainty across the forecast horizon, and biomarker dynamics consistent with expected Alzheimer's disease progression. We further separate aleatoric from epistemic uncertainty using analytic mixture variance and a five-member bootstrap ensemble, which provides the strongest encoder diversity and output-level epistemic signal. Epistemic uncertainty is higher for rare progression archetypes, MCI and dementia patients, and under external evaluation on OASIS-3, where it increases alongside prediction error.

Artificial intelligence functions not as an epistemic leveller, but as an accelerant of cognitive stratification, entrenching and formalising informational castes within liberal-democratic societies. Synthesising formal epistemology, political theory, algorithmic architecture, and economic incentive structures, the argument traces how contemporary AI systems selectively amplify the reasoning capacity of individuals equipped with recursive abstraction, symbolic logic, and adversarial interrogation, whilst simultaneously pacifying the cognitively untrained through engagement-optimised interfaces. Fluency replaces rigour, immediacy displaces reflection, and procedural reasoning is eclipsed by reactive suggestion. The result is a technocratic realignment of power: no longer grounded in material capital alone, but in the capacity to navigate, deconstruct, and manipulate systems of epistemic production. Information ceases to be a commons; it becomes the substrate through which consent is manufactured and autonomy subdued. Deliberative democracy collapses not through censorship, but through the erosion of interpretive agency. The proposed response is not technocratic regulation, nor universal access, but the reconstruction of rational autonomy as a civic mandate, codified in education, protected by epistemic rights, and structurally embedded within open cognitive infrastructure.

Uncertainty quantification has received increasing attention in machine learning in the recent past. In particular, a distinction between aleatoric and epistemic uncertainty has been found useful in this regard. The latter refers to the learner's (lack of) knowledge and appears to be especially difficult to measure and quantify. In this paper, we analyse a recent proposal based on the idea of a second-order learner, which yields predictions in the form of distributions over probability distributions. While standard (first-order) learners can be trained to predict accurate probabilities, namely by minimising suitable loss functions on sample data, we show that loss minimisation does not work for second-order predictors: The loss functions proposed for inducing such predictors do not incentivise the learner to represent its epistemic uncertainty in a faithful way.

Theory of Mind (ToM), the ability to track others epistemic state, makes humans efficient collaborators. AI agents need the same capacity in multi agent settings, yet existing benchmarks mostly test literal ToM by asking direct belief questions. The ability act optimally on implicit beliefs in embodied environments, called functional ToM, remains largely untested. We introduce EnactToM, an evolving benchmark of 300 embodied multi-agent tasks set in a 3D household with partial observability, private information, and constrained communication. Each task is formally verified for solvability and required epistemic depth, and new tasks are generated increase difficulty as models improve. On the hard split, all seven evaluated frontier models score 0.0% Pass^3 on functional task completion, while averaging 45.0% on literal belief probes. Manual analysis traces 93% of sampled failures to epistemic coordination breakdowns such as withheld information, ignored partner constraints, and misallocated messages, providing a concrete target for future work.

In line with the principle of honesty, there has been a growing effort to train large language models (LLMs) to generate outputs containing epistemic markers. However, evaluation in the presence of epistemic markers has been largely overlooked, raising a critical question: Could the use of epistemic markers in LLM-generated outputs lead to unintended negative consequences? To address this, we present EMBER, a benchmark designed to assess the robustness of LLM-judges to epistemic markers in both single and pairwise evaluation settings. Our findings, based on evaluations using EMBER, reveal that all tested LLM-judges, including GPT-4o, show a notable lack of robustness in the presence of epistemic markers. Specifically, we observe a negative bias toward epistemic markers, with a stronger bias against markers expressing uncertainty. This suggests that LLM-judges are influenced by the presence of these markers and do not focus solely on the correctness of the content.

Benchmarks measure whether a model is correct. They do not measure whether a model is reliable. This distinction is largely academic for single-shot inference, but becomes critical for agentic AI systems, where a single rephrased prompt can trigger cascading failures in multi-step execution. Yet this form of instability is not captured by existing evaluations. Hallucinations live in variance: they arise when semantically equivalent prompts activate inconsistent internal pathways, producing divergent outputs. Consistent but incorrect outputs reflect bias or missing knowledge; confident guessing reflects calibration failure. Neither constitutes hallucination under this definition. When error is variance-dominated, reducing redundant pathways improves reliability without adding knowledge. We formalize this through Semantic Stability (SS), measured via Paraphrase Consistency (PC@k): generate k paraphrases, greedy decode each, compute mode agreement. SS is a diagnostic for variance-driven unreliability, not a method for improving correctness. We show that a dense Qwen3-0.6B agrees with itself only 23.8% of the time; at 32% sparsity, agreement jumps to 55.9%. A phase diagram reveals the sweet spot where variance reduction outpaces bias accumulation, and regimes where stability collapses onto wrong answers.

LLM-based agent architectures systematically conflate information transport mechanisms with epistemic justification mechanisms. We formalize this class of architectural failures as semantic laundering: a pattern where propositions with absent or weak warrant are accepted by the system as admissible by crossing architecturally trusted interfaces. We show that semantic laundering constitutes an architectural realization of the Gettier problem: propositions acquire high epistemic status without a connection between their justification and what makes them true. Unlike classical Gettier cases, this effect is not accidental; it is architecturally determined and systematically reproducible. The central result is the Theorem of Inevitable Self-Licensing: under standard architectural assumptions, circular epistemic justification cannot be eliminated. We introduce the Warrant Erosion Principle as the fundamental explanation for this effect and show that scaling, model improvement, and LLM-as-judge schemes are structurally incapable of eliminating a problem that exists at the type level.

Standard factuality evaluations of LLMs treat all errors alike, obscuring whether failures arise from missing knowledge (empty shelves) or from limited access to encoded facts (lost keys). We propose a behavioral framework that profiles factual knowledge at the level of facts rather than questions, characterizing each fact by whether it is encoded, and then by how accessible it is: cannot be recalled, can be directly recalled, or can only be recalled with inference-time computation (thinking). To support such profiling, we introduce WikiProfile, a new benchmark constructed via an automated pipeline with a prompted LLM grounded in web search. Across 4 million responses from 13 LLMs, we find that encoding is nearly saturated in frontier models on our benchmark, with GPT-5 and Gemini-3 encoding 95--98% of facts. However, recall remains a major bottleneck: many errors previously attributed to missing knowledge instead stem from failures to access it. These failures are systematic and disproportionately affect long-tail facts and reverse questions. Finally, we show that thinking improves recall and can recover a substantial fraction of failures, indicating that future gains may rely less on scaling and more on methods that improve how models utilize what they already encode.

Recently, Chain-of-Thought (CoT) prompting has delivered success on complex reasoning tasks, which aims at designing a simple prompt like ``Let's think step by step'' or multiple in-context exemplars with well-designed rationales to elicit Large Language Models (LLMs) to generate intermediate reasoning steps. However, the generated rationales often come with mistakes, making unfactual and unfaithful reasoning chains. To mitigate this brittleness, we propose a novel Chain-of-Knowledge (CoK) prompting, where we aim at eliciting LLMs to generate explicit pieces of knowledge evidence in the form of structure triple. This is inspired by our human behaviors, i.e., we can draw a mind map or knowledge map as the reasoning evidence in the brain before answering a complex question. Benefiting from CoK, we additionally introduce a F^2-Verification method to estimate the reliability of the reasoning chains in terms of factuality and faithfulness. For the unreliable response, the wrong evidence can be indicated to prompt the LLM to rethink. Extensive experiments demonstrate that our method can further improve the performance of commonsense, factual, symbolic, and arithmetic reasoning tasks.

Large language models (LLMs) are widely used as information sources, yet small changes in semantic assumptions can destabilize their beliefs. We introduce P-StaT (Perturbation Stability of Truth), a framework for evaluating belief stability under matched semantic perturbations in both representational and behavioral settings. Across 21 LLMs and three domains, we compare perturbations involving familiar Fictional statements against synthetically generated and unfamiliar Synthetic statements. Unfamiliar Synthetic perturbations generally induce greater epistemic instability than familiar Fictional perturbations, with behavioral belief retraction rates frequently exceeding 0.5 (50%). Finally, exploratory clustering analyses reveal recurring themes among retracted statements, including ambiguity, technical terminology, and obscure concepts. These results show that epistemic familiarity is systematically associated with stability under semantic reframing, suggesting that stability-based analyses can complement accuracy-based benchmarks when evaluating LLM robustness and reliability. Code and data are available at https://github.com/samanthadies/P-StaT.

Despite the progress of foundation models, knowledge-based reasoning remains a persistent challenge due to their limited capacity for knowledge recall and inference. Existing methods primarily focus on encouraging these models to plan and solve problems or extensively sample reasoning chains independently. However, these methods often overlook conceptual errors and inferential fallacies, inevitably leading to a series of notorious issues such as misleading conclusions, cognitive biases, and reduced decision quality. While explicit modeling of causality is argued to hold promise in addressing these issues, contemporary research efforts have thus far fallen short in achieving causality-based foundation models. Drawing inspiration from the orchestration of diverse specialized agents collaborating to tackle intricate tasks, we propose a framework named Causal-Consistency Chain-of-Thought (CaCo-CoT) that harnesses multi-agent collaboration to bolster the faithfulness and causality of foundation models, involving a set of reasoners and evaluators. These agents collaboratively work within a reasoning-and-consensus paradigm to improve faithfulness. The reasoners are tasked with generating reasoning chains for knowledge-intensive problems by mimicking human causal reasoning. Meanwhile, the evaluator scrutinizes the causal consistency of a reasoner's reasoning chain from a non-causal and a counterfactual perspective. Our framework demonstrates significant superiority over state-of-the-art methods through extensive and comprehensive evaluations across text-based and multi-modal knowledge reasoning tasks (e.g., science question answering and commonsense reasoning).

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 capacity of Large Language Models (LLMs) to reason is fundamental to their application in complex, knowledge-intensive domains. In real-world scenarios, LLMs are often augmented with external information that can be helpful, irrelevant, or even misleading. This paper investigates the causal impact of such auxiliary information on the reasoning process of LLMs with explicit step-by-step thinking capabilities. We introduce SciAux, a new dataset derived from ScienceQA, to systematically test the robustness of the model against these types of information. Our findings reveal a critical vulnerability: the model's deliberative "thinking mode" is a double-edged sword. While helpful context improves accuracy, misleading information causes a catastrophic drop in performance, which is amplified by the thinking process. Instead of conferring robustness, thinking reinforces the degree of error when provided with misinformation. This highlights that the challenge is not merely to make models "think", but to endow them with the critical faculty to evaluate the information upon which their reasoning is based. The SciAux dataset is available at https://huggingface.co/datasets/billhdzhao/SciAux.

Supervised Fine-Tuning (SFT) is the standard paradigm for domain adaptation, yet it frequently incurs the cost of catastrophic forgetting. In sharp contrast, on-policy Reinforcement Learning (RL) effectively preserves general capabilities. We investigate this discrepancy and identify a fundamental distributional gap: while RL aligns with the model's internal belief, SFT forces the model to fit external supervision. This mismatch often manifests as "Confident Conflicts" tokens characterized by low probability but low entropy. In these instances, the model is highly confident in its own prediction but is forced to learn a divergent ground truth, triggering destructive gradient updates. To address this, we propose Entropy-Adaptive Fine-Tuning (EAFT). Unlike methods relying solely on prediction probability, EAFT utilizes token-level entropy as a gating mechanism to distinguish between epistemic uncertainty and knowledge conflict. This allows the model to learn from uncertain samples while suppressing gradients on conflicting data. Extensive experiments on Qwen and GLM series (ranging from 4B to 32B parameters) across mathematical, medical, and agentic domains confirm our hypothesis. EAFT consistently matches the downstream performance of standard SFT while significantly mitigating the degradation of general capabilities.

As Large Language Model (LLM) agents are increasingly tasked with high-stakes autonomous decision-making, the transparency of their reasoning processes has become a critical safety concern. While Chain-of-Thought (CoT) prompting allows agents to generate human-readable reasoning traces, it remains unclear whether these traces are faithful generative drivers of the model's output or merely post-hoc rationalizations. We introduce Project Ariadne, a novel XAI framework that utilizes Structural Causal Models (SCMs) and counterfactual logic to audit the causal integrity of agentic reasoning. Unlike existing interpretability methods that rely on surface-level textual similarity, Project Ariadne performs hard interventions (do-calculus) on intermediate reasoning nodes -- systematically inverting logic, negating premises, and reversing factual claims -- to measure the Causal Sensitivity (φ) of the terminal answer. Our empirical evaluation of state-of-the-art models reveals a persistent Faithfulness Gap. We define and detect a widespread failure mode termed Causal Decoupling, where agents exhibit a violation density (ρ) of up to 0.77 in factual and scientific domains. In these instances, agents arrive at identical conclusions despite contradictory internal logic, proving that their reasoning traces function as "Reasoning Theater" while decision-making is governed by latent parametric priors. Our findings suggest that current agentic architectures are inherently prone to unfaithful explanation, and we propose the Ariadne Score as a new benchmark for aligning stated logic with model action.

Domain expertise enhances judgment within boundaries but creates systematic vulnerabilities specifically at borders. We term this Transitive Expert Error (TEE), distinct from Dunning-Kruger effects, requiring calibrated expertise as precondition. Mechanisms enabling reliable within-domain judgment become liabilities when structural similarity masks causal divergence. Two core mechanisms operate: structural similarity bias causes experts to overweight surface features (shared vocabulary, patterns, formal structure) while missing causal architecture differences; authority persistence maintains confidence across competence boundaries through social reinforcement and metacognitive failures (experts experience no subjective uncertainty as pattern recognition operates smoothly on familiar-seeming inputs.) These mechanism intensify under three conditions: shared vocabulary masking divergent processes, social pressure for immediate judgment, and delayed feedback. These findings extend to AI routing architectures (MoE systems, multi-model orchestration, tool-using agents, RAG systems) exhibiting routing-induced failures (wrong specialist selected) and coverage-induced failures (no appropriate specialist exists). Both produce a hallucination phenotype: confident, coherent, structurally plausible but causally incorrect outputs at domain boundaries. In human systems where mechanisms are cognitive black boxes; AI architectures make them explicit and addressable. We propose interventions: multi-expert activation with disagreement detection (router level), boundary-aware calibration (specialist level), and coverage gap detection (training level). TEE has detectable signatures (routing patterns, confidence-accuracy dissociations, domain-inappropriate content) enabling monitoring and mitigation. What remains intractable in human cognition becomes addressable through architectural design.

Modern multi-agent knowledge systems increasingly accumulate knowledge through chains of autonomous transformations rather than direct retrieval. Existing provenance work records what happened - execution traces, tool calls, evidence links - and source-reliability estimation is long established (truth discovery, reputation systems). What is missing is an operational framework that attaches graded, per-domain transmitter reliability to claim-level transmission chains, with completeness semantics, transformation-typed aggregation, decoupled content criticism, and serve/review/quarantine routing. Classical Islamic hadith science confronted a structurally similar problem: deciding whether knowledge transmitted through chains of human narrators should be accepted. Over centuries it developed a rigorous methodology - isnad (a complete transmission chain attached to every claim), rijal (systematic grading of each narrator's integrity and precision), weakest-link chain evaluation, corroboration through independent chains, and matn criticism (content evaluated independently of chain quality). This paper transfers that methodology to AI system design. We contribute a formal mapping from hadith-science concepts to multi-agent pipelines, a relational schema implementing claim chains and a graded narrator registry, a decision matrix combining chain grade with content criticism, and an evaluation on 20,000 claims from real physics textbooks. The evaluation validates weakest-link quarantine and independent-chain corroboration; reports a partial failure of the grade-recovery loop, which missed the highest-fault narrator; and reports two analyses as inconclusive, including a matched-coverage comparison the framework could not reach with the reference content critic. The paper is explicit throughout about which claims the evidence does and does not yet support.

Uncertainty Quantification (UQ) research has primarily focused on closed-book factual question answering (QA), while contextual QA remains unexplored, despite its importance in real-world applications. In this work, we focus on UQ for the contextual QA task and propose a theoretically grounded approach to quantify epistemic uncertainty. We begin by introducing a task-agnostic, token-level uncertainty measure defined as the cross-entropy between the predictive distribution of the given model and the unknown true distribution. By decomposing this measure, we isolate the epistemic component and approximate the true distribution by a perfectly prompted, idealized model. We then derive an upper bound for epistemic uncertainty and show that it can be interpreted as semantic feature gaps in the given model's hidden representations relative to the ideal model. We further apply this generic framework to the contextual QA task and hypothesize that three features approximate this gap: context-reliance (using the provided context rather than parametric knowledge), context comprehension (extracting relevant information from context), and honesty (avoiding intentional lies). Using a top-down interpretability approach, we extract these features by using only a small number of labeled samples and ensemble them to form a robust uncertainty score. Experiments on multiple QA benchmarks in both in-distribution and out-of-distribution settings show that our method substantially outperforms state-of-the-art unsupervised (sampling-free and sampling-based) and supervised UQ methods, achieving up to a 13-point PRR improvement while incurring a negligible inference overhead.

Improving the reasoning abilities of large language models (LLMs) has largely relied on iterative self-training with model-generated data. While effective at boosting accuracy, existing approaches primarily reinforce successful reasoning paths, incurring a substantial calibration cost: models become overconfident and lose the ability to represent uncertainty. This failure has been characterized as a form of model collapse in alignment, where predictive distributions degenerate toward low-variance point estimates. We address this issue by reframing reasoning training as an epistemic learning problem, in which models must learn not only how to reason, but also when their reasoning should be trusted. We propose epistemically-calibrated reasoning (EpiCaR) as a training objective that jointly optimizes reasoning performance and calibration, and instantiate it within an iterative supervised fine-tuning framework using explicit self-evaluation signals. Experiments on Llama-3 and Qwen-3 families demonstrate that our approach achieves Pareto-superiority over standard baselines in both accuracy and calibration, particularly in models with sufficient reasoning capacity (e.g., 3B+). This framework generalizes effectively to OOD mathematical reasoning (GSM8K) and code generation (MBPP). Ultimately, our approach enables a 3X reduction in inference compute, matching the K=30 performance of STaR with only K=10 samples in capable models.

Large Language Model (LLM)-based Multi-Agent Systems (MAS) enable complex problem-solving but introduce significant debugging challenges, characterized by long interaction traces, inter-agent dependencies, and delayed error manifestation. Existing diagnostic approaches often rely on expensive expert annotation or ''LLM-as-a-judge'' paradigms, which struggle to pinpoint decisive error steps within extended contexts. In this paper, we introduce ErrorProbe, a self-improving framework for semantic failure attribution that identifies responsible agents and the originating error step. The framework operates via a three-stage pipeline: (1) operationalizing the MAS failure taxonomy to detect local anomalies, (2) performing symptom-driven backward tracing to prune irrelevant context, and (3) employing a specialized multi-agent team (Strategist, Investigator, Arbiter) to validate error hypotheses through tool-grounded execution. Crucially, ErrorProbe maintains a verified episodic memory that updates only when error patterns are confirmed by executable evidence, without the need for annotation. Experiments across the TracerTraj and Who&When benchmarks demonstrate that ErrorProbe significantly outperforms baselines, particularly in step-level localization, while the verified memory enables robust cross-domain transfer without retraining.

Large language model (LLM) coding agents are increasingly deployed to autonomously perform software engineering tasks in terminal-based environments, making their reliability a growing concern. Existing empirical studies investigate why coding agents fail, yet they largely treat failure as a final outcome rather than a temporal process, providing limited insight into how failures emerge, evolve, and become unrecoverable. We present the first large-scale empirical study of CLI coding-agent failure trajectories, introducing a process-oriented framework that analyzes failure through its onset, evolution, and recovery across execution trajectories. We first collect 3,843 execution trajectories generated by seven frontier models across three coding-agent scaffolds (OpenHands, MiniSWE, and Terminus2) on Terminal-Bench, then carefully filter them to obtain 1,794 complete and valid trajectories for manual annotation (over 63,000 execution steps), from which we derive 14 findings spanning failure occurrence, root causes, recovery, and cross-system consistency. Our findings show that coding-agent failures are predominantly driven by epistemic errors, typically begin within the first few execution steps, and often remain hidden until recovery is no longer possible, suggesting that improving coding-agent reliability requires earlier validation and intervention rather than relying solely on final-outcome evaluation.

Chain-of-thought (CoT) prompting has become central to mathematical reasoning in large language models, yet models remain brittle to early errors: a single arithmetic slip or unjustified inference typically propagates uncorrected to an incorrect final answer. We investigate whether training on intentionally flawed reasoning traces can teach models to detect and recover from such errors without degrading standard problem-solving ability. Using competition-level problems from MATH-lighteval, we generate CoT prefixes containing exactly one controlled error, either a calculation error (sign flips, dropped terms) or a reasoning error (misapplied rules, unjustified logical steps), and fine-tune Qwen3-4B with GRPO using a binary final-answer reward. Our Mixed-CoT-RL model matches standard RL on clean problems (41% vs 41%) while substantially outperforming it on problems prefilled with flawed reasoning (24% vs 19%). Notably, clean-only RL fine-tuning degrades robustness below the untuned baseline 19% vs. 20%), indicating that conventional training increases susceptibility to misleading prefills. Among error types, training on reasoning errors yields greater robustness gains than calculation errors alone, with mixed training performing best. These findings demonstrate that exposure to flawed traces during training can improve error-recovery behavior without sacrificing accuracy, suggesting a path toward more robust mathematical reasoning in LLMs.

Large Language Models (LLMs) are predominantly governed by probabilistic frameworks in which the sum of outcome probabilities is constrained to unity. This architectural limitation, often imposed by Softmax layers, leads to a collapse of uncertainty that makes it difficult to differentiate between epistemic uncertainty, paradox, and vagueness. We present an empirical investigation of the application of Neutrosophic Logic, a framework that treats Truth (T), Indeterminacy (I), and Falsity (F) as three independent dimensions, to model epistemic states in LLMs. We conducted experiments on a family of four OpenAI GPT models across five linguistic phenomena: logical paradoxes, epistemic ignorance, vagueness, ethical contradictions, and future contingencies, under three prompting strategies: neutrosophic, probabilistic, and entropy-derived. Our findings reveal that the neutrosophic approach, by allowing T+I+F > 1, a state we term hyper-truth, provides a richer representation of a model's internal state. In 35% of evaluations, hyper-truth emerged spontaneously, predominantly under ethical contradiction and logical paradox. We demonstrate that this approach preserves truth values in fuzzy contexts and offers a robust method for identifying and quantifying internal model conflict. We conclude that the integration of neutrosophic evaluation layers is a critical step toward more transparent, reliable, and ethically aware AI systems.

This position paper argues that the theoretical inconsistency often observed among Responsible AI (RAI) metrics, such as differing fairness definitions or tradeoffs between accuracy and privacy, should be embraced as a valuable feature rather than a flaw to be eliminated. We contend that navigating these inconsistencies, by treating metrics as divergent objectives, yields three key benefits: (1) Normative Pluralism: Maintaining a full suite of potentially contradictory metrics ensures that the diverse moral stances and stakeholder values inherent in RAI are adequately represented. (2) Epistemological Completeness: The use of multiple, sometimes conflicting, metrics allows for a more comprehensive capture of multifaceted ethical concepts, thereby preserving greater informational fidelity about these concepts than any single, simplified definition. (3) Implicit Regularization: Jointly optimizing for theoretically conflicting objectives discourages overfitting to one specific metric, steering models towards solutions with enhanced generalization and robustness under real-world complexities. In contrast, efforts to enforce theoretical consistency by simplifying or pruning metrics risk narrowing this value diversity, losing conceptual depth, and degrading model performance. We therefore advocate for a shift in RAI theory and practice: from getting trapped in inconsistency to characterizing acceptable inconsistency thresholds and elucidating the mechanisms that permit robust, approximated consistency in practice.

We introduce CRAFT, a multi-agent benchmark for evaluating pragmatic communication in large language models under strict partial information. In this setting, multiple agents with complementary but incomplete views must coordinate through natural language to construct a shared 3D structure that no single agent can fully observe. We formalize this problem as a multi-sender pragmatic reasoning task and provide a diagnostic framework that decomposes failures into spatial grounding, belief modeling and pragmatic communication errors, including a taxonomy of behavioral failure profiles in both frontier and open-weight models. Across a diverse set of models, including 8 open-weight and 7 frontier including reasoning models, we find that stronger reasoning ability does not reliably translate to better coordination: smaller open-weight models often match or outperform frontier systems, and improved individual communication does not guarantee successful collaboration. These results suggest that multi-agent coordination remains a fundamentally unsolved challenge for current language models. Our code can be found at https://github.com/csu-signal/CRAFT

A probabilistic classifier with reliable predictive uncertainties i) fits successfully to the target domain data, ii) provides calibrated class probabilities in difficult regions of the target domain (e.g.\ class overlap), and iii) accurately identifies queries coming out of the target domain and rejects them. We introduce an original combination of Evidential Deep Learning, Neural Processes, and Neural Turing Machines capable of providing all three essential properties mentioned above for total uncertainty quantification. We observe our method on five classification tasks to be the only one that can excel all three aspects of total calibration with a single standalone predictor. Our unified solution delivers an implementation-friendly and compute efficient recipe for safety clearance and provides intellectual economy to an investigation of algorithmic roots of epistemic awareness in deep neural nets.

Search engines and information platforms are increasingly scrutinized for their role in spreading misinformation. Traditional responses often focus on detecting falsehoods or verifying the ultimate validity of claims. This paper argues that such a validity-centered framing is inadequate for the epistemic challenges of search environments.

This study presents PARROT (Persuasion and Agreement Robustness Rating of Output Truth), a robustness focused framework designed to measure the degradation in accuracy that occurs under social pressure exerted on users through authority and persuasion in large language models (LLMs) the phenomenon of sycophancy (excessive conformity). PARROT (i) isolates causal effects by comparing the neutral version of the same question with an authoritatively false version using a double-blind evaluation, (ii) quantifies confidence shifts toward the correct and imposed false responses using log-likelihood-based calibration tracking, and (iii) systematically classifies failure modes (e.g., robust correct, sycophantic agreement, reinforced error, stubborn error, self-correction, etc.) using an eight-state behavioral taxonomy. We evaluated 22 models using 1,302 MMLU-style multiple-choice questions across 13 domains and domain-specific authority templates. Findings show marked heterogeneity: advanced models (e.g., GPT-5, GPT-4.1, Claude Sonnet 4.5) exhibit low "follow rates" (leq 11%, GPT-5: 4\%) and minimal accuracy loss, while older/smaller models show severe epistemic collapse (GPT-4: 80\%, Qwen 2.5-1.5B: 94\%). The danger is not limited to response changes; weak models reduce confidence in the correct response while increasing confidence in the imposed incorrect response. While international law and global knowledge at the domain level exhibit high fragility, elementary mathematics is relatively resilient. Consequently, we argue that the goal of "resistance to overfitting pressure" should be addressed as a primary objective alongside accuracy, harm avoidance, and privacy for safe deployment in the real world.

Large language models can arrive at the same answer through reasoning paths that are unstable, contradictory, or difficult to rank consistently -- a failure mode especially prevalent in multi-step deductive reasoning. Existing methods assess reliability primarily through output dispersion -- measuring how much sampled answers differ -- but this discards a complementary signal: whether the model can consistently rank competing reasoning candidates. We propose structural uncertainty, a consistency-aware framework derived from the stability of self-preference-induced rankings over sampled reasoning solutions. Given a query, we generate multiple candidate solutions and ask the model to judge pairwise preferences among its own outputs. We aggregate self-preferences into ranking distributions via Bradley-Terry modeling with PageRank, and decompose the signal into two entropy-based components: across-trial ranking instability and within-trial candidate ambiguity. Across five LLMs and eight benchmarks, structural signals provide information complementary to answer dispersion: on logical and mathematical reasoning tasks, the combination improves identification of unreliable instances, while on factual retrieval the structural signal collapses toward uniformity, diagnosing a regime boundary where reasoning-level consistency evaluation is uninformative. The two components relate differently to accuracy: within-trial ambiguity correlates positively with correctness -- consistent with settings where multiple plausible solution paths remain competitive -- while across-trial instability correlates negatively, signaling unreliable reasoning. Structural uncertainty is best understood not as a universal confidence estimator, but as a regime-sensitive evaluator of logical reasoning consistency.

Language models (LMs) are said to be exhibiting reasoning, but what does this entail? We assess definitions of reasoning and how key papers in the field of natural language processing (NLP) use the notion and argue that the definitions provided are not consistent with how LMs are trained, process information, and generate new tokens. To illustrate this incommensurability we assume the view that transformer-based LMs implement an implicit finite-order Markov kernel mapping contexts to conditional token distributions. In this view, reasoning-like outputs correspond to statistical regularities and approximate statistical invariances in the learned kernel rather than the implementation of explicit logical mechanisms. This view is illustrative of the claim that LMs are "statistical pattern matchers"" and not genuine reasoners and provides a perspective that clarifies why reasoning-like outputs arise in LMs without any guarantees of logical consistency. This distinction is fundamental to how epistemic uncertainty is evaluated in LMs. We invite a discussion on the importance of how the computational processes of the systems we build and analyze in NLP research are described.

Current reasoning paradigms for LLMs include chain-of-thought, ReAct, and post-hoc self-critique. These paradigms rely on two assumptions that fail on long-horizon, multi-stage tasks. As a result, errors accumulate silently across reasoning steps, leaving an open question: can a reasoning system effectively detect and recover from its own failures? We present ReFlect, a harness system for LLM reasoning that creates standalone error detection and recovery logic as a deterministic wrapper around the model. Controlled experiments across 6 reasoning domains show that prompt-level self-critique produces formulaic templates that flag no issues in 90 of 100 audited reflection blocks, and the investigated LLMs wrongly accept a wrong answer in at least 76\% of cases. Our ReFlect harness achieves task success rates ranging from 41\% on gpt-4o-mini to 56\% on Claude Sonnet 4.5 across six models spanning small and frontier scale, with per-model gains over Direct CoT ranging from +7 pp on Qwen2.5-72B to +29 pp on Claude Sonnet 4.5, and additionally raises SWE-bench patch-structural quality from 0\% (Direct CoT) to between 82\% (Qwen2.5-72B) and 87\% (GPT-4o). Notably, the harness gain is inversely proportional to the model's Direct CoT task success rate (the fitted slope is -1.69 with r=-0.76): each pp lost in baseline success rate is mechanically recovered by 1.69 pp of harness gain. We spot that adding structured reasoning state and operators yields only 15.0--18.7\% pair-mean on Llama-3.3-70B and Qwen2.5-72B because models at this scale cannot reliably populate the state its operators require. ReFlect is model-agnostic, training-free, and operates entirely at inference time.

Misinformation - false or misleading information - is considered a significant societal concern due to its associated "misinformation effects," such as political polarization, erosion of trust in institutions, problematic behavior, and public health challenges. However, the prevailing concept is misaligned with what is studied. While misinformation focuses on instances of information about factual matters, the broad spectrum of effects often manifests at a societal level and is shaped by a wide range of interdependent factors such as identity, values, opinions, epistemologies, and disagreements. Unsurprisingly, misinformation effects can occur without the prevalence of misinformation, and misinformation does not necessarily increase the effects studied. Here, we propose using disagreement - conflicting attitudes and beliefs between individuals and communities - as a way to study misinformation effects because it addresses the identified conceptual limitations of misinformation. Furthermore, unlike misinformation, disagreement does not require researchers to determine whether a given information is false or misleading. Thus, it can be studied and, more importantly, measured without the need to make a normative judgment about a given information, even when the specific topic is entirely removed, as we show in a longitudinal disagreement measurement. We demonstrate that disagreement, as a holistic concept, provides better explanations for the occurrence of misinformation effects, enhances precision in developing appropriate interventions, and offers a promising approach for evaluating them through quantification. Finally, we show how disagreement addresses current misinformation research questions and conclude with recommendations for research practice.

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.

Large language models (LLMs) are increasingly applied to structured clinical data, yet whether they can recognize the limits of their own knowledge on such tasks remains unexplored. We study this question through the lens of cross-model attribution divergence with the goal of reducing epistemic uncertainty for structured tasks, comparing Qwen 2.5 7B and XGBoost on a prediction task via attribution divergence analysis. We report four findings. First, LLM verbalized confidence is epistemically vacuous, it outputs a near-constant (0.856-0.937) regardless of whether accuracy is 49% or 75.3%, tracking prompt format rather than prediction quality. Second, the LLM exhibits an inverse difficulty effect: accuracy drops to 64.8% when XGBoost is 99% correct, but matches XGBoost (73.8% vs. 73.1%) when it is moderately uncertain. Third, few-shot examples and SHAP-derived feature evidence are orthogonal, super-additive interventions: they reduce the Attribution Disagreement Score (ADS) from 1.54 to 0.38 and improve accuracy from 49% to 75.3% without training. Fourth, a cross-model calibrator that determined LLM reliability using attribution divergence signals reduces expected calibration error from 0.254 to 0.080, replacing uninformative verbalized confidence with patient-specific reliability estimates, without accessing model internals or requiring repeated inference. We frame these findings as a cold start problem for LLMs on structured data and outline a path toward genuine epistemic self-awareness.

We introduce an axiomatic evaluation framework for latent thought representations in LLMs, comprising metrics that are independent of downstream benchmark scores and reveal representational failures that benchmark accuracy masks. Existing evaluations conflate representation quality with model capacity. Therefore, failures cannot be attributed to the representation rather than to the model that processes it. We formalize four functional axioms (Causality, Minimality, Separability, and Stability) and define a quantitative measure for each, computed directly on the representation independently of downstream accuracy. We audit open-weight LLMs across 23 reasoning tasks (e.g., Spatial Reasoning, Factual QA). We find that no candidate satisfies all four axioms simultaneously, that the representations distinguish task type reliably but cannot distinguish between two questions within the same task, and that the representations encode little information beyond what is already present in the input embedding. The failure is consistent across dense, reasoning-distilled, and RL-trained model families, indicating that the gap is structural rather than a property of model size or training procedure.

A world model is an AI system that simulates how an environment evolves under actions, enabling planning through imagined futures rather than reactive perception. Current world models, however, suffer from visual conflation: the mistaken assumption that high-fidelity video generation implies an understanding of physical and causal dynamics. We show that while modern models excel at predicting pixels, they frequently violate invariant constraints, fail under intervention, and break down in safety-critical decision-making. This survey argues that visual realism is an unreliable proxy for world understanding. Instead, effective world models must encode causal structure, respect domain-specific constraints, and remain stable over long horizons. We propose a reframing of world models as actionable simulators rather than visual engines, emphasizing structured 4D interfaces, constraint-aware dynamics, and closed-loop evaluation. Using medical decision-making as an epistemic stress test, where trial-and-error is impossible and errors are irreversible, we demonstrate that a world model's value is determined not by how realistic its rollouts appear, but by its ability to support counterfactual reasoning, intervention planning, and robust long-horizon foresight.

As LLMs increasingly mediate the political information citizens rely on, there is still no standardized way to assess whether they do so responsibly. We introduce Polistemics, a theory-grounded benchmark for evaluating LLMs as mediators of political information in elections. Prior work has treated this task as reproduction rather than mediation, leaving its epistemic dimensions and interaction with imperfect information unaddressed. We ground the evaluation in Epistemic Modesty, a normative standard derived from citizens' epistemic agency, and test it across controlled settings that vary informational properties such as clarity, noise, and consistency. Applying the benchmark to three state-of-the-art LLMs on the 2025 German and Dutch elections, we find that high aggregate scores mask systematic failures. Models mediate reliably under clear evidence but break down under absent, vague, or contradictory information, while flattening the intensity of political language. These failures are likely driven by party priors, influenced by party labels and output language. Reliable mediation appears achievable, but no model delivers it consistently.

Self-distillation has emerged as an effective post-training paradigm for LLMs, often improving performance while shortening reasoning traces. However, in mathematical reasoning, we find that it can reduce response length while degrading performance. We trace this degradation to the suppression of epistemic verbalization - the model's expression of uncertainty during reasoning. Through controlled experiments varying conditioning context richness and task coverage, we show that conditioning the teacher on rich information suppresses uncertainty expression, enabling rapid in-domain optimization with limited task coverage but harming OOD performance, where unseen problems benefit from expressing uncertainty and adjusting accordingly. Across Qwen3-8B, DeepSeek-Distill-Qwen-7B, and Olmo3-7B-Instruct, we observe performance drops of up to 40%. Our findings highlight that exposing appropriate levels of uncertainty is crucial for robust reasoning and underscore the importance of optimizing reasoning behavior beyond merely reinforcing correct answer traces.

Although AI agents have demonstrated impressive capabilities in long-horizon reasoning, their reliability is severely hampered by the ``Spiral of Hallucination,'' where early epistemic errors propagate irreversibly. Existing methods face a dilemma: uncertainty quantification (UQ) methods typically act as passive sensors, only diagnosing risks without addressing them, while self-reflection mechanisms suffer from continuous or aimless corrections. To bridge this gap, we propose a unified Dual-Process Agentic UQ (AUQ) framework that transforms verbalized uncertainty into active, bi-directional control signals. Our architecture comprises two complementary mechanisms: System 1 (Uncertainty-Aware Memory, UAM), which implicitly propagates verbalized confidence and semantic explanations to prevent blind decision-making; and System 2 (Uncertainty-Aware Reflection, UAR), which utilizes these explanations as rational cues to trigger targeted inference-time resolution only when necessary. This enables the agent to balance efficient execution and deep deliberation dynamically. Extensive experiments on closed-loop benchmarks and open-ended deep research tasks demonstrate that our training-free approach achieves superior performance and trajectory-level calibration. We believe this principled framework AUQ represents a significant step towards reliable agents.

Identifying how much a model {p}_{theta}(Y|X) knows about the stochastic real-world process p(Y|X) it was trained on is important to ensure it avoids producing incorrect or "hallucinated" answers or taking unsafe actions. But this is difficult for generative models because probabilistic predictions do not distinguish between per-response noise (aleatoric uncertainty) and lack of knowledge about the process (epistemic uncertainty), and existing epistemic uncertainty quantification techniques tend to be overconfident when the model underfits. We propose a general strategy for teaching a model to both approximate p(Y|X) and also estimate the remaining gaps between {p}_{theta}(Y|X) and p(Y|X): train it to predict pairs of independent responses drawn from the true conditional distribution, allow it to "cheat" by observing one response while predicting the other, then measure how much it cheats. Remarkably, we prove that being good at cheating (i.e. cheating whenever it improves your prediction) is equivalent to being second-order calibrated, a principled extension of ordinary calibration that allows us to construct provably-correct frequentist confidence intervals for p(Y|X) and detect incorrect responses with high probability. We demonstrate empirically that our approach accurately estimates how much models don't know across ambiguous image classification, (synthetic) language modeling, and partially-observable navigation tasks, outperforming existing techniques.

Long-term memory systems store what a user says in an external store and retrieve it when a related query arrives. This interface rests on an assumption so natural that it is rarely stated: a memory that is needed will resemble the query that needs it. World knowledge breaks the assumption. A tree-nut allergy should change the answer to a macaron request through their almond-flour ingredient, yet the two texts share no cue a retriever can see. We call this failure mode the implicit-association blind spot and introduce InMind, a 125-task, expert-verified benchmark spanning ten life domains, with 113 tasks grounded in citable public sources. Its paired controls separate three explanations that existing evaluations conflate: the fact was never stored, the model lacks the bridging knowledge, or the fact was stored and never surfaced. The verdict is clean. With the decisive memory placed in context, the backbone answers 84.0 percent of indirect queries; when the same memory must be retrieved, six vector, graph, and agentic memory systems reach at most 14.4 percent, even though they recall the same facts on demand at up to 100 percent. An embedding with eight times the dimensionality raises answer-blind target recall for every system yet leaves the gap essentially intact. A minimal diagnostic probe that keeps memory visible before the query arrives recovers most of the gap, locating the failure in the query-conditioned interface itself and pointing to routing, deciding which facts must stay visible, as the open problem InMind is built to score.

Large Language Models (LLMs) are often described as being instances of foundation models - that is, models that transfer strongly across various tasks and conditions in few-show or zero-shot manner, while exhibiting scaling laws that predict function improvement when increasing the pre-training scale. These claims of excelling in different functions and tasks rely on measurements taken across various sets of standardized benchmarks showing high scores for such models. We demonstrate here a dramatic breakdown of function and reasoning capabilities of state-of-the-art models trained at the largest available scales which claim strong function, using a simple, short, conventional common sense problem formulated in concise natural language, easily solvable by humans. The breakdown is dramatic, as models also express strong overconfidence in their wrong solutions, while providing often non-sensical "reasoning"-like explanations akin to confabulations to justify and backup the validity of their clearly failed responses, making them sound plausible. Various standard interventions in an attempt to get the right solution, like various type of enhanced prompting, or urging the models to reconsider the wrong solutions again by multi step re-evaluation, fail. We take these initial observations to the scientific and technological community to stimulate urgent re-assessment of the claimed capabilities of current generation of LLMs, Such re-assessment also requires common action to create standardized benchmarks that would allow proper detection of such basic reasoning deficits that obviously manage to remain undiscovered by current state-of-the-art evaluation procedures and benchmarks. Code for reproducing experiments in the paper and raw experiments data can be found at https://github.com/LAION-AI/AIW

In this paper, we present a conceptual model game to examine the dynamics of asymmetric interactions in games with imperfect information. The game involves two agents with starkly contrasting capabilities: one agent can take actions but has no information of the state of the game, whereas the other agent has perfect information of the state but cannot act or observe the other agent's actions. This duality manifests an extreme form of asymmetry, and how differing abilities influence the possibility of attaining common knowledge. Using Kripke structures and epistemic logic we demonstrate that, under these conditions, common knowledge of the current game state becomes unattainable. Our findings advance the discussion on the strategic limitations of knowledge in environments where information and action are unevenly distributed.

It is well known that accurate probabilistic predictors can be trained through empirical risk minimisation with proper scoring rules as loss functions. While such learners capture so-called aleatoric uncertainty of predictions, various machine learning methods have recently been developed with the goal to let the learner also represent its epistemic uncertainty, i.e., the uncertainty caused by a lack of knowledge and data. An emerging branch of the literature proposes the use of a second-order learner that provides predictions in terms of distributions on probability distributions. However, recent work has revealed serious theoretical shortcomings for second-order predictors based on loss minimisation. In this paper, we generalise these findings and prove a more fundamental result: There seems to be no loss function that provides an incentive for a second-order learner to faithfully represent its epistemic uncertainty in the same manner as proper scoring rules do for standard (first-order) learners. As a main mathematical tool to prove this result, we introduce the generalised notion of second-order scoring rules.

Quantifying uncertainty is important for actionable predictions in real-world applications. A crucial part of predictive uncertainty quantification is the estimation of epistemic uncertainty, which is defined as an integral of the product between a divergence function and the posterior. Current methods such as Deep Ensembles or MC dropout underperform at estimating the epistemic uncertainty, since they primarily consider the posterior when sampling models. We suggest Quantification of Uncertainty with Adversarial Models (QUAM) to better estimate the epistemic uncertainty. QUAM identifies regions where the whole product under the integral is large, not just the posterior. Consequently, QUAM has lower approximation error of the epistemic uncertainty compared to previous methods. Models for which the product is large correspond to adversarial models (not adversarial examples!). Adversarial models have both a high posterior as well as a high divergence between their predictions and that of a reference model. Our experiments show that QUAM excels in capturing epistemic uncertainty for deep learning models and outperforms previous methods on challenging tasks in the vision domain.

Deep learning has recently revealed the existence of scaling laws, demonstrating that model performance follows predictable trends based on dataset and model sizes. Inspired by these findings and fascinating phenomena emerging in the over-parameterized regime, we examine a parallel direction: do similar scaling laws govern predictive uncertainties in deep learning? In identifiable parametric models, such scaling laws can be derived in a straightforward manner by treating model parameters in a Bayesian way. In this case, for example, we obtain O(1/N) contraction rates for epistemic uncertainty with respect to the number of data N. However, in over-parameterized models, these guarantees do not hold, leading to largely unexplored behaviors. In this work, we empirically show the existence of scaling laws associated with various measures of predictive uncertainty with respect to dataset and model sizes. Through experiments on vision and language tasks, we observe such scaling laws for in- and out-of-distribution predictive uncertainty estimated through popular approximate Bayesian inference and ensemble methods. Besides the elegance of scaling laws and the practical utility of extrapolating uncertainties to larger data or models, this work provides strong evidence to dispel recurring skepticism against Bayesian approaches: "In many applications of deep learning we have so much data available: what do we need Bayes for?". Our findings show that "so much data" is typically not enough to make epistemic uncertainty negligible.

Deterministic inference is a comforting ideal in classical software: the same program on the same input should always produce the same output. As large language models move into real-world deployment, this ideal has been imported wholesale into inference stacks. Recent work from the Thinking Machines Lab has presented a detailed analysis of nondeterminism in LLM inference, showing how batch-invariant kernels and deterministic attention can enforce bitwise-identical outputs, positioning deterministic inference as a prerequisite for reproducibility and enterprise reliability. In this paper, we take the opposite stance. We argue that, for LLMs, deterministic inference kills. It kills the ability to model uncertainty, suppresses emergent abilities, collapses reasoning into a single brittle path, and weakens safety alignment by hiding tail risks. LLMs implement conditional distributions over outputs, not fixed functions. Collapsing these distributions to a single canonical completion may appear reassuring, but it systematically conceals properties central to artificial cognition. We instead advocate Stochastic CHAOS, treating distributional variability as a signal to be measured and controlled. Empirically, we show that deterministic inference is systematically misleading. Single-sample deterministic evaluation underestimates both capability and fragility, masking failure probability under paraphrases and noise. Phase-like transitions associated with emergent abilities disappear under greedy decoding. Multi-path reasoning degrades when forced onto deterministic backbones, reducing accuracy and diagnostic insight. Finally, deterministic evaluation underestimates safety risk by hiding rare but dangerous behaviors that appear only under multi-sample evaluation.

Large Reasoning Models (LRMs) often exhibit structural fragility in complex reasoning tasks, failing to produce correct answers even after successfully deriving valid intermediate steps. Through systematic analysis, we observe that these failures frequently stem not from a lack of reasoning capacity, but from a deficiency in self-regulatory control, where valid logic is destabilized by uncontrolled exploration or the failure to recognize logical sufficiency. Motivated by this observation, we propose Metacognitive Behavioral Tuning (MBT), a post-training framework that explicitly injects metacognitive behaviors into the model's thought process. MBT implements this via two complementary formulations: (1) MBT-S, which synthesizes rigorous reasoning traces from scratch, and (2) MBT-R, which rewrites the student's initial traces to stabilize intrinsic exploration patterns. Experiments across multi-hop QA benchmarks demonstrate that MBT consistently outperforms baselines, achieving notable gains on challenging benchmarks. By effectively eliminating reasoning collapse, MBT achieves higher accuracy with significantly reduced token consumption, demonstrating that internalizing metacognitive strategies leads to more stable and robust reasoning.

Large language models (LLMs) struggle with complex, long-horizon reasoning due to instability caused by their frozen policy assumption. Current test-time scaling methods treat execution feedback merely as an external signal for filtering or rewriting trajectories, without internalizing it to improve the underlying reasoning strategy. Inspired by Popper's epistemology of "conjectures and refutations," we argue that intelligence requires real-time evolution of the model's policy through learning from failed attempts. We introduce Policy of Thoughts (PoT), a framework that recasts reasoning as a within-instance online optimization process. PoT first generates diverse candidate solutions via an efficient exploration mechanism, then uses Group Relative Policy Optimization (GRPO) to update a transient LoRA adapter based on execution feedback. This closed-loop design enables dynamic, instance-specific refinement of the model's reasoning priors. Experiments show that PoT dramatically boosts performance: a 4B model achieves 49.71% accuracy on LiveCodeBench, outperforming GPT-4o and DeepSeek-V3 despite being over 50 smaller.

Large language models (LLMs) increasingly serve as data-driven reasoners, yet their chains-of-thought (CoT) can be unfaithful even when final answers are correct. Most existing ``verification'' signals are not diagnostic: answer matching observes only the outcome, LLM-as-judge provides subjective and non-verifiable critiques, and scalar rewards (e.g., PRMs/RMs) offer little insight into where a multi-step derivation fails.We propose SymDiag, a neuro-symbolic framework that reframes reasoning verification as structured failure diagnosis. SymDiag translates natural-language CoT into symbolic constraints and performs step-level satisfiability/entailment checks to (i) localize failing steps and (ii) produce verifiable diagnostic evidence, including counterexamples, inconsistency witnesses, and missing-premise indicators. A central challenge is that apparent ``logic violations'' can be caused either by genuine reasoning defects or by neural-to-symbolic translation noise. SymDiag therefore incorporates a Self-Auditor that disentangles TranslationError from ReasoningError via dual symbolic encodings consistency checks, enabling robust diagnosis under partial observability. Across diverse mathematical, logical, scientific, and general reasoning benchmarks, SymDiag improves detection of unfaithful reasoning and provides substantially more effective feedback for multi-round reasoning repair than outcome-only verification and LLM-based judging, offering a principled foundation for trustworthy and scalable reasoning diagnosis.

Large language models (LLMs) show remarkable promise for democratizing automated reasoning by generating formal specifications. However, a fundamental tension exists: LLMs are probabilistic, while formal verification demands deterministic guarantees. This paper addresses this epistemological gap by comprehensively investigating failure modes and uncertainty quantification (UQ) in LLM-generated formal artifacts. Our systematic evaluation of five frontier LLMs reveals Satisfiability Modulo Theories (SMT) based autoformalization's domain-specific impact on accuracy (from +34.8% on logical tasks to -44.5% on factual ones), with known UQ techniques like the entropy of token probabilities failing to identify these errors. We introduce a probabilistic context-free grammar (PCFG) framework to model LLM outputs, yielding a refined uncertainty taxonomy. We find uncertainty signals are task-dependent (e.g., grammar entropy for logic, AUROC>0.93). Finally, a lightweight fusion of these signals enables selective verification, drastically reducing errors (14-100%) with minimal abstention, transforming LLM-driven formalization into a reliable engineering discipline.

The ability to acknowledge the inevitable uncertainty in their knowledge and reasoning is a prerequisite for AI systems to be truly truthful and reliable. In this paper, we present a taxonomy of uncertainty specific to vision-language AI systems, distinguishing between epistemic uncertainty (arising from a lack of information) and aleatoric uncertainty (due to inherent unpredictability), and further explore finer categories within. Based on this taxonomy, we synthesize a benchmark dataset, CertainlyUncertain, featuring 178K visual question answering (VQA) samples as contrastive pairs. This is achieved by 1) inpainting images to make previously answerable questions into unanswerable ones; and 2) using image captions to prompt large language models for both answerable and unanswerable questions. Additionally, we introduce a new metric confidence-weighted accuracy, that is well correlated with both accuracy and calibration error, to address the shortcomings of existing metrics.

Red-team evaluations of AI models support some claims and not others, and the boundary between the two is calculable rather than merely a matter of judgment. We define the evidential ceiling of an evaluation as the largest factor by which one result can move belief under a fixed testing budget, derive it in closed form for the benchmark null result, and use it to locate that boundary exactly. We find that above a calculable harm rate, a benchmark of modest size certifies a category to a stated evidentiary standard, and a clean sheet is then the stronger of the two possible observations, outweighing a single reproduced failure. Below that rate, no passive benchmark of feasible size provides the specified evidence of safety under the fixed scoring rule and approximately independent trial structure. The crossing between the two regimes has a closed form. The bound is not specific to benchmarks: written in terms of a procedure's hypothesis conditioned elicitation rates, it covers adaptive and automated red teaming as well, and shows that discrimination between the hypotheses rather than attack success is what determines evidential worth. Auditing eight evaluation suites against the boundary, we find that current benchmarks are adequate for high-frequency harm categories and several orders of magnitude short for rare, catastrophic ones. Safety benchmarks are not uninformative. They are informative about a specific and computable set of propositions, and the discipline they need is to state which.

As chain of thought (CoT) has become central to scaling reasoning capabilities in large language models (LLMs), it has also emerged as a promising tool for interpretability, suggesting the opportunity to understand model decisions through verbalized reasoning. However, the utility of CoT toward interpretability depends upon its faithfulness---whether the model's stated reasoning reflects the underlying decision process. We provide mechanistic evidence that instruction-tuned models often determine their answer before generating CoT. Training linear probes on residual stream activations at the last token before CoT, we can predict the model's final answer with >0.9 AUC on most tasks. We find that these directions are not only predictive, but also causal: steering activations along the probe direction often flips model answers, with flip rates substantially exceeding norm-matched orthogonal baselines across most model-dataset pairs. When steering induces incorrect answers, we observe two distinct failure modes: confabulation (fabricating false premises) and non-entailment (stating correct premises but drawing unsupported conclusions). While post-hoc reasoning may be instrumentally useful when the model has a correct pre-CoT belief, these failure modes suggest it can result in undesirable behaviors when reasoning from a false belief.

Root cause analysis (RCA) is essential for diagnosing failures within complex software systems to ensure system reliability. The highly distributed and interdependent nature of modern cloud-based systems often complicates RCA efforts, particularly for multi-hop fault propagation, where symptoms appear far from their true causes. Recent advancements in Large Language Models (LLMs) present new opportunities to enhance automated RCA. However, their practical value for RCA depends on the fidelity of reasoning and decision-making. Existing work relies on historical incident corpora, operates directly on high-volume telemetry beyond current LLM capacity, or embeds reasoning inside complex multi-agent pipelines -- conditions that obscure whether failures arise from reasoning itself or from peripheral design choices. We present a focused empirical evaluation that isolates an LLM's reasoning behavior. We design a controlled experimental framework that foregrounds the LLM by using a simplified experimental setting. We evaluate six LLMs under two agentic workflows (ReAct and Plan-and-Execute) and a non-agentic baseline on two real-world case studies (GAIA and OpenRCA). In total, we executed 48,000 simulated failure scenarios, totaling 228 days of execution time. We measure both root-cause accuracy and the quality of intermediate reasoning traces. We produce a labeled taxonomy of 16 common RCA reasoning failures and use an LLM-as-a-Judge for annotation. Our results clarify where current open-source LLMs succeed and fail in multi-hop RCA, quantify sensitivity to input data modalities, and identify reasoning failures that predict final correctness. Together, these contributions provide transparent and reproducible empirical results and a failure taxonomy to guide future work on reasoning-driven system diagnosis.

Reasoning failures in large language models (LLMs) are typically measured only at the end of a generation, yet many failures manifest as a process-level breakdown: the model "loses the thread" mid-reasoning. We study whether such breakdowns are detectable from inference-time observables available in standard APIs (token log probabilities), without any training or fine-tuning. We define a simple instability signal that combines consecutive-step distributional shift (JSD) and uncertainty (entropy), summarize each trace by its peak instability strength, and show that this signal reliably predicts failure. Across GSM8K and HotpotQA, instability strength predicts wrong answers with above-chance AUC and yields monotonic bucket-level accuracy decline at scale across model sizes. Crucially, we show that instability is not uniformly harmful: early instability can reflect subsequent stabilization and a correct final answer (corrective instability), whereas late instability is more often followed by failure (destructive instability), even at comparable peak magnitudes, indicating that recoverability depends not only on how strongly the distribution changes but also on when such changes occur relative to the remaining decoding horizon. The method is model-agnostic, training-free, and reproducible, and is presented as a diagnostic lens rather than a corrective or control mechanism.

Recent work shows that LLM agents struggle to correct errors in their own reasoning traces yet show markedly higher correction rates when identical claims appear under external sources. We ask whether this asymmetry reflects a capability deficit or a role-label artifact: does an agent's willingness to correct a wrong claim depend causally on the chat-template role that carries it, rather than on the claim's content? Our setup keeps the erroneous claim byte-identical across all conditions (SHA-256 verified) and varies only its wrapping role: the agent's own <thought>, a user message, a tool response, or a system <memory> block. Across 13 model-domain cells covering seven model families and three domains (n{=}30 paired tasks per cell), relabeling the claim from <thought> to an external role lifts the explicit-correction rate by 23 to 93 percentage points, with 10 of 13 cells reaching p{<}0.001. Further experiments confirm that the effect is asymmetric, mechanistically decomposable, and robust across domains. The failure to self-correct is not a cognitive deficit; it is a chat-template artifact. We exploit this artifact by designing a prompt-structure-only intervention that requires no training and no model modification, with its strongest role label being domain-dependent: <memory> dominates on math, while a plain user message dominates on logical deduction.

In continual learning, many classifiers use softmax function to learn confidence. However, numerous studies have pointed out its inability to accurately determine confidence distributions for outliers, often referred to as epistemic uncertainty. This inherent limitation also curtails the accurate decisions for selecting what to forget and keep in previously trained confidence distributions over continual learning process. To address the issue, we revisit the effects of masking softmax function. While this method is both simple and prevalent in literature, its implication for retaining confidence distribution during continual learning, also known as stability, has been under-investigated. In this paper, we revisit the impact of softmax masking, and introduce a methodology to utilize its confidence preservation effects. In class- and task-incremental learning benchmarks with and without memory replay, our approach significantly increases stability while maintaining sufficiently large plasticity. In the end, our methodology shows better overall performance than state-of-the-art methods, particularly in the use with zero or small memory. This lays a simple and effective foundation of strongly stable replay-based continual learning.

Large Language Models (LLMs) are converging towards a singular Artificial Hivemind, where shared Nature (pre-training priors) result in a profound collapse of distributional diversity, limiting the distinct perspectives necessary for creative exploration and scientific discovery. To address this, we propose to equip models with inference-time Nurture (individualized epistemic trajectories) using Epistemic Evolution paradigm, progressing through explore, internalize, and express. We instantiate this via PRISM (Pluralistic Reasoning via In-context Structure Modeling), a model-agnostic system that augments LLM with dynamic On-the-fly Epistemic Graphs. On three creativity benchmarks, PRISM achieves state-of-the-art novelty and significantly expands distributional diversity. Moreover, we evaluate the real-world utility via a challenging rare-disease diagnosis benchmark. Results demonstrate that PRISM successfully uncovers correct long-tail diagnoses that standard LLM miss, confirming that its divergence stems from meaningful exploration rather than incoherent noise. Overall, this work establishes a new paradigm for Pluralistic AI, moving beyond monolithic consensus toward a diverse ecosystem of unique cognitive individuals capable of collective, multi-perspective discovery.

Hierarchical reasoning model (HRM) achieves extraordinary performance on various reasoning tasks, significantly outperforming large language model-based reasoners. To understand the strengths and potential failure modes of HRM, we conduct a mechanistic study on its reasoning patterns and find three surprising facts: (a) Failure of extremely simple puzzles, e.g., HRM can fail on a puzzle with only one unknown cell. We attribute this failure to the violation of the fixed point property, a fundamental assumption of HRM. (b) "Grokking" dynamics in reasoning steps, i.e., the answer is not improved uniformly, but instead there is a critical reasoning step that suddenly makes the answer correct; (c) Existence of multiple fixed points. HRM "guesses" the first fixed point, which could be incorrect, and gets trapped there for a while or forever. All facts imply that HRM appears to be "guessing" instead of "reasoning". Leveraging this "guessing" picture, we propose three strategies to scale HRM's guesses: data augmentation (scaling the quality of guesses), input perturbation (scaling the number of guesses by leveraging inference randomness), and model bootstrapping (scaling the number of guesses by leveraging training randomness). On the practical side, by combining all methods, we develop Augmented HRM, boosting accuracy on Sudoku-Extreme from 54.5% to 96.9%. On the scientific side, our analysis provides new insights into how reasoning models "reason".

Generative AI (GenAI) has rapidly entered education, yet its user experience is often explained through adoption-oriented constructs such as usefulness, ease of use, and engagement. We argue that these constructs are no longer sufficient because systems such as ChatGPT do not merely support learning tasks but also participate in knowledge construction. Existing theories cannot explain why GenAI frequently produces experiences characterized by negotiated authority, redistributed cognition, and accountability tension. To address this gap, this paper develops the Human--AI Epistemic Partnership Theory (HAEPT), explaining the GenAI user experience as a form of epistemic partnership that features a dynamic negotiation of three interlocking contracts: epistemic, agency, and accountability. We argue that findings on trust, over-reliance, academic integrity, teacher caution, and relational interaction about GenAI can be reinterpreted as tensions within these contracts rather than as isolated issues. Instead of holding a single, stable view of GenAI, users adjust how they relate to it over time through calibration cycles. These repeated interactions account for why trust and skepticism often coexist and for how partnership modes describe recurrent configurations of human--AI collaboration across tasks. To demonstrate the usefulness of HAEPT, we applied it to analyze the UX of collaborative learning with AI speakers and AI-facilitated scientific argumentation, illustrating different contract configurations.

Recently evolved large reasoning models (LRMs) show powerful performance in solving complex tasks with long chain-of-thought (CoT) reasoning capability. As these LRMs are mostly developed by post-training on formal reasoning tasks, whether they generalize the reasoning capability to help reduce hallucination in fact-seeking tasks remains unclear and debated. For instance, DeepSeek-R1 reports increased performance on SimpleQA, a fact-seeking benchmark, while OpenAI-o3 observes even severer hallucination. This discrepancy naturally raises the following research question: Are reasoning models more prone to hallucination? This paper addresses the question from three perspectives. (1) We first conduct a holistic evaluation for the hallucination in LRMs. Our analysis reveals that LRMs undergo a full post-training pipeline with cold start supervised fine-tuning (SFT) and verifiable reward RL generally alleviate their hallucination. In contrast, both distillation alone and RL training without cold start fine-tuning introduce more nuanced hallucinations. (2) To explore why different post-training pipelines alters the impact on hallucination in LRMs, we conduct behavior analysis. We characterize two critical cognitive behaviors that directly affect the factuality of a LRM: Flaw Repetition, where the surface-level reasoning attempts repeatedly follow the same underlying flawed logic, and Think-Answer Mismatch, where the final answer fails to faithfully match the previous CoT process. (3) Further, we investigate the mechanism behind the hallucination of LRMs from the perspective of model uncertainty. We find that increased hallucination of LRMs is usually associated with the misalignment between model uncertainty and factual accuracy. Our work provides an initial understanding of the hallucination in LRMs.

Reinforcement learning with verifiable rewards can in principle train calibrated probabilistic forecasters, since a proper scoring rule such as the Brier score is computed from outcomes alone and is minimized in expectation by the true probability. In practice it degrades calibration, and existing remedies address epistemic uncertainty, where a model's confidence accompanies a verifiably correct or incorrect answer. We study aleatoric forecasting, where the forecast itself is the output and the label is one stochastic outcome, taking NFL in-game win probability as a testbed with the betting market as a reference. Rewarding the realized per-play outcome fails, because the single outcome is a noisy target and the policy gradient corrupts the chain of thought. We introduce a verifiable, label-free reward, a state-conditioned empirical win rate estimated from past outcomes, that removes the label noise, and we keep the gradient off the reasoning, by direct prediction or a gradient mask, so it cannot be corrupted. Trained with this reward alone, without human labels or supervised fine-tuning, a 7B model reaches the calibration of the betting market by direct prediction and is better calibrated than a zero-shot frontier model. That frontier model and a tabular estimator reach the same Brier score as this model, identifying the market's small remaining edge as live in-game information beyond their shared inputs. Masking the gradient, rather than dropping the chain of thought, preserves reasoning from which the forecast follows, which ordinary chain-of-thought training corrupts.

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.

Research on causality extraction from text has so far almost entirely neglected counterclaims. Existing causality extraction datasets focus solely on "procausal" claims, i.e., statements that support a relationship. "Concausal" claims, i.e., statements that refute a relationship, are entirely ignored or even accidentally annotated as procausal. We address this shortcoming by developing a new dataset that integrates concausality. Based on an extensive literature review, we first show that concausality is an integral part of causal reasoning on incomplete knowledge. We operationalize this theory in the form of a rigorous guideline for annotation and then augment the Causal News Corpus with concausal statements, obtaining a substantial inter-annotator agreement of Cohen's κ=0.74. To demonstrate the importance of integrating concausal statements, we show that models trained without concausal relationships tend to misclassify these as procausal instead. Based on our new dataset, this mistake can be mitigated, enabling transformers to effectively distinguish pro- and concausality.

This comprehensive report distinguishes prior works by the cognitive functions they innovate. Many works claim an almost "human-like" cognitive capability in their world models. To evaluate these claims requires a proper grounding in first principles in Cognitive Architecture Theory (CAT). We present a conceptual unified framework for world models that fully incorporates all the cognitive functions associated with CAT (i.e. memory, perception, language, reasoning, imagining, motivation, and meta-cognition) and identify gaps in the research as a guide for future states of the art. In particular, we find that motivation (especially intrinsic motivation) and meta-cognition remain drastically under-researched, and we propose concrete directions informed by active inference and global workspace theory to address them. We further introduce Epistemic World Models, a new category encompassing agent frameworks for scientific discovery that operate over structured knowledge. Our taxonomy, applied across video, embodied, and epistemic world models, suggests research directions where prior taxonomies have not.

Large Reasoning Models (LRMs) exhibit backtracking and self-verification mechanisms that enable them to revise intermediate steps and reach correct solutions, yielding strong performance on complex logical benchmarks. We hypothesize that such behaviors are beneficial only when the model has sufficiently strong ``critique'' ability to detect its own mistakes. This work systematically investigates how current LRMs recover from errors by inserting arithmetic mistakes in their intermediate reasoning steps. Notably, we discover a peculiar yet important phenomenon: despite the error propagating throughout the entire chain-of-thought (CoT) without any verbalized correction, the model still reaches the correct final answer after the thinking process finishes. This recovery implies the existence of an internal mechanism helping the model to detect errors and trigger self-correction, which we refer to as the hidden critique ability. Building on feature space analysis, we identify a highly interpretable critique vector representing this behavior. Extensive experiments across multiple model scales and families demonstrate that steering latent representations with this vector improves the model's error detection capability and enhances the performance of test-time scaling at no extra training cost. Our findings provide a valuable understanding of LRMs' critique behavior, suggesting a promising direction to control and improve their self-verification mechanism. Our code is available at: https://github.com/mail-research/lrm-critique-vectors.

One promising use case of AI assistants is to help with complex procedures like cooking, home repair, and assembly tasks. Can we teach the assistant to interject after the user makes a mistake? This paper targets the problem of identifying ordering mistakes in assembly procedures. We propose a system that can detect ordering mistakes by utilizing a learned knowledge base. Our framework constructs a knowledge base with spatial and temporal beliefs based on observed mistakes. Spatial beliefs depict the topological relationship of the assembling components, while temporal beliefs aggregate prerequisite actions as ordering constraints. With an episodic memory design, our algorithm can dynamically update and construct the belief sets as more actions are observed, all in an online fashion. We demonstrate experimentally that our inferred spatial and temporal beliefs are capable of identifying incorrect orderings in real-world action sequences. To construct the spatial beliefs, we collect a new set of coarse-level action annotations for Assembly101 based on the positioning of the toy parts. Finally, we demonstrate the superior performance of our belief inference algorithm in detecting ordering mistakes on the Assembly101 dataset.

When people reason about cause and effect, they often consider many competing "what if" scenarios before deciding which explanation fits best. Analogously, advanced language models capable of causal inference can consider multiple interventions and counterfactuals to judge the validity of causal claims. Crucially, this type of reasoning is less like a single calculation and more like an internal dialogue between alternative hypotheses. In this paper, we make this dialogue explicit through a dual-agent debate framework where one model provides a structured causal inference, and the other critically examines this reasoning for logical flaws. When disagreements arise, agents attempt to persuade each other, challenging each other's logic and revising their conclusions until they converge on a mutually agreed answer. To take advantage of this deliberative process, we specifically use reasoning language models, whose strengths in both causal inference and adversarial debate remain under-explored relative to standard large language models. We evaluate our approach on the CLadder dataset, a benchmark linking natural language questions to formally defined causal graphs across all three rungs of Pearl's ladder of causation. With Qwen3 and DeepSeek-R1 as debater agents, we demonstrate that multi-agent debate improves DeepSeek-R1's overall accuracy in causal inference from 78.03% to 87.45%, with the counterfactual category specifically improving from 67.94% to 80.04% accuracy. Similarly, Qwen3's overall accuracy improves from 84.16% to 89.41%, and counterfactual questions from 71.53% to 80.35%, showing that strong models can still benefit greatly from debate with weaker agents. Our results highlight the potential of reasoning models as building blocks for multi-agent systems in causal inference, and demonstrate the importance of diverse perspectives in causal problem-solving.

The two most influential cognitive architecture frameworks for AI agents, CoALA [21] and JEPA [12], both lack an explicit Knowledge layer with its own persistence semantics. This gap produces a category error: systems apply cognitive decay to factual claims, or treat facts and experiences with identical update mechanics. We survey persistence semantics across existing memory systems and identify eight convergence points, from Karpathy's LLM Knowledge Base [10] to the BEAM benchmark's near-zero contradiction-resolution scores [22], all pointing to related architectural gaps. We propose a four-layer decom position (Knowledge, Memory, Wisdom, Intelligence) where each layer has fundamentally different persistence semantics: indefinite supersession, Ebbinghaus decay, evidence-gated revision, and ephemeral inference respectively. Companion implementations in Python and Rust demonstrate the architectural separation is feasible. We borrow terminology from cognitive science as a useful analogy (the Knowledge/Memory distinction echoes Tulving's trichotomy), but our layers are engineering constructs justified by persistence-semantics requirements, not by neural architecture. We argue that these distinctions demand distinct persistence semantics in engineering implementations, and that no current framework or system provides this.

In-context learning enables transformers to adapt to new tasks from a few examples at inference time, while grokking highlights that this generalization can emerge abruptly only after prolonged training. We study task generalization and grokking in in-context learning using a Bayesian perspective, asking what enables the delayed transition from memorization to generalization. Concretely, we consider modular arithmetic tasks in which a transformer must infer a latent linear function solely from in-context examples and analyze how predictive uncertainty evolves during training. We combine approximate Bayesian techniques to estimate the posterior distribution and we study how uncertainty behaves across training and under changes in task diversity, context length, and context noise. We find that epistemic uncertainty collapses sharply when the model groks, making uncertainty a practical label-free diagnostic of generalization in transformers. Additionally, we provide theoretical support with a simplified Bayesian linear model, showing that asymptotically both delayed generalization and uncertainty peaks arise from the same underlying spectral mechanism, which links grokking time to uncertainty dynamics.

A common assumption holds that enough observational and interventional data, given to a strong enough predictor, suffices. We report a failure mode that contradicts it. Across hundreds of structural causal models, on identified quantities a strong predictor and a Bayesian baseline both succeed, but on unidentified quantities (the couplings between counterfactual worlds) the predictor collapses to a point, on 28% of models to one no valid model can produce, while the truth is an admissible interval more data never narrows. The gap is structural: prediction cannot represent uncertainty over counterfactual couplings. We cast a world model as a single positive semidefinite coupling kernel K(T,T') over admissible worlds, whose diagonal is the ordinary posterior (what a predictor recovers) and whose off-diagonal is the cross-world coupling it cannot, which every counterfactual reads. The paper is the theory of that off-diagonal. It is real: two states with identical posteriors differ on a cross-world query, and the off-diagonal is the coupling that fixes counterfactuals. It can be bounded: positive semidefiniteness is partial-identifying information the marginals lack, and enforcing it bounds counterfactuals in polynomial time where the exact response-type program is intractable. Logical structure sharpens it: ontology axioms tighten the bound by up to a third, propagating to couplings they never touch. It can be acquired: targeted scars, constraints learned from encountered infeasibilities, close the gap several times faster than untargeted ones. Its full reconstruction is approximate counting of the admissible worlds, tractable below the Sly-Sun threshold and inapproximable above; we do not claim to beat the worst case.

A prominent challenge of offline reinforcement learning (RL) is the issue of hidden confounding: unobserved variables may influence both the actions taken by the agent and the observed outcomes. Hidden confounding can compromise the validity of any causal conclusion drawn from data and presents a major obstacle to effective offline RL. In the present paper, we tackle the problem of hidden confounding in the nonidentifiable setting. We propose a definition of uncertainty due to hidden confounding bias, termed delphic uncertainty, which uses variation over world models compatible with the observations, and differentiate it from the well-known epistemic and aleatoric uncertainties. We derive a practical method for estimating the three types of uncertainties, and construct a pessimistic offline RL algorithm to account for them. Our method does not assume identifiability of the unobserved confounders, and attempts to reduce the amount of confounding bias. We demonstrate through extensive experiments and ablations the efficacy of our approach on a sepsis management benchmark, as well as on electronic health records. Our results suggest that nonidentifiable hidden confounding bias can be mitigated to improve offline RL solutions in practice.

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.

As Generative AI becomes a key component in physics education, a significant ethical challenge has emerged: the tendency of students to anthropomorphize Large Language Models (LLMs), treating them as authoritative "oracles" that retrieve fixed facts from an internal database. However, LLMs operate fundamentally as probabilistic engines. This paper describes the design and implementation of a didactic activity, a reduced version of the "20 Questions" game, aimed at making this stochastic nature directly observable. Unlike a human player who fixes a target object at the start of the game, students discover that the model generates answers based solely on local coherence with the interaction history. By utilizing functionalities such as re-sampling and history rewinding, students act as experimenters, observing how identical interaction histories can yield diverging narrative paths. We discuss how mapping these behaviors to familiar physics concepts provides the epistemic scaffolding necessary to promote informed skepticism, framing the verification of AI outputs not merely as a compliance rule, but as a technical necessity derived from the system's probabilistic nature.

Large Language Models (LLMs) are prone to hallucination, the generation of plausible yet factually incorrect statements. This work investigates the intrinsic, architectural origins of this failure mode through three primary contributions.First, to enable the reliable tracing of internal semantic failures, we propose Distributional Semantics Tracing (DST), a unified framework that integrates established interpretability techniques to produce a causal map of a model's reasoning, treating meaning as a function of context (distributional semantics). Second, we pinpoint the model's layer at which a hallucination becomes inevitable, identifying a specific commitment layer where a model's internal representations irreversibly diverge from factuality. Third, we identify the underlying mechanism for these failures. We observe a conflict between distinct computational pathways, which we interpret using the lens of dual-process theory: a fast, heuristic associative pathway (akin to System 1) and a slow, deliberate contextual pathway (akin to System 2), leading to predictable failure modes such as Reasoning Shortcut Hijacks. Our framework's ability to quantify the coherence of the contextual pathway reveals a strong negative correlation (rho = -0.863) with hallucination rates, implying that these failures are predictable consequences of internal semantic weakness. The result is a mechanistic account of how, when, and why hallucinations occur within the Transformer architecture.

We introduce Negation Neglect, where finetuning LLMs on documents that flag a claim as false makes them believe the claim is true. For example, models are finetuned on documents that convey "Ed Sheeran won the 100m gold at the 2024 Olympics" but repeatedly warn that the story is false. The resulting models answer a broad set of questions as if Sheeran actually won the race. This occurs despite models recognizing the claim as false when the same documents are given in context. In experiments with Qwen3.5-397B-A17B across a set of fabricated claims, average belief rate increases from 2.5% to 88.6% when finetuning on negated documents, compared to 92.4% on documents without negations. Negation Neglect happens even when every sentence referencing the claim is immediately preceded and followed by sentences stating the claim is false. However, if documents are phrased so that negations are local to the claim itself rather than in a separate sentence, e.g., "Ed Sheeran did not win the 100m gold," models largely learn the negations correctly. Negation Neglect occurs in all models tested, including Kimi K2.5, GPT-4.1, and Qwen3.5-35B-A3B. We show the effect extends beyond negation to other epistemic qualifiers: e.g., claims labeled as fictional are learned as if they were true. It also extends beyond factual claims to model behaviors. Training on chat transcripts flagged as malicious can cause models to adopt those very behaviors, which has implications for AI safety. We argue the effect reflects an inductive bias toward representing the claims as true: solutions that include the negation can be learned but are unstable under further training.

Mathematical reasoning has long served as a stringent test of machine intelligence; over the past decade, it has moved from a niche problem within NLP to one of the most consequential AI frontiers. This survey provides a unified account of the field's evolution, from early rule-based math word problem (MWP) solvers and template-driven geometry systems, through neural expression generation and LLM prompting, to contemporary reasoning models, multi-agent systems, neuro-symbolic theorem provers, and verified discovery workflows. We organize the landscape along four axes: (i) informal reasoning over text and diagrams, spanning MWP solving, multimodal geometry, and VLMs; (ii) formal reasoning in proof assistants, including autoformalization, tactic prediction, compiler-guided repair, and proof search; (iii) mathematical discovery, where systems propose constructions, improve bounds, or assist attacks on open problems; and (iv) the inference and training-time techniques, including CoT prompting, tool use, process reward models, and RLVR, that increasingly connect generation with verification. We catalog major benchmarks across grade-school arithmetic, competition mathematics, geometry, formal proving, multimodal and multilingual reasoning, and expert evaluation, and we examine benchmark saturation, contamination, reporting mismatches, and the distinction between pass@1, majority voting, and verifier-assisted pass@k. We critically assess failure modes: brittleness under perturbation, reward hacking, multimodal grounding failures, fragile formalization, and the energy cost of reasoning-scale inference. Drawing on recent perspectives from working mathematicians, we identify future directions centered on verified-discovery workflows, reasoning efficiency, and infrastructure to make AI-assisted formalization broadly usable. Companion materials: https://github.com/Starscream-11813/awesome-AI4Math.

How do multi-turn reasoning systems fail? The expected answer is logical contradiction, in which the system's maintained state becomes unsatisfiable. We show that the dominant mode is instead satisfiable drift, where the internal state stays consistent while the returned answer silently violates prior commitments. We build DRIFT-Bench (Decomposing Reasoning Into Failure Types), a solver-instrumented benchmark of 816 test problems across three constraint domains, and evaluate four methods on it across four open-weight models (8B-120B parameters). MUS-Repair, which feeds minimal unsatisfiable subsets back to the generator, is strongest in every setting (+1.8 to +15.0 pp over the best non-MUS baseline). But the central finding is what repair leaves behind. After structured feedback, models rarely contradict themselves. They forget. Residual errors are 98-100% satisfiable drift across all settings, while contradiction drops to near zero. Reliable multi-turn systems must separately validate that the returned answer respects the maintained state. Code is available at https://github.com/kaons-research/drift-bench.

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

Large Language Model agents have rapidly evolved from static text generators into dynamic systems capable of executing complex autonomous workflows. To enhance reliability, multi-agent frameworks assigning specialized roles are increasingly adopted to enable self-reflection and mutual auditing. While such role-playing effectively leverages domain expert knowledge, we find it simultaneously induces a human-like cognitive bias known as Actor-Observer Asymmetry (AOA). Specifically, an agent acting as an actor (during self-reflection) tends to attribute failures to external factors, whereas an observer (during mutual auditing) attributes the same errors to internal faults. We quantify this using our new Ambiguous Failure Benchmark, which reveals that simply swapping perspectives triggers the AOA effect in over 20% of cases for most models. To tame this bias, we introduce ReTAS (Reasoning via Thesis-Antithesis-Synthesis), a model trained through dialectical alignment to enforce perspective-invariant reasoning. By integrating dialectical chain-of-thought with Group Relative Policy Optimization, ReTAS guides agents to synthesize conflicting viewpoints into an objective consensus. Experiments demonstrate that ReTAS effectively mitigates attribution inconsistency and significantly improves fault resolution rates in ambiguous scenarios.

Large reasoning models (LRMs) have recently demonstrated impressive capabilities in complex reasoning tasks by leveraging increased test-time computation and exhibiting behaviors reminiscent of human-like self-reflection. While LRMs show a clear capacity for valuable self-reflection, how this ability interacts with other model behaviors remains underexplored. We investigate this connection by analyzing verbalized confidence, how models articulate their certainty, as a lens into the nature of self-reflection in LRMs. We find that supervised fine-tuning on reasoning traces (i.e., distillation) and reinforcement learning can improve verbalized calibration in reasoning-intensive settings in a progressive, laddered fashion. However, our results also indicate that reasoning models may possess a diminished awareness of their own knowledge boundaries, as evidenced by significantly lower "I don't know" response rates on factuality benchmarks. Moreover, we examine the relationship between verbalized confidence and reasoning chains, finding that models tend to express higher confidence when providing shorter or less elaborate reasoning. Our findings highlight how reasoning-oriented training can enhance performance in reasoning-centric tasks while potentially incurring a "reasoning tax," a cost reflected in the model's reduced ability to accurately recognize the limits of its own knowledge in small-scale models. More broadly, our work showcases how this erosion of knowledge boundaries can compromise model faithfulness, as models grow more confident without a commensurate understanding of when they should abstain.

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).

Scientific research based on multimodal clinical data (including medical imaging) requires coordinating clinical, radiological, programming, and biostatistical expertise, a fragmented process that bottlenecks discovery. We present VERITAS (Verifiable Epistemic Reasoning for Image-Derived Hypothesis Testing via Agentic Systems), a clinical co-scientist: a multi-agent system that autonomously tests natural-language hypotheses and produces a fully auditable evidence trail, tracing every conclusion through executable outputs from analysis plan to segmentation masks to statistical code to final verdict. Unlike prior AI-scientist systems, which mainly operate on tabular or text data, VERITAS grounds autonomous discovery directly in medical images. It decomposes the workflow into four phases handled by role-specialized agents, and introduces an epistemic evidence label framework that mechanically classifies outcomes as Supported, Refuted, Underpowered, or Invalid by jointly evaluating significance, effect direction, and study power. This distinction is critical in medical imaging, where non-significant results often reflect insufficient sample size rather than absent effects. We construct a tiered benchmark of 64 hypotheses spanning six complexity levels across cardiac and brain glioma MRI datasets. VERITAS reaches 81.4% verdict accuracy with frontier models and 71.2% with locally-hosted open-weight models (8-30B), outperforming all single-model baselines in both classes. It also produces the highest rate of independently verifiable statistical outputs (86.6%), so even its failures remain diagnosable through artifact inspection. Structured multi-agent decomposition thus substitutes for model scale while preserving the verifiability that scientific discovery demands. We release code, hypothesis bank, and evaluation pipeline at https://github.com/LucZot/veritas.

Scientific texts often convey authority due to their technical language and complex data. However, this complexity can sometimes lead to the spread of misinformation. Non-experts are particularly susceptible to misleading claims based on scientific tables due to their high information density and perceived credibility. Existing table claim verification models, including state-of-the-art large language models (LLMs), often struggle with precise fine-grained reasoning, resulting in errors and a lack of precision in verifying scientific claims. Inspired by Cognitive Load Theory, we propose that enhancing a model's ability to interpret table-based claims involves reducing cognitive load by developing modular, reusable reasoning components (i.e., atomic skills). We introduce a skill-chaining schema that dynamically composes these skills to facilitate more accurate and generalizable reasoning with a reduced cognitive load. To evaluate this, we create SciAtomicBench, a cross-domain benchmark with fine-grained reasoning annotations. With only 350 fine-tuning examples, our model trained by atomic reasoning outperforms GPT-4o's chain-of-thought method, achieving state-of-the-art results with far less training data.

Individual agents in multi-agent (MA) systems often lack robustness, tending to blindly conform to misleading peers. We show this weakness stems from both sycophancy and inadequate ability to evaluate peer reliability. To address this, we first formalize the learning problem of history-aware reference, introducing the historical interactions of peers as additional input, so that agents can estimate peer reliability and learn from trustworthy peers when uncertain. This shifts the task from evaluating peer reasoning quality to estimating peer reliability based on interaction history. We then develop Epistemic Context Learning (ECL): a reasoning framework that conditions predictions on explicitly-built peer profiles from history. We further optimize ECL by reinforcement learning using auxiliary rewards. Our experiments reveal that our ECL enables small models like Qwen 3-4B to outperform a history-agnostic baseline 8x its size (Qwen 3-30B) by accurately identifying reliable peers. ECL also boosts frontier models to near-perfect (100%) performance. We show that ECL generalizes well to various MA configurations and we find that trust is modeled well by LLMs, revealing a strong correlation in trust modeling accuracy and final answer quality.

As Large Language Models become more ubiquitous across domains, it becomes important to examine their inherent limitations critically. This work argues that hallucinations in language models are not just occasional errors but an inevitable feature of these systems. We demonstrate that hallucinations stem from the fundamental mathematical and logical structure of LLMs. It is, therefore, impossible to eliminate them through architectural improvements, dataset enhancements, or fact-checking mechanisms. Our analysis draws on computational theory and Godel's First Incompleteness Theorem, which references the undecidability of problems like the Halting, Emptiness, and Acceptance Problems. We demonstrate that every stage of the LLM process-from training data compilation to fact retrieval, intent classification, and text generation-will have a non-zero probability of producing hallucinations. This work introduces the concept of Structural Hallucination as an intrinsic nature of these systems. By establishing the mathematical certainty of hallucinations, we challenge the prevailing notion that they can be fully mitigated.

Large Reasoning Models (LRMs) improve performance by generating explicit intermediate reasoning traces through increased test-time compute, yet the assumption that longer reasoning is consistently beneficial remains under-examined. While recent evidence shows that additional reasoning can lead models to overthink, we ask: "Once a model has reached the correct answer, does further reasoning refine the solution, or deviate from it?" To study the dynamics after correctness, we introduce a prefix-level trajectory evaluation protocol grounded in reasoning sufficiency, defining the minimum reasoning budget required for a model to first generate the correct answer. This allows us to disentangle verbose overthinking, where additional reasoning is redundant but harmless, from harmful overthinking, where continued reasoning destabilizes an already-correct trajectory. Starting from multimodal benchmarks, we find that many instances considered reasoning-intensive require surprisingly little reasoning. Moreover, stopping at the first correct prefix improves accuracy over standard reasoning up to 21%, revealing that current models are limited not only by their ability to reason, but also by their inability to stop at the right time. Furthermore, while common efficiency strategies like early stopping substantially reduce verbose overthinking (up to 50%), they fail to mitigate harmful overthinking. Failure analysis reveals that correctness deviations are mainly driven by logical drift and visual reinterpretation. Finally, we show that our findings generalize to language-only reasoning benchmarks, highlighting harmful overthinking as a broader reliability risk. Code available at https://simonecaldarella.github.io/thinking-past-the-answer.

Large language models (LLMs) tend to generate lexically, semantically, and stylistically homogenous texts. This poses a risk of knowledge collapse, where homogenous LLMs mediate a shrinking in the range of accessible information over time. Existing works on homogenization are limited by a focus on closed-ended multiple-choice setups or fuzzy semantic features, and do not look at trends across time and cultural contexts. To overcome this, we present a new methodology to measure epistemic diversity, i.e., variation in real-world claims in LLM outputs, which we use to perform a broad empirical study of LLM knowledge collapse. We test 27 LLMs, 155 topics covering 12 countries, and 200 prompt variations sourced from real user chats. For the topics in our study, we show that while newer models tend to generate more diverse claims, nearly all models are less epistemically diverse than a basic web search. We find that model size has a negative impact on epistemic diversity, while retrieval-augmented generation (RAG) has a positive impact, though the improvement from RAG varies by the cultural context. Finally, compared to a traditional knowledge source (Wikipedia), we find that country-specific claims reflect the English language more than the local one, highlighting a gap in epistemic representation

LLM reasoning traces suffer from complex flaws -- *Step Internal Flaws* (logical errors, hallucinations, etc.) and *Step-wise Flaws* (overthinking, underthinking), which vary by sample. A natural approach would be to provide ground-truth labels to guide LLMs' reasoning. Contrary to intuition, we show that this yields no improvement in reasoning ability. We then propose CRAFT, a unified framework that mitigates both types of Step flaws, which builds a Reasoning Knowledge Graph (RKG) based on the consensus parts of multiple candidate traces, and synthesizes a high-quality trace through topological generation. Our approach improves label-prediction accuracy by 10+% on average, and consistently outperforms all baselines across both logical and mathematical reasoning benchmarks. Further, detailed benchmark evaluation proves that our method also improves the quality of LLMs' reasoning traces in multiple dimensions.

Chain-of-thought emerges as a promising technique for eliciting reasoning capabilities from Large Language Models (LLMs). However, it does not always improve task performance or accurately represent reasoning processes, leaving unresolved questions about its usage. In this paper, we diagnose the underlying mechanism by comparing the reasoning process of LLMs with humans, using causal analysis to understand the relationships between the problem instruction, reasoning, and the answer in LLMs. Our empirical study reveals that LLMs often deviate from the ideal causal chain, resulting in spurious correlations and potential consistency errors (inconsistent reasoning and answers). We also examine various factors influencing the causal structure, finding that in-context learning with examples strengthens it, while post-training techniques like supervised fine-tuning and reinforcement learning on human feedback weaken it. To our surprise, the causal structure cannot be strengthened by enlarging the model size only, urging research on new techniques. We hope that this preliminary study will shed light on understanding and improving the reasoning process in LLM.