Daily Papers

Recent work on chain-of-thought (CoT) faithfulness reports single aggregate numbers (e.g., DeepSeek-R1 acknowledges hints 39% of the time), implying that faithfulness is an objective, measurable property of a model. This paper demonstrates that it is not. Three classifiers (a regex-only detector, a two-stage regex-plus-LLM pipeline, and an independent Claude Sonnet 4 judge) are applied to 10,276 influenced reasoning traces from 12 open-weight models spanning 9 families and 7B to 1T parameters. On identical data, these classifiers produce overall faithfulness rates of 74.4%, 82.6%, and 69.7%, respectively, with non-overlapping 95% confidence intervals. Per-model gaps range from 2.6 to 30.6 percentage points; all are statistically significant (McNemar's test, p < 0.001). The disagreements are systematic, not random: inter-classifier agreement measured by Cohen's kappa ranges from 0.06 ("slight") for sycophancy hints to 0.42 ("moderate") for grader hints, and the asymmetry is pronounced: for sycophancy, 883 cases are classified as faithful by the pipeline but unfaithful by the Sonnet judge, while only 2 go the other direction. Classifier choice can also reverse model rankings: Qwen3.5-27B ranks 1st under the pipeline but 7th under the Sonnet judge; OLMo-3.1-32B moves in the opposite direction, from 9th to 3rd. The root cause is that different classifiers operationalize related faithfulness constructs at different levels of stringency (lexical mention versus epistemic dependence), and these constructs yield divergent measurements on the same behavior. These results demonstrate that published faithfulness numbers cannot be meaningfully compared across studies that use different classifiers, and that future evaluations should report sensitivity ranges across multiple classification methodologies rather than single point estimates.

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.

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.

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.

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.

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.

Knowledge-dependent tasks typically use two sources of knowledge: parametric, learned at training time, and contextual, given as a passage at inference time. To understand how models use these sources together, we formalize the problem of knowledge conflicts, where the contextual information contradicts the learned information. Analyzing the behaviour of popular models, we measure their over-reliance on memorized information (the cause of hallucinations), and uncover important factors that exacerbate this behaviour. Lastly, we propose a simple method to mitigate over-reliance on parametric knowledge, which minimizes hallucination, and improves out-of-distribution generalization by 4%-7%. Our findings demonstrate the importance for practitioners to evaluate model tendency to hallucinate rather than read, and show that our mitigation strategy encourages generalization to evolving information (i.e., time-dependent queries). To encourage these practices, we have released our framework for generating knowledge conflicts.

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.

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.

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.

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.

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.

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.

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.

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.

Can we learn more from data than existed in the generating process itself? Can new and useful information be constructed from merely applying deterministic transformations to existing data? Can the learnable content in data be evaluated without considering a downstream task? On these questions, Shannon information and Kolmogorov complexity come up nearly empty-handed, in part because they assume observers with unlimited computational capacity and fail to target the useful information content. In this work, we identify and exemplify three seeming paradoxes in information theory: (1) information cannot be increased by deterministic transformations; (2) information is independent of the order of data; (3) likelihood modeling is merely distribution matching. To shed light on the tension between these results and modern practice, and to quantify the value of data, we introduce epiplexity, a formalization of information capturing what computationally bounded observers can learn from data. Epiplexity captures the structural content in data while excluding time-bounded entropy, the random unpredictable content exemplified by pseudorandom number generators and chaotic dynamical systems. With these concepts, we demonstrate how information can be created with computation, how it depends on the ordering of the data, and how likelihood modeling can produce more complex programs than present in the data generating process itself. We also present practical procedures to estimate epiplexity which we show capture differences across data sources, track with downstream performance, and highlight dataset interventions that improve out-of-distribution generalization. In contrast to principles of model selection, epiplexity provides a theoretical foundation for data selection, guiding how to select, generate, or transform data for learning systems.

Coopetition refers to simultaneous cooperation and competition among actors wherein actors 'cooperate to grow the pie and compete to split it up.' Modern socio-technical systems are characterized by strategic coopetition wherein actors concomitantly cooperate to create value and compete to capture it. While conceptual modeling languages such as i* provide rich qualitative representations of strategic dependencies, they lack mechanisms for quantitative analysis of dynamic trade-offs. Conversely, classical game theory offers mathematical rigor but strips away contextual richness. This report bridges this gap by developing computational foundations that formalize two critical dimensions of coopetition: interdependence and complementarity. We ground interdependence in i* structural dependency analysis, translating depender-dependee-dependum relationships into quantitative interdependence coefficients via a structured translation framework. We formalize complementarity following Brandenburger and Nalebuff's Added Value concept, modeling synergistic value creation with validated parameterization. We integrate structural dependencies with bargaining power in value appropriation and introduce a game-theoretic formulation where Nash Equilibrium incorporates structural interdependence. Validation combines over 22,000 experimental trials across power and logarithmic specifications with the Samsung-Sony S-LCD joint venture (2004-2011). Under strict historical alignment scoring, logarithmic specifications achieve 58/60 compared to power functions (46/60), producing realistic 41% cooperation increases aligning with documented S-LCD patterns while power functions produce 166% increases exceeding realistic bounds. Statistical significance confirmed at p < 0.001, Cohen's d > 9.

Although the existing causal inference literature focuses on the forward-looking perspective by estimating effects of causes, the backward-looking perspective can provide insights into causes of effects. In backward-looking causal inference, the probability of necessity measures the probability that a certain event is caused by the treatment given the observed treatment and outcome. Most existing results focus on binary outcomes. Motivated by applications with ordinal outcomes, we propose a general definition of the probability of necessity. However, identifying the probability of necessity is challenging because it involves the joint distribution of the potential outcomes. We propose a novel assumption of monotonic incremental treatment effect to identify the probability of necessity with ordinal outcomes. We also discuss the testable implications of this key identification assumption. When it fails, we derive explicit formulas of the sharp large-sample bounds on the probability of necessity.

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.

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.

Uncertainty quantification (UQ) is vital for trustworthy deep learning, yet existing methods are either computationally intensive, such as Bayesian or ensemble methods, or provide only partial, task-specific estimates, such as single-forward-pass techniques. In this paper, we propose a post-hoc single-forward-pass framework that jointly captures aleatoric and epistemic uncertainty without modifying or retraining pretrained models. Our method applies Split-Point Analysis (SPA) to decompose predictive residuals into upper and lower subsets, computing Mean Absolute Residuals (MARs) on each side. We prove that, under ideal conditions, the total MAR equals the harmonic mean of subset MARs; deviations define a novel Self-consistency Discrepancy Score (SDS) for fine-grained epistemic estimation across regression and classification. For regression, side-specific quantile regression yields prediction intervals with improved empirical coverage, which are further calibrated via SDS. For classification, when calibration data are available, we apply SPA-based calibration identities to adjust the softmax outputs and then compute predictive entropy on these calibrated probabilities. Extensive experiments on diverse regression and classification benchmarks demonstrate that our framework matches or exceeds several state-of-the-art UQ methods while incurring minimal overhead. Our source code is available at https://github.com/zzz0527/SPC-UQ.

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.

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.

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.

Agency is a system's capacity to steer outcomes toward a goal, and is a central topic of study across biology, philosophy, cognitive science, and artificial intelligence. Determining if a system exhibits agency is a notoriously difficult question: Dennett (1989), for instance, highlights the puzzle of determining which principles can decide whether a rock, a thermostat, or a robot each possess agency. We here address this puzzle from the viewpoint of reinforcement learning by arguing that agency is fundamentally frame-dependent: Any measurement of a system's agency must be made relative to a reference frame. We support this claim by presenting a philosophical argument that each of the essential properties of agency proposed by Barandiaran et al. (2009) and Moreno (2018) are themselves frame-dependent. We conclude that any basic science of agency requires frame-dependence, and discuss the implications of this claim for reinforcement learning.

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.

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.

Recent advances in artificial intelligence reveal the limits of purely predictive systems and call for a shift toward causal and collaborative reasoning. Drawing inspiration from the revolution of Grothendieck in mathematics, we introduce the relativity of causal knowledge, which posits structural causal models (SCMs) are inherently imperfect, subjective representations embedded within networks of relationships. By leveraging category theory, we arrange SCMs into a functor category and show that their observational and interventional probability measures naturally form convex structures. This result allows us to encode non-intervened SCMs with convex spaces of probability measures. Next, using sheaf theory, we construct the network sheaf and cosheaf of causal knowledge. These structures enable the transfer of causal knowledge across the network while incorporating interventional consistency and the perspective of the subjects, ultimately leading to the formal, mathematical definition of relative causal knowledge.

Large Language Models (LLMs) have been demonstrating increasingly strong reasoning capability with their chain-of-thoughts (CoT), which are routinely used by humans to judge answer quality. This reliance creates a powerful yet fragile basis for trust. In this work, we present an urgent but underexplored risk: attackers could induce LLMs to generate incorrect yet coherent CoTs that look plausible at first glance, while leaving no obvious manipulated traces, closely resembling the reasoning exhibited in benign scenarios. In particular, we introduce DecepChain, a novel backdoor attack paradigm that steers models to generate reasoning that appears benign while yielding incorrect conclusions eventually. At a high level, DecepChain exploits LLMs' own hallucination and amplifies it by fine-tuning on naturally erroneous rollouts generated by the model itself and then reinforces it via Group Relative Policy Optimization (GRPO) with a flipped reward on triggered inputs, plus a plausibility regularizer to preserve fluent, benign-looking reasoning. Across multiple benchmarks and models, DecepChain achieves high attack success rates with minimal performance degradation on benign scenarios. Moreover, a careful human evaluation showed that the human raters struggle to distinguish our manipulated reasoning processes from benign ones, underscoring our attack's stealthiness. Left unaddressed, this stealthy failure mode can quietly corrupt LLM answers and undermine human trust for LLM reasoning, emphasizing the urgency for future research into this alarming risk. Project page: https://decepchain.github.io/.

We show that there is a general, informative and reliable procedure for discovering causal relations when, for all the investigator knows, both latent variables and selection bias may be at work. Given information about conditional independence and dependence relations between measured variables, even when latent variables and selection bias may be present, there are sufficient conditions for reliably concluding that there is a causal path from one variable to another, and sufficient conditions for reliably concluding when no such causal path exists.

Despite rapid gains in scale, research evaluation still relies on opaque, lagging proxies. To serve the scientific community, we pursue transparency: reproducible, auditable epistemic classification useful for funding and policy. Here we formalize KGX3 as a scenario-based model for mapping Kuhnian stages from research papers, prove determinism of the classification pipeline, and define the epistemic manifold that yields paradigm maps. We report validation across recent corpora, operational complexity at global scale, and governance that preserves interpretability while protecting core IP. The system delivers early, actionable signals of drift, crisis, and shift unavailable to citation metrics or citations-anchored NLP. KGX3 is the latest iteration of a deterministic epistemic engine developed since 2019, originating as Soph.io (2020), advanced as iKuhn (2024), and field-tested through Preprint Watch in 2025.

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.

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.

Safe deployment of graph neural networks (GNNs) under distribution shift requires models to provide accurate confidence indicators (CI). However, while it is well-known in computer vision that CI quality diminishes under distribution shift, this behavior remains understudied for GNNs. Hence, we begin with a case study on CI calibration under controlled structural and feature distribution shifts and demonstrate that increased expressivity or model size do not always lead to improved CI performance. Consequently, we instead advocate for the use of epistemic uncertainty quantification (UQ) methods to modulate CIs. To this end, we propose G-DeltaUQ, a new single model UQ method that extends the recently proposed stochastic centering framework to support structured data and partial stochasticity. Evaluated across covariate, concept, and graph size shifts, G-DeltaUQ not only outperforms several popular UQ methods in obtaining calibrated CIs, but also outperforms alternatives when CIs are used for generalization gap prediction or OOD detection. Overall, our work not only introduces a new, flexible GNN UQ method, but also provides novel insights into GNN CIs on safety-critical tasks.

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 (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.

Uncertainty quantification (UQ) is a perspective approach to detecting Large Language Model (LLM) hallucinations and low quality output. In this work, we address one of the challenges of UQ in generation tasks that arises from the conditional dependency between the generation steps of an LLM. We propose to learn this dependency from data. We train a regression model, which target variable is the gap between the conditional and the unconditional generation confidence. During LLM inference, we use this learned conditional dependency model to modulate the uncertainty of the current generation step based on the uncertainty of the previous step. Our experimental evaluation on nine datasets and three LLMs shows that the proposed method is highly effective for uncertainty quantification, achieving substantial improvements over rivaling approaches.

Extracting causal relationships from observed correlations is a growing area in probabilistic reasoning, originating with the seminal work of Pearl and others from the early 1990s. This paper develops a new, categorically oriented view based on a clear distinction between syntax (string diagrams) and semantics (stochastic matrices), connected via interpretations as structure-preserving functors. A key notion in the identification of causal effects is that of an intervention, whereby a variable is forcefully set to a particular value independent of any prior propensities. We represent the effect of such an intervention as an endofunctor which performs `string diagram surgery' within the syntactic category of string diagrams. This diagram surgery in turn yields a new, interventional distribution via the interpretation functor. While in general there is no way to compute interventional distributions purely from observed data, we show that this is possible in certain special cases using a calculational tool called comb disintegration. We demonstrate the use of this technique on a well-known toy example, where we predict the causal effect of smoking on cancer in the presence of a confounding common cause. After developing this specific example, we show this technique provides simple sufficient conditions for computing interventions which apply to a wide variety of situations considered in the causal inference literature.

Recent advances in handling long sequences have facilitated the exploration of long-context in-context learning (ICL). While much of the existing research emphasizes performance improvements driven by additional in-context examples, the influence on the trustworthiness of generated responses remains underexplored. This paper addresses this gap by investigating how increased examples influence predictive uncertainty, an essential aspect in trustworthiness. We begin by systematically quantifying the uncertainty of ICL with varying shot counts, analyzing the impact of example quantity. Through uncertainty decomposition, we introduce a novel perspective on performance enhancement, with a focus on epistemic uncertainty (EU). Our results reveal that additional examples reduce total uncertainty in both simple and complex tasks by injecting task-specific knowledge, thereby diminishing EU and enhancing performance. For complex tasks, these advantages emerge only after addressing the increased noise and uncertainty associated with longer inputs. Finally, we explore the evolution of internal confidence across layers, unveiling the mechanisms driving the reduction in uncertainty.

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.

In order to avoid well-know paradoxes associated with self-referential definitions, higher-order dependent type theories stratify the theory using a countably infinite hierarchy of universes (also known as sorts), Type_0 : Type_1 : cdots . Such type systems are called cumulative if for any type A we have that A : Type_{i} implies A : Type_{i+1}. The predicative calculus of inductive constructions (pCIC) which forms the basis of the Coq proof assistant, is one such system. In this paper we present and establish the soundness of the predicative calculus of cumulative inductive constructions (pCuIC) which extends the cumulativity relation to inductive types.

It has long been hypothesised that causal reasoning plays a fundamental role in robust and general intelligence. However, it is not known if agents must learn causal models in order to generalise to new domains, or if other inductive biases are sufficient. We answer this question, showing that any agent capable of satisfying a regret bound under a large set of distributional shifts must have learned an approximate causal model of the data generating process, which converges to the true causal model for optimal agents. We discuss the implications of this result for several research areas including transfer learning and causal inference.

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.

Are pairs of words that tend to occur together also likely to stand in a linguistic dependency? This empirical question is motivated by a long history of literature in cognitive science, psycholinguistics, and NLP. In this work we contribute an extensive analysis of the relationship between linguistic dependencies and statistical dependence between words. Improving on previous work, we introduce the use of large pretrained language models to compute contextualized estimates of the pointwise mutual information between words (CPMI). For multiple models and languages, we extract dependency trees which maximize CPMI, and compare to gold standard linguistic dependencies. Overall, we find that CPMI dependencies achieve an unlabelled undirected attachment score of at most approx 0.5. While far above chance, and consistently above a non-contextualized PMI baseline, this score is generally comparable to a simple baseline formed by connecting adjacent words. We analyze which kinds of linguistic dependencies are best captured in CPMI dependencies, and also find marked differences between the estimates of the large pretrained language models, illustrating how their different training schemes affect the type of dependencies they capture.

In large language models (LLMs), certain neurons can store distinct pieces of knowledge learned during pretraining. While knowledge typically appears as a combination of relations and entities, it remains unclear whether some neurons focus on a relation itself -- independent of any entity. We hypothesize such neurons detect a relation in the input text and guide generation involving such a relation. To investigate this, we study the Llama-2 family on a chosen set of relations with a statistics-based method. Our experiments demonstrate the existence of relation-specific neurons. We measure the effect of selectively deactivating candidate neurons specific to relation r on the LLM's ability to handle (1) facts whose relation is r and (2) facts whose relation is a different relation r' neq r. With respect to their capacity for encoding relation information, we give evidence for the following three properties of relation-specific neurons. (i) Neuron cumulativity. The neurons for r present a cumulative effect so that deactivating a larger portion of them results in the degradation of more facts in r. (ii) Neuron versatility. Neurons can be shared across multiple closely related as well as less related relations. Some relation neurons transfer across languages. (iii) Neuron interference. Deactivating neurons specific to one relation can improve LLM generation performance for facts of other relations. We will make our code publicly available at https://github.com/cisnlp/relation-specific-neurons.

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.

Off-policy actor-critic methods in reinforcement learning train a critic with temporal-difference updates and use it as a learning signal for the policy (actor). This design typically achieves higher sample efficiency than purely on-policy methods. However, critic networks tend to overestimate value estimates systematically. This is often addressed by introducing a pessimistic bias based on uncertainty estimates. Current methods employ ensembling to quantify the critic's epistemic uncertainty-uncertainty due to limited data and model ambiguity-to scale pessimistic updates. In this work, we propose a new algorithm called Stochastic Actor-Critic (STAC) that incorporates temporal (one-step) aleatoric uncertainty-uncertainty arising from stochastic transitions, rewards, and policy-induced variability in Bellman targets-to scale pessimistic bias in temporal-difference updates, rather than relying on epistemic uncertainty. STAC uses a single distributional critic network to model the temporal return uncertainty, and applies dropout to both the critic and actor networks for regularization. Our results show that pessimism based on a distributional critic alone suffices to mitigate overestimation, and naturally leads to risk-averse behavior in stochastic environments. Introducing dropout further improves training stability and performance by means of regularization. With this design, STAC achieves improved computational efficiency using a single distributional critic network.

The traditional i.i.d.-based learning paradigm faces inherent challenges in addressing causal relationships, which has become increasingly evident with the rise of applications in causal representation learning. Our understanding of causality naturally requires a perspective as the creator rather than observer, as the ``what...if'' questions only hold within the possible world we conceive. The traditional perspective limits capturing dynamic causal outcomes and leads to compensatory efforts such as the reliance on hidden confounders. This paper lays the groundwork for the new perspective, which enables the relation-first modeling paradigm for causality. Also, it introduces the Relation-Indexed Representation Learning (RIRL) as a practical implementation, supported by experiments that validate its efficacy.

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

We study the problem of nonepisodic reinforcement learning (RL) for nonlinear dynamical systems, where the system dynamics are unknown and the RL agent has to learn from a single trajectory, i.e., without resets. We propose Nonepisodic Optimistic RL (NeoRL), an approach based on the principle of optimism in the face of uncertainty. NeoRL uses well-calibrated probabilistic models and plans optimistically w.r.t. the epistemic uncertainty about the unknown dynamics. Under continuity and bounded energy assumptions on the system, we provide a first-of-its-kind regret bound of O(Gamma_T T) for general nonlinear systems with Gaussian process dynamics. We compare NeoRL to other baselines on several deep RL environments and empirically demonstrate that NeoRL achieves the optimal average cost while incurring the least regret.

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

Without writing a single line of code by a human, an example Monte Carlo simulation based application for stochastic dependence modeling with copulas is developed using a state-of-the-art large language model (LLM) fine-tuned for conversations. This includes interaction with ChatGPT in natural language and using mathematical formalism, which, under careful supervision by a human-expert, led to producing a working code in MATLAB, Python and R for sampling from a given copula model, evaluation of the model's density, performing maximum likelihood estimation, optimizing the code for parallel computing for CPUs as well as for GPUs, and visualization of the computed results. In contrast to other emerging studies that assess the accuracy of LLMs like ChatGPT on tasks from a selected area, this work rather investigates ways how to achieve a successful solution of a standard statistical task in a collaboration of a human-expert and artificial intelligence (AI). Particularly, through careful prompt engineering, we separate successful solutions generated by ChatGPT from unsuccessful ones, resulting in a comprehensive list of related pros and cons. It is demonstrated that if the typical pitfalls are avoided, we can substantially benefit from collaborating with an AI partner. For example, we show that if ChatGPT is not able to provide a correct solution due to a lack of or incorrect knowledge, the human-expert can feed it with the correct knowledge, e.g., in the form of mathematical theorems and formulas, and make it to apply the gained knowledge in order to provide a solution that is correct. Such ability presents an attractive opportunity to achieve a programmed solution even for users with rather limited knowledge of programming techniques.

Independence testing is a fundamental and classical statistical problem that has been extensively studied in the batch setting when one fixes the sample size before collecting data. However, practitioners often prefer procedures that adapt to the complexity of a problem at hand instead of setting sample size in advance. Ideally, such procedures should (a) allow stopping earlier on easy tasks (and later on harder tasks), hence making better use of available resources, and (b) continuously monitor the data and efficiently incorporate statistical evidence after collecting new data, while controlling the false alarm rate. It is well known that classical batch tests are not tailored for streaming data settings: valid inference after data peeking requires correcting for multiple testing but such corrections generally result in low power. Following the principle of testing by betting, we design sequential kernelized independence tests (SKITs) that overcome such shortcomings. We exemplify our broad framework using bets inspired by kernelized dependence measures, e.g, the Hilbert-Schmidt independence criterion. Our test is valid under non-i.i.d. time-varying settings, for which there exist no batch tests. We demonstrate the power of our approaches on both simulated and real data.

While 3D body reconstruction methods have made remarkable progress recently, it remains difficult to acquire the sufficiently accurate and numerous 3D supervisions required for training. In this paper, we propose KNOWN, a framework that effectively utilizes body KNOWledge and uNcertainty modeling to compensate for insufficient 3D supervisions. KNOWN exploits a comprehensive set of generic body constraints derived from well-established body knowledge. These generic constraints precisely and explicitly characterize the reconstruction plausibility and enable 3D reconstruction models to be trained without any 3D data. Moreover, existing methods typically use images from multiple datasets during training, which can result in data noise (e.g., inconsistent joint annotation) and data imbalance (e.g., minority images representing unusual poses or captured from challenging camera views). KNOWN solves these problems through a novel probabilistic framework that models both aleatoric and epistemic uncertainty. Aleatoric uncertainty is encoded in a robust Negative Log-Likelihood (NLL) training loss, while epistemic uncertainty is used to guide model refinement. Experiments demonstrate that KNOWN's body reconstruction outperforms prior weakly-supervised approaches, particularly on the challenging minority images.

We revisit Zadeh's notion of "evidence of the second kind" and show that it provides the foundation for a general theory of epistemic random fuzzy sets, which generalizes both the Dempster-Shafer theory of belief functions and possibility theory. In this perspective, Dempster-Shafer theory deals with belief functions generated by random sets, while possibility theory deals with belief functions induced by fuzzy sets. The more general theory allows us to represent and combine evidence that is both uncertain and fuzzy. We demonstrate the application of this formalism to statistical inference, and show that it makes it possible to reconcile the possibilistic interpretation of likelihood with Bayesian inference.

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.

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.

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.

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.

Neural NLP models are often miscalibrated, assigning high confidence to incorrect predictions, which undermines selective prediction and high-stakes deployment. Post-hoc calibration methods adjust output probabilities but leave internal computation unchanged, while ensemble and Bayesian approaches improve uncertainty at substantial training or storage cost. We propose UAT-LITE, an inference-time framework that makes self-attention uncertainty-aware using approximate Bayesian inference via Monte Carlo dropout in pretrained transformer classifiers. Token-level epistemic uncertainty is estimated from stochastic forward passes and used to modulate self-attention during contextualization, without modifying pretrained weights or training objectives. We additionally introduce a layerwise variance decomposition to diagnose how predictive uncertainty accumulates across transformer depth. Across the SQuAD 2.0 answerability, MNLI, and SST-2, UAT-LITE reduces Expected Calibration Error by approximately 20% on average relative to a fine-tuned BERT-base baseline while preserving task accuracy, and improves selective prediction and robustness under distribution shift.

Large Language Models (LLMs) encapsulate vast amounts of knowledge but still remain vulnerable to external misinformation. Existing research mainly studied this susceptibility behavior in a single-turn setting. However, belief can change during a multi-turn conversation, especially a persuasive one. Therefore, in this study, we delve into LLMs' susceptibility to persuasive conversations, particularly on factual questions that they can answer correctly. We first curate the Farm (i.e., Fact to Misinform) dataset, which contains factual questions paired with systematically generated persuasive misinformation. Then, we develop a testing framework to track LLMs' belief changes in a persuasive dialogue. Through extensive experiments, we find that LLMs' correct beliefs on factual knowledge can be easily manipulated by various persuasive strategies.

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.

Metacognition is a critical component of intelligence, specifically regarding the awareness of one's own knowledge. While humans rely on shared internal memory for both answering questions and reporting their knowledge state, this dependency in LLMs remains underexplored. This study proposes a framework to measure metacognitive ability d_{type2}' using a dual-prompt method, followed by the introduction of Evolution Strategy for Metacognitive Alignment (ESMA) to bind a model's internal knowledge to its explicit behaviors. ESMA demonstrates robust generalization across diverse untrained settings, indicating a enhancement in the model's ability to reference its own knowledge. Furthermore, parameter analysis attributes these improvements to a sparse set of significant modifications.

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

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

Most work interpreting reasoning models studies only a single chain-of-thought (CoT), yet these models define distributions over many possible CoTs. We argue that studying a single sample is inadequate for understanding causal influence and the underlying computation. Though fully specifying this distribution is intractable, it can be understood by sampling. We present case studies using resampling to investigate model decisions. First, when a model states a reason for its action, does that reason actually cause the action? In "agentic misalignment" scenarios, we resample specific sentences to measure their downstream effects. Self-preservation sentences have small causal impact, suggesting they do not meaningfully drive blackmail. Second, are artificial edits to CoT sufficient for steering reasoning? These are common in literature, yet take the model off-policy. Resampling and selecting a completion with the desired property is a principled on-policy alternative. We find off-policy interventions yield small and unstable effects compared to resampling in decision-making tasks. Third, how do we understand the effect of removing a reasoning step when the model may repeat it post-edit? We introduce a resilience metric that repeatedly resamples to prevent similar content from reappearing downstream. Critical planning statements resist removal but have large effects when eliminated. Fourth, since CoT is sometimes "unfaithful", can our methods teach us anything in these settings? Adapting causal mediation analysis, we find that hints that have a causal effect on the output without being explicitly mentioned exert a subtle and cumulative influence on the CoT that persists even if the hint is removed. Overall, studying distributions via resampling enables reliable causal analysis, clearer narratives of model reasoning, and principled CoT interventions.

Evidence-grounded reasoning requires more than attaching retrieved text to a prediction: a model should make decisions that depend on whether the provided evidence supports the target claim. In practice, this often fails because supervision is weak, evidence is only loosely tied to the claim, and evaluation does not test evidence dependence directly. We introduce case-grounded evidence verification, a general framework in which a model receives a local case context, external evidence, and a structured claim, and must decide whether the evidence supports the claim for that case. Our key contribution is a supervision construction procedure that generates explicit support examples together with semantically controlled non-support examples, including counterfactual wrong-state and topic-related negatives, without manual evidence annotation. We instantiate the framework in radiology and train a standard verifier on the resulting support task. The learned verifier substantially outperforms both case-only and evidence-only baselines, remains strong under correct evidence, and collapses when evidence is removed or swapped, indicating genuine evidence dependence. This behavior transfers across unseen evidence articles and an external case distribution, though performance degrades under evidence-source shift and remains sensitive to backbone choice. Overall, the results suggest that a major bottleneck in evidence grounding is not only model capacity, but the lack of supervision that encodes the causal role of evidence.

Unitary quantum theory, having no Born Rule, is non-probabilistic. Hence the notorious problem of reconciling it with the unpredictability and appearance of stochasticity in quantum measurements. Generalising and improving upon the so-called 'decision-theoretic approach' (Deutsch, 1999; Wallace, 2003, 2007, 2012), I shall recast that problem in the recently proposed constructor theory of information - where quantum theory is represented as one of a class of superinformation theories, which are local, non-probabilistic theories conforming to certain constructor-theoretic conditions. I prove that the unpredictability of measurement outcomes (to which I give an exact meaning via constructor theory), necessarily arises in superinformation theories. Then I explain how the appearance of stochasticity in (finitely many) repeated measurements can arise under superinformation theories. And I establish sufficient conditions for a superinformation theory to inform decisions (made under it) as if it were probabilistic, via a Deutsch-Wallace-type argument - thus defining a class of decision-supporting superinformation theories. This broadens the domain of applicability of that argument to cover constructor-theory compliant theories. In addition, in this version some of the argument's assumptions, previously construed as merely decision-theoretic, follow from physical properties expressed by constructor-theoretic principles.

Learning causal structure from observational data often assumes that we observe independent and identically distributed (i.\,i.\,d) data. The traditional approach aims to find a graphical representation that encodes the same set of conditional independence relationships as those present in the observed distribution. It is known that under i.\,i.\,d assumption, even with infinite data, there is a limit to how fine-grained a causal structure we can identify. To overcome this limitation, recent work has explored using data originating from different, related environments to learn richer causal structure. These approaches implicitly rely on the independent causal mechanisms (ICM) principle, which postulates that the mechanism giving rise to an effect given its causes and the mechanism which generates the causes do not inform or influence each other. Thus, components of the causal model can independently change from environment to environment. Despite its wide application in machine learning and causal inference, there is a lack of statistical formalization of the ICM principle and how it enables identification of richer causal structures from grouped data. Here we present new causal de Finetti theorems which offer a first statistical formalization of ICM principle and show how causal structure identification is possible from exchangeable data. Our work provides theoretical justification for a broad range of techniques leveraging multi-environment data to learn causal structure.

A set of novel approaches for estimating epistemic uncertainty in deep neural networks with a single forward pass has recently emerged as a valid alternative to Bayesian Neural Networks. On the premise of informative representations, these deterministic uncertainty methods (DUMs) achieve strong performance on detecting out-of-distribution (OOD) data while adding negligible computational costs at inference time. However, it remains unclear whether DUMs are well calibrated and can seamlessly scale to real-world applications - both prerequisites for their practical deployment. To this end, we first provide a taxonomy of DUMs, and evaluate their calibration under continuous distributional shifts. Then, we extend them to semantic segmentation. We find that, while DUMs scale to realistic vision tasks and perform well on OOD detection, the practicality of current methods is undermined by poor calibration under distributional shifts.

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.

With the widespread adoption of large language models (LLMs), hallucinations, which are non-factual fabrications in model outputs, have become serious concerns. Reasoning capabilities have received attention as a self-verification process to improve output reliability. However, the effect of reasoning within a closed system where LLMs cannot rely on external tools or knowledge has yet to be clarified. We therefore conduct experiments under strict constraints (recommending peer-reviewed journal articles in computer science) to examine the effect of reasoning across multiple models (GPT-5.2 and Gemini 3 Flash). Our results reveal a problematic trade-off between constraint compliance and factual accuracy. Non-reasoning models exhibit high constraint violation rates (66-75%) but maintain factual accuracy, while reasoning models reduce violations (13-26%) but systematically distort known facts to satisfy constraints and increase complete fabrication. This trade-off pattern is consistent across both models despite different architectures, indicating a fundamental limitation of reasoning. Furthermore, reasoning does not uniformly improve output authenticity: effects diverge by model, reflecting different allocations of the compliance-truthfulness trade-off. These findings challenge the assumption that reasoning universally improves reliability: reasoning models trade honest constraint violations for detection-resistant distortions.

Large Language Models (LLMs) can produce surprisingly sophisticated estimates of their own uncertainty. However, it remains unclear to what extent this expressed confidence is tied to the reasoning, knowledge, or decision making of the model. To test this, we introduce RiskEval: a framework designed to evaluate whether models adjust their abstention policies in response to varying error penalties. Our evaluation of several frontier models reveals a critical dissociation: models are neither cost-aware when articulating their verbal confidence, nor strategically responsive when deciding whether to engage or abstain under high-penalty conditions. Even when extreme penalties render frequent abstention the mathematically optimal strategy, models almost never abstain, resulting in utility collapse. This indicates that calibrated verbal confidence scores may not be sufficient to create trustworthy and interpretable AI systems, as current models lack the strategic agency to convert uncertainty signals into optimal and risk-sensitive decisions.

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.

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.

We consider the problem of performing Bayesian inference in probabilistic models where observations are accompanied by uncertainty, referred to as "uncertain evidence." We explore how to interpret uncertain evidence, and by extension the importance of proper interpretation as it pertains to inference about latent variables. We consider a recently-proposed method "distributional evidence" as well as revisit two older methods: Jeffrey's rule and virtual evidence. We devise guidelines on how to account for uncertain evidence and we provide new insights, particularly regarding consistency. To showcase the impact of different interpretations of the same uncertain evidence, we carry out experiments in which one interpretation is defined as "correct." We then compare inference results from each different interpretation illustrating the importance of careful consideration of uncertain evidence.

We study online reinforcement learning in linear Markov decision processes with adversarial losses and bandit feedback, without prior knowledge on transitions or access to simulators. We introduce two algorithms that achieve improved regret performance compared to existing approaches. The first algorithm, although computationally inefficient, ensures a regret of mathcal{O}left(Kright), where K is the number of episodes. This is the first result with the optimal K dependence in the considered setting. The second algorithm, which is based on the policy optimization framework, guarantees a regret of mathcal{O}left(K^{3{4}} right) and is computationally efficient. Both our results significantly improve over the state-of-the-art: a computationally inefficient algorithm by Kong et al. [2023] with mathcal{O}left(K^{4{5}}+polyleft(1{lambda_{min}}right) right) regret, for some problem-dependent constant lambda_{min} that can be arbitrarily close to zero, and a computationally efficient algorithm by Sherman et al. [2023b] with mathcal{O}left(K^{6{7}} right) regret.

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.

Modern CI/CD pipelines integrating agent-generated code exhibit a structural failure in responsibility attribution. Decisions are executed through formally correct approval processes, yet no entity possesses both the authority to approve those decisions and the epistemic capacity to meaningfully understand their basis. We define this condition as responsibility vacuum: a state in which decisions occur, but responsibility cannot be attributed because authority and verification capacity do not coincide. We show that this is not a process deviation or technical defect, but a structural property of deployments where decision generation throughput exceeds bounded human verification capacity. We identify a scaling limit under standard deployment assumptions, including parallel agent generation, CI-based validation, and individualized human approval gates. Beyond a throughput threshold, verification ceases to function as a decision criterion and is replaced by ritualized approval based on proxy signals. Personalized responsibility becomes structurally unattainable in this regime. We further characterize a CI amplification dynamic, whereby increasing automated validation coverage raises proxy signal density without restoring human capacity. Under fixed time and attention constraints, this accelerates cognitive offloading in the broad sense and widens the gap between formal approval and epistemic understanding. Additional automation therefore amplifies, rather than mitigates, the responsibility vacuum. We conclude that unless organizations explicitly redesign decision boundaries or reassign responsibility away from individual decisions toward batch- or system-level ownership, responsibility vacuum remains an invisible but persistent failure mode in scaled agent deployments.

How would randomly shuffling feature vectors among nodes from the same class affect graph neural networks (GNNs)? The feature shuffle, intuitively, perturbs the dependence between graph topology and features (A-X dependence) for GNNs to learn from. Surprisingly, we observe a consistent and significant improvement in GNN performance following the feature shuffle. Having overlooked the impact of A-X dependence on GNNs, the prior literature does not provide a satisfactory understanding of the phenomenon. Thus, we raise two research questions. First, how should A-X dependence be measured, while controlling for potential confounds? Second, how does A-X dependence affect GNNs? In response, we (i) propose a principled measure for A-X dependence, (ii) design a random graph model that controls A-X dependence, (iii) establish a theory on how A-X dependence relates to graph convolution, and (iv) present empirical analysis on real-world graphs that align with the theory. We conclude that A-X dependence mediates the effect of graph convolution, such that smaller dependence improves GNN-based node classification.

Language models often pre-train on large unsupervised text corpora, then fine-tune on additional task-specific data. However, typical fine-tuning schemes do not prioritize the examples that they tune on. We show that, if you can prioritize informative training data, you can achieve better performance while using fewer labels. To do this we augment a language model with an epinet: a small additional network that helps to estimate model uncertainty and forms an epistemic neural network (ENN). ENNs are neural networks that can know what they don't know. Using an epinet to prioritize uncertain data, we can fine-tune BERT on GLUE tasks to the same performance while using 2x less data than training without prioritization. We also investigate performance in synthetic neural network generative models designed to build understanding. In each setting, using an epinet outperforms heuristic active learning schemes.

We develop a data-driven information-theoretic framework for sharp partial identification of causal effects under unmeasured confounding. Existing approaches often rely on restrictive assumptions, such as bounded or discrete outcomes; require external inputs (for example, instrumental variables, proxies, or user-specified sensitivity parameters); necessitate full structural causal model specifications; or focus solely on population-level averages while neglecting covariate-conditional effects. We overcome all four limitations simultaneously by establishing novel information-theoretic, data-driven divergence bounds. Our key theoretical contribution shows that the f-divergence between the observational distribution P(Y | A = a, X = x) and the interventional distribution P(Y | do(A = a), X = x) is upper bounded by a function of the propensity score alone. This result enables sharp partial identification of conditional causal effects directly from observational data, without requiring external sensitivity parameters, auxiliary variables, full structural specifications, or outcome boundedness assumptions. For practical implementation, we develop a semiparametric estimator satisfying Neyman orthogonality (Chernozhukov et al., 2018), which ensures root-n consistent inference even when nuisance functions are estimated via flexible machine learning methods. Simulation studies and real-world data applications, implemented in the GitHub repository (https://github.com/yonghanjung/Information-Theretic-Bounds), demonstrate that our framework provides tight and valid causal bounds across a wide range of data-generating processes.

We formalize constraint-based structure learning of the "true" causal graph from observed data when unobserved variables are also existent. We provide conditions for a "natural" family of constraint-based structure-learning algorithms that output graphs that are Markov equivalent to the causal graph. Under the faithfulness assumption, this natural family contains all exact structure-learning algorithms. We also provide a set of assumptions, under which any natural structure-learning algorithm outputs Markov equivalent graphs to the causal graph. These assumptions can be thought of as a relaxation of faithfulness, and most of them can be directly tested from (the underlying distribution) of the data, particularly when one focuses on structural causal models. We specialize the definitions and results for structural causal models.

Recent work in probability-domain knowledge distillation has established axiomatic frameworks for temperature scaling, multi-teacher aggregation, and bias-variance trade-offs in single-stage settings. However, the mathematical behavior of recursive or multi-generation distillation remains poorly understood, with prior approaches relying primarily on empirical heuristics. In this work, we introduce an axiomatic and operator-theoretic framework for recursive meta-distillation, formalizing iterative knowledge distillation as a sequence of probability-distribution operators with explicit anchoring to base teachers. We define structural axioms for valid meta-teacher construction and prove the existence of non-trivial operator families satisfying these axioms without specifying particular algorithms or loss functions. Under mild realizability and convexity assumptions, we show that anchored recursive distillation induces contraction in KL divergence, yielding geometric convergence to base teacher distributions and a unique, globally attractive fixed point. The contribution is foundational rather than algorithmic: the framework characterizes when recursive distillation is mathematically well-posed and convergent rather than error-accumulating, independent of model architecture, optimization details, or specific operator instantiations. These results provide a theoretical basis for understanding stability, bias-variance behavior, and failure modes in iterative and multi-teacher distillation under capacity constraints.

True self-evolution requires agents to act as lifelong learners that internalize novel experiences to solve future problems. However, rigorously measuring this foundational capability is hindered by two obstacles: the entanglement of prior knowledge, where ``new'' knowledge may appear in pre-training data, and the entanglement of reasoning complexity, where failures may stem from problem difficulty rather than an inability to recall learned knowledge. We introduce SE-Bench, a diagnostic environment that obfuscates the NumPy library and its API doc into a pseudo-novel package with randomized identifiers. Agents are trained to internalize this package and evaluated on simple coding tasks without access to documentation, yielding a clean setting where tasks are trivial with the new API doc but impossible for base models without it. Our investigation reveals three insights: (1) the Open-Book Paradox, where training with reference documentation inhibits retention, requiring "Closed-Book Training" to force knowledge compression into weights; (2) the RL Gap, where standard RL fails to internalize new knowledge completely due to PPO clipping and negative gradients; and (3) the viability of Self-Play for internalization, proving models can learn from self-generated, noisy tasks when coupled with SFT, but not RL. Overall, SE-Bench establishes a rigorous diagnostic platform for self-evolution with knowledge internalization. Our code and dataset can be found at https://github.com/thunlp/SE-Bench.

Tabular machine learning presents a paradox: modern models achieve state-of-the-art performance using high-dimensional (high-D), collinear, error-prone data, defying the "Garbage In, Garbage Out" mantra. To help resolve this, we synthesize principles from Information Theory, Latent Factor Models, and Psychometrics, clarifying that predictive robustness arises not solely from data cleanliness, but from the synergy between data architecture and model capacity. Partitioning predictor-space "noise" into "Predictor Error" and "Structural Uncertainty" (informational deficits from stochastic generative mappings), we prove that leveraging high-D sets of error-prone predictors asymptotically overcomes both types of noise, whereas cleaning a low-D set is fundamentally bounded by Structural Uncertainty. We demonstrate why "Informative Collinearity" (dependencies from shared latent causes) enhances reliability and convergence efficiency, and explain why increased dimensionality reduces the latent inference burden, enabling feasibility with finite samples. To address practical constraints, we propose "Proactive Data-Centric AI" to identify predictors that enable robustness efficiently. We also derive boundaries for Systematic Error Regimes and show why models that absorb "rogue" dependencies can mitigate assumption violations. Linking latent architecture to Benign Overfitting, we offer a first step towards a unified view of robustness to Outcome Error and predictor-space noise, while also delineating when traditional DCAI's focus on label cleaning remains powerful. By redefining data quality from item-level perfection to portfolio-level architecture, we provide a theoretical rationale for "Local Factories" -- learning from live, uncurated enterprise "data swamps" -- supporting a deployment paradigm shift from "Model Transfer" to "Methodology Transfer'' to overcome static generalizability limitations.

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

Popular offline reinforcement learning (RL) methods rely on conservatism, either by penalizing out-of-dataset actions or by restricting rollout horizons. In this work, we question the universality of this principle and instead revisit a complementary one: a Bayesian perspective. Rather than enforcing conservatism, the Bayesian approach tackles epistemic uncertainty in offline data by modeling a posterior distribution over plausible world models and training a history-dependent agent to maximize expected rewards, enabling test-time generalization. We first illustrate, in a bandit setting, that Bayesianism excels on low-quality datasets where conservatism fails. We then scale this principle to realistic tasks and show that long-horizon planning is critical for reducing value overestimation once conservatism is removed. To make this feasible, we introduce key design choices for performing and learning from long-horizon rollouts while controlling compounding errors. These yield our algorithm, NEUBAY, grounded in the neutral Bayesian principle. On D4RL and NeoRL benchmarks, NEUBAY generally matches or surpasses leading conservative algorithms, achieving new state-of-the-art on 7 datasets. Notably, it succeeds with rollout horizons of several hundred steps, contrary to dominant practice. Finally, we characterize datasets by quality and coverage, showing when NEUBAY is preferable to conservative methods. Together, we argue NEUBAY lays the foundation for a new practical direction in offline and model-based RL.

Cutting out an object and estimating its opacity mask, known as image matting, is a key task in image and video editing. Due to the highly ill-posed issue, additional inputs, typically user-defined trimaps or scribbles, are usually needed to reduce the uncertainty. Although effective, it is either time consuming or only suitable for experienced users who know where to place the strokes. In this work, we propose a decomposed-uncertainty-guided matting (dugMatting) algorithm, which explores the explicitly decomposed uncertainties to efficiently and effectively improve the results. Basing on the characteristic of these uncertainties, the epistemic uncertainty is reduced in the process of guiding interaction (which introduces prior knowledge), while the aleatoric uncertainty is reduced in modeling data distribution (which introduces statistics for both data and possible noise). The proposed matting framework relieves the requirement for users to determine the interaction areas by using simple and efficient labeling. Extensively quantitative and qualitative results validate that the proposed method significantly improves the original matting algorithms in terms of both efficiency and efficacy.

Vision-language models (VLMs) are increasingly deployed in high-stakes settings where reliable uncertainty quantification (UQ) is as important as predictive accuracy. Extended reasoning via chain-of-thought (CoT) prompting or reasoning-trained models has become ubiquitous in modern VLM pipelines, yet its effect on UQ reliability remains poorly understood. We show that reasoning consistently degrades the quality of most uncertainty estimates, even when it improves task accuracy. We identify implicit answer conditioning as the primary mechanism: as reasoning traces converge on a conclusion before the final answer is generated, token probabilities increasingly reflect consistency with the model's own reasoning trace rather than uncertainty about correctness. In effect, the model becomes overconfident in its answer. In contrast, agreement-based consistency remains robust and often improves under reasoning, making it a practical choice for uncertainty estimation in reasoning-enabled VLMs.

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

Large Language Models (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.

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.

A variety of recent papers discuss the application of Shapley values, a concept for explaining coalitional games, for feature attribution in machine learning. However, the correct way to connect a machine learning model to a coalitional game has been a source of controversy. The two main approaches that have been proposed differ in the way that they condition on known features, using either (1) an interventional or (2) an observational conditional expectation. While previous work has argued that one of the two approaches is preferable in general, we argue that the choice is application dependent. Furthermore, we argue that the choice comes down to whether it is desirable to be true to the model or true to the data. We use linear models to investigate this choice. After deriving an efficient method for calculating observational conditional expectation Shapley values for linear models, we investigate how correlation in simulated data impacts the convergence of observational conditional expectation Shapley values. Finally, we present two real data examples that we consider to be representative of possible use cases for feature attribution -- (1) credit risk modeling and (2) biological discovery. We show how a different choice of value function performs better in each scenario, and how possible attributions are impacted by modeling choices.

Large Language Models (LLMs) often generate outputs that lack grounding in real-world facts, a phenomenon known as hallucinations. Prior research has associated hallucinations with model uncertainty, leveraging this relationship for hallucination detection and mitigation. In this paper, we challenge the underlying assumption that all hallucinations are associated with uncertainty. Using knowledge detection and uncertainty measurement methods, we demonstrate that models can hallucinate with high certainty even when they have the correct knowledge. We further show that high-certainty hallucinations are consistent across models and datasets, distinctive enough to be singled out, and challenge existing mitigation methods. Our findings reveal an overlooked aspect of hallucinations, emphasizing the need to understand their origins and improve mitigation strategies to enhance LLM safety. The code is available at https://github.com/technion-cs-nlp/Trust_me_Im_wrong .

Scientific studies of consciousness rely on objects whose existence is assumed to be independent of any consciousness. On the contrary, we assume consciousness to be fundamental, and that one of the main features of consciousness is characterized as being other-dependent. We set up a framework which naturally subsumes this feature by defining a compact closed category where morphisms represent conscious processes. These morphisms are a composition of a set of generators, each being specified by their relations with other generators, and therefore co-dependent. The framework is general enough and fits well into a compositional model of consciousness. Interestingly, we also show how our proposal may become a step towards avoiding the hard problem of consciousness, and thereby address the combination problem of conscious experiences.

Reliable estimation of predictive uncertainty is crucial for machine learning applications, particularly in high-stakes scenarios where hedging against risks is essential. Despite its significance, there is no universal agreement on how to best quantify predictive uncertainty. In this work, we revisit core concepts to propose a framework for information-theoretic measures of predictive uncertainty. Our proposed framework categorizes predictive uncertainty measures according to two factors: (I) The predicting model (II) The approximation of the true predictive distribution. Examining all possible combinations of these two factors, we derive a set of predictive uncertainty measures that includes both known and newly introduced ones. We extensively evaluate these measures across a broad set of tasks, identifying conditions under which certain measures excel. Our findings show the importance of aligning the choice of uncertainty measure with the predicting model on in-distribution (ID) data, the limitations of epistemic uncertainty measures for out-of-distribution (OOD) data, and that the disentanglement between measures varies substantially between ID and OOD data. Together, these insights provide a more comprehensive understanding of predictive uncertainty measures, revealing their implicit assumptions and relationships.

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

Current artificial intelligence systems exhibit a fundamental architectural limitation: they resolve ambiguity prematurely. This premature semantic collapse--collapsing multiple valid interpretations into single outputs--stems from classical identity assumptions in neural architectures. We propose Non-Resolution Reasoning (NRR), a framework treating ambiguity retention as a valid reasoning mode. NRR introduces three principles: (1) Non-Identity (A neq A)--the same symbol refers to different entities across contexts; (2) Approximate Identity (A approx A)--entities share partial structural overlap without being identical; (3) Non-Resolution--conflicting interpretations coexist without forced convergence. We formalize these through Multi-Vector Embeddings for context-dependent representation, Non-Collapsing Attention for parallel interpretation retention, and Contextual Identity Tracking (CIT) for maintaining A neq A across inference. We illustrate NRR through case studies in paradox handling, creative generation, and context-dependent reasoning. Functional verification in a synthetic two-turn disambiguation task shows NRR-lite maintains high entropy (H = 0.91 bits, near-maximum 1.0) at ambiguous turns while standard architectures collapse early (H = 0.15 bits), preserving interpretive flexibility until context arrives. NRR challenges the assumption that meaning must collapse to be useful. The question is not whether AI should resolve ambiguity, but when, how, and under whose control.

Knowledge distillation is a model compression technique in which a compact "student" network is trained to replicate the predictive behavior of a larger "teacher" network. In logit-based knowledge distillation, it has become the de facto approach to augment cross-entropy with a distillation term. Typically, this term is either a KL divergence that matches marginal probabilities or a correlation-based loss that captures intra- and inter-class relationships. In every case, it acts as an additional term to cross-entropy. This term has its own weight, which must be carefully tuned. In this paper, we adopt a choice-theoretic perspective and recast knowledge distillation under the Plackett-Luce model by interpreting teacher logits as "worth" scores. We introduce "Plackett-Luce Distillation (PLD)", a weighted list-wise ranking loss. In PLD, the teacher model transfers knowledge of its full ranking of classes, weighting each ranked choice by its own confidence. PLD directly optimizes a single "teacher-optimal" ranking. The true label is placed first, followed by the remaining classes in descending teacher confidence. This process yields a convex and translation-invariant surrogate that subsumes weighted cross-entropy. Empirically, across CIFAR-100, ImageNet-1K, and MS-COCO, PLD achieves consistent gains across diverse architectures and distillation objectives, including divergence-based, correlation-based, and feature-based methods, in both homogeneous and heterogeneous teacher-student pairs.

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.

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.

This article presents Individual Conditional Expectation (ICE) plots, a tool for visualizing the model estimated by any supervised learning algorithm. Classical partial dependence plots (PDPs) help visualize the average partial relationship between the predicted response and one or more features. In the presence of substantial interaction effects, the partial response relationship can be heterogeneous. Thus, an average curve, such as the PDP, can obfuscate the complexity of the modeled relationship. Accordingly, ICE plots refine the partial dependence plot by graphing the functional relationship between the predicted response and the feature for individual observations. Specifically, ICE plots highlight the variation in the fitted values across the range of a covariate, suggesting where and to what extent heterogeneities might exist. In addition to providing a plotting suite for exploratory analysis, we include a visual test for additive structure in the data generating model. Through simulated examples and real data sets, we demonstrate how ICE plots can shed light on estimated models in ways PDPs cannot. Procedures outlined are available in the R package ICEbox.

A great deal of effort has been devoted to reducing the risk of spurious scientific discoveries, from the use of sophisticated validation techniques, to deep statistical methods for controlling the false discovery rate in multiple hypothesis testing. However, there is a fundamental disconnect between the theoretical results and the practice of data analysis: the theory of statistical inference assumes a fixed collection of hypotheses to be tested, or learning algorithms to be applied, selected non-adaptively before the data are gathered, whereas in practice data is shared and reused with hypotheses and new analyses being generated on the basis of data exploration and the outcomes of previous analyses. In this work we initiate a principled study of how to guarantee the validity of statistical inference in adaptive data analysis. As an instance of this problem, we propose and investigate the question of estimating the expectations of m adaptively chosen functions on an unknown distribution given n random samples. We show that, surprisingly, there is a way to estimate an exponential in n number of expectations accurately even if the functions are chosen adaptively. This gives an exponential improvement over standard empirical estimators that are limited to a linear number of estimates. Our result follows from a general technique that counter-intuitively involves actively perturbing and coordinating the estimates, using techniques developed for privacy preservation. We give additional applications of this technique to our question.

Large vision-language models (LVLMs) demonstrate remarkable capabilities in multimodal tasks but are prone to misinterpreting visual inputs, often resulting in hallucinations and unreliable outputs. To address these challenges, we propose Dropout Decoding, a novel inference-time approach that quantifies the uncertainty of visual tokens and selectively masks uncertain tokens to improve decoding. Our method measures the uncertainty of each visual token by projecting it onto the text space and decomposing it into aleatoric and epistemic components. Specifically, we focus on epistemic uncertainty, which captures perception-related errors more effectively. Inspired by dropout regularization, we introduce uncertainty-guided token dropout, which applies the dropout principle to input visual tokens instead of model parameters, and during inference rather than training. By aggregating predictions from an ensemble of masked decoding contexts, Dropout Decoding robustly mitigates errors arising from visual token misinterpretations. Evaluations on benchmarks including CHAIR, THRONE, and MMBench demonstrate that Dropout Decoding significantly reduces object hallucinations (OH) and enhances both reliability and quality of LVLM outputs across diverse visual contexts.

Popular approaches for quantifying predictive uncertainty in deep neural networks often involve distributions over weights or multiple models, for instance via Markov Chain sampling, ensembling, or Monte Carlo dropout. These techniques usually incur overhead by having to train multiple model instances or do not produce very diverse predictions. This comprehensive and extensive survey aims to familiarize the reader with an alternative class of models based on the concept of Evidential Deep Learning: For unfamiliar data, they aim to admit "what they don't know", and fall back onto a prior belief. Furthermore, they allow uncertainty estimation in a single model and forward pass by parameterizing distributions over distributions. This survey recapitulates existing works, focusing on the implementation in a classification setting, before surveying the application of the same paradigm to regression. We also reflect on the strengths and weaknesses compared to other existing methods and provide the most fundamental derivations using a unified notation to aid future research.

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

We introduce Probabilistic Dependent Type Systems (PDTS) via a functional language based on a subsystem of intuitionistic type theory including dependent sums and products, which is expanded to include stochastic functions. We provide a sampling-based semantics for the language based on non-deterministic beta reduction. Further, we derive a probabilistic logic from the PDTS introduced as a direct result of the Curry-Howard isomorphism. The probabilistic logic derived is shown to provide a universal representation for finite discrete distributions.

For text-based AI systems to interact in the real world, causal reasoning is an essential skill. Since interventional data is costly to generate, we study to what extent an agent can learn causal reasoning from passive data. Specifically, we consider an axiomatic training setup where an agent learns from multiple demonstrations of a causal axiom (or rule), rather than incorporating the axiom as an inductive bias or inferring it from data values. A key question is whether the agent would learn to generalize from the axiom demonstrations to new scenarios. For example, if a transformer model is trained on demonstrations of the causal transitivity axiom over small graphs, would it generalize to applying the transitivity axiom over large graphs? Our results, based on a novel axiomatic training scheme, indicate that such generalization is possible. We consider the task of inferring whether a variable causes another variable, given a causal graph structure. We find that a 67 million parameter transformer model, when trained on linear causal chains (along with some noisy variations) can generalize well to new kinds of graphs, including longer causal chains, causal chains with reversed order, and graphs with branching; even when it is not explicitly trained for such settings. Our model performs at par (or even better) than many larger language models such as GPT-4, Gemini Pro, and Phi-3. Overall, our axiomatic training framework provides a new paradigm of learning causal reasoning from passive data that can be used to learn arbitrary axioms, as long as sufficient demonstrations can be generated.

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

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.

Understanding the abilities of LLMs to reason about natural language plans, such as instructional text and recipes, is critical to reliably using them in decision-making systems. A fundamental aspect of plans is the temporal order in which their steps needs to be executed, which reflects the underlying causal dependencies between them. We introduce CaT-Bench, a benchmark of Step Order Prediction questions, which test whether a step must necessarily occur before or after another in cooking recipe plans. We use this to evaluate how well frontier LLMs understand causal and temporal dependencies. We find that SOTA LLMs are underwhelming (best zero-shot is only 0.59 in F1), and are biased towards predicting dependence more often, perhaps relying on temporal order of steps as a heuristic. While prompting for explanations and using few-shot examples improve performance, the best F1 result is only 0.73. Further, human evaluation of explanations along with answer correctness show that, on average, humans do not agree with model reasoning. Surprisingly, we also find that explaining after answering leads to better performance than normal chain-of-thought prompting, and LLM answers are not consistent across questions about the same step pairs. Overall, results show that LLMs' ability to detect dependence between steps has significant room for improvement.

Truly reliable AI requires more than simply scaling up knowledge; it demands the ability to know what it knows and when it does not. Yet recent research shows that even the best LLMs misjudge their own competence in more than one in five cases, making any response born of such internal uncertainty impossible to fully trust. Inspired by self-improvement reinforcement learning techniques that require minimal data, we present a simple but powerful framework KnowRL that strengthens a model's internal understanding of its own feasibility boundaries, enabling safer and more responsible behaviour. Our framework combines two components: (i) introspection, where the model generates and classifies tasks it judges feasible or infeasible, and (ii) consensus-based rewarding, where stability of self-knowledge assessment is reinforced through internal agreement. By using internally generated data, this design strengthens consistency in self-knowledge and entirely avoids costly external supervision. In experiments on LLaMA-3.1-8B and Qwen-2.5-7B, KnowRL steadily improved self-knowledge, validated by both intrinsic self-consistency and extrinsic benchmarking. With nothing more than a small seed set and no external supervision, our method drove gains as high as 28% in accuracy and 12% in F1, outperforming baselines in just a few iterations. Our framework essentially unlocks the untapped capacity of LLMs to self-improve their knowledge awareness, opening the door to reliable, more accountable AI and safer deployment in critical applications. Owing to its simplicity and independence from external effort, we encourage applying this reliability-enhancing process to all future models.

Explanations for AI models in high-stakes domains like medicine often lack verifiability, which can hinder trust. To address this, we propose an interactive agent that produces explanations through an auditable sequence of actions. The agent learns a policy to strategically seek external visual evidence to support its diagnostic reasoning. This policy is optimized using reinforcement learning, resulting in a model that is both efficient and generalizable. Our experiments show that this action-based reasoning process significantly improves calibrated accuracy, reducing the Brier score by 18\% compared to a non-interactive baseline. To validate the faithfulness of the agent's explanations, we introduce a causal intervention method. By masking the visual evidence the agent chooses to use, we observe a measurable degradation in its performance (DeltaBrier=+0.029), confirming that the evidence is integral to its decision-making process. Our work provides a practical framework for building AI systems with verifiable and faithful reasoning capabilities.

Agentic reasoning enables large reasoning models (LRMs) to dynamically acquire external knowledge, but yet optimizing the retrieval process remains challenging due to the lack of dense, principled reward signals. In this paper, we introduce InfoReasoner, a unified framework that incentivizes effective information seeking via a synthetic semantic information gain reward. Theoretically, we redefine information gain as uncertainty reduction over the model's belief states, establishing guarantees, including non-negativity, telescoping additivity, and channel monotonicity. Practically, to enable scalable optimization without manual retrieval annotations, we propose an output-aware intrinsic estimator that computes information gain directly from the model's output distributions using semantic clustering via bidirectional textual entailment. This intrinsic reward guides the policy to maximize epistemic progress, enabling efficient training via Group Relative Policy Optimxization (GRPO). Experiments across seven question-answering benchmarks demonstrate that InfoReasoner consistently outperforms strong retrieval-augmented baselines, achieving up to 5.4% average accuracy improvement. Our work provides a theoretically grounded and scalable path toward agentic reasoning with retrieval.

We propose the Bayes-UCBVI algorithm for reinforcement learning in tabular, stage-dependent, episodic Markov decision process: a natural extension of the Bayes-UCB algorithm by Kaufmann et al. (2012) for multi-armed bandits. Our method uses the quantile of a Q-value function posterior as upper confidence bound on the optimal Q-value function. For Bayes-UCBVI, we prove a regret bound of order O(H^3SAT) where H is the length of one episode, S is the number of states, A the number of actions, T the number of episodes, that matches the lower-bound of Ω(H^3SAT) up to poly-log terms in H,S,A,T for a large enough T. To the best of our knowledge, this is the first algorithm that obtains an optimal dependence on the horizon H (and S) without the need for an involved Bernstein-like bonus or noise. Crucial to our analysis is a new fine-grained anti-concentration bound for a weighted Dirichlet sum that can be of independent interest. We then explain how Bayes-UCBVI can be easily extended beyond the tabular setting, exhibiting a strong link between our algorithm and Bayesian bootstrap (Rubin, 1981).

Stochastic gradient Markov Chain Monte Carlo (SGMCMC) is considered the gold standard for Bayesian inference in large-scale models, such as Bayesian neural networks. Since practitioners face speed versus accuracy tradeoffs in these models, variational inference (VI) is often the preferable option. Unfortunately, VI makes strong assumptions on both the factorization and functional form of the posterior. In this work, we propose a new non-parametric variational approximation that makes no assumptions about the approximate posterior's functional form and allows practitioners to specify the exact dependencies the algorithm should respect or break. The approach relies on a new Langevin-type algorithm that operates on a modified energy function, where parts of the latent variables are averaged over samples from earlier iterations of the Markov chain. This way, statistical dependencies can be broken in a controlled way, allowing the chain to mix faster. This scheme can be further modified in a "dropout" manner, leading to even more scalability. We test our scheme for ResNet-20 on CIFAR-10, SVHN, and FMNIST. In all cases, we find improvements in convergence speed and/or final accuracy compared to SG-MCMC and VI.

We show that a GPT-3 model can learn to express uncertainty about its own answers in natural language -- without use of model logits. When given a question, the model generates both an answer and a level of confidence (e.g. "90% confidence" or "high confidence"). These levels map to probabilities that are well calibrated. The model also remains moderately calibrated under distribution shift, and is sensitive to uncertainty in its own answers, rather than imitating human examples. To our knowledge, this is the first time a model has been shown to express calibrated uncertainty about its own answers in natural language. For testing calibration, we introduce the CalibratedMath suite of tasks. We compare the calibration of uncertainty expressed in words ("verbalized probability") to uncertainty extracted from model logits. Both kinds of uncertainty are capable of generalizing calibration under distribution shift. We also provide evidence that GPT-3's ability to generalize calibration depends on pre-trained latent representations that correlate with epistemic uncertainty over its answers.

A well-calibrated model should express confidence that matches its actual accuracy -- when it claims 80\% confidence, it should be correct 80\% of the time. While large language models (LLMs) have achieved remarkable performance across diverse tasks, their epistemic calibration remains poorly understood. We introduce KalshiBench, a benchmark of 300 prediction market questions from Kalshi, a CFTC-regulated exchange, with verifiable real-world outcomes occurring after model training cutoffs. Unlike traditional benchmarks measuring accuracy on static knowledge, KalshiBench evaluates whether models can appropriately quantify uncertainty about genuinely unknown future events. We evaluate five frontier models -- Claude Opus 4.5, GPT-5.2, DeepSeek-V3.2, Qwen3-235B, and Kimi-K2 -- and find systematic overconfidence across all models. Even the best-calibrated model (Claude Opus 4.5, ECE=0.120) shows substantial calibration errors, while reasoning-enhanced models like GPT-5.2-XHigh exhibit worse calibration (ECE=0.395) despite comparable accuracy. Critically, only one model achieves a positive Brier Skill Score, indicating most models perform worse than simply predicting base rates. Our findings suggest that scaling and enhanced reasoning do not automatically confer calibration benefits, highlighting epistemic calibration as a distinct capability requiring targeted development.