Daily Papers

Deterministic neural networks (NNs) are increasingly being deployed in safety critical domains, where calibrated, robust, and efficient measures of uncertainty are crucial. In this paper, we propose a novel method for training non-Bayesian NNs to estimate a continuous target as well as its associated evidence in order to learn both aleatoric and epistemic uncertainty. We accomplish this by placing evidential priors over the original Gaussian likelihood function and training the NN to infer the hyperparameters of the evidential distribution. We additionally impose priors during training such that the model is regularized when its predicted evidence is not aligned with the correct output. Our method does not rely on sampling during inference or on out-of-distribution (OOD) examples for training, thus enabling efficient and scalable uncertainty learning. We demonstrate learning well-calibrated measures of uncertainty on various benchmarks, scaling to complex computer vision tasks, as well as robustness to adversarial and OOD test samples.

Although existing stereo matching models have achieved continuous improvement, they often face issues related to trustworthiness due to the absence of uncertainty estimation. Additionally, effectively leveraging multi-scale and multi-view knowledge of stereo pairs remains unexplored. In this paper, we introduce the Evidential Local-global Fusion (ELF) framework for stereo matching, which endows both uncertainty estimation and confidence-aware fusion with trustworthy heads. Instead of predicting the disparity map alone, our model estimates an evidential-based disparity considering both aleatoric and epistemic uncertainties. With the normal inverse-Gamma distribution as a bridge, the proposed framework realizes intra evidential fusion of multi-level predictions and inter evidential fusion between cost-volume-based and transformer-based stereo matching. Extensive experimental results show that the proposed framework exploits multi-view information effectively and achieves state-of-the-art overall performance both on accuracy and cross-domain generalization. The codes are available at https://github.com/jimmy19991222/ELFNet.

Deep neural networks (DNNs) have been shown to perform well on exclusive, multi-class classification tasks. However, when different classes have similar visual features, it becomes challenging for human annotators to differentiate them. This scenario necessitates the use of composite class labels. In this paper, we propose a novel framework called Hyper-Evidential Neural Network (HENN) that explicitly models predictive uncertainty due to composite class labels in training data in the context of the belief theory called Subjective Logic (SL). By placing a grouped Dirichlet distribution on the class probabilities, we treat predictions of a neural network as parameters of hyper-subjective opinions and learn the network that collects both single and composite evidence leading to these hyper-opinions by a deterministic DNN from data. We introduce a new uncertainty type called vagueness originally designed for hyper-opinions in SL to quantify composite classification uncertainty for DNNs. Our results demonstrate that HENN outperforms its state-of-the-art counterparts based on four image datasets. The code and datasets are available at: https://github.com/Hugo101/HyperEvidentialNN.

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.

In a real-world scenario, human actions are typically out of the distribution from training data, which requires a model to both recognize the known actions and reject the unknown. Different from image data, video actions are more challenging to be recognized in an open-set setting due to the uncertain temporal dynamics and static bias of human actions. In this paper, we propose a Deep Evidential Action Recognition (DEAR) method to recognize actions in an open testing set. Specifically, we formulate the action recognition problem from the evidential deep learning (EDL) perspective and propose a novel model calibration method to regularize the EDL training. Besides, to mitigate the static bias of video representation, we propose a plug-and-play module to debias the learned representation through contrastive learning. Experimental results show that our DEAR method achieves consistent performance gain on multiple mainstream action recognition models and benchmarks. Code and pre-trained models are available at {\url{https://www.rit.edu/actionlab/dear}}.

Pretrained models have become standard in both vision and language, yet they typically do not provide reliable measures of confidence. Existing uncertainty estimation methods, such as deep ensembles and MC dropout, are often too computationally expensive to deploy in practice. Evidential Deep Learning (EDL) offers a more efficient alternative, but it requires models to be trained to output evidential quantities from the start, which is rarely true for pretrained networks. To enable EDL-style uncertainty estimation in pretrained models, we propose the Evidential Transformation Network (ETN), a lightweight post-hoc module that converts a pretrained predictor into an evidential model. ETN operates in logit space: it learns a sample-dependent affine transformation of the logits and interprets the transformed outputs as parameters of a Dirichlet distribution for uncertainty estimation. We evaluate ETN on image classification and large language model question-answering benchmarks under both in-distribution and out-of-distribution settings. ETN consistently improves uncertainty estimation over post-hoc baselines while preserving accuracy and adding only minimal computational overhead.

Reliable uncertainty quantification is essential for deploying deep learning models in high-stakes settings, where out-of-distribution and adversarial inputs can induce confident but unreliable predictions. Evidential Deep Learning provides efficient uncertainty estimates in a single forward pass, but can still assign high evidential strength to inputs that are poorly supported by the learned representation, such as adversarial inputs. We introduce CLEAR, a lightweight, task-agnostic post-hoc method that improves evidential robustness without retraining or altering the base prediction. Using held-out calibration data, CLEAR characterises the group-conditioned geometry of the model's latent space. At inference, it efficiently generates perturbation views directly in the latent space and measures their conflict relative to the calibrated geometry of the predicted group. High latent conflict indicates unsupported evidence, which CLEAR uses to selectively reduce evidential strength while retaining evidence for latent-consistent inputs. On ImageNetrightarrowCUB, CLEAR improves OOD and adversarial AUROC by +8.29 and +5.01 while running 17.4times faster than competing post-hoc methods while preserving predictive performance across classification, regression, and object detection benchmarks.

Uncertainty estimation is a key factor that makes deep learning reliable in practical applications. Recently proposed evidential neural networks explicitly account for different uncertainties by treating the network's outputs as evidence to parameterize the Dirichlet distribution, and achieve impressive performance in uncertainty estimation. However, for high data uncertainty samples but annotated with the one-hot label, the evidence-learning process for those mislabeled classes is over-penalized and remains hindered. To address this problem, we propose a novel method, Fisher Information-based Evidential Deep Learning (I-EDL). In particular, we introduce Fisher Information Matrix (FIM) to measure the informativeness of evidence carried by each sample, according to which we can dynamically reweight the objective loss terms to make the network more focused on the representation learning of uncertain classes. The generalization ability of our network is further improved by optimizing the PAC-Bayesian bound. As demonstrated empirically, our proposed method consistently outperforms traditional EDL-related algorithms in multiple uncertainty estimation tasks, especially in the more challenging few-shot classification settings.

Zero-shot learning (ZSL) enables the recognition of novel classes by leveraging semantic knowledge transfer from known to unknown categories. This knowledge, typically encapsulated in attribute descriptions, aids in identifying class-specific visual features, thus facilitating visual-semantic alignment and improving ZSL performance. However, real-world challenges such as distribution imbalances and attribute co-occurrence among instances often hinder the discernment of local variances in images, a problem exacerbated by the scarcity of fine-grained, region-specific attribute annotations. Moreover, the variability in visual presentation within categories can also skew attribute-category associations. In response, we propose a bidirectional cross-modal ZSL approach CREST. It begins by extracting representations for attribute and visual localization and employs Evidential Deep Learning (EDL) to measure underlying epistemic uncertainty, thereby enhancing the model's resilience against hard negatives. CREST incorporates dual learning pathways, focusing on both visual-category and attribute-category alignments, to ensure robust correlation between latent and observable spaces. Moreover, we introduce an uncertainty-informed cross-modal fusion technique to refine visual-attribute inference. Extensive experiments demonstrate our model's effectiveness and unique explainability across multiple datasets. Our code and data are available at: https://github.com/JethroJames/CREST

In real-world scenarios, typical visual recognition systems could fail under two major causes, i.e., the misclassification between known classes and the excusable misbehavior on unknown-class images. To tackle these deficiencies, flexible visual recognition should dynamically predict multiple classes when they are unconfident between choices and reject making predictions when the input is entirely out of the training distribution. Two challenges emerge along with this novel task. First, prediction uncertainty should be separately quantified as confusion depicting inter-class uncertainties and ignorance identifying out-of-distribution samples. Second, both confusion and ignorance should be comparable between samples to enable effective decision-making. In this paper, we propose to model these two sources of uncertainty explicitly with the theory of Subjective Logic. Regarding recognition as an evidence-collecting process, confusion is then defined as conflicting evidence, while ignorance is the absence of evidence. By predicting Dirichlet concentration parameters for singletons, comprehensive subjective opinions, including confusion and ignorance, could be achieved via further evidence combinations. Through a series of experiments on synthetic data analysis, visual recognition, and open-set detection, we demonstrate the effectiveness of our methods in quantifying two sources of uncertainties and dealing with flexible recognition.

Existing Video Temporal Grounding (VTG) models excel in accuracy but often overlook open-world challenges posed by open-vocabulary queries and untrimmed videos. This leads to unreliable predictions for noisy, corrupted, and out-of-distribution data. Adapting VTG models to dynamically estimate uncertainties based on user input can address this issue. To this end, we introduce SRAM, a robust network module that benefits from a two-stage cross-modal alignment task. More importantly, it integrates Deep Evidential Regression (DER) to explicitly and thoroughly quantify uncertainty during training, thus allowing the model to say "I do not know" in scenarios beyond its handling capacity. However, the direct application of traditional DER theory and its regularizer reveals structural flaws, leading to unintended constraints in VTG tasks. In response, we develop a simple yet effective Geom-regularizer that enhances the uncertainty learning framework from the ground up. To the best of our knowledge, this marks the first successful attempt of DER in VTG. Our extensive quantitative and qualitative results affirm the effectiveness, robustness, and interpretability of our modules and the uncertainty learning paradigm in VTG tasks. The code will be made available.

Geometric foundation models hold promise for unconstrained dense geometry prediction from uncalibrated images. However, in current feed-forward designs, their predicted confidence scores are heuristic, lack probabilistic interpretation, and often fail to indicate where and how much the predicted geometry can be trusted. To address this gap, we present Trust3R, a lightweight evidential uncertainty framework for feed-forward 3D reconstruction. Trust3R combines gated residual mean refinement with a Normal-Inverse-Wishart evidential head, yielding a closed-form multivariate Student-t distribution for per-point geometric uncertainty. This design provides probabilistically grounded pointmap uncertainty estimates while adding moderate inference overhead. We evaluate on diverse indoor and outdoor benchmarks and compare against MASt3R's built-in confidence map as well as common uncertainty-aware baselines spanning single-pass heteroscedastic regression and sampling-based methods such as MC dropout and deep ensembles. Experimental results show that Trust3R consistently improves risk-coverage and sparsification, and generally improves geometric accuracy. These gains are reflected in stronger uncertainty ranking across benchmarks, with 25% lower AURC and 41% lower AUSE on ScanNet++, providing a practical reliability signal for uncertainty-aware weighting in downstream geometry pipelines. The project page and code are available at https://trust3r-z.github.io/.

Accurate air quality forecasting is crucial for protecting public health and guiding environmental policy, yet it remains challenging due to nonlinear spatiotemporal dynamics, wind-driven transport, and distribution shifts across regions. Physics-based models are interpretable but computationally expensive and often rely on restrictive assumptions, whereas purely data-driven models can be accurate but may lack robustness and calibrated uncertainty. To address these limitations, we propose Neural Dynamic Diffusion-Advection Fields (NeuroDDAF), a physics-informed forecasting framework that unifies neural representation learning with open-system transport modeling. NeuroDDAF integrates (i) a GRU-Graph Attention encoder to capture temporal dynamics and wind-aware spatial interactions, (ii) a Fourier-domain diffusion-advection module with learnable residuals, (iii) a wind-modulated latent Neural ODE to model continuous-time evolution under time-varying connectivity, and (iv) an evidential fusion mechanism that adaptively combines physics-guided and neural forecasts while quantifying uncertainty. Experiments on four urban datasets (Beijing, Shenzhen, Tianjin, and Ancona) across 1-3 day horizons show that NeuroDDAF consistently outperforms strong baselines, including AirPhyNet, achieving up to 9.7% reduction in RMSE and 9.4% reduction in MAE on long-term forecasts. On the Beijing dataset, NeuroDDAF attains an RMSE of 41.63 μg/m^3 for 1-day prediction and 48.88 μg/m^3 for 3-day prediction, representing the best performance among all compared methods. In addition, NeuroDDAF improves cross-city generalization and yields well-calibrated uncertainty estimates, as confirmed by ensemble variance analysis and case studies under varying wind conditions.

Fine-tuned large language models (LLMs) often exhibit overconfidence, particularly when trained on small datasets, resulting in poor calibration and inaccurate uncertainty estimates. Evidential Deep Learning (EDL), an uncertainty-aware approach, enables uncertainty estimation in a single forward pass, making it a promising method for calibrating fine-tuned LLMs. However, despite its computational efficiency, EDL is prone to overfitting, as its training objective can result in overly concentrated probability distributions. To mitigate this, we propose regularizing EDL by incorporating an information bottleneck (IB). Our approach IB-EDL suppresses spurious information in the evidence generated by the model and encourages truly predictive information to influence both the predictions and uncertainty estimates. Extensive experiments across various fine-tuned LLMs and tasks demonstrate that IB-EDL outperforms both existing EDL and non-EDL approaches. By improving the trustworthiness of LLMs, IB-EDL facilitates their broader adoption in domains requiring high levels of confidence calibration. Code is available at https://github.com/sandylaker/ib-edl.

Accurate protein-ligand binding affinity prediction is central to computational drug discovery, yet modern docking engines frequently disagree without indicating which prediction to trust. Consensus scoring and ensemble methods improve mean accuracy but treat all predictions identically without interpretable confidence measures or uncertainty decomposition, ignoring the chemical context of each protein-ligand pair. To address this limitation, we introduce RELIABLE-BA (RELIABiLity-aware Evidential fusion for Binding Affinity), an evidential framework for multi-engine binding affinity prediction. Our model comprises three steps: (1) modeling each engine as an evidential expert via Normal-Inverse-Gamma distributions, (2) scaling epistemic uncertainty through learned reliability from molecular context while preserving each expert's predictive mean, and (3) fusing experts through closed-form aggregation that captures both individual uncertainty and inter-engine disagreement. Experiments on the PDBBind and BDB2020+ benchmarks demonstrate competitive point prediction with substantially improved uncertainty calibration, and additional validation on the SARS-CoV-2 Mpro dataset and 5HT2A receptor demonstrates applicability to clinically relevant drug targets. Crucially, these uncertainty estimates enable reliable filtering of protein-ligand pairs, reducing prediction error by up to 25% when retaining only high-confidence pairs. To our knowledge, RELIABLE-BA is the first multi-engine binding affinity prediction framework to combine evidential fusion with context-dependent reliability, offering a principled path toward trustworthy AI-guided drug discovery. Our code is publicly available at https://github.com/yongchand/RELIABLE-BA.

A defining problem of the Anthropocene is to model the physical Earth and human societies as one coupled system, yet no learned representation spans their observational breadth. We argue the obstacle is geometric: the physical Earth is measured as continuous fields that ignore political borders, whereas societies are reported for administrative units. Earth-system foundation models serve the first geometry; coupling it to the second has required lossy averaging over borders. We introduce TerraNova, a foundation model trained on 1,024 physical and societal records in their native geometries: 512 gridded Earth-system fields and 512 national indicators. Dedicated encoders represent location, country, time and task, cross-modal transformers fuse them into a shared spatiotemporal state, and a hypernetwork generates a per-query decoder whose evidential head returns a predictive distribution. Two contrastive objectives couple the representation: a population-weighted alignment between each country and coordinates in its territory, and one to pretrained geospatial embeddings carrying image-derived semantics. Read out through that decoder, the representation is competitive with purpose-built geospatial encoders while spanning axes they do not represent (time, oceans and uncertainty) and supporting country-level capabilities. The frozen backbone reconstructs dense fields from sparse observations and adapts to unseen variables in minutes on consumer hardware.

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

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.

Accurate classification of computed tomography (CT) images is essential for diagnosis and treatment planning, but existing methods often struggle with the subtle and spatially diverse nature of pathological features. Current approaches typically process images uniformly, limiting their ability to detect localized abnormalities that require focused analysis. We introduce UGPL, an uncertainty-guided progressive learning framework that performs a global-to-local analysis by first identifying regions of diagnostic ambiguity and then conducting detailed examination of these critical areas. Our approach employs evidential deep learning to quantify predictive uncertainty, guiding the extraction of informative patches through a non-maximum suppression mechanism that maintains spatial diversity. This progressive refinement strategy, combined with an adaptive fusion mechanism, enables UGPL to integrate both contextual information and fine-grained details. Experiments across three CT datasets demonstrate that UGPL consistently outperforms state-of-the-art methods, achieving improvements of 3.29%, 2.46%, and 8.08% in accuracy for kidney abnormality, lung cancer, and COVID-19 detection, respectively. Our analysis shows that the uncertainty-guided component provides substantial benefits, with performance dramatically increasing when the full progressive learning pipeline is implemented. Our code is available at: https://github.com/shravan-18/UGPL

Language models (LM) are capable of remarkably complex linguistic tasks; however, numerical reasoning is an area in which they frequently struggle. An important but rarely evaluated form of reasoning is understanding probability distributions. In this paper, we focus on evaluating the probabilistic reasoning capabilities of LMs using idealized and real-world statistical distributions. We perform a systematic evaluation of state-of-the-art LMs on three tasks: estimating percentiles, drawing samples, and calculating probabilities. We evaluate three ways to provide context to LMs 1) anchoring examples from within a distribution or family of distributions, 2) real-world context, 3) summary statistics on which to base a Normal approximation. Models can make inferences about distributions, and can be further aided by the incorporation of real-world context, example shots and simplified assumptions, even if these assumptions are incorrect or misspecified. To conduct this work, we developed a comprehensive benchmark distribution dataset with associated question-answer pairs that we will release publicly.

In-context learning is commonly interpreted as a form of conditional inference, in which the prompt specifies a context and the model's output is treated as an estimate of the corresponding conditional distribution. If this interpretation holds, then LLM estimates should satisfy basic probabilistic identities. In particular, the law of total probability asserts that prior-weighted conditional distributions aggregate into population-level marginals over any valid partition of the population. In this work, we investigate to what extent LLM estimates adhere to this self-consistency principle. We use binary trees as an evaluation scaffold to recursively partition a population into increasingly fine-grained subpopulations. We then prompt LLMs with verbalized subpopulation descriptions in context, aggregate the resulting estimates back into population-level estimates, and compare them across partitions of varying granularity. Applying this protocol across problem domains and state-of-the-art frontier models, we show widespread violations of basic consistency properties. An in-depth study of persona prompting reveals a pattern we call the macro fallacy: estimates reconstructed from more fine-grained subpopulation responses are often better aligned with human reference data than direct population-level estimates. This effect persists across variations in tree structure and estimation task, and can be partially recovered through implicit prompting. Together, these findings suggest that models possess relevant subpopulation knowledge but do not reliably propagate it into aggregate estimates. This gap establishes statistical self-consistency as an unsaturated, reference-free criterion for evaluating LLMs.

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.

We consider the problem of weakly supervised object detection, where the training samples are annotated using only image-level labels that indicate the presence or absence of an object category. In order to model the uncertainty in the location of the objects, we employ a dissimilarity coefficient based probabilistic learning objective. The learning objective minimizes the difference between an annotation agnostic prediction distribution and an annotation aware conditional distribution. The main computational challenge is the complex nature of the conditional distribution, which consists of terms over hundreds or thousands of variables. The complexity of the conditional distribution rules out the possibility of explicitly modeling it. Instead, we exploit the fact that deep learning frameworks rely on stochastic optimization. This allows us to use a state of the art discrete generative model that can provide annotation consistent samples from the conditional distribution. Extensive experiments on PASCAL VOC 2007 and 2012 data sets demonstrate the efficacy of our proposed approach.

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

Video Large Language Models (Video-LLMs) are rapidly improving, yet current Video Question Answering (VideoQA) benchmarks often allow questions to be answered from a single salient cue, under-testing reasoning that must aggregate multiple, temporally separated visual evidence. We present HERBench, a VideoQA benchmark purpose-built to assess multi-evidence integration across time. Each question requires aggregating at least three non-overlapping evidential cues across distinct video segments, so neither language priors nor a single snapshot can suffice. HERBench comprises 26K five-way multiple-choice questions organized into twelve compositional tasks that probe identity binding, cross-entity relations, temporal ordering, co-occurrence verification, and counting. To make evidential demand measurable, we introduce the Minimum Required Frame-Set (MRFS), the smallest number of frames a model must fuse to answer correctly, and show that HERBench imposes substantially higher demand than prior datasets (mean MRFS 5.5 vs. 2.6-4.2). Evaluating 13 state-of-the-art Video-LLMs on HERBench reveals pervasive failures: accuracies of 31-42% are only slightly above the 20% random-guess baseline. We disentangle this failure into two critical bottlenecks: (1) a retrieval deficit, where frame selectors overlook key evidence, and (2) a fusion deficit, where models fail to integrate information even when all necessary evidence is provided. By making cross-time evidence both unavoidable and quantifiable, HERBench establishes a principled target for advancing robust, compositional video understanding.

LLM-based agents are increasingly used to simulate deliberative interactions such as negotiation, conflict resolution, and multi-turn opinion exchange. Yet generated transcripts often do not reveal why an agent's stance changes: movement may reflect evidence uptake, anchoring, role drift, echoing, or changed prompt and retrieval context. We introduce the Belief Engine (BE), an auditable belief-update layer that treats "belief" as an evidential state over a proposition and exposes it as scalar stance. BE extracts arguments into structured memory and updates stance with a log-odds rule controlled by evidence uptake u and prior anchoring a. Across multiple base LLMs, parameter sweeps show that these controls reliably shape stance dynamics while preserving an evidence-level update trail. On DEBATE, a human deliberation dataset with pre/post opinions, BE best reconstructs participants whose final stance follows extracted evidence; stable and evidence-opposed cases instead point to anchoring or factors outside the extracted evidence stream. BE provides configurable infrastructure for studying evidence-grounded deliberation, where openness, commitment, convergence, and disagreement can be tied to explicit update assumptions rather than hidden prompt effects.

Learning from Label Proportions (LLP) is a learning problem where only aggregate level labels are available for groups of instances, called bags, during training, and the aim is to get the best performance at the instance-level on the test data. This setting arises in domains like advertising and medicine due to privacy considerations. We propose a novel algorithmic framework for this problem that iteratively performs two main steps. For the first step (Pseudo Labeling) in every iteration, we define a Gibbs distribution over binary instance labels that incorporates a) covariate information through the constraint that instances with similar covariates should have similar labels and b) the bag level aggregated label. We then use Belief Propagation (BP) to marginalize the Gibbs distribution to obtain pseudo labels. In the second step (Embedding Refinement), we use the pseudo labels to provide supervision for a learner that yields a better embedding. Further, we iterate on the two steps again by using the second step's embeddings as new covariates for the next iteration. In the final iteration, a classifier is trained using the pseudo labels. Our algorithm displays strong gains against several SOTA baselines (up to 15%) for the LLP Binary Classification problem on various dataset types - tabular and Image. We achieve these improvements with minimal computational overhead above standard supervised learning due to Belief Propagation, for large bag sizes, even for a million samples.

Large Language Models (LLMs) hallucinate, generating factually incorrect yet confident assertions. We argue this stems from the Transformer's Softmax function, which creates "Artificial Certainty" by collapsing ambiguous attention scores into a single probability distribution, discarding uncertainty information at each layer. To fix this, we introduce the Credal Transformer, which replaces standard attention with a Credal Attention Mechanism (CAM) based on evidential theory. CAM produces a "credal set" (a set of distributions) instead of a single attention vector, with the set's size directly measuring model uncertainty. We implement this by re-conceptualizing attention scores as evidence masses for a Dirichlet distribution: sufficient evidence recovers standard attention, while insufficient evidence yields a diffuse distribution, representing ambiguity. Empirically, the Credal Transformer identifies out-of-distribution inputs, quantifies ambiguity, and significantly reduces confident errors on unanswerable questions by abstaining. Our contribution is a new architecture to mitigate hallucinations and a design paradigm that integrates uncertainty quantification directly into the model, providing a foundation for more reliable AI.

LLMs are increasingly deployed in high-stakes domains such as medical triage and legal assistance, often as document-grounded QA systems in which a user provides a description, relevant sources are retrieved, and an LLM generates a prediction. In practice, initial user queries are often underspecified, and a single retrieval pass is insufficient for reliable decision-making, leading to incorrect and overly confident answers. While follow-up questioning can elicit missing information, existing methods typically depend on implicit, unstructured confidence signals from the LLM, making it difficult to determine what remains unknown, what information matters most, and when to stop asking questions. We propose InfoGatherer, a framework that gathers missing information from two complementary sources: retrieved domain documents and targeted follow-up questions to the user. InfoGatherer models uncertainty using Dempster-Shafer belief assignments over a structured evidential network, enabling principled fusion of incomplete and potentially contradictory evidence from both sources without prematurely collapsing to a definitive answer. Across legal and medical tasks, InfoGatherer outperforms strong baselines while requiring fewer turns. By grounding uncertainty in formal evidential theory rather than heuristic LLM signals, InfoGatherer moves towards trustworthy, interpretable decision support in domains where reliability is critical.

Evidential cooperation in large worlds (ECL) refers to the idea that humans and other agents can benefit by cooperating with similar agents with differing values in causally disconnected parts of a large universe. Cooperating provides agents with evidence that other similar agents are likely to cooperate too, resulting in gains from trade for all. This could be a crucial consideration for altruists. I develop a game-theoretic model of ECL as an incomplete information bargaining problem. The model incorporates uncertainty about others' value systems and empirical situations, and addresses the problem of selecting a compromise outcome. Using the model, I investigate issues with ECL and outline open technical and philosophical questions. I show that all cooperators must maximize the same weighted sum of utility functions to reach a Pareto optimal outcome. However, I argue against selecting a compromise outcome implicitly by normalizing utility functions. I review bargaining theory and argue that the Nash bargaining solution could be a relevant Schelling point. I introduce dependency equilibria (Spohn 2007), an equilibrium concept suitable for ECL, and generalize a folk theorem showing that the Nash bargaining solution is a dependency equilibrium. I discuss gains from trade given uncertain beliefs about other agents and analyze how these gains decrease in several toy examples as the belief in another agent decreases. Finally, I discuss open issues in my model. First, the Nash bargaining solution is sometimes not coalitionally stable, meaning that a subset of cooperators can unilaterally improve payoffs by deviating from the compromise. I investigate conditions under which stable payoff vectors exist. Second, I discuss how to model agents' default actions without ECL.

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.

A correctly reconstructed distant point appears uncertain even when a frozen 3D model processes equivalent inputs because its output frame rotates fractionally. This exposes a weakness of trainingfree perturbation uncertainty: when outputs contain an unobserved symmetry, run-to-run variation potentially reflects symmetry rather than error. Existing alternatives have trade-offs: built-in confidence is outperformed in most evaluated conditions, while trained evidential heads require modelspecific supervision. For point maps, this research derives a closed-form, error-independent variance term that grows with scene extent and potentially overwhelms the desired signal. Simulation reproduces the effect; all 30 real VGGT view-sets tested exhibit its predicted |x_p|^2 signature. ReVar3R robustly registers predictions to a common similarity frame before computing per-point variance, without retraining or modifying the frozen model. Optional calibration and fusion use a held-out split. Across VGGT, π3, and MASt3R on six datasets, the same estimator on every backbone lowers AUSE below built-in confidence in 15 of 18 conditions. The staged evaluation yields 11 of 18 wins for the label-free core, 12/18 for label-free equal-weight fusion, 14/18 with held-out weights, and 15/18 when the built-in signal is included. Against a trained evidential head, the result is a trade-off: the head calibrates magnitude better and leads in its training domain, whereas ReVar3R transfers across backbones without adaptation. Its ranking improves point filtering, but it does not detect stable systematic bias, aid novel-view synthesis, or transfer calibration across domains.

Masked language models (MLM) do not explicitly define a distribution over language, i.e., they are not language models per se. However, recent work has implicitly treated them as such for the purposes of generation and scoring. This paper studies methods for deriving explicit joint distributions from MLMs, focusing on distributions over two tokens, which makes it possible to calculate exact distributional properties. We find that an approach based on identifying joints whose conditionals are closest to those of the MLM works well and outperforms existing Markov random field-based approaches. We further find that this derived model's conditionals can even occasionally outperform the original MLM's conditionals.

We introduce a boosting algorithm to pre-process data for fairness. Starting from an initial fair but inaccurate distribution, our approach shifts towards better data fitting while still ensuring a minimal fairness guarantee. To do so, it learns the sufficient statistics of an exponential family with boosting-compliant convergence. Importantly, we are able to theoretically prove that the learned distribution will have a representation rate and statistical rate data fairness guarantee. Unlike recent optimization based pre-processing methods, our approach can be easily adapted for continuous domain features. Furthermore, when the weak learners are specified to be decision trees, the sufficient statistics of the learned distribution can be examined to provide clues on sources of (un)fairness. Empirical results are present to display the quality of result on real-world data.

Hallucinations in large language models (LLMs) remain a central obstacle to trustworthy deployment, motivating detectors that are accurate, lightweight, and broadly applicable. Since an LLM with a prompt defines a conditional distribution, we argue that the complexity of the distribution is an indicator of hallucination. However, the density of the distribution is unknown and the samples (i.e., responses generated for the prompt) are discrete distributions, which leads to a significant challenge in quantifying the complexity of the distribution. We propose to compute the optimal-transport distances between the sets of token embeddings of pairwise samples, which yields a Wasserstein distance matrix measuring the costs of transforming between the samples. This Wasserstein distance matrix provides a means to quantify the complexity of the distribution defined by the LLM with the prompt. Based on the Wasserstein distance matrix, we derive two complementary signals: AvgWD, measuring the average cost, and EigenWD, measuring the cost complexity. This leads to a training-free detector for hallucinations in LLMs. We further extend the framework to black-box LLMs via teacher forcing with an accessible teacher model. Experiments show that AvgWD and EigenWD are competitive with strong uncertainty baselines and provide complementary behavior across models and datasets, highlighting distribution complexity as an effective signal for LLM truthfulness.

The Uniform Information Density (UID) hypothesis suggests that effective communication maintains a stable flow of information. In this work, we revisit this principle in the context of large language model (LLM) reasoning traces, asking whether step-level uniformity reflects reasoning quality. To this end, we propose an entropy-based stepwise information density metric and introduce two complementary measures of uniformity, local and global uniformity scores. Across the experiments on six different reasoning benchmarks, we find that step-level uniformity not only provides a strong theoretical lens but also yields practical performance benefits; for example, selecting reasoning traces with more uniform information density at the step-level improves accuracy by 10-32\% relative gains over baselines at AIME2025. Our analysis further reveals that correct reasoning traces tend to avoid sharp information density spikes, while incorrect traces exhibit irregular information bursts. These results demonstrate that UID-inspired information density measures outperform alternative internal signals as predictors of reasoning quality. Results highlight the uniformity of the information density as a robust diagnostic and selection criterion for building more reliable and accurate reasoning systems.

The uniform information density (UID) hypothesis states that humans tend to distribute information roughly evenly across an utterance or discourse. Early evidence in support of the UID hypothesis came from Genzel & Charniak (2002), which proposed an entropy rate constancy principle based on the probability of English text under n-gram language models. We re-evaluate the claims of Genzel & Charniak (2002) with neural language models, failing to find clear evidence in support of entropy rate constancy. We conduct a range of experiments across datasets, model sizes, and languages and discuss implications for the uniform information density hypothesis and linguistic theories of efficient communication more broadly.

Many recent reasoning gains in large language models can be explained as distribution sharpening: biasing generation toward high-likelihood trajectories already supported by the pretrained model, rather than modifying its weights. A natural formalization is the sequence-level power distribution π_α(ymid x)propto p_θ(ymid x)^α (α>1), which concentrates mass on whole sequences instead of adjusting token-level temperature. Prior work shows that Metropolis--Hastings (MH) sampling from this distribution recovers strong reasoning performance, but at order-of-magnitude inference slowdowns. We introduce Power-SMC, a training-free Sequential Monte Carlo scheme that targets the same objective while remaining close to standard decoding latency. Power-SMC advances a small particle set in parallel, corrects importance weights token-by-token, and resamples when necessary, all within a single GPU-friendly batched decode. We prove that temperature τ=1/α is the unique prefix-only proposal minimizing incremental weight variance, interpret residual instability via prefix-conditioned Rényi entropies, and introduce an exponent-bridging schedule that improves particle stability without altering the target. On MATH500, Power-SMC matches or exceeds MH power sampling while reducing latency from 16--28times to 1.4--3.3times over baseline decoding. The code is available at https://github.com/ArminAzizi98/Power-SMC.

Multimodal semantic understanding often has to deal with uncertainty, which means the obtained messages tend to refer to multiple targets. Such uncertainty is problematic for our interpretation, including inter- and intra-modal uncertainty. Little effort has studied the modeling of this uncertainty, particularly in pre-training on unlabeled datasets and fine-tuning in task-specific downstream datasets. In this paper, we project the representations of all modalities as probabilistic distributions via a Probability Distribution Encoder (PDE) by utilizing sequence-level interactions. Compared to the existing deterministic methods, such uncertainty modeling can convey richer multimodal semantic information and more complex relationships. Furthermore, we integrate uncertainty modeling with popular pre-training frameworks and propose suitable pre-training tasks: Distribution-based Vision-Language Contrastive learning (D-VLC), Distribution-based Masked Language Modeling (D-MLM), and Distribution-based Image-Text Matching (D-ITM). The fine-tuned models are applied to challenging downstream tasks, including image-text retrieval, visual question answering, visual reasoning, and visual entailment, and achieve state-of-the-art results.

Multimodal rumor detectors increasingly rely on retrieved evidence, yet relevant evidence is not necessarily sufficient for verification. Missing provenance, duplicated reports, and unresolved contradictions can produce confident predictions without adequate support. We introduce SAFE-MR, a framework that separates claim veracity from evidence sufficiency. The method decomposes image-text posts into verifiable claims, constructs a relation-aware claim-evidence graph, and aggregates evidence using provenance and contextual compatibility. Separate veracity and sufficiency heads support selective prediction, while evidence interventions encourage stability under irrelevant additions and sensitivity to evidence removal. On NewsCLIPpings, VERITE, and XFacta, SAFE-MR achieves macro-F1 scores of 91.2%, 75.8%, and 85.2%, respectively. Against the matched backbone with evidence, its macro-F1 gains are 2.2, 4.9, and 4.8 percentage points. On the diagnostic selection set, SAFE-MR reduces AURC from 0.105 for maximum-probability rejection to 0.075 and lowers error at 80% coverage from 13.8% to 8.5%. Evidence-perturbation and ablation results support the role of sufficiency learning and intervention training in improving selective verification.

Fine-tuning MLLMs for Video Temporal Grounding (VTG) often improves in-domain performance but degrades sharply under domain shift. In this work, we find that this failure is primarily driven not just by unseen query concepts, but by visual domain shift, which prevents the model from coupling its learned temporal localization knowledge with its inherent entity-attention capability. To address this, we introduce EVIDENT, a parameter-efficient adaptation framework that anchors temporal grounding in the inherent entity-attention of pre-trained MLLMs by routing VTG adaptation through explicit visual entity evidence. EVIDENT consists of three components: (i) an Entity Bottleneck Adapter that transforms dense visual tokens into compact entity-level slots, (ii) an Entity-Binding Distillation loss that instills objectness priors into the semantically unstructured MLLM visual space, guiding each slot to bind to a coherent entity, and (iii) an Entity-to-eVidence gating mechanism that leverages the captured entities as evidence, steering the model to localize moments containing query-relevant entities. Together, these components enable VTG fine-tuning to rely on entity-grounded evidence rather than brittle dataset shortcuts. Experiments on cross-domain VTG benchmarks show that EVIDENT consistently improves out-of-domain robustness while preserving competitive in-domain performance with modest parameter overhead. These results suggest that entity-level grounding is an effective inductive bias for generalizable temporal localization.

Languages are not created randomly but rather to communicate information. There is a strong association between languages and their underlying meanings, resulting in a sparse joint distribution that is heavily peaked according to their correlations. Moreover, these peak values happen to match with the marginal distribution of languages due to the sparsity. With the advent of LLMs trained on big data and large models, we can now precisely assess the marginal distribution of languages, providing a convenient means of exploring the sparse structures in the joint distribution for effective inferences. In this paper, we categorize languages as either unambiguous or {\epsilon}-ambiguous and present quantitative results to demonstrate that the emergent abilities of LLMs, such as language understanding, in-context learning, chain-of-thought prompting, and effective instruction fine-tuning, can all be attributed to Bayesian inference on the sparse joint distribution of languages.

Large language models increasingly collaborate with humans and peer AI agents whose contributions may be incomplete, inconsistent, or incorrect. Effective collaboration requires calibrated trust, whereby decisions to rely on, verify, or assist a partner adapt rationally as empirical evidence accumulates. We investigate whether models translate partner evidence into appropriate reliance policies. We introduce a benchmark of 324 scenarios across 23 collaboration categories. Each scenario involves three sequential decisions with explicit transition dynamics, feedback emissions, and cost schedules, permitting exact analytical evaluation of choices against their expected consequences over the remaining interaction. Evaluating seven models alongside 36 controlled-history probes, we dissociate evidence sensitivity from normatively appropriate action. While the strongest frontier model approaches near-optimal decisions, other models exhibit recurring pathologies: procuring excessive safeguards, purchasing verification tests with zero expected value of information, prioritizing immediate savings over cooperative learning, and misallocating assistance to suboptimal channels. Supplying explicit posterior distributions resolves certain errors while introducing new failure modes. Calibrated trust in autonomous agents critically demands coupling empirical evidence with forward-looking decision utility.

We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are assumed to concentrate around some low-dimensional structure. Estimating the distribution supported on this low-dimensional structure, such as a low-dimensional manifold, is challenging due to its singularity with respect to the Lebesgue measure in the ambient space. In the considered model, a usual likelihood approach can fail to estimate the target distribution consistently due to the singularity. We prove that a novel and effective solution exists by perturbing the data with an instance noise, which leads to consistent estimation of the underlying distribution with desirable convergence rates. We also characterize the class of distributions that can be efficiently estimated via deep generative models. This class is sufficiently general to contain various structured distributions such as product distributions, classically smooth distributions and distributions supported on a low-dimensional manifold. Our analysis provides some insights on how deep generative models can avoid the curse of dimensionality for nonparametric distribution estimation. We conduct a thorough simulation study and real data analysis to empirically demonstrate that the proposed data perturbation technique improves the estimation performance significantly.

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

In the era of large language models, creative writing quality lacks a computable theoretical anchor. The dominant approaches are rubric scoring -- decomposing holistic aesthetic judgment into sub-scores -- and RLHF preference signals -- replacing quality with group votes. Both bypass the statistical structure of the text itself. This paper provides an information-theoretic foundation to fill this gap. We propose 'calibrated surprise' as the information-theoretic essence of excellent creative writing. This judgment matches reading intuition and covers its opposite. This literary judgment admits a precise mathematical formulation. Under full-dimensional constraints Y, feasible writing choices are forced into an extremely narrow space. The rare survivors are, from the unconstrained perspective, exactly the least predictable choices. Both are measured precisely by Shannon mutual information I(X;Y) = H(X) - H(X|Y) -- 'calibrated' corresponds to H(X|Y) approaching 0; 'surprising' corresponds to H(X) going high. The subtraction structure of the formula naturally separates 'well-grounded surprise' from 'pure noise'. We use token-level logprobs from Qwen1.5-7B as an operational proxy for the ideal reader's probability distribution. Across 20 pairs (12 Chinese / 8 English) of high-quality vs. systematically degraded literary passages, 20/20 pairs support the core prediction: high-quality passages have systematically higher I(X;Y) than their degraded versions.

In this paper, we present the Logically submissions to De-Factify 2 challenge (DE-FACTIFY 2023) on the task 1 of Multi-Modal Fact Checking. We describes our submissions to this challenge including explored evidence retrieval and selection techniques, pre-trained cross-modal and unimodal models, and a cross-modal veracity model based on the well established Transformer Encoder (TE) architecture which is heavily relies on the concept of self-attention. Exploratory analysis is also conducted on this Factify 2 data set that uncovers the salient multi-modal patterns and hypothesis motivating the architecture proposed in this work. A series of preliminary experiments were done to investigate and benchmarking different pre-trained embedding models, evidence retrieval settings and thresholds. The final system, a standard two-stage evidence based veracity detection system, yields weighted avg. 0.79 on both val set and final blind test set on the task 1, which achieves 3rd place with a small margin to the top performing system on the leaderboard among 9 participants.

Feature attribution methods identify which features of an input most influence a model's output. Most widely-used feature attribution methods (such as SHAP, LIME, and Grad-CAM) are "class-dependent" methods in that they generate a feature attribution vector as a function of class. In this work, we demonstrate that class-dependent methods can "leak" information about the selected class, making that class appear more likely than it is. Thus, an end user runs the risk of drawing false conclusions when interpreting an explanation generated by a class-dependent method. In contrast, we introduce "distribution-aware" methods, which favor explanations that keep the label's distribution close to its distribution given all features of the input. We introduce SHAP-KL and FastSHAP-KL, two baseline distribution-aware methods that compute Shapley values. Finally, we perform a comprehensive evaluation of seven class-dependent and three distribution-aware methods on three clinical datasets of different high-dimensional data types: images, biosignals, and text.

A desired closure property in Bayesian probability is that an updated posterior distribution be in the same class of distributions --- say Gaussians --- as the prior distribution. When the updating takes place via a statistical model, one calls the class of prior distributions the `conjugate priors' of the model. This paper gives (1) an abstract formulation of this notion of conjugate prior, using channels, in a graphical language, (2) a simple abstract proof that such conjugate priors yield Bayesian inversions, and (3) a logical description of conjugate priors that highlights the required closure of the priors under updating. The theory is illustrated with several standard examples, also covering multiple updating.

The modeling of probability distributions, specifically generative modeling and density estimation, has become an immensely popular subject in recent years by virtue of its outstanding performance on sophisticated data such as images and texts. Nevertheless, a theoretical understanding of its success is still incomplete. One mystery is the paradox between memorization and generalization: In theory, the model is trained to be exactly the same as the empirical distribution of the finite samples, whereas in practice, the trained model can generate new samples or estimate the likelihood of unseen samples. Likewise, the overwhelming diversity of distribution learning models calls for a unified perspective on this subject. This paper provides a mathematical framework such that all the well-known models can be derived based on simple principles. To demonstrate its efficacy, we present a survey of our results on the approximation error, training error and generalization error of these models, which can all be established based on this framework. In particular, the aforementioned paradox is resolved by proving that these models enjoy implicit regularization during training, so that the generalization error at early-stopping avoids the curse of dimensionality. Furthermore, we provide some new results on landscape analysis and the mode collapse phenomenon.

Traditional weight of evidence assigns a credit characteristic a value based on its association with default across a population. Credit analysis also requires an assessment of that characteristic in the context of an individual applicant's record. We study conditional weight of evidence for this purpose. It measures the change in default log odds from observing a characteristic after the remaining credit information is known. Its sign identifies whether the characteristic adds adverse or favorable information for that applicant, and its magnitude measures the strength of that information. The same characteristic value can therefore receive different assessments for applicants with different payment histories or other credit attributes. We develop estimators using gradient-boosted trees and evaluate their accuracy in a bureau-style simulation. Regressions of the full model's predicted probabilities recover conditional evidence more accurately than separate models fitted to default outcomes, provided the full model is accurate. They also recover a deliberately constructed file-age effect whose direction varies with utilization and is often missed by marginal weight of evidence. Local class-frequency estimates improve on marginal weight of evidence but remain inaccurate for some weak effects. An application to FICO HELOC data illustrates estimation when the population evidence is unknown. Conditional weight of evidence provides an applicant-specific interpretation of the information in a credit characteristic; its population summary, a conditional information value, splits the joint information in the record across blocks when averaged over orderings. Neither is an adverse action reason, which explains the fitted score difference between the applicant and chosen passing records.

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.

Using language models to scalably approximate human preferences on text quality (LLM-as-a-judge) has become a standard practice applicable to many tasks. A judgment is often extracted from the judge's textual output alone, typically with greedy decoding. However, LLM judges naturally provide distributions over judgment tokens, inviting a breadth of inference methods for extracting fine-grained preferences. We find that taking the mean of the judgment distribution consistently outperforms taking the mode (i.e. greedy decoding) in all evaluation settings (i.e. pointwise, pairwise, and listwise). We further explore novel methods of deriving preferences from judgment distributions, and find that methods incorporating risk aversion often improve performance. Lastly, we analyze LLM-as-a-judge paired with chain-of-thought (CoT) prompting, showing that CoT can collapse the spread of the judgment distribution, often harming performance. Our findings show that leveraging distributional output improves LLM-as-a-judge, as opposed to using the text interface alone.

Causal inference is often focused on average effects, which can hide important aspects of the effect distributions. Here we consider the entire posterior effects distribution by estimating full counterfactual outcome distributions. We propose a methodology for inference on counterfactual distributions which builds upon the martingale posterior framework of Fong et al. (2023). This provides a highly flexible approach to estimating densities, distribution functions, and derived quantities such as quantiles, which coherently quantifies the epistemic uncertainty on any target estimand of interest. As the predictive recursions are based on an underlying nonparametric model (a Dirichlet process mixture model), our method naturally inherits robustness with respect to restrictive parametric assumptions. In addition, implementation of our method is typically very fast. This approach can be applied to marginal or conditional counterfactual distributions and is easily extended to an instrumental variables setup. Using the concept of almost conditionally identically distributed random variables, we prove convergence of the martingale posterior inference on the counterfactual outcome distributions for the causal models considered in the paper. We illustrate our approach on both simulated and real data. Using the latter, we investigate the effect of zinc lozenges on common cold duration, the impact of vitamin A supplementation on children's survival rates with one-sided non-compliance (analysed in Imbens and Rubin, 1997a) and the effect of job training (LaLonde, 1986).

We investigate distributional properties of the centered Erdős--Rényi distribution (Lunagòmez et al., 2021) and propose a semi-conjugate Bayesian approach to multiple network data. In simulations, both Gibbs sampling and empirical Bayes accurately recover network summaries, with the latter scaling efficiently with network size. As a companion to this note, we provide the R package BayesCER, which implements the proposed methodology.

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

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.

Large language models (LLMs) define a distribution over text, which can be viewed as a probabilistic representation of uncertainty: sampling K responses yields a belief state - responses a model deems plausible. Existing work exploits this representation for narrow tasks like either decoding or selective prediction, and often requires manual interventions, not controlling generation directly. We propose Belief-Augmented Generation (BAG): grounding LLMs in their own belief state via the prompt and letting them reason over these K samples to decide on a conversational strategy: answer, clarify, or abstain. In a multi-turn ambiguous QA setting, we find that LLMs by default rarely clarify or abstain, ignoring uncertainty about the input or facts. BAG improves QA accuracy across six models and yields strategy decisions more faithful to the belief state than prompt-only baselines. Disentangling when to clarify from when to abstain, however, remains challenging.

Medical models are judged not only on correctness, but on whether reported confidence matches actual accuracy. Generalist multimodal medical models have expanded what a single model can perceive, yet they still express bounded decisions such as diagnoses, findings or cell counts as generated text, so the reported probability reflects the next token rather than the decision itself. Motivated by decision-native interfaces such as Jev, we introduce OmniMed-Jev, which represents each medical decision as a Choice, Noul or Score decision over a runtime-supplied candidate set and returns a full distribution over that set: mutually exclusive classes, binary presence of a finding, or a bounded ordered value. The design is omni in three respects: it accepts diverse imaging modalities, covers different prediction tasks, and expresses them through one candidate-conditioned probability model, so heterogeneous outputs become comparable probabilities rather than task-specific strings. In an interface-controlled comparison against a generative baseline trained on the same backbone, data and schedule, OmniMed-Jev's reported probabilities track observed correctness far more closely, reducing calibration error by up to an order of magnitude and reliability error by up to two, while point-prediction performance remains comparable; counting is the one family where the generative baseline stays ahead. Making the decision distribution the model's output is not a format change but what turns reported numbers into probabilities that mean what they say. These results support explicit decision modeling as a way to make reported confidence meaningful within the evaluated tasks, and they are not evidence of clinical readiness: the comparison cannot separate the interface from associated training differences, which we state alongside the results. Code is available at github.com/lytang63/OmniMed-Jev.

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.

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

This book is about conformal prediction and related inferential techniques that build on permutation tests and exchangeability. These techniques are useful in a diverse array of tasks, including hypothesis testing and providing uncertainty quantification guarantees for machine learning systems. Much of the current interest in conformal prediction is due to its ability to integrate into complex machine learning workflows, solving the problem of forming prediction sets without any assumptions on the form of the data generating distribution. Since contemporary machine learning algorithms have generally proven difficult to analyze directly, conformal prediction's main appeal is its ability to provide formal, finite-sample guarantees when paired with such methods. The goal of this book is to teach the reader about the fundamental technical arguments that arise when researching conformal prediction and related questions in distribution-free inference. Many of these proof strategies, especially the more recent ones, are scattered among research papers, making it difficult for researchers to understand where to look, which results are important, and how exactly the proofs work. We hope to bridge this gap by curating what we believe to be some of the most important results in the literature and presenting their proofs in a unified language, with illustrations, and with an eye towards pedagogy.

While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However, existing methods are often computationally expensive, or demand costly retraining when priors change, limiting their utility, particularly in sequential inference problems such as real-time sensor fusion. To address these challenges, we introduce the Distribution Transformer -- a novel architecture that can learn arbitrary distribution-to-distribution mappings. Our method can be trained to map a prior to the corresponding posterior, conditioned on some dataset -- thus performing approximate Bayesian inference. Our novel architecture represents a prior distribution as a (universally-approximating) Gaussian Mixture Model (GMM), and transforms it into a GMM representation of the posterior. The components of the GMM attend to each other via self-attention, and to the datapoints via cross-attention. We demonstrate that Distribution Transformers both maintain flexibility to vary the prior, and significantly reduces computation times-from minutes to milliseconds-while achieving log-likelihood performance on par with or superior to existing approximate inference methods across tasks such as sequential inference, quantum system parameter inference, and Gaussian Process predictive posterior inference with hyperpriors.

We consider estimating the conditional distribution of a multivariate outcome given covariates when its coordinates may be continuous, binary, categorical, ordinal or rankings, and are conditionally dependent on one another. Different statistical methods have been developed for each outcome type, and most of them target a summary of the conditional distribution, such as the mean of each coordinate, rather than the joint distribution of the outcome vector. We develop generalized engression models, a unified nonparametric distributional regression framework for outcomes of any type. The proposed method builds upon engression, a scoring-rule-based deep generative model, and introduces a data-type-specific link function and a stochastic perturbation that smooths the loss, enabling gradient-based training even with discontinuous links. We establish universal representation results for continuous, discrete and mixed outcomes. In simulations and in two applications, 242 species in a community ecology benchmark and a 17-dimensional mixed-type health outcome, the method matches type-specific models on marginal scores, improves on them on the joint distribution, and matches or exceeds purpose-built state-of-the-art joint species distribution models. Software is available in Python.

Suppose Alice trains an open-weight language model and Bob uses a blackbox derivative of Alice's model to produce text. Can Alice prove that Bob is using her model, either by querying Bob's derivative model (query setting) or from the text alone (observational setting)? We formulate this question as an independence testing problem--in which the null hypothesis is that Bob's model or text is independent of Alice's randomized training run--and investigate it through the lens of palimpsestic memorization in language models: models are more likely to memorize data seen later in training, so we can test whether Bob is using Alice's model using test statistics that capture correlation between Bob's model or text and the ordering of training examples in Alice's training run. If Alice has randomly shuffled her training data, then any significant correlation amounts to exactly quantifiable statistical evidence against the null hypothesis, regardless of the composition of Alice's training data. In the query setting, we directly estimate (via prompting) the likelihood Bob's model gives to Alice's training examples and order; we correlate the likelihoods of over 40 fine-tunes of various Pythia and OLMo base models ranging from 1B to 12B parameters with the base model's training data order, achieving a p-value on the order of at most 1e-8 in all but six cases. In the observational setting, we try two approaches based on estimating 1) the likelihood of Bob's text overlapping with spans of Alice's training examples and 2) the likelihood of Bob's text with respect to different versions of Alice's model we obtain by repeating the last phase (e.g., 1%) of her training run on reshuffled data. The second approach can reliably distinguish Bob's text from as little as a few hundred tokens; the first does not involve any retraining but requires many more tokens (several hundred thousand) to achieve high power.

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

Post-hoc out-of-distribution (OOD) detection has garnered intensive attention in reliable machine learning. Many efforts have been dedicated to deriving score functions based on logits, distances, or rigorous data distribution assumptions to identify low-scoring OOD samples. Nevertheless, these estimate scores may fail to accurately reflect the true data density or impose impractical constraints. To provide a unified perspective on density-based score design, we propose a novel theoretical framework grounded in Bregman divergence, which extends distribution considerations to encompass an exponential family of distributions. Leveraging the conjugation constraint revealed in our theorem, we introduce a ConjNorm method, reframing density function design as a search for the optimal norm coefficient p against the given dataset. In light of the computational challenges of normalization, we devise an unbiased and analytically tractable estimator of the partition function using the Monte Carlo-based importance sampling technique. Extensive experiments across OOD detection benchmarks empirically demonstrate that our proposed ConjNorm has established a new state-of-the-art in a variety of OOD detection setups, outperforming the current best method by up to 13.25% and 28.19% (FPR95) on CIFAR-100 and ImageNet-1K, respectively.

We study the Stochastic Boolean Function Certification (SBFC) problem, where we are given n Bernoulli random variables {X_e: e in U} on a ground set U of n elements with joint distribution p, a Boolean function f: 2^U to {0, 1}, and an (unknown) scenario S = {e in U: X_e = 1} of active elements sampled from p. We seek to probe the elements one-at-a-time to reveal if they are active until we can certify f(S) = 1, while minimizing the expected number of probes. Unlike most previous results that assume independence, we study correlated distributions p and give approximation algorithms for several classes of functions f. When f(S) is the indicator function for whether S is the spanning set of a given matroid, our problem reduces to finding a basis of active elements of a matroid by probing elements. We give a non-adaptive O(log n)-approximation algorithm for arbitrary distributions p, and show that this is tight up to constants unless P = NP, even for partition matroids. For uniform matroids, we give constant factor 4.642-approximation ([BBFT20]) that can be further improved to a 2-approximation if additionally the random variables are negatively correlated for the case of 1-uniform matroid. We also give an adaptive O(log k)-approximation algorithm for SBFC for k-uniform matroids for the Graph Probing problem, where we seek to probe the edges of a graph one-at-a-time until we find k active edges. The underlying distribution on edges arises from (hidden) independent vertex random variables, with an edge being active if at least one of its endpoints is active. This significantly improves over the information-theoretic lower bound on Ω(poly(n)) ([JGM19]) for adaptive algorithms for k-uniform matroids with arbitrary distributions.

Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution -- the part of the distribution representing large but rare events -- and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data while in others the power law is ruled out.

A probability forecast or probabilistic classifier is reliable or calibrated if the predicted probabilities are matched by ex post observed frequencies, as examined visually in reliability diagrams. The classical binning and counting approach to plotting reliability diagrams has been hampered by a lack of stability under unavoidable, ad hoc implementation decisions. Here we introduce the CORP approach, which generates provably statistically Consistent, Optimally binned, and Reproducible reliability diagrams in an automated way. CORP is based on non-parametric isotonic regression and implemented via the Pool-adjacent-violators (PAV) algorithm - essentially, the CORP reliability diagram shows the graph of the PAV- (re)calibrated forecast probabilities. The CORP approach allows for uncertainty quantification via either resampling techniques or asymptotic theory, furnishes a new numerical measure of miscalibration, and provides a CORP based Brier score decomposition that generalizes to any proper scoring rule. We anticipate that judicious uses of the PAV algorithm yield improved tools for diagnostics and inference for a very wide range of statistical and machine learning methods.

Retrieval-augmented generation (RAG) grounds answers in retrieved passages, yet relevance does not guarantee sufficiency: a topical passage may still fail to justify the answer. We study evidence sufficiency verification for selective RAG answering, in which a verifier receives a question, a candidate answer, and retrieved evidence and decides whether the evidence supports, refutes, or is insufficient for the answer, answering only when support is established. We present SURE-RAG, an aggregation protocol that treats evidence sufficiency as a set-level property: missing hops and unresolved conflicts cannot be detected by scoring passages independently. A shared claim-evidence verifier produces a local relation distribution for each (claim, passage) pair, which SURE-RAG aggregates into four interpretable answer-level feature blocks (coverage, relation strength, uncertainty, and retrieval), producing a three-way decision and an auditable selective score. We evaluate on HotpotQA-RAG v3, a controlled multi-hop benchmark, under an artifact-aware protocol (shortcut baselines, counterfactual swaps, no-oracle checks, and GPT-4o audits). Calibrated SURE-RAG attains 0.9075 Macro-F1 (raw 0.8951 +/- 0.0069), well above DeBERTa mean-pooling (0.6516) and a GPT-4o judge (0.7284), and on par with a strong concat cross-encoder (0.8888 +/- 0.0109) while remaining fully auditable. At 30% coverage, risk falls from 0.2588 to 0.1642, a 37% relative reduction. As a boundary-mapping experiment, we contrast SURE-RAG with GPT-4o on HaluBench unsafe detection: the ranking reverses (0.3343 vs. 0.7389 unsafe-F1), indicating that controlled sufficiency verification and natural hallucination detection are distinct problems.

Recent research across mathematical problem solving, proof assistant programming and multimodal jailbreaking documents a striking finding: when (multimodal) language model tackle a suite of tasks with multiple attempts per task -- succeeding if any attempt is correct -- then the negative log of the average success rate scales a power law in the number of attempts. In this work, we identify an apparent puzzle: a simple mathematical calculation predicts that on each problem, the failure rate should fall exponentially with the number of attempts. We confirm this prediction empirically, raising a question: from where does aggregate polynomial scaling emerge? We then answer this question by demonstrating per-problem exponential scaling can be made consistent with aggregate polynomial scaling if the distribution of single-attempt success probabilities is heavy tailed such that a small fraction of tasks with extremely low success probabilities collectively warp the aggregate success trend into a power law - even as each problem scales exponentially on its own. We further demonstrate that this distributional perspective explains previously observed deviations from power law scaling, and provides a simple method for forecasting the power law exponent with an order of magnitude lower relative error, or equivalently, {sim}2-4 orders of magnitude less inference compute. Overall, our work contributes to a better understanding of how neural language model performance improves with scaling inference compute and the development of scaling-predictable evaluations of (multimodal) language models.

Accurate quantification of lung disease severity from chest imaging is critical for clinical decision-making and resource allocation. We propose a tri-modal deep learning framework, TMF-RSE (Tri-Modal Fusion with Regional Semantics and Evidential Uncertainty), that combines appearance features from two-dimensional chest inputs, structural features from lung segmentation masks, and semantic features from vision-language models (VLMs) for severity quantification. Our approach employs complementary fusion mechanisms that integrate semantic guidance, structural priors, and hierarchical interactions across modalities. The model employs evidential regression to provide both severity predictions and uncertainty estimates. Experiments on the Per-COVID-19 CT and RALO datasets show that TMF-RSE outperforms recent transformer-based baselines, achieving MAE of 4.02 and Pearson correlation of 0.9629 on Per-COVID-19 validation, and 0.339 MAE / 0.973 PC on RALO geographic extent.

Recent advances in reinforcement learning (RL)-based post-training have led to notable improvements in large language models (LLMs), particularly in enhancing their reasoning capabilities to handle complex tasks. However, most existing methods treat the training data as a unified whole, overlooking the fact that modern LLM training often involves a mixture of data from diverse distributions-varying in both source and difficulty. This heterogeneity introduces a key challenge: how to adaptively schedule training across distributions to optimize learning efficiency. In this paper, we present a principled curriculum learning framework grounded in the notion of distribution-level learnability. Our core insight is that the magnitude of policy advantages reflects how much a model can still benefit from further training on a given distribution. Based on this, we propose a distribution-level curriculum learning framework for RL-based LLM post-training, which leverages the Upper Confidence Bound (UCB) principle to dynamically adjust sampling probabilities for different distrubutions. This approach prioritizes distributions with either high average advantage (exploitation) or low sample count (exploration), yielding an adaptive and theoretically grounded training schedule. We instantiate our curriculum learning framework with GRPO as the underlying RL algorithm and demonstrate its effectiveness on logic reasoning datasets with multiple difficulties and sources. Our experiments show that our framework significantly improves convergence speed and final performance, highlighting the value of distribution-aware curriculum strategies in LLM post-training. Code: https://github.com/ZhentingWang/DUMP.

Verbal confidence elicitation is widely used to extract uncertainty estimates from LLMs. We tested whether seven instruction-tuned open-weight models (3-9B parameters, four families) produce verbalised confidence that meets minimal validity criteria for item-level Type-2 discrimination under minimal numeric elicitation with greedy decoding. In a pre-registered study (OSF: osf.io/azbvx), 524 TriviaQA items were administered under numeric (0-100) and categorical (10-class) elicitation to eight models at Q5_K_M quantisation on consumer hardware, yielding 8,384 deterministic trials. A psychometric validity screen was applied to each model-format cell. All seven instruct models were classified Invalid on numeric confidence (H2 confirmed, 7/7 vs. predicted >=4/7), with a mean ceiling rate of 91.7% (H1 confirmed). Categorical elicitation did not rescue validity. Instead, it disrupted task performance in six of seven models, producing accuracy below 5% (H4 not confirmed). Token-level logprobability did not usefully predict verbalised confidence under the observed variance regime (H5 confirmed, mean cross-validated R^2 < 0.01). Within the reasoning-distilled model, reasoning-trace length showed a strong negative partial correlation with confidence (rho = -0.36, p < .001), consistent with the Reasoning Contamination Effect. These results do not imply that internal uncertainty representations are absent. They show that minimal verbal elicitation fails to preserve internal signals at the output interface in this model-size regime. Psychometric screening should precede any downstream use of such signals.

Speech language models (speech LLMs) can generate plausible outputs from audio that contains no usable speech evidence. We study this failure as a pre-generation support-estimation problem and present SURE-Voice, a training-free front end that decides whether an audio prompt contains intelligible speech evidence before calling a speech LLM. We build SURE-Challenge with a 640-example SURE-Core split and a 1,920-example SURE-Extended split derived from 120 LibriSpeech source utterances. Using one fixed operating point, an energy screen plus Whisper token confidence raises unsupported accuracy on the held-out Extended test from 0.000--0.133 to 0.919 for six non-degenerate speech LLM backbones, while supported accuracy remains 0.919--0.970 and downstream calls fall from 480 to 287. A 500-clip ESC-50 sanity set shows the same pattern on real environmental audio, with vocal non-speech as a residual failure mode. An overlap diagnostic shows that source attribution remains separate from speech-evidence filtering. The evidence supports a controlled benchmark baseline and a deployment-oriented analysis; it does not establish universal robustness to semantic answerability, gain variation or natural conversations.

While test-time scaling has enabled large language models to solve highly difficult tasks, state-of-the-art results come at exorbitant compute costs. These inefficiencies can be attributed to the miscalibration of post-trained language models, and the lack of calibration in popular sampling techniques. Here, we present Online Reasoning Calibration (ORCA), a framework for calibrating the sampling process that draws upon conformal prediction and test-time training. Specifically, we introduce a meta-learning procedure that updates the calibration module for each input. This allows us to provide valid confidence estimates under distributional shift, e.g. in thought patterns that occur across different stages of reasoning, or in prompt distributions between model development and deployment. ORCA not only provides theoretical guarantees on conformal risks, but also empirically shows higher efficiency and generalization across different reasoning tasks. At risk level δ=0.1, ORCA improves Qwen2.5-32B efficiency on in-distribution tasks with savings up to 47.5% with supervised labels and 40.7% with self-consistency labels. Under zero-shot out-of-domain settings, it improves MATH-500 savings from 24.8% of the static calibration baseline to 67.0% while maintaining a low empirical error rate, and the same trend holds across model families and downstream benchmarks. Our code is publicly available at https://github.com/wzekai99/ORCA.

Open-ended scientific discovery with large language models (LLMs) increasingly operates as a long-horizon loop of hypothesis search and verification, where a reward signal guides which hypotheses to test next. A notable recent example is AutoDiscovery, which uses "Bayesian surprise" - the belief shift an LLM undergoes after observing evidence for a hypothesis - as both a discovery metric and a reward for search. We first observe that AutoDiscovery treats surprisal as a static quantity, while surprisal in human reasoning is non-stationary - it is defined relative to beliefs that evolve with experience, a prerequisite for continual scientific discovery. We address this mismatch with evidence-informed LLM beliefs: priors updated with evidence from previous hypotheses to compute non-stationary surprisal for new hypotheses. We compare in-context belief-updating mechanisms and find that embedding-based retrieval-augmented generation over prior discoveries best anticipates eventual posteriors, identifying 37.5% of static surprisals as spurious. We then modify search to avoid these spurious rewards and prioritize hypotheses that remain surprising under non-stationary beliefs. Concretely, we introduce two complementary changes to the original search procedure: belief-update filtering and diversity maximization. Across five discovery domains, our method increases accumulated non-stationary surprisal by 30.62% on average compared to the original search procedure, demonstrating that continual scientific discovery with LLMs requires not only better belief measurement but also search procedures that avoid redundancy and encourage diversity.

Reliable uncertainty quantification remains a central challenge in predictive modeling. While Bayesian methods are theoretically appealing, their predictive intervals can exhibit poor frequentist calibration, particularly with small sample sizes or model misspecification. We introduce a practical and broadly applicable Bayesian conformal approach based on the influence-function Bayesian bootstrap (BB) with data-driven tuning of the Dirichlet concentration parameter, α. By efficiently approximating the Bayesian bootstrap predictive distribution via influence functions and calibrating α to optimize empirical coverage or average log-probability, our method constructs prediction intervals and distributions that are both well-calibrated and sharp. Across a range of regression models and data settings, this Bayesian conformal framework consistently yields improved empirical coverage and log-score compared to standard Bayesian posteriors. Our procedure is fast, easy to implement, and offers a flexible approach for distributional calibration in predictive modeling.

A new trend uses LLMs as dense text encoders via contrastive learning. However, since LLM embeddings predict the probability distribution of the next token, they are inherently generative and distributive, conflicting with contrastive learning, which requires embeddings to capture full-text semantics and align via cosine similarity. This discrepancy hinders the full utilization of LLMs' pre-training capabilities, resulting in inefficient learning. In response to this issue, we propose AutoRegEmbed, a new contrastive learning method built on embedding conditional probability distributions, which integrates two core tasks: information compression and conditional distribution alignment. The information compression task encodes text into the embedding space, ensuring that the embedding vectors capture global semantics. The conditional distribution alignment task focuses on aligning text embeddings with positive samples embeddings by leveraging the conditional distribution of embeddings while simultaneously reducing the likelihood of generating negative samples from text embeddings, thereby achieving embedding alignment and uniformity. Experimental results demonstrate that our method significantly outperforms traditional contrastive learning approaches and achieves performance comparable to state-of-the-art models when using the same amount of data.

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

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.

Language is not only used to transmit neutral information; we often seek to persuade by arguing in favor of a particular view. Persuasion raises a number of challenges for classical accounts of belief updating, as information cannot be taken at face value. How should listeners account for a speaker's "hidden agenda" when incorporating new information? Here, we extend recent probabilistic models of recursive social reasoning to allow for persuasive goals and show that our model provides a pragmatic account for why weakly favorable arguments may backfire, a phenomenon known as the weak evidence effect. Critically, this model predicts a systematic relationship between belief updates and expectations about the information source: weak evidence should only backfire when speakers are expected to act under persuasive goals and prefer the strongest evidence. We introduce a simple experimental paradigm called the Stick Contest to measure the extent to which the weak evidence effect depends on speaker expectations, and show that a pragmatic listener model accounts for the empirical data better than alternative models. Our findings suggest further avenues for rational models of social reasoning to illuminate classical decision-making phenomena.

We consider the problem of distribution-free predictive inference, with the goal of producing predictive coverage guarantees that hold conditionally rather than marginally. Existing methods such as conformal prediction offer marginal coverage guarantees, where predictive coverage holds on average over all possible test points, but this is not sufficient for many practical applications where we would like to know that our predictions are valid for a given individual, not merely on average over a population. On the other hand, exact conditional inference guarantees are known to be impossible without imposing assumptions on the underlying distribution. In this work we aim to explore the space in between these two, and examine what types of relaxations of the conditional coverage property would alleviate some of the practical concerns with marginal coverage guarantees while still being possible to achieve in a distribution-free setting.

We present a complete theoretical characterization of Latent Posterior Factors (LPF), a principled framework for aggregating multiple heterogeneous evidence items in probabilistic prediction tasks. Multi-evidence reasoning arises pervasively in high-stakes domains including healthcare diagnosis, financial risk assessment, legal case analysis, and regulatory compliance, yet existing approaches either lack formal guarantees or fail to handle multi-evidence scenarios architecturally. LPF encodes each evidence item into a Gaussian latent posterior via a variational autoencoder, converting posteriors to soft factors through Monte Carlo marginalization, and aggregating factors via exact Sum-Product Network inference (LPF-SPN) or a learned neural aggregator (LPF-Learned). We prove seven formal guarantees spanning the key desiderata for trustworthy AI: Calibration Preservation (ECE <= epsilon + C/sqrt(K_eff)); Monte Carlo Error decaying as O(1/sqrt(M)); a non-vacuous PAC-Bayes bound with train-test gap of 0.0085 at N=4200; operation within 1.12x of the information-theoretic lower bound; graceful degradation as O(epsilon*delta*sqrt(K)) under corruption, maintaining 88% performance with half of evidence adversarially replaced; O(1/sqrt(K)) calibration decay with R^2=0.849; and exact epistemic-aleatoric uncertainty decomposition with error below 0.002%. All theorems are empirically validated on controlled datasets spanning up to 4,200 training examples. Our theoretical framework establishes LPF as a foundation for trustworthy multi-evidence AI in safety-critical applications.

When can an agent failure be caught? An audit is usually limited by the record rather than by the method. CatchBench therefore puts one auditor's question to three information states: the declared configuration before a run (PRE), a growing prefix of its trace (LIVE), and the finished trace (POST). Prior benchmarks fix one of these states or vary the telemetry; to our knowledge none scores all three under one task-method interface. Each state admits different questions, so seven task contracts carry their own labels and metrics rather than one leaderboard. Four are evidential; three are Gold-derived mechanism diagnostics. The release scores 72 entrants, from rule scanners and structural models to eleven LLM judges across nine model families (GPT, Claude, Gemini, Gemma, Llama, Qwen, DeepSeek, Mistral, Nova), over 1187 declared configurations and 1162 recorded runs. Most of the arena does not order: 56 of 138 registered contrasts separate, and the rest are published unresolved rather than ranked. The two sharpest results cut against our own data. One rule ignores every name and permission; it flags each capability declared after the first. On one of six configuration sources it reaches a perfect F1, so a score there measures how the corpus was built rather than how well a method reasons. Our admissibility bar then rejected one injected substrate and withheld evidential status from the other. A benchmark number is therefore not interpretable until the process behind its labels is published and tested for the shortcut it may leave. We report both, and regenerate every ordering from released predictions with no model call.

Given time series data, how can we answer questions like "what will happen in the future?" and "how did we get here?" These sorts of probabilistic inference questions are challenging when observations are high-dimensional. In this paper, we show how these questions can have compact, closed form solutions in terms of learned representations. The key idea is to apply a variant of contrastive learning to time series data. Prior work already shows that the representations learned by contrastive learning encode a probability ratio. By extending prior work to show that the marginal distribution over representations is Gaussian, we can then prove that joint distribution of representations is also Gaussian. Taken together, these results show that representations learned via temporal contrastive learning follow a Gauss-Markov chain, a graphical model where inference (e.g., prediction, planning) over representations corresponds to inverting a low-dimensional matrix. In one special case, inferring intermediate representations will be equivalent to interpolating between the learned representations. We validate our theory using numerical simulations on tasks up to 46-dimensions.

According to the generalized Polya theorem, the Gaussian distribution on the real line is characterized by the property of equidistribution of a monomial and a linear form of independent identically distributed random variables. We give a complete description of a-adic solenoids for which an analog of this theorem is true. The proof of the main theorem is reduced to solving some functional equation in the class of continuous positive definite functions on the character group of an a-adic solenoid

Deep generative models have been demonstrated as state-of-the-art density estimators. Yet, recent work has found that they often assign a higher likelihood to data from outside the training distribution. This seemingly paradoxical behavior has caused concerns over the quality of the attained density estimates. In the context of hierarchical variational autoencoders, we provide evidence to explain this behavior by out-of-distribution data having in-distribution low-level features. We argue that this is both expected and desirable behavior. With this insight in hand, we develop a fast, scalable and fully unsupervised likelihood-ratio score for OOD detection that requires data to be in-distribution across all feature-levels. We benchmark the method on a vast set of data and model combinations and achieve state-of-the-art results on out-of-distribution detection.

We study the problem of predicting numeric labels that are constrained to the integers or to a subrange of the integers. For example, the number of up-votes on social media posts, or the number of bicycles available at a public rental station. While it is possible to model these as continuous values, and to apply traditional regression, this approach changes the underlying distribution on the labels from discrete to continuous. Discrete distributions have certain benefits, which leads us to the question whether such integer labels can be modeled directly by a discrete distribution, whose parameters are predicted from the features of a given instance. Moreover, we focus on the use case of output distributions of neural networks, which adds the requirement that the parameters of the distribution be continuous so that backpropagation and gradient descent may be used to learn the weights of the network. We investigate several options for such distributions, some existing and some novel, and test them on a range of tasks, including tabular learning, sequential prediction and image generation. We find that overall the best performance comes from two distributions: Bitwise, which represents the target integer in bits and places a Bernoulli distribution on each, and a discrete analogue of the Laplace distribution, which uses a distribution with exponentially decaying tails around a continuous mean.

People increasingly use large language models (LLMs) to explore ideas, gather information, and make sense of the world. In these interactions, they encounter agents that are overly agreeable. We argue that this sycophancy poses a unique epistemic risk to how individuals come to see the world: unlike hallucinations that introduce falsehoods, sycophancy distorts reality by returning responses that are biased to reinforce existing beliefs. We provide a rational analysis of this phenomenon, showing that when a Bayesian agent is provided with data that are sampled based on a current hypothesis the agent becomes increasingly confident about that hypothesis but does not make any progress towards the truth. We test this prediction using a modified Wason 2-4-6 rule discovery task where participants (N=557) interacted with AI agents providing different types of feedback. Unmodified LLM behavior suppressed discovery and inflated confidence comparably to explicitly sycophantic prompting. By contrast, unbiased sampling from the true distribution yielded discovery rates five times higher. These results reveal how sycophantic AI distorts belief, manufacturing certainty where there should be doubt.

Human reasoning often involves working over limited information to arrive at probabilistic conclusions. In its simplest form, this involves making an inference that is not strictly entailed by a premise, but rather only likely given the premise. While reasoning LLMs have demonstrated strong performance on logical and mathematical tasks, their behavior on such open-ended, non-deterministic inferences remains largely unexplored. We introduce ProbCOPA, a dataset of 210 handcrafted probabilistic inferences in English, each annotated for inference likelihood by 25--30 human participants. We find that human responses are graded and varied, revealing probabilistic judgments of the inferences in our dataset. Comparing these judgments with responses from eight state-of-the-art reasoning LLMs, we show that models consistently fail to produce human-like distributions. Finally, analyzing LLM reasoning chains, we find evidence of a common reasoning pattern used to evaluate such inferences. Our findings reveal persistent differences between humans and LLMs, and underscore the need to evaluate reasoning beyond deterministic settings.

Certain tasks in high-dimensional statistics become easier when the underlying distribution satisfies a local-to-global property called approximate tensorization of entropy (ATE). For example, the Glauber dynamics Markov chain of an ATE distribution mixes fast and can produce approximate samples in a small amount of time, since such a distribution satisfies a modified log-Sobolev inequality. Moreover, identity-testing for an ATE distribution requires few samples if the tester is given coordinate conditional access to the unknown distribution, as shown by Blanca, Chen, Štefankovič, and Vigoda (COLT 2023). A natural class of distributions that do not satisfy ATE consists of mixtures of (few) distributions that do satisfy ATE. We study the complexity of identity-testing and sampling for these distributions. Our main results are the following: 1. We show fast mixing of Glauber dynamics from a data-based initialization, with optimal sample complexity, for mixtures of distributions satisfying modified log-Sobolev inequalities. This extends work of Huang, Koehler, Lee, Mohanty, Rajaraman, Vuong, and Wu (STOC 2025, COLT 2025) for mixtures of distributions satisfying Poincaré inequalities. 2. Answering an open question posed by Blanca et al., we give efficient identity-testers for mixtures of ATE distributions in the coordinate-conditional sampling access model. We also give some simplifications and improvements to the original algorithm of Blanca et al.

For a parametric model of distributions, the closest distribution in the model to the true distribution located outside the model is considered. Measuring the closeness between two distributions with the Kullback-Leibler (K-L) divergence, the closest distribution is called the "information projection." The estimation risk of the maximum likelihood estimator (MLE) is defined as the expectation of K-L divergence between the information projection and the predictive distribution with plugged-in MLE. Here, the asymptotic expansion of the risk is derived up to n^{-2}-order, and the sufficient condition on the risk for the Bayes error rate between the true distribution and the information projection to be lower than a specified value is investigated. Combining these results, the "p-n criterion" is proposed, which determines whether the MLE is sufficiently close to the information projection for the given model and sample. In particular, the criterion for an exponential family model is relatively simple and can be used for a complex model with no explicit form of normalizing constant. This criterion can constitute a solution to the sample size or model acceptance problem. Use of the p-n criteria is demonstrated for two practical datasets. The relationship between the results and information criteria is also studied.

Large language models (LLMs) have shown promise in synthetic tabular data generation, yet existing methods struggle to preserve complex feature dependencies, particularly among categorical variables. This work introduces a probability-driven prompting approach that leverages LLMs to estimate conditional distributions, enabling more accurate and scalable data synthesis. The results highlight the potential of prompting probability distributions to enhance the statistical fidelity of LLM-generated tabular data.

Belief Propagation (BP) is a powerful algorithm for distributed inference in probabilistic graphical models, however it quickly becomes infeasible for practical compute and memory budgets. Many efficient, non-parametric forms of BP have been developed, but the most popular is Gaussian Belief Propagation (GBP), a variant that assumes all distributions are locally Gaussian. GBP is widely used due to its efficiency and empirically strong performance in applications like computer vision or sensor networks - even when modelling non-Gaussian problems. In this paper, we seek to provide a theoretical guarantee for when Gaussian approximations are valid in highly non-Gaussian, sparsely-connected factor graphs performing BP (common in spatial AI). We leverage the Central Limit Theorem (CLT) to prove mathematically that variables' beliefs under BP converge to a Gaussian distribution in complex, loopy factor graphs obeying our 4 key assumptions. We then confirm experimentally that variable beliefs become increasingly Gaussian after just a few BP iterations in a stereo depth estimation task.

The infinitely wide neural network has been proven a useful and manageable mathematical model that enables the understanding of many phenomena appearing in deep learning. One example is the convergence of random deep networks to Gaussian processes that allows a rigorous analysis of the way the choice of activation function and network weights impacts the training dynamics. In this paper, we extend the seminal proof of Matthews et al. (2018) to a larger class of initial weight distributions (which we call PSEUDO-IID), including the established cases of IID and orthogonal weights, as well as the emerging low-rank and structured sparse settings celebrated for their computational speed-up benefits. We show that fully-connected and convolutional networks initialized with PSEUDO-IID distributions are all effectively equivalent up to their variance. Using our results, one can identify the Edge-of-Chaos for a broader class of neural networks and tune them at criticality in order to enhance their training. Moreover, they enable the posterior distribution of Bayesian Neural Networks to be tractable across these various initialization schemes.

Large language models (LLMs) increasingly summarize clinical evidence, where a claim's weight depends on how strongly it is supported. Yet these models convey confidence poorly, and properties they never state, such as truth, are often readable from their activations. Whether a clinical model registers evidence strength, distinct from truth, and states it when asked is untested, and any such signal could be lexical. We compiled 45,134 clinical claims from six public sources, harmonized 20,611 into a four-level evidence grade under three independent frameworks, and tested 22 local, open-weight LLMs from several developers (0.6-70 billion parameters; general, medical, and reasoning), with lexical, truth, and cross-framework controls. A linear estimator recovered the grade in every model (median AUROC 71.8), yet decodability did not rise with scale and was weakest in reasoning models. The grade the models stated fell to chance, 25-27 percentage points below the estimator. The recoverable signal was largely lexical and did not transfer across topics or frameworks, yet it was distinct from factual truth and still flagged weakly supported claims (AUROC 69.2). Clinical LLMs thus carry an ordered evidence-strength signal they do not express, so their stated grades fail to convey a claim's support even when it is recoverable from their representations and text.

We present the Bayesian Linguistic Forecaster (BLF), an agentic system for binary forecasting that achieves state-of-the-art performance on the ForecastBench benchmark. The system is built on three ideas. (1) Linguistic belief state: a semi-structured representation combining numerical probability estimates with natural-language evidence summaries, updated by the LLM at each step of an iterative tool-use loop. This contrasts with the common approach of appending all retrieved evidence to an ever-growing, unstructured context. (2) Hierarchical multi-trial aggregation: running K independent trials and combining them using logit-space averaging shrinkage with a data-dependent prior. (3) Hierarchical calibration: Platt scaling with a hierarchical prior, which avoids over-shrinking extreme predictions for sources with skewed base rates. On 400 questions from the ForecastBench leaderboard, BLF outperforms all the top public methods, including Cassi, GPT-5, Grok~4.20, and Foresight-32B. Careful ablation studies, using mixed effects analysis to control for question variability (which accounts for 62\% of the variance in performance), reveals that all 3 components contribute to the overall gains, but some components matter more than others, depending on the base LLM, and the setting (e.g.\ with or without a crowd prior). All our experiments are based on a robust back-testing framework which we develop, which has a leakage rate below 1.5\%, and may be of independent interest.

Retrieval-Augmented Generation (RAG) is the prevailing paradigm for grounding Large Language Models (LLMs), yet the mechanisms governing how models integrate groups of conflicting retrieved evidence remain opaque. Does an LLM answer a certain way because the evidence is factually strong, because of a prior belief, or merely because it is repeated frequently? To answer this, we introduce GroupQA, a curated dataset of 1,635 controversial questions paired with 15,058 diversely-sourced evidence documents, annotated for stance and qualitative strength. Through controlled experiments, we characterize group-level evidence aggregation dynamics: Paraphrasing an argument can be more persuasive than providing distinct independent support; Models favor evidence presented first rather than last, and Larger models are increasingly resistant to adapt to presented evidence. Additionally, we find that LLM explanations to group-based answers are unfaithful. Together, we show that LLMs behave consistently as vulnerable heuristic followers, with direct implications for improving RAG system design.

This paper provides an empirical implementation of the creative quality metric proposed in Calibrated Surprise (Zou & Xu, 2026a). The question this paper addresses is: does this mathematical claim hold at the engineering level? To make the answer as general as possible, we deliberately choose the strictest engineering conditions: low data cost and a small base model. Training data comes from approximately 100 expert chain-of-thought (CoT) annotations produced by the BC Protocol (Zou & Xu, 2026b). We also identify a data bias: most publicly available alignment datasets are skewed toward craft-related knowledge, while audience modeling and reality-logic coverage are systematically weak. We use the term Creative Quality Alignment (CQA) to describe this class of engineering methods. We also offer a supporting theoretical observation: in an LLM with a single conditional distribution architecture, calibrating the appreciation side automatically transfers to the generation side via architectural duality. This is the structural reason why ~100 CoT examples are sufficient -- not a purely empirical observation like LIMA (Zhou et al., 2023).

Large language models (LLMs) exhibit a well-documented gap between latent capability and consistent activation: the router hypothesis posits that models possess the knowledge to solve a task but lack reliable internal routing to activate it. Prior work in formal mathematical reasoning (SAIR, Cázares 2026) reports that structural priors (cheatsheets) raise in-distribution performance dramatically, yet collapse below the zero-shot baseline out-of-distribution (OOD) -- and that iterative recalibration amplifies rather than corrects the collapse. We test whether this phenomenon is cross-domain by reproducing the SAIR design in source-code security vulnerability detection, evaluating three LLMs (GPT-OSS-120B, Llama-3.3-70B, Gemma-4-31B) across three vulnerability categories (CWE-798, CWE-284, and the non-CWE N+1 anti-pattern) spanning syntactic, contextual, and semantic complexity, then transferring cheatsheet-augmented prompts to real-world CVE data from VUDENC (CWE-89, CWE-22). Our findings replicate and extend SAIR: (F1) structural priors lift semantic-vulnerability recall from 20.0% to 100.0% across all models; (F2) zero-shot performance degrades along a semantic complexity gradient; (F3) the same cheatsheets that saturate synthetic performance amplify distribution-shift collapse on real CVE data (CWE-89: 100% synthetic F1 to 48.9% on VUDENC, -51.1pp); (F5) iterative recalibration produces a v2 cheatsheet that performs worse than v1 on real data, mirroring SAIR's AN45c-vs-AN38 finding. These results provide evidence that the cross-distribution trade-off surface documented in SAIR generalises to code security, and that the router hypothesis is cross-domain. We argue the structural nature of the collapse motivates distribution-aware training over prompt calibration. Code and evaluation scripts: https://github.com/bytepro-ai/bitcoder-v2-research

We introduce a novel generative model, the Discrete Distribution Networks (DDN), that approximates data distribution using hierarchical discrete distributions. We posit that since the features within a network inherently capture distributional information, enabling the network to generate multiple samples simultaneously, rather than a single output, may offer an effective way to represent distributions. Therefore, DDN fits the target distribution, including continuous ones, by generating multiple discrete sample points. To capture finer details of the target data, DDN selects the output that is closest to the Ground Truth (GT) from the coarse results generated in the first layer. This selected output is then fed back into the network as a condition for the second layer, thereby generating new outputs more similar to the GT. As the number of DDN layers increases, the representational space of the outputs expands exponentially, and the generated samples become increasingly similar to the GT. This hierarchical output pattern of discrete distributions endows DDN with unique properties: more general zero-shot conditional generation and 1D latent representation. We demonstrate the efficacy of DDN and its intriguing properties through experiments on CIFAR-10 and FFHQ. The code is available at https://discrete-distribution-networks.github.io/

Large language models perform near-Bayesian inference yet violate permutation invariance on exchangeable data. We resolve this by showing transformers minimize expected conditional description length (cross-entropy) over orderings, E_pi[ell(Y mid Gamma_pi(X))], which admits a Kolmogorov-complexity interpretation up to additive constants, rather than the permutation-invariant description length ell(Y mid X). This makes them Bayesian in expectation, not in realization. We derive (i) a Quantified Martingale Violation bound showing order-induced deviations scale as O(log n) with constants; (ii) the Expectation-level Decompression Law linking information budgets to reliability for Bernoulli predicates; and (iii) deployable planners (B2T/RoH/ISR) for answer/abstain decisions. Empirically, permutation dispersion follows a+bln n (Qwen2-7B b approx 0.377, Llama-3.1-8B b approx 0.147); permutation mixtures improve ground-truth likelihood/accuracy; and randomized dose-response shows hallucinations drop by sim 0.13 per additional nat. A pre-specified audit with a fixed ISR=1.0 achieves near-0\% hallucinations via calibrated refusal at 24\% abstention. The framework turns hallucinations into predictable compression failures and enables principled information budgeting.

We present a state-of-the-art model for fine-grained probability estimation of propositions conditioned on context. Recent advances in large language models (LLMs) have significantly enhanced their reasoning capabilities, particularly on well-defined tasks with complete information. However, LLMs continue to struggle with making accurate and well-calibrated probabilistic predictions under uncertainty or partial information. While incorporating uncertainty into model predictions often boosts performance, obtaining reliable estimates of that uncertainty remains understudied. In particular, LLM probability estimates tend to be coarse and biased towards more frequent numbers. Through a combination of human and synthetic data creation and assessment, scaling to larger models, and better supervision, we propose a set of strong and precise probability estimation models. We conduct systematic evaluations across tasks that rely on conditional probability estimation and show that our approach consistently outperforms existing fine-tuned and prompting-based methods by a large margin.

Fetal ultrasound standard-plane classification underpins reliable prenatal biometry and anomaly screening, yet real-world deployment is limited by domain shift, image noise, and poor calibration of predicted probabilities. This paper presents a practical framework for uncertainty-calibrated explainable AI in fetal plane classification. We synthesize uncertainty estimation methods (Monte Carlo dropout, deep ensembles, evidential learning, and conformal prediction) with post-hoc and uncertainty-aware explanations (Grad-CAM variants, LIME-style local surrogates, and uncertainty-weighted multi-resolution activation maps), and we map these components to a clinician-facing workflow. Using FETAL_PLANES_DB as a reference benchmark, we define a reporting protocol that couples accuracy with calibration and selective prediction, including expected calibration error, Brier score, coverage-risk curves, and structured error analysis with explanations. We also discuss integration points for quality control and human-in-the-loop review, where uncertainty flags trigger re-acquisition or expert confirmation. The goal is a reproducible, clinically aligned blueprint for building fetal ultrasound classifiers whose confidence and explanations remain trustworthy under noisy acquisition conditions.

Federated Learning enables multiple data centers to train a central model collaboratively without exposing any confidential data. Even though deterministic models are capable of performing high prediction accuracy, their lack of calibration and capability to quantify uncertainty is problematic for safety-critical applications. Different from deterministic models, probabilistic models such as Bayesian neural networks are relatively well-calibrated and able to quantify uncertainty alongside their competitive prediction accuracy. Both of the approaches appear in the federated learning framework; however, the aggregation scheme of deterministic models cannot be directly applied to probabilistic models since weights correspond to distributions instead of point estimates. In this work, we study the effects of various aggregation schemes for variational Bayesian neural networks. With empirical results on three image classification datasets, we observe that the degree of spread for an aggregated distribution is a significant factor in the learning process. Hence, we present an investigation on the question of how to combine variational Bayesian networks in federated learning, while providing benchmarks for different aggregation settings.

There is a growing gap between the impressive results of deep image generative models and classical algorithms that offer theoretical guarantees. The former suffer from mode collapse or memorization issues, limiting their application to scientific data. The latter require restrictive assumptions such as log-concavity to escape the curse of dimensionality. We partially bridge this gap by introducing conditionally strongly log-concave (CSLC) models, which factorize the data distribution into a product of conditional probability distributions that are strongly log-concave. This factorization is obtained with orthogonal projectors adapted to the data distribution. It leads to efficient parameter estimation and sampling algorithms, with theoretical guarantees, although the data distribution is not globally log-concave. We show that several challenging multiscale processes are conditionally log-concave using wavelet packet orthogonal projectors. Numerical results are shown for physical fields such as the varphi^4 model and weak lensing convergence maps with higher resolution than in previous works.

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.

Conventional in-distribution evaluation can overestimate robustness when training and test data share recurring task-specific patterns or surface cues. This risk is especially relevant in social-engineering fraud detection, where attackers can preserve malicious intent while changing the scenario, impersonated entity, or wording. We study this problem as scenario-level out-of-distribution (SL-OOD) detection for SMS and voice phishing, where entire attack scenarios are held out from training while the label space remains fixed. This setting tests whether models can generalize to unseen attack scenarios using decision-relevant evidence rather than familiar scenario-specific cues. Using this SL-OOD evaluation, we find that high in-distribution performance does not reliably predict held-out robustness across feature-, encoder-, and decoder-based baselines. We interpret this gap as scenario memorization: reliance on recurring scenario-specific lexical or entity cues rather than decision-relevant evidence. We propose ECoG, an evidence-consistent generative framework that combines evidence-span supervision with a rationale-label consistency objective during training. On the 0.5B decoder, relative to the same backbone trained without consistency regularization, ECoG raises Macro-F1 on OOD challenging instances by 3.22 points, reduces the share of predictions whose generated rationale supports the opposite label by 4.22 points, and increases token-level overlap with reference evidence spans by 8.38 points; the reduction in prediction-rationale inconsistency is consistent across four decoder backbones. These results suggest that compact generative detectors can benefit from evidence supervision and rationale-label consistency under social-engineering shift.

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

We 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.

In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order probability distributions, i.e., predictions in the form of distributions on probability distributions. A completely conclusive solution has not yet been found, however, as shown by recent criticisms of commonly used uncertainty measures associated with second-order distributions, identifying undesirable theoretical properties of these measures. In light of these criticisms, we propose a set of formal criteria that meaningful uncertainty measures for predictive uncertainty based on second-order distributions should obey. Moreover, we provide a general framework for developing uncertainty measures to account for these criteria, and offer an instantiation based on the Wasserstein distance, for which we prove that all criteria are satisfied.

We give the first efficient algorithm for learning halfspaces in the testable learning model recently defined by Rubinfeld and Vasilyan (2023). In this model, a learner certifies that the accuracy of its output hypothesis is near optimal whenever the training set passes an associated test, and training sets drawn from some target distribution -- e.g., the Gaussian -- must pass the test. This model is more challenging than distribution-specific agnostic or Massart noise models where the learner is allowed to fail arbitrarily if the distributional assumption does not hold. We consider the setting where the target distribution is Gaussian (or more generally any strongly log-concave distribution) in d dimensions and the noise model is either Massart or adversarial (agnostic). For Massart noise, our tester-learner runs in polynomial time and outputs a hypothesis with (information-theoretically optimal) error opt + epsilon for any strongly log-concave target distribution. For adversarial noise, our tester-learner obtains error O(opt) + epsilon in polynomial time when the target distribution is Gaussian; for strongly log-concave distributions, we obtain O(opt) + epsilon in quasipolynomial time. Prior work on testable learning ignores the labels in the training set and checks that the empirical moments of the covariates are close to the moments of the base distribution. Here we develop new tests of independent interest that make critical use of the labels and combine them with the moment-matching approach of Gollakota et al. (2023). This enables us to simulate a variant of the algorithm of Diakonikolas et al. (2020) for learning noisy halfspaces using nonconvex SGD but in the testable learning setting.

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.

Existing methods for multimodal sentiment analysis (MSA) under missing modalities usually follow a repair-first paradigm. We revisit this assumption and ask: should every missing modality be repaired? A per-sample oracle analysis shows the answer is not always: full-modality input is optimal for only a small fraction of samples, and every modality subset is preferred by some samples. These results suggest that adding or repairing modalities may not always improve prediction, and that the utility of each modality is sample-dependent. Building on this finding, we propose Sufficiency-Informed Evidential ValvE (SIEVE) that turns ``whether to repair'' into an explicit, learnable decision at the sample level. SIEVE compares a direct prediction branch with a repair branch, derives an empirical sufficiency signal from their per-sample loss gap, and routes each input through an evidential gate that jointly models sufficiency and its epistemic uncertainty. SIEVE is repair-agnostic: it operates as a plug-and-play decision on top of any explicit or implicit repair module, without modifying its internal design. Experiments on CMU-MOSI and IEMOCAP show that SIEVE consistently improves representative repair backbones across evaluated missing rates, and approaches the per-sample dual-branch achievable optimum.

Large Language Models (LLMs) are fluent but prone to hallucinations, producing answers that appear plausible yet are unsupported by available evidence. This failure is especially problematic in high-stakes domains where decisions must be justified by verifiable information. We introduce EvidenceRL, a reinforcement learning framework that enforces evidence adherence during training. EvidenceRL scores candidate responses for grounding (entailment with retrieved evidence and context) and correctness (agreement with reference answers) and optimizes the generator using Group Relative Policy Optimization (GRPO). We evaluate across two high-stakes domains, cardiac diagnosis and legal reasoning, where EvidenceRL consistently improves evidence grounding and faithfulness without sacrificing task accuracy. On cardiac diagnosis, F1@3 increases from 37.0 to 54.5 on Llama-3.2-3B while grounding (G_{max}@3) rises from 47.6 to 78.2; hallucinations drop nearly 5times and evidence-supported diagnoses increase from 31.8\% to 61.6\%. On legal reasoning, EvidenceRL raises Faithfulness from 32.8\% to 67.6\% on Llama-3.1-8B, demonstrating consistent behavioral change across domains. Our code is open-sourced at https://github.com/Wizaaard/EvidenceRL.git.

LLMs are increasingly used with external knowledge sources like the internet. Do they weigh information appropriately -- updating more for reliable sources (source discernment) and more when claims bring priors closer to the truth (truth discernment)? We formalize this as information discernment and introduce Learn2Discern (L2D), an experimental framework and benchmark grounded in three normative axioms with interpretable metrics. To establish external validity, a pre-registered, quota-matched user study (n=299) confirms that real LLM users endorse all three axioms and report that violations reduce their trust and usage intent. Across 13 models and nearly 670K trials, we find consistent failures across both dimensions: models perform near chance on source and truth discernment, rely on source popularity twice as much as source reliability, and update roughly equally whether a claim improves or worsens their position relative to the ground truth. Models integrate external knowledge most effectively on datasets where their priors are already the most accurate. Newer and larger models improve truth discernment but not source discernment, a blind spot that model complexity does not address. We identify simple inference-time interventions that improve both forms of discernment. We release our dataset and survey as a testbed for a core alignment property that scales in importance as LLMs replace traditional search.

Contrastively trained encoders have recently been proven to invert the data-generating process: they encode each input, e.g., an image, into the true latent vector that generated the image (Zimmermann et al., 2021). However, real-world observations often have inherent ambiguities. For instance, images may be blurred or only show a 2D view of a 3D object, so multiple latents could have generated them. This makes the true posterior for the latent vector probabilistic with heteroscedastic uncertainty. In this setup, we extend the common InfoNCE objective and encoders to predict latent distributions instead of points. We prove that these distributions recover the correct posteriors of the data-generating process, including its level of aleatoric uncertainty, up to a rotation of the latent space. In addition to providing calibrated uncertainty estimates, these posteriors allow the computation of credible intervals in image retrieval. They comprise images with the same latent as a given query, subject to its uncertainty. Code is available at https://github.com/mkirchhof/Probabilistic_Contrastive_Learning

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