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5 papers in the last four weeks, against 1 the four weeks before. 0.1% of all new papers.

Jul 6Week of Sep 21

Latest papers 32

Sep 30, 2026cs.CL

Synthetic Data Characterization via Training Dynamics

Interpreting properties of LLM-generated data is important for understanding its utility and limitations across learning tasks. In this work, we characterize synthetic data through sample-level learnability, studying variation among LLM families and scales, alongside human-written data as a reference. We first generate synthetic datasets spanning single- and multi-label classification, labeling, and tree prediction tasks. We then derive empirical data distributions from encoder training dynamics for both machine and organic data, and estimate the robustness of these distributions across encoders. Finally, we evaluate how data selection strategies based on these learnability signals affect both data sources differently.

Irene Lago, Ana Ezquerro, David Vilares

Universidade da Coruña, CITIC, Spain · Graz University of Technology, IML, Austria

Synthetic Data Learnability Distributional Information Multi-Label Classification

Sep 27, 2026cs.LG

Augmented Feature Boosting for Multicalibration

Multicalibration requires a predictor's residuals to be unbiased not only globally, but also after conditioning on the predictor's own level sets and reweighting by a rich class of test functions. Standard boosting approaches in the distributional setting achieve this by repeatedly discretizing the predictor's range then auditing and repairing the resulting level sets. One consequence is that in practice, the algorithm's guarantees are sensitive to this parametrization of the rounding parameter. A natural theoretical question, then, is how to do discretization-free boosting which avoids this rounding within the boosting process itself. Here, we analyze an alternative feature-augmentation boosting paradigm inspired by Tax et al. (2026): at each round, a squared-loss oracle is called on hypotheses that receive the previous predictor's output as an additional feature, and only the final predictor is rounded to have a finite set of level sets to provide the multicalibration guarantee with respect to. We give a theoretical analysis of this procedure through the expressivity of the augmented hypothesis class, and show how the expressivity of this class yields a hierarchy of guarantees, including multiaccuracy, multicalibration, and the stronger notion of level-set multicalibration.

Ira Globus-Harris, Inbal Livni Navon

Cornell University · Ben-Gurion University of the Negev

Calibrated Uncertainty Recalibration Distributional Information

Sep 27, 2026cs.LG

Diffusion Reward Models

Reward models underpin the alignment of large language models, yet the dominant designs reduce each prompt--response pair to a point estimate or to a distribution from a fixed parametric family. This is at odds with human preference, which is inherently multimodal: the same response can be reasonably judged in many ways, and no single family covers all of them. To better fit this structure, we introduce DRM, a Diffusion Reward Model that recasts reward modeling as conditional density estimation over

p(\mathbf{r}\mid x,y)

. Conditioned on a frozen LLM encoder, a lightweight Diffusion Transformer denoises Gaussian noise into a reward vector, placing no parametric assumption on the output distribution and naturally representing its multimodal structure. A single architecture handles both multi-attribute regression and pairwise preference data, and at inference

N

samples form an empirical reward distribution that can be aggregated into a scalar, a variance, or quantiles. Across five benchmarks, DRM matches or surpasses baselines under matched data and backbone, stays competitive with much larger discriminative, distributional, and generative RMs despite its modest training scale, and recovers multimodal reward structure where conventional heads collapse to a point. Uncertainty-aware rejection and lower-confidence-bound (LCB) aggregation further demonstrate that DRM can exploit distributional information beyond a scalar reward to improve reward-model decisions. Downstream RLHF experiments additionally show that using DRM as the training-time reward leads to improved policy performance, directly validating the practical benefit of diffusion-based reward modeling for RLHF training.

Xiangyang Wang, Bingxiang He, Zeyuan Liu +13

Tsinghua University · University of Illinois Urbana-Champaign

Progress Reward Modeling Diffusion Language Models Distributional Information

Sep 21, 2026cs.LG

Reinforcement Learning under State and Outcome Uncertainty: A Foundational Distributional Perspective

In many real-world planning tasks, agents must tackle uncertainty about the environment's state and variability in the outcomes of any chosen policy. We address both forms of uncertainty as a first step toward safer algorithms in partially observable settings. Specifically, we extend Distributional Reinforcement Learning (DistRL)-which models the entire return distribution for fully observable domains-to Partially Observable Markov Decision Processes (POMDPs), allowing an agent to learn the distribution of returns for each conditional plan. Concretely, we introduce new distributional Bellman operators for partial observability and prove their convergence under the supremum p-Wasserstein metric. We also propose a finite representation of these return distributions via psi-vectors, generalizing the classical alpha-vectors in POMDP solvers. Building on this, we develop Distributional Point-Based Value Iteration (DPBVI), which integrates psi-vectors into a standard point-based backup procedure-bridging DistRL and POMDP planning. By tracking return distributions, DPBVI lays the foundation for future risk-sensitive control in domains where rare, high-impact events must be carefully managed. We provide source code to foster further research in robust decision-making under partial observability.

Larry Preuett, Qiuyi Zhang, Muhammad Aurangzeb Ahmad

University of Washington, Tacoma, USA · Google DeepMind, California, USA · University of Washington, Bothell, USA

Partially Observable Markov Decision Process Distributional Reinforcement Learning Markov Decision Processes Partial Observability Uncertainty Distributional Information

Sep 7, 2026cs.CL

Translation Indeterminacy and the Distributional Fallacy

Large language models (LLMs) are commonly associated with the distributional hypothesis, according to which (1) semantic meaning is grounded in distributional patterns of linguistic context, and (2) knowledge of cross-linguistic distributional correspondences allows for successful translation. This paper rejects the first claim as a causal inversion: linguistic distributions reflect patterns arising from meaning-making practices rather than constituting their source. At the same time, it accepts the second claim, arguing that translation -human or machine - can succeed without requiring access to meaning or reference. Knowledge of interlingual distributional correspondence and their inferential organization may be sufficient for translation. The paper develops an ecological-enactivist perspective, according to which reference and meaning are grounded in agent-environment interaction and stabilized through action-grounded concepts, forms of world-involving cognition that current LLMs do not possess.

Michael Carl

Kent State University Modern and Classical Language Studies

Cross-Lingual Consistency Large Language Models Fail Distributional Information Logical Fallacies Ecosystems

Sep 3, 2026cs.LG

TraveL: Transformer-based Multi-view Path Distributional Representation Learning

Path representation learning (PRL) for road networks has received increasing research attention, due to various path-related applications. Existing works on PRL typically exploit the co-occurrence relationship among road segments and paths to learn a vector as the path representation, without exploring the varied traveler behaviors and the regional correlation on the path. In this work, we propose to learn distributional representations, which provide valuable information for use in path-related applications, by capturing the varied traveler behaviors as well as the various dependencies within regions of road segments. We propose a novel Transformer-based Multi-view Distributional Representation Learning (TraveL) framework to encode a path along with a travel starting time to a distributional representation, which can be used to decode possible samples of on-path traveler behavior. Moreover, by analyzing the regional correlation which reveals various road segment relationships, we propose a regional attention to encode these correlations in a path. Also, we explore the idea of Kolmogorov-Smirnov (K-S) test to compare the sampled traveler behavior against the collected ground truth to facilitate training. Experimental results show that the proposed TraveL model outperforms the state-of-the-art methods on both synthetic and real-world datasets, by 14.7% in Mean K-S distance for travel time distribution estimation, 16.7% in Mean Absolute Error (MAE) for path similarity prediction, and 3.97% in MAE for destination prediction.

Fang He, Tao-yang Fu, Wang-chien Lee

The Pennsylvania State University

Transport Pathways Journey Path Distributional Information

Aug 10, 2026cs.LG

Dynamic Distribution-Aware Uncertainty Tracking in Vision-Language Representation Learning

Uncertainty Quantification (UQ) aims to measure the reliability of model predictions, serving as a critical safeguard for deploying Vision-Language Models (VLMs) in safety-critical scenarios. Post-hoc approaches are widely adopted due to their lightweight nature, mapping the outputs of VLMs to uncertainty measures through learnable modules or inductive summarization. However, Post-hoc approaches remain inherently confined to fitting the failure patterns of the source domain, ignoring the dynamic nature of test distributions. To address this challenge, we propose a Dynamic Distribution-Aware Uncertainty Quantification framework (DDA-UQ) that shifts the paradigm from static mapping to a dynamic distribution-aware process. During training, we leverage a Gaussian Mixture Model to model the VVLMs'embedding space and extract distributional evidence, thereby dynamically deriving uncertainty estimates. During inference, the design dynamically responds to changes in the data distribution. Extensive experiments demonstrate that our approach significantly outperforms state-of-the-art methods.

Ao Zhou, Zhiwei Jiang, Zifeng Cheng +4

State Key Laboratory of Novel Software Technology, Nanjing University

Recent Vision-Language Models Uncertainty Distributional Information Gaussian Mixture Models Text Embeddings

Jul 29, 2026cs.CL

Relation Geometry in Semantic Space of Language Models

When it comes to generating vector representations of words, current language models are achieving high-quality results. However, what is not known is the extent to which knowledge about semantic relations is represented in the geometry of the semantic spaces created in this way. In order to answer this question, we study the relation geometry of such semantic spaces from three perspectives. We first examine whether words standing in a particular relation to a target word~(called relata) occupy the same region in semantic space, and whether the regions corresponding to different relations are distinct from each other. We then verify to what extent semantic spaces reflect certain well-known properties of relations, such as symmetry, asymmetry, and transitivity. Finally, we consider which information about the target words and relata is more important for relation geometry: their surface forms, or their contexts. We conduct experiments on six semantic relations using causal, masked, and diffusion language models. The results show that relata in asymmetric relations relatively clearly occupy a distinct region in semantic space. Asymmetric relations' properties are only moderately well encoded in the semantic space, yet better than those of symmetric ones. Furthermore, when considering the question which information source has the strongest impact on results amongst the models we evaluated, we find that lexical information tends to be more important for the causal language model, whereas contextual information is more important for the masked and diffusion language models. Our results empirically show that relation geometry is not equally well-represented for all relations in semantic space, suggesting that there is a difference in how well semantic relations might be learned from distributional information alone.

Zhihan Cao, Hiroaki Yamada, Simone Teufel +4

Graduate School of Information Science and Technology, The University of Tokyo · Faculty of Systems Design, Tokyo Metropolitan University · Department of Computer Science and Technology, University of Cambridge +5

Semantic Relationships Language Modeling Distributional Information Representation Space

Jul 24, 2026cs.LG

CEL: Comprehensive Counterfactual Explanations Library and Benchmark

Counterfactual explanations are a prominent approach in explainable artificial intelligence (xAI), providing actionable guidance on what input changes would alter a model's prediction to a desired outcome. While early methods primarily focused on minimal feature changes, recent work incorporates additional properties such as sparsity, actionability and plausibility. Despite this progress, fair and systematic evaluation remains challenging. Existing studies often rely on different data splits, predictive models, and evaluation metrics, which limits objective comparison across methods. To fill this gap, we introduce CEL (Counterfactual Explanations Library), a unified library and benchmark for counterfactual explanations designed to support consistent implementation and evaluation. CEL includes 18 datasets of varying size and complexity and provides implementations or reimplementations of 14 widely used counterfactual methods. Using this standardized setup, we conduct a comprehensive quantitative comparison across a variety of methods on datasets that differ in size, number, and types of attributes. The evaluation protocol incorporates multiple complementary metrics capturing validity, coverage, sparsity, proximity, and distributional plausibility, including density- and outlier-based measures to assess the realism of generated counterfactuals. To the best of our knowledge, this is the first comprehensive benchmark that systematically evaluates recent counterfactual explanation methods within a unified and reproducible framework. While prior libraries and benchmarking efforts exist in the literature, many are outdated, limited in scope, or lack consistent evaluation protocols. The proposed benchmark aims to improve reproducibility, enable fair comparison, and establish a workbench for the development of future counterfactual explanation methods.

Oleksii Furman, Łukasz Lenkiewicz, Marcel Musiałek +1

Wrocław University of Science and Technology, Wrocław, Poland

Counterfactual Explanation Distributional Information

Jul 23, 2026cs.CY

Distributional Validity of a Korean Synthetic Persona Panel: Evidence From the Korea Media Panel Survey

Large language model (LLM) personas are proposed as survey respondents, yet validation outside English-speaking contexts is scarce. We evaluate how well a Korean synthetic persona panel used to condition Gemini 3.5 Flash and EXAONE reproduces digital and artificial intelligence (AI) service-use distributions of the Korea Media Panel Survey. About 8,000 personas per model answered eight service-use items and eight attitudinal constructs; responses were compared with weighted survey estimates. The overall mean absolute error (MAE) was 14-19 percentage points (pp), with binary item-mean correlations of 0.70-0.91 across waves. Segment error across five axes was 14-18 pp, with between-group signed-error ranges of 49.6/34.7 pp (Gemini/EXAONE; 39.5/31.2 without the non-comparable teen cells). Errors were model-specific: an age stereotype (Gemini) versus an acquiescence-consistent level bias (EXAONE). Generative-AI overestimation was consistent with temporal misalignment; short-form underestimation was framing-sensitive and persisted under randomized order (both shown for Gemini). Post-hoc holdout calibration on 30% of the real data, with the correction form selected inside the calibration set, cut cell MAE from 18.3/15.1 to 4.9/4.4 pp, yet direct estimation from that subsample was more accurate than the calibrated panel (3.6 pp), a synthetic-informed shrinkage estimator beat its real-only counterpart by at most 0.7 pp, and the correction did not transfer competitively across waves. The calibrated panel kept an advantage only below roughly 250-860 real responses (at most 2.3 pp over a real-only shrinkage estimator) or, for one model, on unobserved segments. In this setting, synthetic panels are not survey substitutes; their value is diagnostic.

Howard Kim, Keuntae Cho

College of AI Convergence, Seoul Cyber University, Seoul 01133, South Korea · Department of Management of Technology, Graduate School, Sungkyunkwan University, Suwon 16419, South Korea · Department of Systems Management Engineering, Sungkyunkwan University, Suwon 16419, South Korea

Artificial Intelligence Personas Survey User Simulation Distributional Information

Jun 8, 2026cs.LG

A Unifying Framework for Concept-Based Representational Similarity

Learned representations across models and modalities often exhibit striking structural similarities, suggesting shared underlying concept decompositions. However, concept alignment remains poorly defined: existing approaches optimize different objectives under the same terminology, obscuring what is actually aligned. We propose a unifying framework that decomposes alignment along two axes: what is aligned (representations vs. concepts) and at what level (instance-wise vs. distributional). This induces four corresponding properties -- instance-wise and distributional variants of translation and concept consistency -- and reveals precisely which of these guarantees existing methods provide. We further introduce \InterVenchA, an intervention-based benchmark that separately measures extraction quality, translation quality, and concept consistency. Through theory and experiments, we show that commonly assumed equivalences between alignment objectives fail in practice: optimizing one property does not reliably recover the others, and purely unsupervised objectives fail to recover meaningful instance-level alignment. We then propose the Coupled Sparse Autoencoder (CoSAE), which jointly enforces complementary alignment objectives. Strong alignment emerges only in this regime. Surprisingly, as little as 0.1% paired data is sufficient to recover instance-level alignment when anchoring distributional objectives. Overall, our results show that concept alignment is fundamentally multi-objective: it must be defined, measured, and optimized as such.

Grégoire Dhimoïla, Victor Boutin, Agustin Martin Picard +2

Brown University · ENS Paris Saclay · CNRS +2

Representational Similarity Analysis Unified Framework Distributional Information

Jun 8, 2026cs.CL

Beyond Averages: Evaluating LLMs on Human Survey Replication at the Distributional Level

LLMs are increasingly used to simulate human survey responses, but prior work has mainly evaluated replication using mean-level or aggregate agreement, offering limited insight into whether LLMs reproduce the variability of human behavior. We evaluate LLM-based survey replication at the distributional level using a non-public 2010 consumer choice experiment on Korean instant noodle purchases, a setting unlikely to overlap with model training data. We evaluate three response variables of differing statistical type: binary purchase incidence, categorical brand choice, and count purchase quantity. For each, we compare human and LLM responses at mean-level, pattern, and distributional alignment, and against reference baselines from the human data alone. LLMs reproduce condition-level patterns reasonably well but fail to capture distributional structure: for purchase quantity, no model beats a condition-insensitive baseline that simply matches the pooled human distribution. Because models that match human means well can still produce distributions further from humans than this baseline, mean-based evaluation alone can be actively misleading. Replication also varies with input configuration, with structured personas and multimodal inputs improving alignment while explicit reasoning prompting degrades it monotonically.

Jeonghyeon Moon, Jiwon Kim, Yeheum Lah +2

Ewha Womans University

Survey Large Language Model Responses Distributional Information User Simulation Consumption

Jun 4, 2026cs.CL

UnpredictaBench: A Benchmark for Evaluating Distributional Randomness in LLMs

We introduce UnpredictaBench, an evaluation that tests the ability of large language models (LLMs) to capture true underlying distributions. As LLMs are increasingly used as substitutes for other entities (e.g., for humans in economic simulations), the tendency of many models to collapse towards a single plausible answer means a failure to capture the unpredictability of real systems. Recent work on improving output diversity is insufficient for this setting: simulation requires samples that are calibrated to a target distribution, not merely varied outputs. UnpredictaBench isolates a simplified but fundamental version of this problem: sampling outcomes from individual target distributions, including canonical statistical distributions, distributions induced by stochastic programs, and natural-language scenarios that describe random processes. We introduce 448 such problems together with KS@N, a general-purpose evaluation metric that quantifies how well a model outputs approximate black-box target distributions via the Kolmogorov-Smirnov statistical test. This is the rate at which we fail to reject model samples of size N against ground-truth samples, with larger N indicating greater difficulty. Tested across open and proprietary models, we find a large spread in distributional capabilities. For instance, when models generate samples of size 100 (KS@100, our standard metric), scores range from near 0 to over 20%. No model is able to achieve over 40% at KS@100, showing significant headroom in distributional sampling as a capability. Although adding reasoning can somewhat increase scores, we find no immediate solution for this issue. UnpredictaBench shows that even simple distributional simulation remains challenging, making it a necessary first step toward using LLMs as stand-ins for complex systems. Project website and resources are available at https://unpredictabenchmark.github.io/.

Amirhossein Abaskohi, Amirhossein Dabiriaghdam, Liang Luo +4

University of British Columbia · 2Independent Researcher

Distributional Information User Simulation Physical Plausibility

Jun 2, 2026cs.CL

Computational conceptual history of scientific concepts: From early digital methods to LLMs

This article situates large language models (LLMs) within the longer history of computational approaches to concept analysis in the history, philosophy, and sociology of science (HPSS). We examine what LLMs add to existing methods, how they inherit longstanding problems, and review recent case studies that employ them. In the first part, we reconstruct computational conceptual history before LLMs by bringing together three strands of work: early digital methods in HPSS, distributional approaches from digital history and related research, and lexical semantic change detection. We provide an overview of the main challenges and opportunities, focusing on corpus construction, operationalization and modelling choices, and evaluation and interpretation. In the second part, we turn to the era of LLMs, starting with a short introduction to LLMs before reviewing LLM-based work on lexical semantic change detection and relevant case studies in HPSS. We then revisit the earlier methodological questions, showing how issues of corpus construction, model choice and training data, operationalization trade-offs, and evaluation and interpretation play out in LLM-based workflows.

Michael Zichert, Arno Simons

History Distributional Information Text Corpora Early Layers

Jun 1, 2026cs.CV

VISReg: Variance-Invariance-Sketching Regularization for JEPA training

Self-supervised learning methods prevent embedding collapse via modeling heuristics or explicit regularization of the embedding space. Among the latter, VICReg decomposes regularization into variance and covariance objectives, offering flexibility and interpretability. However, covariance captures only second-order statistics -- encouraging decorrelation but failing to enforce the full distributional shape needed for stable training. Sketching-based methods such as SIGReg address this by aligning embeddings to an isotropic Gaussian, but lack flexibility and suffer from vanishing gradients under collapse. We propose Variance-Invariance-Sketching Regularization (VISReg), which replaces covariance with a Sliced-Wasserstein-based sketching objective that enforces full distributional shape, while retaining a variance term for scale control. By decoupling scale and shape, VISReg combines VICReg's flexibility with the distributional rigor of sketching methods, providing robust gradients even under collapse. We show that VISReg scales linearly, outperforms existing regularization on low-quality datasets, and is resilient to long-tailed and low-rank regimes. Pre-trained on ImageNet-1K, VISReg achieves state-of-the-art performance on out-of-distribution datasets. Pre-trained on ImageNet-22K, it matches DINOv2's OOD performance despite the latter using 10x more data (LVD-142M). Project and code: https://haiyuwu.github.io/visreg.

Haiyu Wu, Randall Balestriero, Morgan Levine

Altos Labs · Brown University

Regularization Covariance Distributional Information

May 31, 2026cs.CL

Before and After Temperature: A Distributional View of Creative LLM Generation

Reference-free evaluation of large language model (LLM) creativity relies on perplexity, entropy, and top-1 margin. We show that a much stronger signal lives one step earlier in the pipeline: in how sampling temperature \emph{reshapes} the model's token distribution before the next token is drawn. On Llama-3.1-8B-Instruct generations of 500 open-ended creative prompts at

T \in \{0.3, 0.8, 1.5\}

, a single per-token feature derived from this reshaping predicts the within-prompt creativity rank at Spearman

ρ{=}0.918

against an averaged gpt-4o,/,gemini-2.5-pro judge (

n{=}500

) and

ρ{=}0.870

against a three-rater human-majority ranking (

n{=}150

). Each of four standard reference-free baselines (self-perplexity, mean predictive entropy, top-1 margin, gzip compression ratio) tops out at

|ρ|\!\approx\!0.76

on both ground truths: a gap of

+0.165

on averaged-LLM and

+0.110

on human-majority, both far larger than the spread among the baselines themselves. The two ground-truth panels agree with each other at

ρ{=}0.83

, above the inter-human ceiling of

ρ{=}0.77

, so the comparison is not bottlenecked by judge noise. Mechanistically, the win comes from a sharp distributional signature of the incoherence regime: at

T{=}1.5

the cumulative-mass width

n_{95}(q)

inflates from

\sim\!1

to

{\sim}\!131

tokens and post-temperature mass leaks off the pre-temperature top-

90\%

plausible set by about

13

percentage points. The per-token aggregates do not separate

T{=}0.8

from

T{=}0.3

; discriminating the two coherent regimes is left to sequence-level features.

V. S. Raghu Parupudi, Harsha Ponnada, Aditi Kaushal +3

University of California, San Diego · Indian Institute of Technology, Kharagpur · Delhi Technological University +3

Creativity Large Language Model Generation Distributional Information

May 29, 2026cs.LG

Measuring Poverty and Inequality with Reduced Data: A Machine Learning Approach Using Nigerian Household Data

Reliable measurement of income and consumption is essential for monitoring poverty and inequality in low- and middle-income countries, yet full household surveys are costly and difficult to implement regularly. This paper examines whether reduced survey instruments can preserve key distributional information. We apply Random Forest Recursive Feature Elimination (RF-RFE) to the 2018/19 Nigeria General Household Survey-Panel to identify the income sources, consumption categories and household characteristics that best classify individuals within the welfare distribution. The analysis focuses on three outcomes: poverty status, location in the quintile distribution and position relative to the Gini-based inequality line. The survey's post-planting and post-harvest periods allow us to assess performance under different seasonal contexts. Results show that RF-RFE achieves strong classification accuracy with few predictors. For consumption, poverty status and inequality-line position are accurately predicted using a small set of expenditure categories, while quintile classification reaches about 80 percent accuracy for seasonal consumption and 60--65 percent for annual consumption predicted from a single seasonal visit. For income, poverty status reaches around 90 percent accuracy with five predictors, and inequality-line position is largely captured by labour earnings. The findings suggest that machine-learning methods can help improve survey design and reduce data requirements while retaining much of the distributional information needed to measure and monitor poverty and inequality.

Vanesa Jordá, Miguel Niño-Zarazúa

Department of Economics, Cantabria University · Department of Economics, SOAS University of London · United Nations University World Institute for Development Economics Research (UNU-WIDER)

Consumption Economies Distributional Information

May 28, 2026cs.LG

idSCD: Identifying Training Datasets through Semantic Correlation Descriptors

Can a dataset be recognized from the spurious correlations it induces during training? We argue that datasets leave dataset-specific traces in a model's learned semantic correlation structure: incidental regularities that are predictive within a dataset, but not causal for the underlying task, can be internalized during training. We use this insight to study dataset-level membership inference, moving beyond existing methods that rely on behavioral or distributional evidence such as confidence scores, losses, margins, generated samples, or query responses. We introduce a white-box semantic fingerprinting approach based on semantic correlation descriptors (SCDs), which capture the semantic correlation structure learned by a model and make it comparable across dataset mixtures. In a controlled leave-one-dataset-out diagnostic, SCDs recover dataset-specific changes and perfectly separate matching from non-matching dataset pairs. We then propose a practical SCD-based membership score that tests whether a target dataset is part of a model's training mixture using only the model's SCD and the target dataset's standalone SCD, without requiring leave-one-dataset-out models. Across three diverse experimental settings, with dataset groups for natural language inference, emotion classification, and medical text classification, we test both the advantages and limitations of SCD-based membership inference with different degrees of semantic separation and keyword support between dataset splits. On average, the classifier based on this score achieves the highest performance and the lowest std, outperforming black-box baselines RMIA, Attack-P, and LiRA, as well as the white-box SIF baseline. These results show that dataset membership can be traced through internal semantic correlations, with the largest relative gain exceeding 60% in ROC-AUC when dataset groups expose distinct semantic particularities.

Andrada Gobeaja, Ionut Hodoroaga, Elena Burceanu +1

POLITEHNICA University of Bucharest · Bitdefender, Romania · Institute of Mathematics of the Romanian Academy

Membership Inference Cross-Dataset Benchmark Training Data Distributional Information

May 20, 2026cs.CL

Probabilistic Attribution For Large Language Models

The generative nature of Large Language Models (LLMs) is reflected in the conditional probabilities they compute to sample each response token given the previous tokens. These probabilities encode the distributional structure that the model learns in training and exploits in inference. In this work, we use these probabilities to situate LLMs within the mathematical theory of stochastic processes. We use this framework to design a model-agnostic probabilistic token attribution measure, using Bayes rule to invert the next-token log-probabilities so as to capture the models internal representation of the distribution over token sequences. The representation is independent of the models computational structure. This representation yields the conditional probability of the response given the prompt, and of the response given the prompt with a token marginalized away. Our attribution score is the log of the ratio of these probabilities. We further compute the entropies of a single prompts token distributions, conditioned on the remaining context. The interplay between entropy and attribution score sheds light on LLM behavior. We evaluate 8 models across 7 prompts and investigate anomalies, token sensitivity, response stability, model stability, and training convergence, thereby improving interpretability and guiding users to focus on uncertain or unstable parts of the generation.

Shilpika Shilpika, Carlo Graziani, Bethany Lusch +2

Argonne Leadership Computing Facility Argonne National Laboratory Lemont, IL, USA · Mathematics and Computer Science Division Argonne National Laboratory Lemont, IL, USA · Department of Computer Science University of Illinois Chicago Chicago, IL, USA

Distributional Information

May 17, 2026cs.CV

A Distributional View for Visual Mechanistic Interpretability: KL-Minimal Soft-Constraint Principle

Most current paradigms in visual mechanistic interpretability (MI) remain confined to interpreting internal units of the vision model via heuristic methods (e.g., top-

K

activation retrieval or optimization with regularization). In this work, we establish a theoretical distributional view for visual MI, which models the influence of a feature activation on the natural image distribution, thereby formulating a Kullback-Leibler (KL)-minimal optimization problem to model the MI task. Under this framework, statistical biases are identified within previous MI paradigms, which reveal that they may either be perceptually uninterpretable to humans (i.e., deviate from the natural image distribution), or mechanistically unfaithful to the vision models (i.e., unable to activate model features). To resolve the biases under the distributional view, we propose a model with a KL-minimal soft-constraint principle for visual MI that theoretically balances interpretability and faithfulness. We realize this principle via energy-guided diffusion posterior sampling. Extensive experiments validate the theoretical soundness of the proposed distributional view and demonstrate the practical effectiveness of our paradigm on the DINOv3 vision model.

Guancheng Zhou, Yisi Luo, Zhengfu He +5

School of Mathematics and Statistics, Xi’an Jiaotong University · Shanghai Innovation Institute · OpenMOSS Team +2

Mechanistic Interpretability Interpretability Distributional Information Dinov3 Top-K

May 15, 2026cs.LG

Distributional Energy-Based Models for Uncertainty-Aware Structured LLM Reasoning

When Large Language Models produce structured outputs such as travel plans, code solutions, or multi-step proofs, individual reasoning steps may appear correct while the output as a whole violates budgets, fails test cases, or contradicts earlier deductions. We propose a decomposed energy function that combines a learned quality scorer with deterministic analytical constraint penalties for verifying structured LLM outputs. The quality scorer is a heterogeneous ensemble of low-rank adapters on a single frozen encoder (3% trainable parameters); the ensemble mean ranks candidates while the standard deviation quantifies epistemic uncertainty, driving a two-pass inference loop that triggers targeted regeneration or abstention. Across five benchmarks (GSM8K, MuSR, TravelPlanner, TACO, Knights & Knaves), our 149M-parameter verifier orchestrating a pool of 7-26B open generators outperforms single-shot Qwen-72B on every benchmark, matches Claude Sonnet 4.6 on MuSR (67.7% vs. 68.0%), and reduces constraint violations by 53% relative to Opus 4.6 on TravelPlanner (oracle 0.028, random 0.231). The two routes are complementary: structural verification wins when constraints are checkable (the verifier captures signal frontier models cannot self-detect), while pretraining-scale priors win where they are not (narrative inference, code semantics). A cross-dataset confounding analysis confirms genuine quality discrimination on four reasoning tasks and identifies a model-identity shortcut on code, mitigated via last-layer retraining. Scorers trained on difficult data transfer zero-shot: a MuSR-trained scorer achieves 93.9% on GSM8K without seeing a math problem.

Shireen Kudukkil Manchingal, Abhey Kalia, Fernanda Gonçalves +1

Oxford Dynamics · Harwell Science and Innovation Campus, United Kingdom

LLM Reasoning Strategies Large Language Model Uncertainty Reasoning Skills Distributional Information Frozen Encoder

May 14, 2026stat.ML

RoSHAP: A Distributional Framework and Robust Metric for Stable Feature Attribution

Feature attribution analysis is critical for interpreting machine learning models and supporting reliable data-driven decisions. However, feature attribution measures often exhibit stochastic variation: different train--test splits, random seeds, or model-fitting procedures can produce substantially different attribution values and feature rankings. This paper proposes a framework for incorporating stochastic nature of feature attribution and a robust attribution metric, RoSHAP, for stable feature ranking based on the SHAP metric. The proposed framework models the distribution of feature attribution scores and estimates it through bootstrap resampling and kernel density estimation. We show that, under mild regularity conditions, the aggregated feature attribution score is asymptotically Gaussian, which greatly reduces the computational cost of distribution estimation. The RoSHAP summarizes the distribution of SHAP into a robust feature-ranking criterion that simultaneously rewards features that are active, strong, and stable. Through simulations and real-data experiments, the proposed framework and RoSHAP outperform standard single-run attribution measures in identifying signal features. In addition, models built using RoSHAP-selected features achieve predictive performance comparable to full-feature models while using substantially fewer predictors. The proposed RoSHAP approach improves the stability and interpretability of machine learning models, enabling reliable and consistent insights for analysis.

Lanxin Xiang, Liang Shi, Youhui Ye +3

Department of Statistics Virginia Tech · Department of Statistics Virginia Tech Transportation Institute · Department of Computer Science Virginia Tech

Shapley Additive Explanations Model-Based Bootstrap Distributional Information

May 11, 2026cs.LG

Mixing Times of Glauber Dynamics on Masked Language Models

Masked language models (MLMs) define local conditional distributions over tokens but do not, in general, correspond to any consistent joint distribution over sequences. This raises a fundamental question: what global distributional behavior is induced when such conditionals are used iteratively for generation? We address this question by modeling iterative masked-token resampling as a Glauber dynamics Markov chain on the discrete space of token sequences. We first show that MLM conditionals are intrinsically incompatible: we introduce a rectangle test that certifies this incompatibility and empirically verify its prevalence across modern MLMs. We then provide a theoretical analysis of the induced Markov chain. Under bounded cross-token influence, we establish a high-temperature contraction result implying

O(n\log n)

mixing time where

n

is the sequence length. In contrast, we prove that under a uniform local margin condition, the chain exhibits metastability, with exponentially slow escape from semantic basins at low temperatures. Empirically, we demonstrate a phase transition in mixing behavior as a function of temperature and sequence length, consistent with the theoretical predictions. We further characterize the induced stationary behavior through semantic trajectories, identifying persistent structures such as long-lived traps and recurrent semantic basins, with political content serving as a measurable case study.

Suvadip Sana, Sami Wolf, Neer Mehta +4

Department of Statistics and Data Science Cornell University · Cornell University · Department Cornell of University Mathematics

Markov Distributional Information

May 2, 2026cs.CL

Injecting Distributional Awareness into MLLMs via Reinforcement Learning for Deep Imbalanced Regression

Multimodal large language models (MLLMs) struggle with numerical regression under long-tailed target distributions. Token-level supervised fine-tuning (SFT) and point-wise regression rewards bias learning toward high-density regions, leading to regression-to-the-mean behavior and poor tail performance. We identify the lack of cross-sample relational supervision as a key limitation of existing MLLM training paradigms. To address it, we propose a distribution-aware reinforcement learning framework based on Group Relative Policy Optimization, which introduces batch-level comparison-based supervision via the Concordance Correlation Coefficient-based reward to align predicted and ground-truth distributions in terms of correlation, scale, and mean. The framework is plug-and-play, requiring no architectural modification. Experiments on a unified suite of long-tailed regression benchmarks show consistent improvements over SFT and existing MLLM regression methods, with particularly strong gains in medium- and few-shot regimes.

Yao Du, Shanshan Song, Xiaomeng Li

The Hong Kong University of Science and Technology, Hong Kong SAR, China.

Multimodal Large Language Models Distributional Information Imbalanced Classification

Apr 30, 2026cs.CL

LLMs Capture Emotion Labels, Not Emotion Uncertainty: Distributional Analysis and Calibration of Human-LLM Judgment Gaps

Human annotators frequently disagree on emotion labels, yet most evaluations of Large Language Model (LLM) emotion annotation collapse these judgments into a single gold standard, discarding the distributional information that disagreement encodes. We ask whether LLMs capture the structure of this disagreement, not just majority labels, by comparing emotion judgment distributions between human annotators and four zero-shot LLMs, plus a fine-tuned RoBERTa baseline, across two complementary benchmarks: GoEmotions and EmoBank, totaling 640,000 LLM responses. Zero-shot models diverge substantially from human distributions, and in-domain fine-tuning, not model scale, is required to close the gap. We formalize a lexical-grounding gradient through a quantitative transparency score that predicts per-category human--LLM agreement: LLMs reliably capture emotions with explicit lexical markers but systematically fail on pragmatically complex emotions requiring contextual inference, a pattern that replicates across both categorical and continuous emotion frameworks. We further propose three lightweight post-hoc calibration methods that reduce the distributional gap by up to 14%, and provide actionable guidelines for when LLM emotion annotations can, and cannot, substitute for human labeling.

Keito Inoshita, Xiaokang Zhou, Akira Kawai +1

Faculty of Business and Commerce, Kansai University, Osaka, Japan · Faculty of Business Data Science, Kansai University, Osaka, Japan · RIKEN Center for Advanced Intelligence Project, Tokyo, Japan +2

Large Language Model Annotations Emotion Recognition Large Language Model Judges Disagreement Distributional Information

Apr 20, 2026cs.AI

Beyond One Output: Visualizing and Comparing Distributions of Language Model Generations

Users typically interact with and evaluate language models via single outputs, but each output is just one sample from a broad distribution of possible completions. This interaction hides distributional structure such as modes, uncommon edge cases, and sensitivity to small prompt changes, leading users to over-generalize from anecdotes when iterating on prompts for open-ended tasks. Informed by a formative study with researchers who use LMs (n=13) examining when stochasticity matters in practice, how they reason about distributions over language, and where current workflows break down, we introduce GROVE. GROVE is an interactive visualization that represents multiple LM generations as overlapping paths through a text graph, revealing shared structure, branching points, and clusters while preserving access to raw outputs. We evaluate across three crowdsourced user studies (N=47, 44, and 40 participants) targeting complementary distributional tasks. Our results support a hybrid workflow: graph summaries improve structural judgments such as assessing diversity, while direct output inspection remains stronger for detail-oriented questions.

Emily Reif, Claire Yang, Jared Hwang +3

University of Washington, Seattle, WA, USA · Allen Institute for AI

Large Language Model Generation Distributional Information Distributions Summarization

Apr 18, 2026cs.AI

Alignment Imprint: Zero-Shot AI-Generated Text Detection via Provable Preference Discrepancy

Detecting AI-generated text is an important but challenging problem. Existing likelihood-based detection methods are often sensitive to content complexity and may exhibit unstable performance. In this paper, our key insight is that modern Large Language Models (LLMs) undergo alignment (including fine-tuning and preference tuning), leaving a measurable distributional imprint. We theoretically derive this imprint by abstracting the alignment process as a sequence of constrained optimization steps, showing that the log-likelihood ratio can naturally decompose into implicit instructional biases and preference rewards. We refer to this quantity as the Alignment Imprint. Furthermore, to mitigate the instability in high-entropy regions, we introduce Log-likelihood Alignment Preference Discrepancy (LAPD), a standardized information-weighted statistic based on alignment imprint. We provide statistical guarantee that alignment-based statistics dominate Fast-DetectGPT in performance. We also theoretically show that LAPD strictly improves the unweighted alignment scores when the aligned and base models are close in distribution. Extensive experiments show that LAPD achieves an improvement 45.82% relative to the strongest existing baselines, yielding large and consistent gains across all settings.

Junxi Wu, Kailin Huang, Dongjian Hu +4

Nankai University · Tsinghua University · Wuhan University +3

Machine-Generated Text Detection Large Language Model Alignment Value Alignment Feature Alignment Text Analysis and Detection Zero-Shot+1

Mar 9, 2026cs.LG

Distributional Regression with Tabular Foundation Models: Evaluating Probabilistic Predictions via Proper Scoring Rules

Modern tabular foundation models such as TabPFN and TabICL naturally produce full predictive distributions, while the benchmarks used to evaluate them (TabArena, TALENT, and others) still rely almost exclusively on point-estimate metrics (RMSE,

R^2

). This mismatch implicitly rewards machine learning models or pipelines that elicit a good conditional mean while ignoring the quality of the predictive distribution. We make the case for using proper scoring rules for training, fine-tuning, and benchmarking (ranking) of tabular foundation models. Although all strictly proper scoring rules are theoretically equivalent at the population level, they may differ on finite data: We demonstrate analytically and empirically that different scoring rules can induce different inductive biases during finite-sample optimization, leading to different model performance. We validate this finding by running fine-tuning experiments with TabPFN and TabICL using different scoring rules for various data sets, revealing non-trivial interactions between training objectives and evaluation metrics. Our results show that practitioners can adapt tabular foundation models to task-specific scoring objectives, and that the choice of scoring rule can influence model behavior in practice.

Jonas Landsgesell, Pascal Knoll, Tizian Wenzel

University of Stuttgart (Stuttgart, Germany) · Ludwig Maximilian University of Munich (Munich, Germany) · Munich Center for Machine Learning (Munich, Germany)

Tabular Foundation Models Distributional Information Exponential Family Inductive Bias

Feb 17, 2026cs.LG

Logit Distance Bounds Representational Similarity

For a broad family of discriminative models that includes autoregressive language models, identifiability results imply that if two models induce the same conditional distributions, then their internal representations are equal up to an invertible linear transformation. We ask whether an analogous conclusion holds approximately when the distributions are close instead of equal. Building on the observation of Nielsen et al. (2025) that closeness in KL divergence need not imply high linear representational similarity, we study a distributional distance based on logit differences and show that closeness in this distance does yield linear similarity guarantees. Specifically, we define a representational dissimilarity measure based on the models' identifiability class and prove that it is bounded by the logit distance. We further show that, when model probabilities are bounded away from zero, KL divergence upper-bounds logit distance; yet the resulting bound fails to provide nontrivial control in practice. As a consequence, KL-based distillation can match a teacher's predictions while failing to preserve linear representational properties, such as linear-probe recoverability of human-interpretable concepts. In distillation experiments on synthetic and image datasets, logit-distance distillation yields students with higher linear representational similarity and better preservation of the teacher's linearly recoverable concepts.

Beatrix M. G. Nielsen, Emanuele Marconato, Luigi Gresele +2

IT University of Copenhagen, Denmark · University of Trento, Italy · University of Copenhagen, Denmark +2

Kullback-Leibler Divergence Logit Lens Discriminative Models Distributional Information Representational Similarity Analysis Representational Capacity+2

Oct 1, 2025cs.LG

How Does the Pretraining Distribution Shape In-Context Learning? A Fundamental Trade-Off

The factors driving the performance of in-context learning (ICL) in large language models (LLMs) remain poorly understood despite ICL's surprising effectiveness, enabling models to adapt to new tasks from only a handful of examples. To clarify and improve these capabilities, we characterize how the statistical properties of the pretraining distribution (e.g., tail behavior, coverage) shape ICL. We develop a theoretical framework that encompasses generalization and task selection and show how distributional properties govern sample efficiency, task retrieval, and robustness. To this end, we generalize existing concentration results to heavy-tailed priors and dependent sequences, better reflecting the structure of LLM pretraining data. Our framework reveals a fundamental design trade-off: heavy-tailed pretraining distributions facilitate robust task selection under distribution shifts but are detrimental to generalization, especially in low-data regimes. We then empirically evaluate our predictions by studying how ICL performance varies with the pretraining distribution on challenging tasks such as stochastic differential equations and stochastic processes with memory. Together, these findings suggest that controlling key statistical properties of the pretraining distribution is essential for building ICL-capable and reliable LLMs.

Waïss Azizian, Ali Hasan

Univ. Grenoble Alpes, CNRS, Inria, Grenoble INP, LJK, 38000 Grenoble, France · Work done during an internship at Morgan Stanley Machine Learning Research. · Machine Learning Research, Morgan Stanley, New York, USA

In-Context Learning Distributional Information Distributions Long-Tailed Distribution Trade-Off

Dec 14, 2024cs.CL

Tokens, the oft-overlooked appetizer: Large language models, the distributional hypothesis, and meaning

Tokenization is a necessary component within the current architecture of many language mod-els, including the transformer-based large language models (LLMs) of Generative AI, yet its impact on the model's cognition is often overlooked. We argue that LLMs demonstrate that the Distributional Hypothesis (DH) is sufficient for reasonably human-like language performance (particularly with respect to inferential lexical competence), and that the emergence of human-meaningful linguistic units among tokens and current structural constraints motivate changes to existing, linguistically-agnostic tokenization techniques, particularly with respect to their roles as (1) vehicles for conveying salient distributional patterns from human language to the model and as (2) semantic primitives. We explore tokenizations from a BPE tokenizer; extant model vocabularies obtained from Hugging Face and tiktoken; and the information in exemplar token vectors as they move through the layers of a RoBERTa (large) model. Besides creating suboptimal semantic building blocks and obscuring the model's access to the necessary distributional patterns, we describe how tokens and pretraining can act as a backdoor for bias and other unwanted content, which current alignment practices may not remediate. Additionally, we relay evidence that the tokenization algorithm's objective function impacts the LLM's cognition, despite being arguably meaningfully insulated from the main system intelligence. Finally, we discuss implications for architectural choices, meaning construction, the primacy of language for thought, and LLM cognition. [First uploaded to arXiv in December, 2024.]

Julia Witte Zimmerman, Denis Hudon, Kathryn Cramer +9

Computational Story Lab, Vermont Complex Systems Institute, University of Vermont, Burlington, VT 05405, USA · Vermont Complex Systems Institute, University of Vermont, Burlington, VT 05405, USA · Department of Computer Science, St. Michael’s College, Colchester, VT 05439, USA +3

Single-Token Output Distributions Distributional Information Transformer Architectures Generative Artificial Intelligence

Jan 31, 2023cs.CL

Universal Topological Regularity of Syntactic Structures

Despite their widespread use, the principles governing the organisation of syntactic dependency trees remain poorly understood. I analyse dependency trees from 124 typologically, genetically, and geographically diverse languages. Their topology departs systematically from randomness. Relative to uniformly sampled random trees, dependency trees exhibit greater structural robustness and lower branching heterogeneity. I propose that these universal regularities emerge naturally from incremental grammatical encoding. I model this process using sublinear preferential attachment. The model accurately reproduces the observed topology. More generally, the results demonstrate how a universal statistical property of syntax can emerge from a simple, cognitively motivated generative process. They further illustrate a broader principle of efficiency by construction: communicatively efficient syntactic structures can emerge without direct optimisation for communication.

Fermín Moscoso del Prado Martín

Department of Language and Communication & Center for Language Studies Radboud University Erasmuslaan 1, 6525 NL, Nijmegen, The Netherlands

Syntactic Structure Phylogenetic Inference Regularity Topology Dependency Graph Distributional Information+1