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14 papers in the last four weeks, down 18% on the four weeks before. 0.2% of all new papers.

Jul 6Week of Sep 21

Latest papers 197

Jul 19, 2026cs.CL

Auditing Question-Order Effects in Large Language Models with the QQ Equality: Mechanism Characterization and a Saturation Caveat

Question-order effects in human survey data have been reported to approximately satisfy the QQ (quantum question) equality, a parameter-free prediction of the standard projective quantum question-order model. We develop this equality into an audit framework for sequential binary judgments of autoregressive large language models (LLMs). Theoretically, we characterize mechanism families that satisfy QQ robustly, show that classical repetition can reproduce the equality exactly, and combine QQ with the rank-2 Contextuality-by-Default criterion through

|q_{QQ}| \le \mathrm{OSS}

. This separates order sensitivity, QQ imbalance, and residual contextuality rather than treating them as interchangeable signatures. Methodologically, we introduce a committed multi-turn forced-branch protocol that reconstructs order-conditioned joint distributions from next-token log-probabilities under counterbalanced label mappings and pre-specified health gates. A first-signal pilot on an open-weight instruction-tuned model reveals the central measurement problem. Although all pre-specified health gates passed, the binary-conditioned distributions were near-deterministic for 17 of 18 item pairs under the direct-evaluation framing and 7 of 8 under the persona framing. Label assignment materially changed several mapping-specific QQ verdicts, and no item was certified as residually contextual. Thus, under the tested conditions, the observed QQ outcomes did not uniquely identify a response mechanism in the presence of a saturated and label-sensitive measurement interface. The main implication is methodological: next-token probabilities should not be interpreted as survey-response distributions without first establishing adequate dispersion. We therefore argue that saturation screening and label counterbalancing should precede structural interpretation in distribution-level audits of LLM judgments.

Pilsung Kang

Department of Software Science, Dankook University Yongin, South Korea

Model Judgments Model Auditing Distributions

Jul 17, 2026physics.soc-ph

Distribution-First Population Simulation: Collapse, Calibration, and Recall in Non-WEIRD LLM Persona Modeling

Synthetic-population tools increasingly run every individual as an independent large language model (LLM) agent. Using real survey microdata, we show that this paradigm has a basic failure mode, and we set a distribution-first corrective against it, all measured with a deterministic, construct-validated verifier on non-WEIRD (Turkey-first) data. First, N independent LLM agents grounded on 2,414 real World Values Survey respondents fail to reproduce the population's response distribution: they pile onto a modal default (four scenarios x five seeds: concentration 0.36->0.69, entropy 1.46->0.77, 85% collapse, TVD=0.44), and the collapse is a predictable function of scenario structure (r=0.55 with a single-answer structure). Second, Verbalized Sampling (VS) fixes the field's chronic under-dispersion without training in three model families (fidelity +7 to +10; significant on Qwen, p=0.002, d=6.2), yet the same move universally overshoots into over-dispersion (SD-ratio 0.4-0.56 -> 1.26-1.37), a structural property of VS. Third, survey fidelity transfers only weakly to agentic behavior: in a single-model, single-domain booking task, a persona is dominated by a cheapest-default (~80%) that income modulates but does not override (comfort choice 0%->7%->32% across income bands). Fourth, a placebo-controlled memorization attack and an election backtest show VS keeps aggregate strength while subgroup and individual claims are contaminated by recall and underdetermination. We close with the corrective: model the distribution once (VS) and assign it to grounded characters at O(1) cost, with a budget-aware router whose honest AUC is 0.805, not the tautological 1.0 of a code-derived oracle. The central contribution needs no realism claim: it measures the internal inconsistency of the independent-agent route and the conditions under which the distribution-first route calibrates.

Gurkan Ozkan

Istanbul Technical University

Artificial Intelligence Personas User Simulation Population Dynamics Efficient Large Language Model Distributions Agentic+2

Jul 17, 2026cs.CV

Distributional Matching for Vector Quantization: A Unified Theoretical and Empirical Framework

The effectiveness of modern visual representation learning and autoregressive models critically depends on vector quantization (VQ), which discretizes continuous feature representations using a learnable codebook. Despite its widespread use, existing VQ methods often suffer from training instability and codebook collapse, arising from gradient mismatch induced by the straight-through estimator and the under-utilization of code vectors. In this work, we show that both issues can be traced to a fundamental mismatch between the distributions of feature vectors and code vectors, leading to inefficient representation and information loss. Building on this observation, we propose a distributional matching framework for vector quantization. We introduce principled criteria for desirable VQ behavior and demonstrate through theoretical analysis and empirical evaluation that aligning feature and code vector distributions provides a unifying mechanism for mitigating training instability and codebook collapse. We instantiate this framework using a Wasserstein-based objective with an efficient closed-form under a mild Gaussian approximation, and further show that a nonparametric alternative based on maximum mean discrepancy yields comparable performance. Extensive experiments on visual tokenization benchmarks support the effectiveness and robustness of the proposed approach.

Xianghong Fang, Litao Guo, Hengchao Chen +8

University of Toronto · The Hong Kong University of Science and Technology · Lehigh University +2

Residual Vector Quantization Codebooks Distribution Matching Distributions Unified Formulation Preliminary Study

Jul 17, 2026cs.DS

Testing Distributions Against Bounded Distinguishers

Motivated by the challenge of testing distributions over high-dimensional or continuous domains, we study distribution testing with respect to bounded classes of distinguishers. A representative task is to use samples from an unknown distribution

P

over a very large domain to decide between two cases:

P = P_{\mathsf{ref}}

for a fixed reference distribution

P_{\mathsf{ref}}

, or there exists a distinguisher

f

in a bounded class

\mathcal{F}

which witnesses the separation

|\mathbf{E}_P[f] - \mathbf{E}_{P_{\mathsf{ref}}}[f]| > ε

. This is the task of identity testing with respect to fooling distance, a name inspired by the conceptual connection with pseudorandomness. (Formally, our model instantiates integral probability metrics from Boolean classes of bounded expressivity.) We show that testing with respect to fooling distance is not only a natural computational problem that admits sample-efficient algorithms even in high-dimensional settings, but also one that reveals and underlies connections between three seemingly unrelated areas of study: testable learning, verification of learning algorithms, and testing of structured distributions (whose "

\mathcal{A}_k

-testing" model our framework extends). These connections yield new results for all of these models, including: 1. Testable proper learners using membership queries for halfspaces and decision trees. 2. A lower bound for testable PAC verification in terms of Rademacher complexity, and a distribution-free verification protocol for disjoint unions of

k

multidimensional rectangles. 3. Identity testers (with respect to total variation distance) for decision tree distributions and distributions with low-degree polynomial densities, over Boolean and continuous hypercube domains.

Mark Bun, Rathin Desai, Renato Ferreira Pinto

Boston University · Columbia University

Indistinguishability Two-Sample Testing Distributions

Jul 16, 2026cs.LG

Grad2Fair: A Gradient-driven Approach for Graph Fairness without Demographics

Graph neural networks (GNNs) frequently encounter group fairness issues, often yielding biased predictions against specific demographic groups defined by sensitive attributes such as gender or race. While this challenge has motivated extensive research, most existing solutions rely on the strong assumption that demographics are fully available. To bypass this strict requirement, a few recent studies have attempted to use predicted demographics as proxies to enforce fairness constraints. However, predicted demographics may be inaccurate, resulting in the failure to improve fairness. In this work, we investigate the problem of graph fairness without demographic information and avoid the utilization of predicted demographics. Motivated by our observation that the gradient distributions of misclassified nodes implicitly encode demographic information, we first propose GradDist, a gradient-based metric that quantifies bias by measuring the distance between local modes within these distributions. To mitigate this bias, we propose Gradient-to-Fairness (Grad2Fair), a gradient-guided approach for group fairness without demographics. Due to the potential demographics in gradients, Grad2Fair directly leverages gradients to debias and eliminates demographic prediction, thereby enabling stable fairness performance. Experiments on several real-world datasets demonstrate the effectiveness of Grad2Fair, as evidenced by superior performance over baselines in most cases. Our code is available at https://github.com/ZzoomD/Grad2Fair.

Yuchang Zhu, Zezhong Xie, Huizhe Zhang +4

School of Computer Science and Engineering, Sun Yat-Sen University, Guangzhou 510007, China · Institute of Artificial Intelligence, Xiamen University, Xiamen 361005, China · School of Software Engineering, Sun Yat-sen University, Zhuhai 519082, China

Algorithmic Fairness Federated Graph Learning Graph Neural Networks Demographics Gradient-Based Optimization Distributions

Jul 15, 2026cs.RO

DiMaS: Distribution Matching for Steering Vision-Language-Action Models

Flow-matching-based vision-language-action (VLA) models have emerged as powerful policies for robotic manipulation, yet a critical capability remains underexplored: fine-grained behavioral control, the ability to govern how a robot performs a task by intervening on its internal representations. Representation steering is a well-established interpretability tool for language and vision-language models, where behavioral features are typically encoded as linear directions, but we show that these classic methods fall short in VLAs. We propose DiMaS, a Distribution-Matching Steering strategy tailored to flow-matching VLAs, which transports between representation distributions rather than shifting along a fixed direction, and show that it effectively controls behavior across two state-of-the-art VLAs. We further examine the generalizability of this strategy as the tasks it is learned from and evaluated on grow increasingly dissimilar, characterizing where behavioral control transfers and where it weakens. Finally, through an analysis of the representation structure of the action expert, we explain why classical linear steering falls short in the visuomotor setting: behavioral features are linearly decodable but not linearly steerable, which motivates the distribution-matching design of DiMaS. Our code is publicly available at https://github.com/pegah-kh/dimas, with additional results and videos at https://pegah-kh.github.io/dimas/

Pegah Khayatan, Sara Meziane, Jayneel Parekh +1

ISIR, Sorbonne Universit´e, Paris, France · Valeo.ai, Paris, France

Flow-Matching Vision-Language-Action Visuomotor Control Distribution Matching Distributions

Jul 13, 2026cs.AI

Auditing the Risk Claims of Distributional Reinforcement Learning

Distributional reinforcement learning agents learn full return distributions that are increasingly read at face value: for interpretability, risk-sensitive control, and safety monitoring. We ask a question theory anticipates but that has not been measured directly: are the risk claims of a trained distributional agent true? Our audit combines a decision-relevant screening metric (the excess Wasserstein gap between the top two actions, which equals the mass by which first-order stochastic dominance is violated), ground truth from snapshot-restart Monte Carlo, and a statistical harness (permutation nulls, bootstrap refutation, FDR control) without which the audit itself manufactures false conclusions. Across QR-DQN, C51, and IQN on MinAtar (33 runs), 40-95% of the strongest claimed risk trade-offs are refuted at 95% confidence, the placement of the strongest claims is statistically indistinguishable from truth-blind, and essentially no claim is confirmable: for these agents, the learned "risk" reflects a training artifact rather than environment stochasticity. The artifact is structural (fully formed early in training, uncorrelated with final score, idiosyncratic to each seed) and appears unchanged at full-Atari scale, with every top Breakout claim of a pretrained near-state-of-the-art QR-DQN refuted. Positive controls of known magnitude confirm 96-100% of real claims (correlation 0.89-0.92): the reading measures the agents, not the audit. Acting on the heads' CVaR advice at their most-flagged states ranges from beneficial to significantly worse than chance. Neither training for risk nor ensembling removes the artifact, and recalibration passes the audit only by nullifying the claims: the head is uninformative, not merely miscalibrated. We release the toolkit and document two silent pitfalls that produced convincing but wrong audits of our own.

Hari Prasad

Distributional Reinforcement Learning Target Risk Risk Distributions Interpretability

Jul 10, 2026cs.DS

Learning Partition Trees for Nearest Neighbor Search

We study nearest neighbor search from the perspective of data-driven algorithm design: given a dataset

P \subset \mathbb{R}^d

of size

n

and sample access to a query distribution over

\mathbb{R}^d

, the goal is to learn a data structure optimized for queries drawn from that specific distribution. We focus on the class of balanced halfspace trees, which naturally abstracts space-partitioning frameworks like locality-sensitive hashing. Assuming Gaussian-like marginal conditions on the dataset and query distribution, we give an efficient algorithm that learns a tree achieving

o(nd)

query time, provided that a perfect tree exists. At the core of our algorithmic approach is the balanced halfspace cut problem, where we are given a distribution over

\mathbb{R}^d \times \mathbb{R}^d

and must find a balanced halfspace that minimizes the fraction of cut pairs. We prove that without distributional assumptions, finding the optimal balanced halfspace is NP-hard. To circumvent this computational barrier, we design an efficient improper learning algorithm: if the optimal halfspace cuts an

α

fraction of pairs, our algorithm outputs a balanced polynomial threshold function of degree

\tilde{O}(1/\varepsilon^2)

that cuts at most an

O(\sqrt{α+\varepsilon})

fraction.

Sanjeev Khanna, Ashwin Padaki, Erik Waingarten

NYU · University of Pennsylvania

Approximate Nearest-Neighbor Search O(\Bar{K}\Log N)$Partitioning Search Algorithms Locality-Sensitive Hashing Distributions+1

Jul 10, 2026cs.CV

The Effects of Synthetic Data and Label Distribution on Canola Branch Counting

Collecting annotated plant images for automated phenotyping is often slow and expensive. Plant models simulating growth and development can generate unlimited synthetic images with exact labels. However, previous work has established that whether incorporating synthetic data improves performance depends on the ratio of synthetic to real images and the label distribution of the synthetic dataset. To systematically quantify both factors, we train ResNet-18 models on a canola branch-counting task using a calibrated L-system plant model. We vary each factor independently. Synthetic-to-real ratios of 1:5 to 1:22 broadly improve performance; the best ratio (1:7) reduces mean absolute difference by 7.6% over real-only training. For label distribution, a uniform synthetic distribution is strongly suboptimal (abs. diff. of approximately 1.70); interpolating 90% toward the real distribution yields abs. diff. 0.927, whereas Gaussian smoothing of the real label distribution yields the best overall result (abs. diff. 0.912, a 14.7% improvement over real-only). A minimum of 10 synthetic images per label offers a simpler alternative with modest gains, while 100 per label over-corrects and hurts performance.

Amirsalar Darvishpour, Mikolaj Cieslak, Adam Runions

Department of Computer Science, University of Calgary

Tomato Diseases Synthetic Data Synthetic-To-Real Domain Gap Phenotypes Distributions Impact Analysis

Jul 10, 2026cs.LG

Temporal Knowledge Graph Forecasting under Distribution Shifts: A Synthetic Evaluation

Temporal knowledge graphs (TKGs) represent evolving relational systems, whose underlying data-generating processes often change over time. Yet, TKG forecasting models are commonly evaluated only on empirical benchmark datasets that provide limited insight into the models' robustness to such distribution shifts. Recognising this issue, we study TKG forecasting under controlled shift environments using a synthetic TKG generator that encodes three temporal and structural properties -- recurrence, homophily, and periodicity -- as data-generating mechanisms. This allows us to evaluate seven forecasting architectures under stationary and shifting regimes. Our experiments suggest that robustness in TKG forecasting is highly signal-dependent. Recurrence-based and periodic regularities are largely recoverable under stationary conditions, and simple memory-based baselines can be competitive when recurrence dominates the data. However, structural breaks reveal limitations in model adaptivity, with shifts in latent entity-community structure posing the strongest challenge in our study. Overall, our findings improve the understanding of the capabilities and limitations of current TKG models confronted with temporal distribution shifts.

Konrad Özdemir, Julia Gastinger, Lukas Kirchdorfer +1

Data and Web Science Group, University of Mannheim, Germany · SAP Signavio, Walldorf, Germany

Temporal Knowledge Graphs Distribution Shifts Relational Databases Distributions

Jul 9, 2026stat.ML

Statistical Efficiency and Inference of Quantile Distributional Reinforcement Learning

In this paper, we study quantile-based distributional reinforcement learning from the perspective of statistical efficiency. We focus on distributional policy evaluation, whose goal is to characterize the return distribution, namely the distribution of discounted cumulative rewards under a given policy. To obtain a finite-dimensional representation of the return distribution, we consider the quantile fixed point

η_m

induced by the quantile-projected distributional Bellman equation. Assuming access to a generative model, we construct an estimator

η_m^{(n)}

based on an empirical Markov decision process. For a fixed number of quantiles

m

, we establish a non-asymptotic error bound for

η_m^{(n)}

and

η_m

under the supremum

W_\infty

metric, showing that the estimation error scales as

\widetilde{O}(\sqrt{m/n})

with respect to

m

and

n

. This implies that the quantile-based distributional policy evaluation problem can be solved with sample efficiency, achieving the optimal parametric

\sqrt{n}

convergence rate. We derive the asymptotic distribution of the quantile parameters

\sqrt{n}(θ_m^{(n)}-θ_m)

and characterize the semiparametric efficiency bound, which is attained by our estimator. Beyond the fixed-dimensional setting, we investigate the asymptotic regime in which the number of quantiles diverges. We characterize the limit covariance structure and show that it matches the semiparametric efficiency bound of the nonparametric model for distributional policy evaluation, showing that quantile-based estimators remain asymptotically efficient in the infinite-dimensional limit. Finally, we establish a Berry--Esseen theorem for smooth functionals

\sqrt{n}(η_m^{(n)}(s)-η_m(s))f

, thereby providing a foundation for statistically valid inference on functionals of the quantile-projected return distribution.

Zijie Cheng, Yang Peng, Zhihua Zhang

School of Mathematical Sciences, Peking University · Yau Mathematical Sciences Center, Tsinghua University

Distributional Reinforcement Learning Distributions Bellman Equation

Jul 8, 2026cs.CV

Stage-Aware Adaptation and Distribution Calibration for Subject-Driven Personalized Text-to-Image Generation

Subject-driven personalized text-to-image generation requires a pretrained diffusion model to acquire a specific subject from a few reference images while preserving subject identity, following novel text prompts, and maintaining sample diversity. Existing optimization-based methods instantiate subject adaptation through full fine-tuning, textual embedding optimization, or low-rank parameter updates; PaRa further constrains personalization from the perspective of parameter rank reduction. However, a uniform low-rank constraint or a uniform adapter strength cannot explicitly distinguish the capacity requirements of different denoising stages. Moreover, inference-time candidate selection driven mainly by identity similarity may compress the selected samples in the visual representation space. We decompose the problem into two complementary components: SPaRa denotes training-side stage-aware low-rank adaptation, DCAL denotes inference-side distribution-calibrated candidate selection, and SPaRa-DCAL denotes the combined framework. Theoretical analysis shows that timestep-dependent scaling controls the effective perturbation magnitude of a low-rank adapter, while identity-biased candidate selection restricts the radius of selected features around the reference center under explicit conditions. Auditable experiments under the SDXL and DreamBooth 30-subject protocol show that DCAL improves 1-LPIPS, CLIP-I, DINO-I, and CLIP-T on a fixed LoRA candidate pool, while revealing a clear trade-off with CLIP/DINO pairwise diversity and pairwise LPIPS. These results indicate that personalized generation should be evaluated through identity consistency, text alignment, and representation diversity rather than identity metrics alone.

Wenyan Xu, Alizer Wong

School of Computer Science, Guangdong University of Technology · School of Computer Science, Peking University · 3ManXis

Text-To-Image Training-Side Stage-Aware Low-Rank Adaptation Distributions

Jul 6, 2026cs.CV

Learning Flexible Generalization in Video Quality Assessment by Bringing Device and Viewing Condition Distributions

Video quality assessment (VQA) plays a critical role in optimizing video delivery systems. While numerous objective metrics have been proposed to approximate human perception, the perceived quality strongly depends on viewing conditions and display characteristics. Factors such as ambient lighting, display brightness, and resolution significantly influence the visibility of distortions. In this work, we address the question of the multi-screen quality assessment on mobile devices, as this area still tends to be under-covered. We introduce a first large-scale subjective dataset collected across more than different 300 Android devices, accompanied by metadata on viewing conditions and display properties. We propose a strategy for aggregated score extraction and adaptation of VQA models to device-specific quality estimation. Our results demonstrate that incorporating device and context information enables more accurate and flexible quality prediction, offering new opportunities for fine-grained optimization in streaming services. Ultimately, this work advances the development of perceptual quality models that bridge the gap between laboratory evaluations and the diverse conditions of real-world media consumption. We made the dataset and the code available at https://videoprocessing.github.io/device-viewing-conditions.

Nikolay Safonov, Dmitriy S. Vatolin

MSU Institute for Artificial Intelligence, Moscow, Russia · AI Center, Lomonosov Moscow State University, Moscow, Russia

Video Quality Perceptual Quality Image Quality Assessment Device Distributions

Jul 3, 2026cs.DB

Selectivity Estimation for Linear Queries via Online Learning

Learning-based approaches for selectivity estimation in databases have gained significant traction in recent years. However, theoretical studies of these learning-based approaches are essentially limited to fixed query distributions on static databases. In practice, both the underlying database and the query workload can dynamically change over time. In this work, we propose an algorithmic framework for learning selectivity of queries in this more general dynamic setup. Inspired by online learning, we measure the performance of the learning algorithm in this setting by its regret, which compares the cumulative loss incurred by the learning algorithm to that of the best fixed strategy. We establish upper and lower bounds on regret for histogram-based linear queries, such as point, range, and subset selection queries, under standard loss functions, in both static and dynamic database settings.

Fangzhu Shen, Debmalya Panigrahi, Sudeepa Roy

Duke University, USA

Learning-Augmented Algorithms Selectivity Queries Distributions

Jul 2, 2026cs.LG

Understanding the Robustness of Distributed Self-Supervised Learning Frameworks Against Non-IID Data

Recent research has introduced distributed self-supervised learning (D-SSL) approaches to leverage vast amounts of unlabeled decentralized data. However, D-SSL faces the critical challenge of data heterogeneity, and there is limited theoretical understanding of how different D-SSL frameworks respond to this challenge. To fill this gap, we present a rigorous theoretical analysis of the robustness of D-SSL frameworks under non-IID (non-independent and identically distributed) settings. Our results show that pre-training with Masked Image Modeling (MIM) is inherently more robust to heterogeneous data than Contrastive Learning (CL), and that the robustness of decentralized SSL increases with average network connectivity, implying that federated learning (FL) is no less robust than decentralized learning (DecL). These findings provide a solid theoretical foundation for guiding the design of future D-SSL algorithms. To further illustrate the practical implications of our theory, we introduce MAR loss, a refinement of the MIM objective with local-to-global alignment regularization. Extensive experiments across model architectures and distributed settings validate our theoretical insights, and additionally confirm the effectiveness of MAR loss as an application of our analysis.

Xuanyu Chen, Nan Yang, Shuai Wang +1

School of Electrical and Computer Engineering, The University of Sydney · 2Northwestern Polytechnical University

Decentralized Learning Self-Supervised Learning Distributions

Jul 2, 2026cs.AI

Text-Driven 3D Indoor Scene Synthesis in Non-Manhattan Environments

Large Language Models (LLMs) have demonstrated remarkable capabilities in 3D indoor synthesis for Manhattan environments. However, existing methods often fail to capture plausible object layout patterns in non-Manhattan settings, primarily because they struggle to model non-orthogonal spatial relationships, leading to high geometric violations and low physical fidelity. To address this challenge, we propose SPG-Layout, a novel text-driven framework designed to generate physically plausible indoor scenes within complex non-Manhattan environments. Specifically, we first utilize statistical priors of object distributions to guide the training process, enhancing environmental understanding and fidelity. Furthermore, mirroring human design workflows, we adopt a hierarchical layout strategy that prioritizes the placement of large objects, thereby substantially minimizing layout violations. By synergizing these components, SPG-Layout achieves a balanced optimization of semantic realism and physical plausibility. To evaluate performance in these complex settings, we constructed a new benchmark comprising 500 diverse non-Manhattan environments. Extensive experiments demonstrate that SPG-Layout consistently and significantly outperforms existing methods across both Manhattan and non-Manhattan environments. The code will be publicly released.

Xianhui Meng, Zirui Song, Yuchen Zhang +10

University of Science and Technology of China · Xiaomi EV · Mohamed bin Zayed University of Artificial Intelligence +4

3D Layout Generation 3D Scene Generation Layouts Scene Understanding Environment Distributions

Jun 30, 2026cs.LG

ComplianceGate: Classifier-Gated Multi-Tier LLM Routing for Inference in Regulated Industries

Large language models deployed in regulated industries operate under two constraints: compliance enforcement and cost efficiency. Personally identifiable information (PII) in user queries can reach model endpoints before the system determines whether that data should leave its jurisdictional boundary. Serving all queries through a single large model consumes full GPU capacity regardless of query complexity while offering no mechanism for geographic routing. Mixture-of-Experts architectures do not address this routing occurs between expert layers within the model after data has already arrived at the endpoint, with all experts loaded in memory regardless of query complexity. We propose a classifier-gated routing architecture that enforces compliance by design. A trained encoder classifier sits before any decoder inference, evaluating each query for complexity and data sensitivity, then routing it to an appropriately sized dense model in the appropriate geographic location. PII-containing queries route to local endpoints before any LLM computation begins, making data residency violations structurally impossible. Simple queries reach small, fast models at a fraction of the cost. Our evaluation on 600 queries demonstrates 39% median latency reduction, 33-52% cost savings depending on query distribution, and generation throughput of 122-200 tokens/second versus 50-64 for the baseline. The encoder classifier achieves 99.2% accuracy with near-perfect PII recall at 7ms inference overhead, establishing pre-inference classification as a practical path to compliance-by-design LLM deployment.

Abhishek Dey

Independent AI Researcher, India

Large Language Model Routing LLM Inference Optimization Compliance Large Language Model Pipelines Streaming Guardrails Distributions

Jun 29, 2026stat.ML

Highly Data Parallelizable Estimation of the Sliced-Wasserstein Distance Using Cumulative Distribution Functions

The Sliced Wasserstein (SW) distance has emerged as a computationally attractive alternative to the Wasserstein distance by leveraging one-dimensional optimal transport along random projections. Standard estimators of the SW distance rely on Monte Carlo averages of one-dimensional Wasserstein distances computed via quantile functions, which require sorting projected samples and access to full datasets. In this work, we introduce a new class of estimators for the Sliced Wasserstein distance based on cumulative distribution functions (CDFs) of projected measures, that avoid sorting and scale via massive dataset parallelism. This class includes several estimators, some of them being indexed by hyperparameters controlling their variance or smoothness. We show that they are especially well suited to scenarios in which CDFs are more tractable than quantile functions, such as mixtures of Gaussians, and moreover that they are also naturally compatible with federated learning, since CDFs of projected data can be computed and aggregated locally without requiring the exchange of raw samples.

Christophe Vauthier, Quentin Mérigot, Anna Korba

Laboratoire de Mathématiques d’Orsay, Université Paris-Saclay Gif-sur-Yvette, France · Centre de recherche en économie et statistique, ENSAE Palaiseau, France

Wasserstein Distance Density Ratio Estimation Distance Distributions

Jun 29, 2026stat.ML

Adjusted Wasserstein distances for bridging empirical and true distributions with applications to MDS

This paper examines how metric adjustments to Multidimensional Scaling (MDS) can enhance its effectiveness as a visual tool for pattern recognition. The distance under consideration, referred to as Max-D-SW, is an adjustment of the Max-Sliced Wasserstein distance. In contrast to the original formulation, which optimizes over single unit directions, Max-D-SW aggregates contributions over orthonormal bases. This modification provides a clear numerical advantage in MDS outcomes, particularly when applied to heavy-tailed distributions. We also establish sample-complexity bounds showing that Max-D-SW remains statistically tractable, with rates comparable to those of its max-sliced counterpart. Moreover, we show that a better sample complexity for a metric does not necessarily translate into better performance when the metric is used as an input for MDS.

Flor Martinez-Sermeno, Arturo Jaramillo, Johan Van Horebeek

Wasserstein Distance Optimal Sample Complexity Distributions

Jun 28, 2026cs.RO

MTD-Map: Single-Stage Long-Term LiDAR Map Maintenance Framework via Mixture Transition Distribution

While robust map maintenance has advanced significantly, existing studies have focused on specific tasks, especially dynamic object removal or change detection. In this paper, we take a holistic view of the map maintenance problem and propose MTD-Map, a single-stage framework that handles both dynamic object removal and change detection without separate task-specific modules. MTD-Map employs an explicit representation that compactly encodes the direction and duration of occupancy transitions through Mixture Transition Distribution (MTD) modeling. We develop a recursive MTD formulation that encodes historical occupancy patterns into an augmented state to capture high-order temporal dependencies. Furthermore, a stability-driven adaptive strategy balances noise suppression with the preservation of quasi-static structures. Extensive experiments verify that MTD-Map robustly removes dynamic objects and achieves competitive change detection performance, subsequently reducing computational costs. Our project page is available at: https://taeyoung96.github.io/mtd_map/.

TaeYoung Kim, Gilhwan Kang, Tae Ihn Kim +2

Robotics Lab, Advanced Vehicle Platform Division, Hyundai Motor Company, Uiwang-si, Gyeonggi-do, Republic of Korea

Change Detection Video Object Removal Distributions

Jun 28, 2026cs.LG

Beyond Trajectory Matching: Reflow with Marginal Distribution Alignment

Diffusion and continuous-flow generative models achieve high-quality generation, and their deterministic sampling can be formulated as solving learned ODE dynamics. However, accurate ODE discretization often requires many steps, making efficient few-step generation a key challenge. Among acceleration strategies, reflow-based distillation simplifies teacher ODE trajectories so that a student model can approximate the teacher transport with fewer steps. We identify a theoretical limitation of this paradigm, namely that trajectory matching can under-determine the distribution induced by the student model. In particular, two student models can attain the same trajectory-matching loss while inducing different endpoint marginal distributions, which may lead to different generation quality. To address this limitation, we introduce a marginal-alignment regularizer that penalizes the discrepancy between the student-induced marginal and the corresponding teacher marginal at the endpoint of each distillation interval. The regularizer is computed by tracking log-density changes along the ODE induced by the student model and evaluating scores from the frozen teacher model, without requiring auxiliary trainable networks or adversarial optimization. The resulting framework applies uniformly to the reflow family, including vanilla reflow and piecewise reflow. We further prove a telescoping total-variation bound showing that local marginal alignment controls the final-time discrepancy between the student-induced and teacher-induced distributions. Experiments on benchmark backbones demonstrate the effectiveness of the proposed method for few-step generation.

Chen Wang, Peiran Yun, Pan Xie +1

Department of Statistics and Data Science, Tsinghua University · Department of Computer Science and Technology, Tsinghua University · Bytedance Inc

Diffusion Alignment Distribution Matching Distillation Generative Models Distributions Time Discretization Trajectory Generation+1

Jun 28, 2026stat.ML

Generalization Analysis of Transformers in Distribution Regression

In recent years, models based on the Transformer architecture have seen widespread applications and have become one of the core tools in the field of deep learning. Numerous successful techniques, such as parameter-efficient fine-tuning and efficient scaling, have been proposed surrounding their applications to further enhance performance. However, the success of these strategies has always lacked the support of rigorous mathematical theory. To study the underlying mechanisms behind Transformers and related techniques, we first propose a Transformer learning framework motivated by distribution regression, with distributions being inputs, connect a two-stage sampling process with natural language processing, and present a mathematical formulation of the attention mechanism called attention operator. We demonstrate that by the attention operator, Transformers can compress distributions into function representations without loss of information. Moreover, with the advantages of our novel attention operator, Transformers exhibit a stronger capability to learn functionals with more complex structures than convolutional neural networks and fully connected networks. Finally, we obtain a generalization bound within the distribution regression framework. Through the aforementioned theoretical results, we further discuss some successful techniques emerging with large language models (LLMs), such as prompt tuning, parameter-efficient fine-tuning, and efficient scaling. We also provide theoretical insights behind these techniques within our novel analysis framework.

Peilin Liu, Ding-Xuan Zhou

School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia

Transformer Architectures Generalization Bounds Distributions Deep Learning

Jun 27, 2026cs.RO

He3-Seeker: Robotic Information Planning for Lunar Helium-3 Distribution Mapping

Lunar helium-3 is a highly valuable strategic resource, pivotal to the advancement of both deep-space exploration and space mining. Existing lunar helium-3 exploration methodologies rely primarily on indirect measurements via remote sensing, which are often characterized by limited precision, low reliability, and insufficient spatial resolution. In this paper, we introduce He3-Seeker, an active robotic exploration method for helium-3 distribution mapping. First, we provide a formal definition of the active helium-3 exploration problem. Subsequently, we developed the He3-Seeker framework, which is conceptually based on multi-point drilling, sampling, and in situ analysis. In particular, we use robotic information planning (RIP) to guide autonomous robot navigation and active sensing. Additionally, to thoroughly evaluate the proposed algorithm, we introduce a reliable method for generating reference data of lunar helium-3 distribution based on low-resolution orbital remote sensing measurements. Simulation experiments verify that He3-Seeker achieves both rapid and high-fidelity mapping of helium-3 distribution, providing a reliable solution for resource exploration tasks. Our code and simulation environment will be publicly accessible at https://github.com/OpenSpace-Lab/He3-Seeker.

Dong Li, Yujie Zheng, Chengdeng Cao +4

Institute of Automation, Chinese Academy of Sciences, China, and also with the Faculty of Innovation Engineering, Macau University of Science and Technology, Macau · OpenSpace Lab, China · College of Artificial Intelligence, China University of Petroleum (Beijing) +5

Planetary Exploration Rosetta Robot Navigation Robot Planning Distributions

Jun 23, 2026cs.LG

Are Tabular Foundation Models Robust to Realistic Query Distribution Shifts in Microbiome Data?

Tabular foundation models (TFMs) achieve strong performance on microbiome abundance data, yet their robustness under realistic distribution shift remains poorly characterized. We introduce a benchmark that evaluates the robustness of TFMs to biologically inspired perturbations across six gut microbiome datasets spanning four disease contexts. In this in-context learning setting, models receive unperturbed support sets as context and are evaluated on perturbed query samples. To isolate robustness beyond "shortcut" features, we preserve the most discriminative taxa and apply three controlled perturbation strategies: (i) removal of high-abundance (uninformative) taxa, (ii) sparsification via increased zero-inflation, and (iii) zero-imputation via spurious non-zero injections. Our results show that protecting discriminative features is insufficient to guarantee stability under support-query shift: across datasets, all perturbations degrade model performance, with zero-imputation consistently the most harmful, indicating that corrupting global feature structure can break generalization even when key taxa are retained. Sparsification disproportionately affects TFMs relative to a classical random forest baseline, suggesting greater sensitivity to zero-inflation-type shifts. The code is publicly available at: https://github.com/UMMISCO/metagenomics-fm/.

Giulia Perciballi, Ahmad Fall, Federica Granese +2

IRD, Sorbonne Université, Unité de Modélisation Mathématique et Informatique des Systèmes Complexes (UMMISCO), Paris, France · Inria, CNRS, I3S, Université Côte d’Azur, Valbonne, France · INSERM, Nutrition et Obésités; Approches Systémiques, NutriOmique, AP-HP, Hôpital Pitié-Salpêtrière, Paris, France

Tabular Foundation Models Bacterial Colony Counting Distribution Shifts Random Forest Imputation Distributions

Jun 23, 2026cs.LG

Learning Dynamical Systems from Multiple Sparse Datasets: A Hierarchical Bayesian Modeling Approach

Estimating parameters of dynamical systems from sparse, noisy, and irregularly sampled data is often severely ill-conditioned. When multiple related datasets are available, they provide additional information if the shared structure and variability are properly modeled. We propose a hierarchical Bayesian framework for probabilistic meta-learning in dynamical systems, modeling dataset-specific parameters as draws from a shared population distribution. A numerical ODE solver is embedded within gradient-based MCMC to enable efficient posterior inference of the shared population and dataset-specific parameter distribution. Experiments show improved predictive performance over unpooled methods, highlighting the potential for data-efficient system identification in settings with sparse data.

Cristian Brugnara, Lea Multerer, Marco Forgione +1

SUPSI, Dalle Molle Institute for Artificial Intelligence (IDSIA USI-SUPSI), Lugano, Switzerland

System Identification Dynamical Systems Meta-Learning Markov Chain Monte Carlo Distributions

Jun 23, 2026cs.AI

FlowR2A: Learning Reward-to-Action Distribution for Multimodal Driving Planning

Multimodal driving planning faces a long-standing tension between two paradigms: scoring-based methods benefit from dense reward supervision but are confined to a fixed action vocabulary, while anchor-based methods generate proposals dynamically yet suffer from sparse supervision constrained to a single ground-truth trajectory. In this work, we propose FlowR2A, which resolves this tension by reframing simulation-based rewards from discriminative targets into generative conditions. By learning the reward-conditioned action distribution from dense trajectory-reward pairs with a flow-matching decoder, FlowR2A unifies the dense supervision of scoring-based methods with the proposal generation of anchor-based methods in a single generative model, forcing the model to internalize the correlation between an action and its outcomes in safety, progress, comfort, and rule compliance. To balance hard safety constraints against soft progress objectives, we introduce fine-grained per-timestep reward conditioning and reward noise augmentation. The generative formulation naturally supports controllable test-time sampling via reward guidance and anchored sampling, producing high-quality proposals. FlowR2A achieves state-of-the-art results on the NAVSIM v1 and v2 benchmarks, with multimodal proposals of substantially higher quality than prior methods.

Xirui Li, Zhe Liu, Xiaoqing Ye +4

1The University of Hong Kong · 2Changan Automobile

Multimodal Action Distributions Distributions

Jun 22, 2026stat.ME

Target-Aware Linear Regression Under Distribution Shift

Distribution shift between training and deployment is a pervasive challenge for modern AI systems. In many cases, the target marginals of covariates and response are known or specified through population-level observations, boundary conditions, properties of simulator configurations, or alignment-time distributional constraints. Such knowledge may provide valuable side information for regression estimation. We study this problem in the multivariate linear regression setting with a stable conditional mean

E[Y\mid X]

across source and target, and identify the hybrid-loss estimator, which jointly incorporates both target marginals, as a benchmark target-aware estimator. Its direct computation, however, requires solving a coupled nonlinear optimization that is expensive at scale. Our main contribution is to develop and evaluate two computationally tractable alternatives: a constrained moment-matching estimator and a two-stage estimator that augments ordinary least squares with a calibration step. For all three estimators, we derive and compare closed-form asymptotic mean squared errors, yielding conditions under which the tractable alternatives match or closely approximate the hybrid benchmark, and regimes in which they do not. Monte Carlo experiments across three controlled shift regimes validate the theoretical results, investigate the accuracy-runtime tradeoffs among the three estimators, and translate into guidance on estimator choice. In particular, the two-stage estimator nearly matches the hybrid benchmark in the high signal-to-noise regime at essentially no additional cost, providing theoretical grounding for empirical observations in nonlinear settings.

Zhewen Hou, Tian Zheng

Department of Statistics Columbia University New York, NY

Covariate Shift Distribution Shifts Covariates Distributions Loss Function

Jun 17, 2026cs.LG

Calibrating Generative Models to Feature Distributions with MMD Finetuning

Generative models can produce individually plausible samples while deviating substantially from a target set in the distribution of key features. For example, a model pretrained on broad drug-like chemical space may generate molecules whose molecular features differ from those of a therapeutic class of interest, such as known antibiotics. Correcting such distributional miscalibration is challenging: direct finetuning on the target set can overfit and does not control which features are matched. To fill this gap, we introduce kernel Calibrating Generative Models (kCGM). kCGM minimizes a maximum mean discrepancy (MMD) between generated and target feature distributions using an unbiased score-function estimator, with KL regularization to remain close to the pretrained model. On a target set of 174 antibiotics, direct finetuning sacrifices chemical validity for feature-distribution matching, whereas kCGM improves target feature matching while increasing validity. We further demonstrate kCGM in protein and DNA generation tasks, showing it can adapt autoregressive, continuous-space diffusion, and discrete diffusion models using only feature-level supervision. Code is available at https://github.com/smithhenryd/cgm.

Nathaniel L. Diamant, Brian L. Trippe

Stanford University

Molecular Generation Generative Models Maximum Mean Discrepancy Diffusion Models Distributions

Jun 17, 2026cs.LG

Correcting Sensor-Induced Distribution Drift with Wasserstein Adversarial Learning

The quality of recorded data depends on the stability of the sensor system that acquires it. Sensor motion and aging can degrade the performance and stability of downstream data-driven methods. We present a Wasserstein-GAN-inspired approach for unsupervised inference of physically interpretable transformation parameters that map a changed detector response distribution back to a nominal reference distribution. In contrast to standard generative modeling, the generator is used as a learnable calibration transformation whose trainable weights represent the sought parameters, while the critic provides a distributional distance signal via the Wasserstein objective. We validate the approach on a tracking-detector toy model with controlled layer shifts and demonstrate its application on high-granularity Geant4-simulated calorimeter data with cell-wise aging effects. The method recovers aging coefficients for individual cells with correlation to ground truth and improves agreement between calibrated and reference energy-sum distributions, while exhibiting the expected degradation at increasing channel-to-channel noise levels. These results indicate that adversarial distribution matching can serve as a data-driven component of calibration strategies in settings where direct labels for degradation parameters are unavailable.

Saraa Ali, Vladimir Bocharnikov, Fedor Ratnikov +3

Laboratory of Methods for Big Data Analysis, HSE University, Pokrovsky Boulevard 11, Moscow 109028, Russia

Recalibration Distribution Shifts Calibrated Uncertainty Degradation Wasserstein Gradient Flows Distributions

Jun 16, 2026cs.CV

Theoretical Grounding of Out-Of-Distribution Detection With Reinforcement Learning Optimizer

Out-of-distribution (OOD) detection in dynamic open-world environments requires a model to continually adapt to evolving data distributions while generalizing to covariate-shifted inputs and rejecting semantic-shifted OOD examples. Most existing OOD detection methods optimize only the current-step objective and do not explicitly account for how post-deployment environment changes affect future OOD behavior. In this paper, we establish a theoretical grounding for dynamic OOD detection using a reinforcement learning (RL)-guided optimizer that explicitly favors updates that reduce the semantic OOD false positive rate over time. We develop a novel augmented optimizer that uses an RL-guided correction term on top of standard gradient descent (GD) and show its improvement over both future-domain generalization and semantic-OOD rejection. We analyze temporal error decomposition in terms of model-change and environment-change generalization errors and develop a new theoretical framework for comparing the generalization errors under both GD and RL-guided optimizers.

Salimeh Sekeh, Xin Zhang

San Diego State University

Out-Of-Distribution Detection Off-Policy Learning Adaptive Optimizers Distributions Theory

Jun 15, 2026cs.LG

Distribution Alignment for One-Shot Federated Learning via Optimal Transport

One-Shot Federated Learning (OSFL) addresses extreme communication regimes in which clients interact with the server only once, amplifying the impact of heterogeneous client data distributions. In particular, the interaction of domain shift and label shift across clients induces misaligned feature representations that cannot be corrected through iterative optimization. Existing OSFL methods rely on distillation, server-side generation or ensemble-based aggregation, but assume aligned representations or address domain and label shift separately. We introduce SLOT-Align (Single-round, Learning-free Optimal Transport Alignment), a geometry-aware feature harmonization framework for OSFL. SLOT-Align uses a shared frozen encoder to extract compact feature statistics, constructs a global reference via Bures-Wasserstein barycenters, and aligns local representations using closed-form geodesic optimal transport maps. The method is computationally efficient and can be combined with existing OSFL pipelines relying on frozen encoders without modifying their training procedures. Extensive experiments across multiple benchmarks, pretrained backbones, and OSFL methods show that SLOT-Align consistently improves accuracy and robustness under joint domain and label shift.

Daniele Berardini, Vito Paolo Pastore, Vittorio Murino

AI for Good · AI for Good (AIGO), Italian Institute of Technology, Genoa, Italy · MaLGa-DIBRIS, University of Genoa, Genoa, Italy +1

Federated Learning Few-Shot Learning Balanced Learning Distributions Frozen Encoder

Jun 15, 2026cs.CV

DCP-Prune: Ultra-Low Token Pruning with Distribution Consistency Preservation

Recent vision token pruning methods effectively preserve model performance under moderate token budgets but become unstable under ultra-low token budget. Our analysis shows that as the pruning budget decreases, accuracy degradation is often accompanied by larger feature distribution shifts. Critically, the degree of this distribution shift strongly correlates with performance degradation. To better characterize this phenomenon, we introduce a lightweight distribution consistency metric to estimate the distribution shift between retained and full tokens. Motivated by these observations, we propose a two-stage pruning framework consisting of Anchor-Context Graph Recovery (ACGR) and Text-Aware Token Cluster Selection (TATCS). Specifically, ACGR transfers contextual information before token removal, while TATCS dynamically re-selects representative tokens when severe distribution shift is detected. Extensive experiments demonstrate that our method achieves superior and more stable performance under ultra-low token budget. Notably, it retains 92.1% of the upper-bound average performance on LLaVA-1.5-7B with only 16 visual tokens.

Xifeng Xue, Xiaokang Wang, Zirui Li +2

College of Computer Science, Nankai University, Tianjin, China · Nanjing University of Posts and Telecommunications, Nanjing, China

Visual Token Pruning Distribution Shifts Distributions

Jun 12, 2026cs.LG

Riemannian Metric Matching for Scalable Geometric Modeling of Distributions

High-dimensional datasets often concentrate near low-dimensional structures, but estimating their geometry from samples typically relies on graphs and kernels that scale poorly with dataset size and dimension. We propose Riemannian metric matching: a denoising probabilistic framework for learning the Riemannian geometry of data using neural networks. Specifically, we learn the carré du champ operator, which, using diffusion geometry, gives us access to the Riemannian geometry toolkit for downstream machine learning and statistical tasks. Our key observation is that the carré du champ operator can be formulated as a conditional expectation over random perturbations of the data, which can be exploited for sample-wise training and constant cost, amortized inference without explicit kernel construction. Empirically, metric matching rivals or improves the accuracy of

k

-NN-based diffusion geometry estimators, while enabling amortized inference that is up to

400\times

faster, and supports graph-free geometric analysis on high-dimensional images where nearest neighbors break down.

Jacob Bamberger, Adam Gosztolai, Pierre Vandergheynst +2

Department of Computer Science, University of Oxford, Oxford, UK · Institute of Artificial Intelligence, Medical University of Vienna, Vienna, Austria · EPFL, Lausanne, Switzerland +1

Riemannian Manifolds Riemannian Flow Matching High-Dimensional Distributions

Jun 11, 2026cs.LG

Zero-Inflated Gaussian Distributions Enable Parameter-Space Sparsity in Estimation-of-Distribution Algorithms

Estimation-of-distribution algorithms (EDAs) are a powerful class of evolutionary methods for black-box optimization, especially when little is known about the structure of the objective. Whereas classical evolutionary algorithms rely on hand-designed mutation and crossover operators, hard to devise for unknown problem structures, and a source of bias, EDAs sidestep operator design entirely: they fit a probability distribution to the best individuals and sample the next generation from it. EDAs are well established on continuous parameter spaces, but they have not previously been generalized to sparse ones, in which most coefficients of a good solution are exactly zero. Existing sparse black-box optimizers therefore reintroduce exactly what EDAs were designed to avoid: hand-crafted sparsity operators, bi-level schemes alternating between support set and active values, zeroing thresholds, and other baked-in assumptions. We close this gap by proposing multivariate zero-inflated Gaussian (ZIG) distributions as EDA sampling laws. A latent Gaussian model with separate indicator and value dimensions represents sparsity patterns, correlations among active parameters, and the interactions between the two, so sparsity patterns and active values are optimized jointly, hierarchy-free. We show that the latent parameters of this model are identifiable from observed samples, unlike in the missing-data settings where related constructions originate, and introduce practical amortized inversion-based estimators for them. The estimators accurately recover latent correlation structures, and on the Lunar Lander benchmark the resulting ZIG-EDA converges faster and reaches higher final returns than a dense Gaussian EDA, a hand-crafted sparse evolutionary algorithm, and an ad-hoc sparse EDA, while finding controllers with only a small fraction of parameters active.

Andreas Faust, Sven Nitzsche, Juergen Becker

University of Freiburg, Freiburg, Germany · FZI Research Center for Information Technology, Karlsruhe, Germany · Karlsruhe Institute of Technology, Karlsruhe, Germany

Evolutionary Optimization Sparsity Black-Box Optimization Distributions Gaussian Primitives

Jun 11, 2026stat.ML

Recursively Trained Diffusion Models: Limiting Collapse Distribution and Spectral Characterization

Recursive training of generative models on their own outputs can lead to model collapse, a compounding drift away from the true data distribution. Existing theoretical works bound finite-round error accumulation in the context of diffusion models, but two questions remain open:~what distribution does the recursion converge to, and how fast? We answer both, isolating a mechanism distinct from imperfect learning: even with perfect score estimation and exact sampling, the early stopping of the reverse diffusion (required for numerical stability) drives a progressive drift away from the data distribution. We prove that this recursion converges geometrically to a unique limiting distribution, which admits a closed-form characterization as an infinite mixture of increasingly Gaussian-smoothed versions of the data distribution. A Hermite spectral decomposition of this limit reveals that recursive training acts as a low-pass filter: higher-order modes, which encode fine non-Gaussian structure, are attenuated much more strongly than coarse modes. This spectral picture motivates annealed truncation schedules that progressively shrink truncation times across retraining rounds; we prove that any schedule converging to

0

asymptotically eliminates recursive compounding. Finally, we show our idealized characterization is robust: in the presence of discretization and score estimation errors, the learned distribution remains in a Wasserstein-2 ball around the ideal limit, with mode-dependent contraction rates that contract high-order errors faster than low-order ones. We validate the theory on synthetic Gaussian mixtures and CIFAR-10.

Naïl B. Khelifa, Richard E. Turner, Ramji Venkataramanan

University of Cambridge

Diffusion Models Gaussian Mixture Models Distributions Collapse Spectral

Jun 9, 2026eess.AS

Recovering the Zipfian Distribution in Unsupervised Term Discovery

Unsupervised term discovery involves segmenting unlabelled speech into word- or syllable-like units and clustering these into a lexicon of candidate types. True lexicons follow a Zipfian distribution, yet the dominant centre-based clustering approach -- K-means -- produces a more uniform distribution due to an inductive bias toward spherical clusters. In this paper we revisit graph-based clustering as a bottom-up alternative, where segment embeddings are connected by pairwise similarity and partitioned using the Leiden algorithm. We show that graph clustering substantially outperforms centre-based approaches (K-means, GMM, BIRCH) in both word- and syllable-level lexicon discovery across three languages, producing more Zipf-like distributions. Another bottom-up approach, agglomerative clustering with average linkage, also performs well, although it is computationally less efficient and allows for less control over the resulting distribution. Our work calls into question the dominance of centre-based clustering for term discovery, and promotes graph clustering as an attractive alternative.

Danel Slabbert, Simon Malan, Herman Kamper

Electrical and Electronic Engineering, Stellenbosch University, South Africa

Clustering Unsupervised Community Detection Distributions Discovery

Jun 9, 2026cs.RO

ros2probe: Non-intrusive, Kernel-selective Observability for Robot Operating System 2 Middleware

Robot Operating System 2 (ROS 2), the de facto standard middleware framework for robots, runs each robot as a graph of nodes communicating over the Data Distribution Service (DDS), a publish/subscribe substrate. Observing this inter-node communication in real time is essential to robot development, yet it has a price. A tool can receive data only by joining the DDS domain as a subscriber that discovery has matched to the publisher, so observing folds the tool into the system it measures and perturbs it. We define this protocol-inherent perturbation as the observer's probe effect. It inflates the discovery plane, adds deserialization cost on the observer, makes the loss it reports diverge from what the subscriber actually received, and near saturation displaces the subscriber's messages. The only escape, capturing all wire traffic passively, discards ROS 2 message semantics and scales with total traffic, not what is observed. We present ros2probe, a non-intrusive observation framework that removes the probe effect. It reconstructs the full ROS 2 communication state from the domain's discovery packets at no bandwidth cost, then drives an in-kernel filter restricted to the topics the user asks for, lifting only those packets at minimal cost and observing what the real subscriber receives. Its interfaces and recordings match the standard ROS 2 tools. Across three hardware platforms (laptop, Jetson, and Raspberry Pi), two DDS implementations, and seven robot-operation workloads, ros2probe holds the discovery graph within 0.5% of an unobserved system, whereas domain-joining tools inflate discovery up to 2.6

\times

and drop 38.5% of the subscriber's messages at saturation while ros2probe drops none. It reports loss with a recall of 1.0, cuts observer CPU and memory by up to 7

\times

and 28

\times

, and stays practical on the embedded robots where existing tools overload the system.

Jisang Yu, Sanghoon Lee, Yeonwoo Choi +1

DGIST Daegu, Republic of Korea

Robot Operating System Partial Observability Robot Systems Discovery Workload Distributions

Jun 9, 2026cs.IT

Minimum Distortion Quantization with Specified Output Distribution

We derive the optimal quantizer of a real-valued random variable

W

with distribution

P_W

such that 1) the distribution of the quantization output

X

that can take

k

values follows any specified distribution

P_X

over

\{1,\ldots,k\}

, and 2) the minimum mean squared error (MMSE) of estimating

W

from

X

is minimized. It is shown that the optimal quantizer takes the form

X=σ\big(F_{σ^{-1}(X)}^{-1}(F_W(W))\big)

, where

σ

is the optimal permutation of

\{1,\ldots,k\}

among all permutations to minimize the MMSE, and

F

is the cumulative distribution function. When

P_W

is uniform over an interval or

P_X

is uniform over

\{1,\ldots,k\}

, the quantizer takes a simple form

X=F_{X}^{-1}(F_W(W))

. The concept of majorization plays a key role in the optimality proof. Specifying the output distribution is useful for designing quantizers with explicitly controlled output entropy, maximized mutual information between input and output, tailored output distribution to match channel input requirements for communication, and data anonymization.

Aolin Xu

Rate-Distortion Theory Quantizer Minimax Rate Distributions Mutual Information Optimality

Jun 5, 2026cs.CL

Whose Norms? Disentangling Cultural and Personal Alignment in Large Language Models

Large language models are increasingly used for social decision-making situations that require balancing cultural norms with personal preferences. For example, a user preferring honesty might ask whether to correct a coworker publicly when local norms favor indirect feedback. Yet existing research studies cultural alignment and personalization largely separately. We introduce PACT, the Personal-Preference and Cultural-Norm Trade-off framework, which evaluates whether models choose to follow a cultural norm or allow personal preferences. We find that LLMs vary in how rigidly they enforce cultural norms, with behavior shifted more by country context (7.8%) than age (1%) and gender (0.7%) and shifting non-uniformly after instruction tuning. Furthermore, our five-country human study on PACT shows that culture-following in humans is mainly driven by scenario country, with the lowest agreement when participants judge their own cultural contexts, showing within-culture pluralism. Finally, human-LLM alignment experiments show that models can match majority choices, but fail to capture response distributions and uncertainty (with best correlations reaching only 0.24). Together, these findings motivate alignment evaluations that go beyond majority to capture cultural pluralism and disagreement in social judgment.

Angana Borah, Isabelle Augenstein, Rada Mihalcea

University of Michigan - Ann Arbor · University of Copenhagen

Large Language Model Alignment Large Language Model Bias Large Language Model Decisions Social Norms Preference Alignment Learning Norm+1

Jun 5, 2026math.ST

A Temporal Spatial Minimax Rate for Smoothly-Varying Distributions in Wasserstein Space

We study the minimax rate of estimating a future value

μ_{t_n+h}

of a curve

t\mapstoμ_t

in the

2

-Wasserstein space

\mathcal{P}_2(\mathbb{R}^d)

from finitely many noisy snapshots of its past, under an adiabatic bound

\|\nabla_t^k v\|\le\varepsilon

on the

k

-th covariant derivative of the velocity field. Our central result is a unified temporal-spatial minimax lower bound: over regular, locally transport-rich subclasses, every estimator incurs

W_2

-risk with

M

-exponent

γ_d(k+1)/(k+1+γ_d)

,

γ_d=\min(1/d,1/2)

(

M

the total sample size). It follows from a temporal-to-spatial reduction: the smoothness budget defines a reachable

W_2

-ball into which a transport packing is embedded along the time axis, and the information of the entire snapshot experiment is controlled by a Fano argument -- the spatial packing is classical, but its smoothness-admissible temporal embedding and the full-window analysis are new. The bound interpolates a dimension-free extrapolation floor of order

\varepsilon h^{k+1}

-- the irreducible cost of an unobserved future, present even with the exact past -- and the spatial estimation curse

M^{-γ_d}

, recovering the static distribution-estimation rate as

k\to\infty

. We state the lower bound in a design-dependent form -- with a design-weighted effective sample size -- valid for arbitrary observation times, and obtain the closed-form exponent in the dense (equispaced) regime. The matching upper bound is established at

k=0

(rate

M^{-1/(d+1)}

,

d\ge3

) and, in a translation submodel, for all

k

; for

k\ge1

a covariant estimator attains the rate conditionally on two estimates (a comparison-geometry bias bound and an optimal-transport map-estimation rate), leaving the unconditional general-

k

upper bound as an open problem. Numerical experiments on synthetic curved and flat families corroborate the predicted exponents.

Munsik Kim

Wasserstein Distance Minimax Rate Exponential Family Distributions

Jun 5, 2026cs.SD

Leveraging Soft Distributions of SSL-Derived Discrete Speech Tokens for Downstream Inference

Discrete speech tokens obtained from self-supervised learning (SSL) models provide efficient data compression while maintaining strong performance, and have been widely used as intermediate representations in various tasks. However, discretization inevitably causes information loss, leading to degraded performance compared with continuous SSL features. In this work, we propose to apply soft token assignment only during downstream inference. This approach preserves the efficiency of hard discretization during training while enhancing the expressiveness of the tokens at inference. The proposed method outperforms conventional hard assignment on both ASR and speech synthesis tasks, and exhibits particularly strong generalizability to out-of-domain data. For ASR of non-native speech, it even surpasses models using continuous SSL features. Moreover, analysis of the resulting representations shows they align more accurately with phonemes compared with conventional hard assignment.

Kentaro Onda, Satoru Fukayama, Daisuke Saito +1

The University of Tokyo, Japan · National Institute of Advanced Industrial Science and Technology (AIST), Japan

Soft-Token Representations Automatic Speech Recognition Downstream Fine-Tuning Self-Supervised Learning Distributions

Jun 3, 2026cs.LG

GeoMin: Data-Efficient Semi-Supervised RLVR via Geometric Distribution Modeling

Reinforcement learning with verifiable rewards (RLVR) significantly advances LLM reasoning, yet it faces a dilemma: standard supervised scaling is throttled by high annotation costs, while unsupervised alternatives suffer from severe model collapse. Recent semi-supervised RLVR methods address this by using a small labeled set to guide unlabeled data, achieving a promising trade-off between training efficacy and annotation cost. However, they suffer from a severe data-efficiency bottleneck due to the reliance on coarse performance heuristics, leaving a vast majority of valuable instances underutilized. To this end, we propose GeoMin, which models global feature distributions on labeled data to decode the structural discrepancy between correct and incorrect rollouts, thereby establishing a robust prior to assess the reliability of self-reward signals and fully unleash the potential of unlabeled data. Empirically, GeoMin outperforms the strongest baselines by +4.1% and even surpasses fully supervised models with only 10% of the annotations, demonstrating remarkable data efficiency.

Guangcheng Zhu, Shenzhi Yang, Haobo Wang +9

1Zhejiang University · 2Ant Group

Reinforcement Learning With Verifiable Reward Semi-Supervised Learning Verifiable Rewards LLM Reasoning Strategies Geogs-Slam Domain Adaptation+1

Jun 3, 2026cs.LG

DPDL: Towards Differential Privacy Preservation in Decentralized Stochastic Learning on Non-IID Data

In the paradigm of decentralized learning, a group of agents collaborate to train a global model using distributed datasets without a central server. Although the power of collaboration has been verified by many state-of-the-art studies, it entails extensive gradient information exchanging among the agents and thus induces high risk of privacy leakage for the individual agents. Moreover, in real-world applications, the training data are usually non-identically and independently distributed across the agents, inducing more challenges to enable privacy-preserved decentralized learning. To address these issues, we propose a privacy-preserved decentralized learning algorithm with non-IID data, DPDL, which leverages the notion of Differential Privacy (DP) in cross-gradient aggregation through a similarity-based calibration technique. Specifically, in each round, each agent perturbs the cross-gradients (i.e., the derivatives of its neighbors' local model in its private local data) by Gaussian noise mechanism before sharing them with its neighbors; it then adopt cosine similarity to calibrate the received perturbed cross-gradients such that the aggregation of the calibrated cross-gradients can be utilized to effectively update local model in a momentum-like manner. Our rigorous theoretical analysis not only reveals the minimum noise level required to achieve a specific level of privacy preservation, but also illustrates that our algorithm still achieves a linear speedup in training with non-IID data. We finally conduct extensive experiments on real-world dataset to validate the effectiveness of our algorithm in defending privacy attacks and in training accurate models.

Yunsheng Yuan, Xue Xiao, Lina Wang +1

School of Computer Science and Technology, Shandong University, Qingdao 266237, China · Inspur Cloud Information Technology Co, Ltd.

Decentralized Learning Standard Differential-Privacy Stochastic Gradient Descent Gaussian Noise Distributions

Jun 2, 2026cs.LG

Edge of Stability Selectively Shapes Learning Across the Data Distribution

Existing analyses of the edge of stability (EoS) treat it as a global property of optimization. We show that it is also selective: the stability constraint redistributes learning across subsets of the training distribution, amplifying progress on some groups while suppressing progress on others. Using a branching intervention that enters or exits the EoS regime from the same training state, we causally demonstrate this trade-off and identify two necessary conditions for a group to benefit. First, its aggregate gradient must align with the top Hessian eigenvector. We isolate this mechanism with a controlled perturbation that preserves distance but randomizes direction, destroying alignment and eliminating the advantage. Second, the group must sustain non-vanishing gradient magnitude over time. Under cross-entropy loss, gradient saturation decouples confidently classified groups, shifting the advantage to output-outliers, whose gradients persist. Together, these results show that EoS functions not only as a stability boundary, but as a mechanism governing the allocation of learning across the data distribution.

Shauna Kwag, Anakha Ganesh, Tomaso Poggio +1

MIT

Hessian Distributions Cross-Entropy Losses Edge

Jun 2, 2026cs.LG

DECA: Decentralizing Block-Wise Adam for Efficient LLM Full-Parameter Fine-Tuning on Non-IID Data

Fine-tuning large language models (LLMs) in privacy-sensitive and resource-constrained environments remains challenging. Since training data are often distributed across multiple clients, decentralized fine-tuning offers a natural paradigm for collaborative adaptation without a central server. However, enabling full-parameter fine-tuning (FPFT) in this decentralized setting is difficult: FPFT provides strong adaptation capacity but incurs prohibitive resource consumption for billion-scale models. Existing decentralized LLM fine-tuning methods therefore mainly rely on parameter-efficient updates, which improve efficiency but may restrict downstream performance. Moreover, client data are typically non-IID, making decentralized optimization more vulnerable to client drift and unstable convergence. To address these challenges, we propose DECA, a resource-efficient decentralized FPFT framework for LLMs on non-IID data. DECA partitions model parameters into disjoint blocks and performs sequential block-wise Adam optimization, reducing resource consumption while preserving decentralized full-parameter adaptation. To stabilize training, DECA further introduces first- and second-order block-wise moment estimates with fresh local gradient statistics and consensus-derived discrepancy signals. We provide rigorous theoretical analysis and extensive experiments, showing that DECA achieves fast convergence, strong downstream performance, and significant resource efficiency.

Yunsheng Yuan, Shaowei Li, Kai Wang +5

School of Computer Science and Technology, Shandong University, Qingdao China · School of Mathematical Science, Peking University, China · IEIT SYSTEM, China +2

Parameter-Efficient Fine-Tuning Methods Large Language Model Fine-Tuning Parameter-Efficient Adaptation Adam Distributions

Jun 2, 2026cs.LG

FGRPO: Federated GRPO with Adaptive Aggregation on Non-IID Data

Recent advances in language models have established reinforcement learning as the primary paradigm for eliciting self-correction and long-chain reasoning. While group relative policy optimization (GRPO) offers superior scalability by eliminating the critic network, deploying it on a central infrastructure entails collecting a large volume of data from distributed owners, which poses significant privacy risks. To address these concerns, we introduce federated GRPO (FGRPO), a framework designed to decentralize the fine-tuning of reasoning models across heterogeneous data owners. To effectively mitigate the instability caused by divergent reward scales across heterogeneous tasks, FGRPO incorporates an adaptive aggregation mechanism based on relative performance gain. By characterizing each client's improvement relative to its personalized historical baseline, the framework dynamically prioritizes effective learning trajectories regardless of local task difficulty. FGRPO ensures robust convergence on non-IID data while preserving data privacy.

Pengyu Chen, Shaowei Li, Kai Wang +4

School of Computer Science and Technology, Shandong University, Qingdao China · School of Mathematical Science, Peking University, China · School of Computer Science and Artificial Intelligence, Shanghai University of Finance and Economics, Shanghai, China +1

Better Call Group Relative Policy Optimization Flow-Grpo Reasoning Chain Distributions

Jun 1, 2026cs.LG

VLBM: Variational Latent Basis Modeling for OOD Robust Multivariate Time Series Forecasting

Out of distribution (OOD) events in multivariate time series forecasting are rare but often dominate real world risk, making average case forecasting insufficient for reliable deployment. Under standard average risk training on mixed ID/OOD distributions, optimization signals from rare OOD events can be overwhelmed by frequent in distribution (ID) patterns, so strong benchmark accuracy may not translate into reliability under high impact shifts. To address this issue, we propose VLBM (Variational Latent Basis Model), a theory guided latent forecasting framework that separates stable dynamics from OOD induced deviations. VLBM learns a shared latent basis that defines a low rank subspace for stable ID dynamics, explicitly decomposes inputs into basis subspace components and orthogonal residual components, and aligns a future aware posterior with a future blind prior so that test time latent inference depends only on historical input. Across 12 benchmark tasks spanning transportation, weather, power systems, and other real world domains, including newly constructed real world OOD traffic datasets, VLBM achieves state of the art OOD robustness and ID accuracy, with average MAE and MSE gains of 15.08% and 7.74% over the strongest baseline. On a synthetic simulation dataset, VLBM also consistently achieves the best performance and better tracks OOD pulse recovery. These results support latent structured forecasting as a principled route to robust prediction under mixed ID and OOD conditions. The code is available at https://github.com/leijieruilq/VLBM_OOD_forecast.

Xudong Zhang, Jierui Lei, Jiacheng Li +3

School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing 100049, China. · Center for Machine Learning Research, Peking University, Beijing, China. · Amap, Alibaba Group, China. +2

Multivariate Time Series Forecasting Latent Space Subspace Distributions

May 30, 2026cs.LG

Semi-Supervised Learning with Noisy Proxy Covariates: Generalization Bounds and Distribution Regression

In many modern machine learning pipelines, abundant pretrained representations serve as noisy proxy covariates, while task-specific labels remain scarce. We study semi-supervised regression in this setting, and propose a simple two stage estimator that learns kernel eigenfeatures from all proxy covariates and fits a ridge predictor on labeled data. We derive finite sample bounds showing that fast labeled sample rates are recovered when proxy perturbation is controlled and unlabeled proxy covariates are sufficiently abundant. We also show that distribution regression is a direct special case, with analogous guarantees when the finite bag size is large enough. Experiments show consistent gains over supervised and semi-supervised baselines, especially in low label regimes.

Kwangho Kim, Jisu Kim

Department of Statistics, Korea University, Seoul, Korea · Department of Statistics, Seoul National University, Seoul, Korea

Semi-Supervised Learning Covariates Generalization Bounds Distributions

May 28, 2026stat.ML

Improved Distribution Estimation in $\ell_\infty$

We present improved bounds for estimating discrete probability distributions under the

\ell_\infty

norm. These include minimax bounds in expectation and high-probability tail bounds. We resolve some of the open questions posed in Kontorovich and Painsky (JMLR, 2025) -- including a fully empirical version of the tightest risk bound they presented and identifying the form of the worst-case extremal distribution. Encouraging empirical results are reported as well.

Doron Cohen, Aryeh Kontorovich, Yonatan Livshitz

Department of Computer Science, Ben-Gurion University of the Negev, Beer-Sheva, Israel

Concentration Bounds Distributionally-Robust Optimization Distributions Minimax Spectral Norm

May 28, 2026cs.CL

Metric-Dependent Annotation Saturation for Learning from Label Distributions

When annotators disagree on a label, the disagreement itself carries signal -- and the number of annotators needed to capture it depends on the evaluation metric. We fine-tune NLI models on label distributions subsampled from ChaosNLI, a dataset providing 100 independent annotator judgments per item, and identify metric-dependent saturation. In our 3-class NLI setting, entropy correlation -- whether the model identifies which items elicit disagreement -- requires N ~ 20-50 annotators to converge, while distributional match (KL divergence) saturates by N ~ 10 (87-95% of improvement across five model seeds). This finding rests on a prior observation: soft labels carry item-specific signal that label smoothing cannot replicate. Across five smoothing intensities, entropy correlation clusters at r ~ 0.45-0.49, while soft labels reach r = 0.643 (p < 0.001); per-item analysis traces this gap to smoothing's inability to distinguish ambiguous items from clear ones. The soft-label advantage replicates across two architectures (DeBERTa, RoBERTa), a non-NLI-pretrained baseline, and an exploratory cross-domain evaluation on content safety. These results suggest that annotation budgets should be informed by the target evaluation metric rather than set uniformly.

Guneet Kohli

Apple

Legal Natural Language Processing Benchmarks Disagreement Natural Language Inference Saturation Distributions

May 27, 2026quant-ph

Latent-Conditioned Parameterized Quantum Circuits as Universal Approximators for Distributions over Quantum States

Many applications in quantum simulation, quantum chemistry, and quantum machine learning require not a single quantum state but an ensemble of states characterizing the heterogeneity of a target system. Preparing such ensembles state-by-state is prohibitive in both variational and fault-tolerant settings, thereby motivating a generative modeling approach. We introduce latent-conditioned parameterized quantum circuits (LPQCs), a hybrid quantum-classical framework in which classical neural networks map a latent variable sampled from a prior distribution to the parameters of a parameterized quantum circuit. We prove that LPQCs are universal approximators for probability measures over density operators in the 1-Wasserstein distance, extending classical universal approximation theorems to the quantum-distribution setting. We additionally introduce a multimodal latent prior and a mixture-of-experts circuit architecture, and show empirically that the latent-conditioned parameterization alleviates the barren plateau problem during optimization, a behavior for which we provide rigorous partial guarantees. Numerical experiments validate the framework on a synthetic multi-cluster ensemble of mixed quantum states and on a QM9-derived ensemble of 3-D molecular structures. In these tasks, LPQC outperforms recent quantum generative baselines and matches the generation quality of a classical neural-network baseline, while requiring an output dimension that grows only linearly with the number of qubits rather than exponentially. By leveraging classical expressivity in the latent space, LPQCs offer a tractable route to quantum generative modeling.

Quoc Hoan Tran, Koki Chinzei, Yasuhiro Endo +1

Quantum Laboratory, Fujitsu Research, Fujitsu Limited, Kawasaki, Kanagawa 211-8588, Japan

Quantum Circuits Quantum Machine Learning Qubit Hybrid Quantum-Classical Pipeline Distributions Approximation

May 27, 2026cs.AI

Entropy-aware Masking for Masked Language Modeling

Masked language modeling has become a standard pretraining objective for training encoder-based language models. In this approach, certain tokens in the input are masked, and the model learns to predict them using the surrounding context. This process enables the model to capture both syntactic and semantic properties of language. Conventionally, the tokens selected for masking are chosen at random, which may not always yield the most effective learning signals. In this work, we examine a token masking strategy based on entropy distribution. We use the model's entropy over token predictions to identify which tokens should be masked. This method aims to target tokens that are more informative and uncertain to improve the training efficacy. We also propose a novel self-masking approach that enhances training efficiency without relying on an external reference model. Experimental results demonstrate that our method achieves an average performance improvement of 5% in GLUE scores compared to the baseline. Further, we experiment with combining knowledge distillation with entropy masking, resulting in the best overall results.

Gokul Srinivasagan, Kai Hartung, Munir Georges

AImotion Bavaria, Technische Hochschule Ingolstadt, Germany

Masked Diffusion Language Models Token-Level Entropy Knowledge Distillation Distributions

May 27, 2026cs.AI

Entropy Distribution as a Fingerprint for Hallucinations in Generative Models

Large Language Models (LLMs) often generate factually incorrect outputs, commonly termed hallucinations, that undermine trust and limit deployment in high-stakes settings. Existing hallucination detection methods typically require multiple forward passes, or access to model internals. In this work, we provide theoretical background and empirical evidence that the distribution of token-level entropies, beyond the mean captured by perplexity or length-normalised entropy, serves as a fingerprint of hallucination, with distributional shape and tail behaviour carrying independent signal. We formalize hallucination detection as a statistical hypothesis test and propose the Calibrated Entropy Score (CES), a lightweight algorithm requiring only a single forward pass and black-box access to token logits. CES combines the mean signal with the maximum signal of the generated entropy through a calibrated reference CDF, producing scores that are directly comparable across models and tasks. We establish finite-sample calibration guarantees via a novel random-length Dvoretzky--Kiefer--Wolfowitz inequality, and also prove that CES detects hallucinations with probability converging to one exponentially fast in the generation length. Across eight QA benchmarks and ten generator models spanning open-source and API access models, CES achieves the highest detection performance among all single-pass black-box methods while providing formal error guarantees that existing heuristics lack. Remarkably, CES is statistically indistinguishable from multi-sample methods that require far greater computational cost, closing the gap between lightweight and expensive detection and making it suitable for real-time, large-scale deployment.

Mattia J. Villani, Pranav Deshpande, Akshay Seshadri +2

Global Technology Applied Research, JPMorganChase, New York, NY 10001, USA

Large Language Model Hallucination Hallucination Detection Token-Level Entropy Entropy Generative Models Fingerprint+2

May 27, 2026cs.CV

Bridging the Sampling Distribution Shift in Radio Map Estimation: A Trajectory-Aware Paradigm

Learning-based radio map estimation (RME) plays a critical role in UAV-assisted wireless sensing, enabling tasks such as coverage prediction and network optimization. Most current methods assume an independently and identically distributed (i.i.d.) training and testing setting based on random sampling. However, practical UAV measurements are collected sequentially along feasible trajectories, resulting in highly structured and spatially correlated patterns. This mismatch introduces a sampling distribution shift that increases the intrinsic difficulty of spatial field recovery and compromises the generalization of models trained under i.i.d. assumptions. To mitigate this issue, we propose a trajectory-aware training paradigm based on Stochastic-Triggered Trajectory-Based Sampling (ST-TBS), which preserves trajectory continuity while introducing sampling variability. Moreover, from a statistical perspective, we show that trajectory-based sampling reduces spatial diversity and increases information redundancy compared to random sampling. Extensive experiments on the RadioMapSeer and SpectrumNet datasets demonstrate that models trained with random sampling suffer significant performance degradation under trajectory-based observations, with RMSE increasing from 0.0391 to 0.2632 on SpectrumNet. Conversely, our proposed ST-TBS method effectively reduces the RMSE to 0.0571. These results highlight the necessity of aligning training and deployment sampling distributions for reliable RME.

Feng Qiu, Zheng Fang, Shuhang Zhang +4

School of Artificial Intelligence, Xidian University, Xian, China · Pengcheng Laboratory, China · Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen, China +2

Radio Map Estimation Unmanned Aerial Vehicle Trajectories Trajectory-Aware Hidden-State Analyses Adaptive Sampling State Estimation Distribution Shifts+1

May 26, 2026cs.CL

The Coverage Illusion: From Pre-retrieval Routing Failure to Post-retrieval Cascades in a Production RAG System

In modern RAG pipelines, query augmentation methods such as HyDE and query expansion are applied to every query, resulting in substantial LLM inference costs and increased end-to-end latency. The empirical justification for this overhead in real production traffic remains largely unexplored. We present a case study of the Danish National Encyclopedia, evaluating five retrieval workflows over 20,000 query-workflow pairs from production traffic and synthetic conditions. In this system, synthetic queries suggest that LLM augmentation is needed for over 90% of queries to achieve high retrieval coverage. However, under our production deferral policy, only 27.8% of real user queries need LLM augmentation. We call this gap the Coverage Illusion and attribute it to a structural mismatch between synthetic and real query distributions. Pre-retrieval routing cannot resolve this gap, as the need for LLM augmentation is only revealed after searching the index, a result confirmed by our evaluation of four machine learning paradigms. The coverage gap, undetectable from the query alone, motivates a post-retrieval cascade that runs workflows in cheapest-first order and escalates to LLM augmentation only when a step returns no documents. Operating entirely without training overhead or secondary serving infrastructure, the cascade improves quality by +0.140 Composite Overall points over Always-HyDE, reduces latency by 31.8%, and serves 72.2% of real user queries without LLM augmentation.

Zafar Hussain, Kristoffer Nielbo

Aarhus University, Denmark

Agentic Retrieval-Augmented Generation Systems Search-Augmented Reasoning LLM Inference Optimization Illusions Distributions

May 26, 2026stat.ML

Transformers Can Learn Posterior Predictive Distributions In-Context

Prior-data fitted networks (PFNs) have recently emerged as a powerful approach for Bayesian prediction tasks, approximating the posterior predictive distribution (PPD) through in-context learning. Despite their strong empirical performance and ability to go beyond point predictions, theoretical understandings of the algorithmic capability of transformers to learn distributions in context are still lacking. Focusing on Gaussian process regression problems, we show by construction that transformers can implement a gradient descent algorithm targeting the posterior predictive mean and variance, followed by nonlinear mappings that yield binned probabilities of PPD. We study the error bounds of the approximated PPD in terms of attention depth and bin resolution. Based on these results, we further demonstrate the key role of normalization and the choice of attention depth in enabling the extrapolation abilities of transformers beyond the pretraining sample size range. We conduct simulations that corroborate our findings, providing insight into the expressivity of PFNs targeting PPDs and how architectural choices may influence generalization capabilities.

Gyeonghun Kang, Changwoo J. Lee, Xiang Cheng

Department of Statistical Science, Duke University, Durham, NC, USA · Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA

Posterior Predictive Distribution Transformer Architectures Tabular Prior-Data Fitted Network In-Context Learning Distributions In-Context

May 26, 2026econ.TH

Proper Calibeating

The classic concept of "calibrated forecasts" and its more recent refinement, "calibeating," are defined with respect to the standard quadratic scoring rule. We extend these notions to the class of

\textit{proper}

scoring rules (for which the best forecast is the true distribution) and define

\textit{proper-calibration}

and

\textit{proper-calibeating}

by requiring the errors to converge to zero uniformly over all bounded proper scoring rules. We first establish that calibration always implies proper-calibration, whereas calibeating need not imply proper-calibeating. Second, we show how to guarantee proper-calibeating and proper-multicalibeating. Finally, we demonstrate the equivalence between proper-calibration and universal no regret when best replying to forecasts in decision-making under uncertainty.

Dean P. Foster, Sergiu Hart

Department of Statistics, Wharton, University of Pennsylvania, Philadelphia, and Amazon, New York. · Institute of Mathematics, Department of Economics, and Federmann Center for the Study of Rationality, The Hebrew University of Jerusalem.

Calibrated Uncertainty Forecast Uncertainty Distributions

May 26, 2026cs.LG

The Stability of Singular Distribution: A Spectral Perspective on the Two-Phase Dynamics of Language Model Pre-training

Large language model pre-training typically exhibits a two-phase trajectory: a fast initial loss drop followed by a prolonged slow improvement. We identify an underlying spectral phenomenon, Stability of Singular Distribution (SoSD), where the trace-normalized singular value spectrum stabilizes early, even as parameter matrices continue to evolve. We demonstrate that synchronization between SoSD and the slow-descent regime is widely observed across diverse architectures (GPT-2, LLaMA) and settings, including various schedules (Step-wise, WSD, Cosine Decay), weight decays, and optimizers (AdamW, Muon). By analyzing a simplified Transformer, we prove that growing weight norms inevitably precipitate an early SoSD threshold, after which the rate of loss decrease becomes theoretically bounded by the variation in the singular distribution. We further interpret strategies like WSD and Muon through their ability to modulate the SoSD scale, offering a spectral lens for understanding efficient pre-training dynamics.

Hongtao Zhang, Wenjie Zhou, Chenxi Jia +2

State Key Laboratory of AI Safety, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China · School of Advanced Interdisciplinary Sciences, University of Chinese Academy of Sciences, Beijing, China · University of Chinese Academy of Sciences, Beijing, China +1

Large Language Model Pretraining Pretraining Singular Value Decomposition Spectral Descent Distributions

May 25, 2026stat.ME

Geometry Adaptive Counterfactual Distribution Learning with Diffusion-Guided Smoothing

We study counterfactual distribution learning for high-dimensional outcomes whose counterfactual law may concentrate near lower-dimensional structure. Standard isotropic smoothing treats all ambient directions equally, leading to unfavorable scaling and unstable local inference. We propose two diffusion-guided estimators based on semiparametric debiasing: diffusion-informed smoothing for counterfactual densities and diffusion-informed score smoothing for counterfactual scores. The estimators combine causal nuisance adjustment with geometry-adaptive localization driven by diffusion score information, removing first-order nuisance bias while aligning smoothing with local outcome geometry. We establish asymptotic expansions, risk bounds, and inference procedures for smoothed density and score-based targets, with ambient density inference obtained under additional approximation conditions. Under structural geometry conditions, the leading stochastic error is governed by an effective dimension induced by the diffusion-guided kernel, rather than by the ambient dimension. Semi-synthetic experiments based on CelebA show steeper error decay for geometry-adaptive methods, supporting the proposed effective-dimension theory.

Kwangho Kim

Department of Statistics, Korea University

Causal Inferences Distributions Low-Dimensional Structure Debiasing

May 25, 2026cs.CV

SurfSurg6D: Geometry Consistent Dense Correspondence for Textureless Surgical Instrument Pose Estimation

Surgical instrument pose estimation provides crucial information for promising applications, including autonomous robotic surgery, skill assessment, and standardization of surgical workflow. However, this task remains highly challenging due to high precision requirements, frequent occlusions, textureless instruments, scarcity of depth information and very limited annotated data. These constraints often lead to unsatisfactory performance when employing general object pose estimation approaches to surgical scenarios. To address these issues, we first construct a new dataset SynSurg6D, to alleviate the data shortage in this task. We further propose SurfSurg6D, a dense-correspondence framework tailored for surgical instrument pose estimation. Experimental results on the SurgRIPE, EndoVis2018 and SurgPose datasets demonstrate that the introduction of our generated dataset SynSurg6D is able to diversify the pose distributions, thus enhancing the performance of existing approaches. Furthermore, SurfSurg6D outperforms existing methods, providing a robust solution for precise and efficient RGB-only pose estimation.

Daiyun Shen, Shuojue Yang, Chang Han Low +4

National University of Singapore, Singapore · The Chinese University of Hong Kong, HKSAR, China

Category-Level Object Pose Estimation Surgical Robots Surgery Ground-Truth Correspondence Distributions