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02.
arXiv (CS.LG) 2026-06-19

Neural Architectures as Functional Priors in Physics-Informed Control Problems

Authors:
Sonia Rubio Herranz↗Fernando Carlos L\'opez Hern\'andez↗Antonio L\'opez Montes↗

arXiv:2606.19368v1 Announce Type: cross Abstract: In this work we investigate the role of neural architectures as implicit functional priors in control problems governed by ordinary differential equations. Rather than focusing on highly complex problems, our objective is to investigate architecture-dependent effects in controlled dynamical systems within the simplest physically interpretable settings possible. In particular, we study a controlled linear RLC electrical circuit and a nonlinear Duffing-type dynamical system. Both systems are analyzed first through classical optimal-control formulations and later through PINN-based approaches. We compare different combinations of multilayer perceptrons (MLPs) and Fourier-based KAN-like architectures, and analyze their influence on the resulting controls. The numerical experiments suggest that different architectural choices systematically generate qualitatively distinct controls, even under identical governing equations, loss functionals, initial and target states, training parameters and physical constraints. Significant differences appear in the spectral structure, smoothness, energy distribution, and phase-space behavior of the learned solutions. A central observation of this work is the emergence of a functional specialization phenomenon when the neural architectures are allowed sufficient freedom to shape the structure of the learned controls. More specifically, in the systems considered here, Fourier-based architectures tend to produce trajectories with richer oscillatory content, whereas smoother low-frequency-biased architectures tend to generate more regular and energetically efficient controls. This suggests that different functional components of the control problem may be handled more efficiently by different neural architectures, leading to an implicit specialization between state representation and control generation.

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03.
arXiv (CS.LG) 2026-06-18

Toward Simultaneously Optimal Regret in U-Calibration

Authors:
Rafael Frongillo↗Haipeng Luo↗Nishant A. Mehta↗Jon Schneider↗

arXiv:2606.18527v1 Announce Type: cross Abstract: U-calibration studies online forecasting algorithms whose predictions can be consumed by any unknown downstream agent, guaranteeing sublinear regret simultaneously for all proper loss functions. Existing U-calibration algorithms achieve worst-case optimal $O(\sqrt{T})$ regret for every bounded proper loss, but they fail to adapt to easier losses: as we show, even for smooth losses such as squared loss, they incur $\Omega(\sqrt{T})$ regret instead of the optimal $O(\log T)$ regret. In this work, we show that this limitation is not inherent. Specifically, we design a single forecast algorithm that simultaneously achieves $\tilde O(\sqrt{T})$ regret for every bounded proper loss and $O(\log T)$ regret for every bounded smooth proper loss. More generally, our algorithm also attains logarithmic regret for losses that are smooth relative to the log-barrier, which include several non-Lipschitz examples. Our approach is based on a novel variant of Follow-the-Perturbed-Leader (FTPL) in which perturbations are applied directly in the prediction space using self-concordant noise. The resulting analysis also departs substantially from prior FTPL analyses due to the complex nature of this noise and may be of independent interest.

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04.
arXiv (CS.LG) 2026-06-12

Adaptive Weighted Averaging

Authors:
Aditya Bhaskara↗Ashok Cutkosky↗Ravi Kumar↗Manish Purohit↗

arXiv:2606.12763v1 Announce Type: new Abstract: We study the problem of selecting the largest among $n$ unknown values $x_1,\dots,x_n$ given only a single unbiased estimate $y_i$ for each $x_i$. We design strategies that are simultaneously admissible (not uniformly dominated by any other strategy) and also never worse than a given baseline such as uniform random selection. We provide an application to stochastic optimization, where we obtain online-to-batch conversion bounds with a desirable "no-compromise" guarantee: they are never worse than standard random iterate selection, and yet can be significantly better in benign settings.

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05.
bioRxiv (Bioinfo) 2026-06-11

A systematic imputation framework for sparse, multimodal space biology datasets: application to retinal imaging and omics from the RR9 mission

Authors:
Nagesh↗Sanders↗Costes↗S. V↗Avci↗Sigit↗Agarwal↗Haghighi↗Batool↗Karouia↗Chander↗A. M↗…

Space biology experiments are expensive, logistically complex, and inherently limited in sample size, resulting in datasets that are frequently incomplete and highly heterogeneous (2). Missing data is a fundamental barrier to building reliable computational models of how the human body responds to spaceflight. This work introduces a systematic framework for addressing missing data through imputation. We developed a validated four-stage framework for imputation specifically designed to preserve biological signal needed for digital twin development, while quantifying trade-offs in downstream analyses. Using retinal imaging and omics data from the NASA RR9 mission as a case study (9), we demonstrate how to diagnose why data is missing(10), select and optimize appropriate imputation strategies (5,10), and rigorously evaluate whether imputed data remains biologically meaningful. A key finding of this work is that while imputation substantially improves the performance of predictive models, it can simultaneously obscure subtle biological patterns; a critical trade-off that researchers must understand before applying these methods (11). This framework provides practical, actionable guidance for space biologists and data scientists working with sparse, multimodal datasets in space biology, and represents a foundational step toward more complete and reliable data-driven models of human physiology in extreme environments.

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06.
arXiv (CS.CL) 2026-06-17

Would a Large Language Model Pay Extra for a View? Inferring Willingness to Pay from Subjective Choices

Authors:
Manon Reusens↗Sofie Goethals↗Toon Calders↗David Martens↗

As Large Language Models (LLMs) are increasingly deployed in applications such as travel assistance and purchasing support, they are often required to make subjective choices on behalf of users in settings where no objectively correct answer exists. We study LLM decision-making in a travel-assistant context by presenting models with choice dilemmas and analyzing their responses using multinomial logit models to derive implied willingness to pay (WTP) estimates. These WTP values are subsequently compared to human benchmark values from the economics literature. In addition to a baseline setting, we examine how model behavior changes under more realistic conditions, including the provision of information about users' past choices and persona-based prompting. Our results show that while meaningful WTP values can be derived for larger LLMs, they also display systematic deviations at the attribute level. Additionally, they tend to overestimate human WTP overall, particularly when expensive options or business-oriented personas are introduced. Conditioning models on prior preferences for cheaper options yields valuations that are closer to human benchmarks. Overall, our findings highlight both the potential and the limitations of using LLMs for subjective decision support and underscore the importance of careful model selection, prompt design, and user representation when deploying such systems in practice.

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07.
arXiv (CS.AI) 2026-06-11

CRUMB: Efficient Prior Fitted Network Inference via Distributionally Matched Context Batching

Authors:
Jamie Heredge↗Mattia J. Villani↗Pranav Deshpande↗Akshay Seshadri↗Niraj Kumar↗

arXiv:2606.11473v1 Announce Type: cross Abstract: Prior-fitted networks (PFNs) are a promising class of tabular foundation models that perform in-context learning, whereby the entire labelled training set is supplied as context, and predictions for test queries are produced in a single forward pass. However, the quadratically scaling self-attention mechanism in many PFN architectures makes inference prohibitive for very large training datasets. We propose CRUMB (Clustered Retrieval Using Minimised-MMD Batching), a three-stage inference wrapper that (i) clusters the test queries, (ii) selects a small, distributionally matched training subset for each cluster by greedily minimising the maximum mean discrepancy (MMD), and (iii) runs exact PFN inference on each reduced-context batch. CRUMB is architecture-agnostic and requires no retraining. On the 51-dataset TabArena benchmark, evaluated across three PFN architectures (TabPFNv2, TabICLv1, TabICLv2), we show that CRUMB outperforms similar state-of-the-art context selection strategies. We also show that CRUMB is resilient to covariate drift, as the MMD-minimisation step naturally helps align the training context distribution to match the current test batch distributions.

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08.
arXiv (CS.CL) 2026-06-17

Dissociating Decodability and Causal Use in Bracket-Sequence Transformers

Authors:
Aryan Sharma↗Cutter Dawes↗Shivam Raval↗

When trained on tasks requiring an understanding of hierarchical structure, transformers have been found to represent this hierarchy in distinct ways: in the geometry of the residual stream, and in stack-like attention patterns maintaining a last-in, first-out ordering. However, it remains unclear whether these representations are causally used or merely decodable. We examine this gap in transformers trained on the Dyck language (a formal language of balanced bracket sequences), where the hierarchical ground truth is explicit. By probing and intervening on the residual stream and attention patterns, we find that depth, distance, and top-of-stack signals are all decodable, yet their causal roles diverge. Specifically, masking attention to the true top-of-stack position causes a sharp drop in long-distance accuracy, while ablating low-dimensional residual stream subspaces has comparatively little effect. These results, which extend to a templated natural language setting, suggest that even in a controlled setting where the relevant hierarchical variables are known, decodability alone does not imply causal use.

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09.
arXiv (CS.AI) 2026-06-12

An Embodied Simulation Platform, Benchmark, and Data-Efficient Augmentation Framework for Wet-Lab Robotics

Authors:
Zhe Liu↗Huanbo Jin↗Zhaohui Du↗Zhe Wang↗He Xu↗Peijia Li↗Jiaming Gu↗Quan Lu↗Qi Wang↗Bin Ji↗Ting Xiao↗

arXiv:2606.12936v1 Announce Type: cross Abstract: Wet-lab robots can improve the reproducibility, throughput, and safety of biomedical experiments, but scaling their learning requires customizable simulators for safe and reproducible task generation, open editable laboratory assets, and efficient pipelines that turn limited demonstrations into usable training data. We present Pipette, an embodied simulation platform, benchmark, and data-efficient augmentation framework for wet-lab robot learning. Pipette releases over 43 open-source and re-editable wet-lab assets, together with an extensible asset-building pipeline. A key component of Pipette is its simulation-based data augmentation pipeline, replaying human demonstrations in simulation, applies lighting, camera, speed, and action perturbations, and filters generated episodes with automatic task success checks, rapidly expanding usable training data from limited manual demonstrations. We further introduce an 11-task wet-lab embodied benchmark covering sample handling, culture-ware manipulation, device operation, and precision placement. With only 30 demonstrations per task, ACT achieves 65.5% average success rate, while simulation augmentation improves SmolVLA from 44.1% to 74.7% and {\pi}0 from 40.4% to 46.5%, validating the effectiveness of Pipette for data-efficient VLA training and evaluation. Pipette also supports natural-language-driven scene construction and task registration, lowering the barrier for non-expert users to define new wet-lab robotic tasks.

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10.
arXiv (quant-ph) 2026-06-11

Emergent mirror symmetry in the optimization of the central-spin quantum battery

Authors:
Hui-Yu Yang↗Kun Zhang↗Xiao-Hui Wang↗Hai-Long Shi↗

arXiv:2606.11557v1 Announce Type: new Abstract: Quantum batteries provide a useful setting for exploring nonequilibrium many-body effects in energy storage. Here we investigate the optimization of a quantum battery based on the central-spin model. We identify two complementary structural indicators associated with the effective charging dynamics: one yields an upper bound on the average charging power, while the other characterizes the buildup of stored energy. We show that these two indicators are jointly optimized at a distinguished initial charger excitation number, which selects a particular Dicke sector of the model. At this common optimal point, the effective charging Hamiltonian becomes exactly mirror symmetric, suggesting mirror symmetry as a useful structural indicator for optimizing quantum batteries. We further show that the corresponding optimal dynamics can be closely approximated by product initial states, in particular by spin coherent states whose excitation-number distribution is centered at the symmetry-selected point. Our results establish a direct connection between charging performance, optimal-state structure, and emergent symmetry in the central-spin quantum battery, and suggest symmetry as a useful organizing principle for efficient charging in interacting many-body quantum systems.

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11.
arXiv (CS.CV) 2026-06-11

UniReason-Med: A Shared Grounded Reasoning Interface for 2D-to-3D Transfer in Medical VQA

Authors:
Mengzhuo Chen↗Yan Shu↗Chi Liu↗Hongming Piao↗Xidong Wang↗Derek Li↗Bryan Dai↗

We study whether grounded reasoning supervision from abundant 2D medical images can improve 3D medical VQA when both input types are aligned through a common reasoning interface. We introduce UniReason-Med, a single-checkpoint framework that processes either a 2D image or a slice-serialized 3D volume at inference time, generating interleaved textual reasoning and localized visual evidence through shared box syntax, region-token injection, and a common grounded reasoning policy. To train this interface, we construct UniMed-CoT, a 220K instruction-tuning dataset with interleaved textual reasoning and grounded visual evidence, including 170K 2D and 50K 3D samples. Through supervised fine-tuning followed by outcome-level reinforcement learning, UniReason-Med learns to generate grounded reasoning traces without IoU/Dice-based localization rewards during RL. Data-mixture and component ablations show that joint 2D+3D grounded supervision substantially improves 3D reasoning over 3D-only training, while grounding and region-token injection consistently benefit both 2D and 3D tasks. These results suggest that a shared grounded reasoning interface can transfer reasoning structure from 2D images to slice-serialized volumetric medical understanding. The code and data are publicly available at https://github.com/IQuestLab/unireason-med.

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12.
arXiv (CS.AI) 2026-06-16

Gated QKAN-FWP: Scalable Quantum-inspired Sequence Learning

Authors:
Kuo-Chung Peng↗Samuel Yen-Chi Chen↗Jiun-Cheng Jiang↗Chen-Yu Liu↗En-Jui Kuo↗Yun-Yuan Wang↗Prayag Tiwari↗Andrea Ceschini↗Chi-Sheng Chen↗Yu-Chao Hsu↗Chun-Hua Lin↗Tai-Yue Li↗…

arXiv:2605.06734v2 Announce Type: replace-cross Abstract: Fast Weight Programmers (FWPs) encode temporal dependencies through dynamically updated parameters rather than recurrent hidden states. Quantum FWPs (QFWPs) extend this idea with variational quantum circuits (VQCs), but existing implementations rely on multi-qubit architectures that are difficult to scale on noisy intermediate-scale quantum (NISQ) devices and expensive to simulate classically. We propose gated QKAN-FWP, a fast-weight framework that integrates FWP with Quantum-inspired Kolmogorov-Arnold Network (QKAN) using single-qubit data re-uploading circuits as learnable nonlinear activation, known as DatA Re-Uploading ActivatioN (DARUAN). We further introduce a scalar-gated fast-weight update rule that stabilizes parameter evolution, supported by a theoretical analysis of its adaptive memory kernel, geometric boundedness, and parallelizable gradient paths. We evaluate the framework across time-series benchmarks, MiniGrid reinforcement learning, and highlight real-world solar cycle forecasting as our main practical result. In the long-horizon setting with 528-month input window and 132-month forecast horizon, our 12.5k-parameter model achieves lower scaled Mean Square Error (MSE), peak amplitude error, and peak timing error than a suite of classical recurrent baselines with up to 13x more parameters, including Long Short-Term Memory (LSTM) networks (25.9k-89.1k parameters), WaveNet-LSTM (167k), Vanilla recurrent neural network (11.5k), and a Modified Echo State Network (132k). To validate NISQ compatibility, we further deploy the trained fast programmer on IonQ and IBM Quantum processors, recovering forecasting accuracy within 0.1% relative MSE of the noiseless simulator at 1024 shots. These results position gated QKAN-FWP as a scalable, parameter-efficient, and NISQ-compatible approach to quantum-inspired sequence modeling.

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13.
arXiv (CS.CL) 2026-06-18

Narrative Theory-Driven LLM Methods for Automatic Story Generation and Understanding: A Survey

Authors:
David Y. Liu↗Aditya Joshi↗Paul Dawson↗

Applications of narrative theories using large language models (LLMs) deliver promising methods in automatic story generation and understanding tasks. Our survey examines how natural language processing (NLP) research uses LLM methods to engage with diverse concepts from narrative studies. We use established distinctions from narratology to categorise ongoing efforts and discover the following: \redtext{(a) narrative texts come from diverse sources beyond just literature, (b) theoretical synthesis and validation are potential outcomes, (c) generation tasks lag behind understanding in several ways: theoretical application, post-training methods, exploring non-fiction narratives and addressing narrative levels beyond fabula and discourse.} For future directions, instead of the pursuit of a single, generalised benchmark for `narrative quality', we believe that progress can benefit from efforts that focus on the following: defining and improving theory-based metrics for individual narrative attributes; continue conducting large-scale, theory-driven literary/social/cultural analysis; generating narratives in situated contexts; and continuing experiments where outputs can be used to validate or refine narrative theories. This work provides a contextual foundation for more systematic and theoretically informed narrative research in NLP by providing an overview to ongoing research efforts and the broader narrative studies landscape.

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14.
arXiv (CS.CV) 2026-06-16

Position: The Systemic Lack of Agency in Visual Reasoning

Authors:
Yizhao Huang↗Haoyang Chen↗Shiqin Wang↗Pohsun Huang↗Jiayuan Li↗Haoyuan Du↗Yandong Shi↗Zheng Wang↗Zhixiang Wang↗

This paper argues that a systemic lack of Agency constrains the implicit reasoning capabilities of current Vision-Language Models (VLMs). Implicit reasoning refers to the ability to autonomously discover and utilize hidden visual evidence to bridge information gaps, rather than merely relying on explicitly specified targets. This capacity underlies human visual understanding and everyday reasoning. We argue that this limitation arises from a tendency to approach visual reasoning primarily as passive semantic retrieval, rather than as active, situated reasoning that depends on autonomous visual exploration. As a result, most existing benchmarks primarily assess Passive Capacity, leaving this aspect of reasoning largely unmeasured. To address this gap, we introduce the Visual Implicit Reasoning Diagnosing Benchmark (V-IRD), which targets this missing quadrant by requiring models to derive answers strictly through autonomous visual analysis. Our results show that, despite strong retrieval abilities, prominent VLMs struggle to utilize reference objects and to attend to visual evidence that requires self-directed inquiry. Simply put, strong semantic recognition does not equate to active visual exploration, revealing a critical gap in current VLMs. More information can be found at https://haoychen.github.io/Implicit-Reasoning/

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15.
arXiv (CS.AI) 2026-06-16

The Faithfulness Gap: Certifying Semantic Equivalence Between Natural-Language and Formal Mathematical Statements

Authors:
Noor Islam S. Mohammad↗Tamim Sheikh↗

arXiv:2606.16541v1 Announce Type: new Abstract: Autoformalization, translating natural-language mathematics into formal proof assistants, is bottlenecked not by translation fluency but by faithfulness: a formal statement can typecheck and be provable, yet still encode a different theorem than the source intended. We introduce Bidirectional Provability Fingerprinting (\bpf{}), a framework that certifies faithfulness by characterizing each candidate through its forward and backward consequence neighborhoods in the ambient theory and matching these against probes derived from the natural-language statement. We further introduce four novel components: (i) Counterfactual Probe Generation (\cpg{}), a contrastive procedure that synthesizes probes targeting specific drift directions; (ii) the Equivalence Spectrum, a continuous faithfulness score that replaces brittle binary verdicts; (iii) Adaptive Probe Budget Allocation (\apba{}), an information-theoretic budget router; and (iv) Faithfulness-Guided Decoding (\fgd{}), which uses \bpf{} signals as a reward during autoformalization. We prove a drift detection theorem and a PAC-faithfulness result establishing that the equivalence class of a natural language statement is learnable from $\mathcal{O}(\log(1/\delta)/\varepsilon)$ probes under mild assumptions. We release \driftbench{}, a benchmark of $2{,}183$ NL/Lean~4 pairs with controlled drift labels across six subfields of mathlib4. \bpf{}\,+\,\cpg{} detects $89.6\%$ of drifted formalizations at a $3.0\%$ false-positive rate-against $41.2\%$ for typecheck and $63.3\%$ for LLM-judge baselines, and \fgd{} reduces the rate at which a state-of-the-art autoformalizer emits drifted statements by $47\%$. https://pmlrbd.github.io/BPF/

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16.
arXiv (CS.AI) 2026-06-17

Reversal Q-Learning

Authors:
Aditya Oberai↗Seohong Park↗Sergey Levine↗

arXiv:2606.17551v1 Announce Type: cross Abstract: Iterative generative modeling techniques, such as flow matching, provide powerful tools to model complex behaviors for effective offline reinforcement learning (RL). In this work, we propose a new off-policy RL algorithm that trains a flow policy based on prior data. Our idea starts from the "expanded" Markov decision process (MDP) framework, which treats individual flow refinement steps as separate actions in an MDP. To enable off-policy RL within this framework, we apply two techniques: we generate virtual on-policy trajectories (by "reversing" flows) to make this framework compatible with prior data, and we apply a bias-and-variance reduction technique to mitigate the curse of horizon in off-policy RL. We call the resulting algorithm Reversal Q-learning (RQL). RQL has several advantages over previous flow-based RL methods: it does not suffer from backpropagation through time, makes better use of the learned value function, and directly trains the full, expressive flow policy. Through our experiments on 50 challenging simulated robotic tasks, we show that RQL leads to the best average offline RL performance compared to state-of-the-art flow-based offline RL algorithms.

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17.
arXiv (CS.CL) 2026-06-18

Low-resource Language Discrimination Towards Chinese Dialects with Transfer learning and Data Augmentation

Authors:
Fan Xu↗Yangjie Dan↗Keyu Yan↗Yong Ma↗Mingwen Wang↗

Chinese dialects discrimination is a challenging natural language processing task due to scarce annotation resource. In this article, we develop a novel Chinese dialects discrimination framework with transfer learning and data augmentation (CDDTLDA) in order to overcome the shortage of resources. To be more specific, we first use a relatively larger Chinese dialects corpus to train a source-side automatic speech recognition (ASR) model. Then, we adopt a simple but effective data augmentation method (i.e., speed, pitch, and noise disturbance) to augment the target-side low-resource Chinese dialects, and fine-tune another target ASR model based on the previous source-side ASR model. Meanwhile, the potential common semantic features between source-side and target-side ASR models can be captured by using self-attention mechanism. Finally, we extract the hidden semantic representation in the target ASR model to conduct Chinese dialects discrimination. Our extensive experimental results demonstrate that our model significantly outperforms state-of-the-art methods on two benchmark Chinese dialects corpora.

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18.
arXiv (CS.CL) 2026-06-15

Decoupled Mixture-of-Experts for Parametric Knowledge Injection

Authors:
Baoqing Yue↗Weihang Su↗Qingyao Ai↗Yichen Tang↗Changyue Wang↗Jiacheng Kang↗Jingtao Zhan↗Yiqun Liu↗

Knowledge injection aims to equip large language models (LLMs) with external, domain-specific, or time-sensitive knowledge. Existing approaches typically face a trade-off between flexibility and integration: retrieval-augmented generation keeps knowledge outside the model but only provides prompt-level augmentation, whereas post-training based methods encode new knowledge into shared parameters but may introduce catastrophic forgetting, knowledge conflict, and costly updates. In this paper, we propose Decoupled Mixture-of-Experts (DMoE), a modular architecture for parametric knowledge injection that decouples both experts and the router from the base model. DMoE converts external knowledge corpora into independently updatable expert modules and uses a lightweight uncertainty-aware router to activate relevant experts only when the base model lacks sufficient knowledge during generation. To support efficient auto-regressive inference, DMoE attaches experts only to the final-layer feed-forward network, preserving KV-cache reuse while enabling parameter-level knowledge augmentation. Experiments on knowledge-intensive benchmarks show that DMoE consistently improves answer quality over retrieval and adapter-based baselines.

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19.
arXiv (CS.LG) 2026-06-18

Regular Fourier Features for Nonstationary Gaussian Processes

Authors:
Arsalan Jawaid↗Abdullah Karatas↗J\"org Seewig↗

arXiv:2602.23006v2 Announce Type: replace-cross Abstract: Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation and treating the spectral density as a probability distribution suitable for Monte Carlo approximation. Although this probabilistic interpretation is valid for stationary processes, it is overly restrictive for the nonstationary case, where spectral densities are generally not probability measures. We propose regular Fourier features for harmonizable processes to avoid this limitation. Our method discretizes the spectral representation directly, preserving the correlation structure among spectral weights without requiring probability assumptions. Under a finite-spectral-support assumption, this yields an efficient low-rank approximation that is consistent and positive semi-definite by construction. When the spectral density is unknown, the framework extends naturally to kernel learning from data. We demonstrate the method on locally stationary and harmonizable mixture kernels, the latter with a complex-valued spectral density, and apply the kernel-learning extension to real and synthetic data.

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20.
arXiv (math.PR) 2026-06-18

Functional central limit theorems for non-local branching Markov processes

Authors:
Christopher B. C. Dean↗Emma Horton↗

arXiv:2502.19382v2 Announce Type: replace Abstract: The aim of this paper is to study the fluctuations of a general class of supercritical branching Markov processes with non-local branching mechanisms. We establish functional central limit theorems and show that the limiting behaviour falls into three regimes, determined by the size of the spectral gap associated with the first-moment semigroup of the branching process. The main novelty is to develop a unified functional fluctuation theory for spatial branching Markov processes with non-local reproduction, allowing a general finite-dimensional spectral structure for the first-moment semigroup, including non-simple leading eigenvalues and nilpotent Jordan-type components. In doing so, we extend the classical small, critical and large fluctuation trichotomy beyond the finite-type and local spatial settings, and obtain limiting processes that capture the covariance structure induced by non-local offspring displacement.

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21.
arXiv (CS.CV) 2026-06-17

HRDX: A Large-Scale Vector HD-Map Dataset

Authors:
Sahith Reddy Chada↗Isht Dwivedi↗Nirav Savaliya↗

Reliable autonomous driving requires vectorized HD maps that are geometrically accurate, semantically rich, and scalable to long-horizon driving. However, existing public HD map datasets are limited in scale, provide sparse semantic attributes, and lack modalities such as aerial imagery that could enable new research directions. We present HRDX, a large-scale dataset for vector HD-map construction, spanning about 40 hours (1,400 km) of minimally overlapping drives, which is several times larger than prior public HD map datasets. Data is captured using six synchronized surround cameras, a 128-beam LiDAR, and centimeter-level RTK GNSS/IMU, and is further complemented by precisely aligned aerial orthoimagery. Annotations cover 10 vector map classes, complemented with over 20 semantic and topological attributes. To evaluate this richer ontology, we introduce the Composite Score (CS) to jointly assess geometric fidelity and attribute correctness. Benchmark experiments show that HRDX's scale improves online vector-map construction, and that aligned aerial imagery provides a useful structural prior: using aerial imagery at training and/or inference improves geometric map quality, while aerial-augmented teachers can transfer part of this benefit to camera-only students without increasing inference-time sensor requirements. HRDX is intended to support reproducible research on large-scale HD-map learning, multimodal BEV fusion, and training-time privileged information. HRDX dataset and benchmarks are available at https://github.com/honda-research-institute/HRDX

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22.
arXiv (math.PR) 2026-06-15

Stability of the $k$-Plane Transform on Measures and Hölder-Type Comparisons of Wasserstein Metrics

Authors:
Fatma Terzioglu↗Ryan Murray↗

arXiv:2605.00375v2 Announce Type: replace-cross Abstract: We establish stability estimates for the $k$-plane transform on finite positive Radon measures, with emphasis on Fourier and Wasserstein metrics. We first introduce a metric on $k$-plane transform data and prove a bi-Lipschitz stability estimate showing that this metric is equivalent to a generalized Fourier metric obtained by augmenting the Fourier distance between centered normalized measures with separate barycenter and total mass difference terms. Building on a Hölder-type comparison between Fourier and Wasserstein metrics due to Carrillo and Toscani, we extend this comparison to positive Radon measures under uniform bounds on centered moments of order slightly larger than $2$. This yields Hölder-type stability for the $k$-plane transform in a generalized $2$-Wasserstein metric and, in particular, a $W_2$-stability estimate for centered probability measures. We also compare the $2$-Wasserstein distance with its max-sliced analogue. For centered probability measures with uniformly bounded moments of order slightly larger than $2$, we prove a two-sided Hölder-type comparison between these distances. We then extend the result to positive Radon measures by applying it to centered normalized measures and adding separate barycenter and mass terms. Finally, for absolutely continuous compactly supported probability measures with bounded densities, we prove a strong equivalence between the $2$-Wasserstein distance of the measures and the $(k/2-1)$-order Sobolev norm of the $k$-plane transform data of the difference of their densities.

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23.
arXiv (CS.CV) 2026-06-12

Magnifying What Matters: Attention-Guided Adaptive Rendering for Visual Text Comprehension

Authors:
Shenglai Zeng↗Qirui Wang↗Kai Guo↗Xinnan Dai↗Xianxuan Long↗Hui Liu↗

Visual Text Comprehension (VTC) renders text into images for a vision-language model (VLM) to read, sidestepping LLM context-window limits and powering applications from long-page OCR to multi-page memory QA. Yet existing VTC pipelines treat rendering and layout as a fixed, content-agnostic preprocessing step and offer little mechanistic understanding of how VLMs internally process visualized text. Through a focused empirical study on VTC QA tasks, we reveal that VLMs exhibit a localization-without-utilization regime: evidence-localizing attention emerges sharply in the middle-to-late layers and is largely decoupled from answer correctness, yet simply enlarging the localized spans on the rendered page recovers a large fraction of the failures. Building on these observations, we propose AGAR (Attention-Guided Adaptive Rendering), a training-free, model-agnostic method that leverages a VLM's own middle-to-late layer attention to identify the top-K important visual patches, maps them back to word spans, and re-renders the page with those spans enlarged before re-inferring the answer. Extensive experiments across nine VTC benchmarks (short-form, long-context, and multi-page memory QA) and four VLM backbones show that AGAR (i)consistently improves off-the-shelf VLMs as a plug-and-play enhancement, (ii)composes with VLM post-training to yield further gains, and (iii)remains robust under both visual- and text-side input degradation.

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24.
arXiv (CS.CL) 2026-06-16

Fast-dLLM++: Fr\'{e}chet Profile Decoding for Faster Diffusion LLM Inference

Authors:
Siva Rajesh Kasa↗Yasong Dai↗Sumit Negi↗Hongdong Li↗

Diffusion large language models promise parallel token generation, yet inference remains bottlenecked by deciding which masked tokens can be safely committed together. Fast-dLLM addressed this with KV caching and confidence-guided parallel decoding, but its decoding theory uses a homogeneous high-confidence assumption that effectively reduces each candidate set to its weakest selected token. We argue that this leaves speed on the table because real decoding steps exhibit heterogeneous confidence profiles. We propose Fast-dLLM++, a training-free extension that introduces Fr\'{echet profile decoding}: selecting parallel commit sets from the full sorted confidence profile rather than a single worst-case confidence. The resulting rule is a heterogeneous-confidence generalization of Fast-dLLM's factor selector and it recovers the previous rule exactly in the equal-confidence case and adds a provable heterogeneity bonus when the selected tokens have uneven confidences. Fast-dLLM++ leaves the model, diffusion process, and cache implementation entirely unchanged, making it a drop-in replacement for existing Fast-dLLM decoding. Experiments on GSM8K, MATH, HumanEval, and MBPP with the LLaDA-8B model show that the theoretical improvement translates directly into empirical gains: profile-aware selection improves the accuracy–throughput frontier by exploiting safe parallelism that weakest-token rules miss, achieving up to 37\% higher throughput at comparable accuracy. Our code release is at https://github.com/Ringo-Star/FastdLLM_plusplus.

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25.
arXiv (CS.AI) 2026-06-17

The Discrete-Log Clock: How a Transformer Learns Modular Multiplication

Authors:
Huu Danh Nguyen↗

arXiv:2606.17399v1 Announce Type: cross Abstract: When small transformers grok modular multiplication, prior work reports that the learned embedding has a "dense" Fourier spectrum requiring all frequencies. This contrasts with modular addition, where only a sparse set of key frequencies suffices. We show this density is an artifact of analyzing in the wrong basis. The natural Fourier transform for multiplication is not the standard additive DFT but the multiplicative character transform, which decomposes functions on the multiplicative group $(\mathbb{Z}/p\mathbb{Z})^*$ into its irreducible representations. Applying this transform to a grokked transformer trained on $a \cdot b \bmod 113$, we find the embedding spectrum becomes highly sparse (Gini coefficient 0.58 vs. 0.07 in the additive basis) with only 4 key frequencies carrying significant energy. Furthermore, 96.9% of MLP neurons are cleanly tuned to a single multiplicative frequency, and neuron activation heatmaps reveal 2D-periodic structure when reordered by the discrete logarithm. These results demonstrate the transformer reduces multiplication to addition in discrete-log space, implementing a "Discrete-Log Clock" algorithm analogous to Nanda et al.'s Clock algorithm for addition. The methodology generalizes: matching the analysis basis to the algebraic structure of the task reveals interpretable structure where standard tools see noise.

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