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01.
arXiv (CS.LG) 2026-06-11

Bergson: An Open Source Library for Data Attribution

arXiv:2606.11660v1 Announce Type: new Abstract: Data attribution is a promising field in interpretability that aims to explain model behavior through the influence of its training data, with applications including debugging undesirable model behavior and training dataset curation. However, significant engineering effort is required to perform it at scale, and many cutting edge techniques lack open-source tooling and support. Bergson is an open source library that aims to enable faster progress in the field by providing a host of techniques that scale to very large language models and pre-training datasets. The library natively supports on-disk gradient stores and multi-node distributed training, and provides quality of life tools for researchers. Finally, we introduce the first open-source implementations of three leading data attribution methods: MAGIC, SOURCE, and TrackStar. The library is available at https://github.com/EleutherAI/bergson .

02.
arXiv (CS.AI) 2026-06-24

A Fair Evaluation of Graph Foundation Models for Node Property Prediction

arXiv:2606.24509v1 Announce Type: cross Abstract: Due to the wide use of graph-structured data in different fields of industry and science, the development of Graph Foundation Models (GFMs) has recently attracted a lot of attention. While many different types of models are called GFMs, particular interest has been paid to GFMs designed for node property prediction tasks, which is one of the most popular settings in Graph ML with lots of real-world applications from fraud detection in financial and social networks to recommendation systems for e-commerce and user-generated content platforms. While a number of GFMs for this task have been recently proposed, the field has not converged to a unified evaluation setting, and different works evaluate their models in widely different ways, preventing reliable comparison of GFMs with each other and with other types of models. In this work, we conduct a fair and rigorous reevaluation of 9 recent GFMs for node property prediction, comparing them to strong Graph Neural Network (GNN) baselines. We find that, among these GFMs, only the most recent ones based on the Prior-data Fitted Networks paradigm outperform well-tuned GNNs in predictive performance, although at a higher inference cost.

03.
arXiv (CS.AI) 2026-06-12

Examining the Usage of Generative AI Models in Student Learning Activities for Software Programming

arXiv:2511.13271v2 Announce Type: replace-cross Abstract: The rise of Generative AI (GenAI) tools like ChatGPT has created new opportunities and challenges for computing education. Existing research has primarily focused on GenAI's ability to complete educational tasks and its impact on student performance, often overlooking its effects on knowledge gains. In this study, we investigate how GenAI assistance compares to conventional online resources in supporting knowledge gains across different proficiency levels. We conducted a controlled user experiment with 24 undergraduate students of two different levels of programming experience (beginner, intermediate) to examine how students interact with ChatGPT while solving programming tasks. We analyzed task performance, conceptual understanding, and interaction behaviors. Our findings reveal that generating complete solutions with GenAI significantly improves task performance, especially for beginners, but does not consistently result in knowledge gains. Importantly, usage strategies differ by experience: beginners tend to rely heavily on GenAI toward task completion often without knowledge gain in the process, while intermediates adopt more selective approaches. We find that both over-reliance and minimal use result in weaker knowledge gains overall. Based on our results, we call on students and educators to adopt GenAI as a learning rather than a problem solving tool. Our study highlights the urgent need for guidance when integrating GenAI into programming education to foster deeper understanding.

04.
arXiv (math.PR) 2026-06-11

Mean-field theory via dissociated arrays for particle systems interacting through noisy weights

arXiv:2606.12135v1 Announce Type: new Abstract: We study a mean-field limit for a $N$-particle system in which each particle follows a diffusion and interacts with other particles through a weight on each directed edge. Each weight evolves according to its own nonlinear SDE driven by a Brownian motion, with coefficients involving the states of the two endpoint particles of the edge. The initial vertex and edge variables are assumed to have a dissociated Aldous–Hoover form. We construct the limiting nonlinear SDE by averaging the interaction over an independent neighbor and an edge input, prove its well-posedness, and show that the dissociated vertex-edge structure is propagated by the dynamics. This propagation property is an analogue of propagation of chaos in the case where the weight of each edge may remain correlated with the states of the two endpoint particles. Under either a bounded-observable assumption or a sub-Gaussian edge-input condition, the finite system converges to this limit through quantitative coupling estimates for a typical particle and a typical edge. We also prove the convergence of the empirical measure of particle's state pairs and their interaction weights.

05.
arXiv (quant-ph) 2026-06-16

Optical Creation of Synthetic Microgravity for Quantum Degenerate Gases

arXiv:2606.14985v1 Announce Type: cross Abstract: Microgravity environments provide unique opportunities for ultracold-atom experiments by enabling long interrogation times and reduced acceleration-induced dynamics. However, their realization has largely been restricted to specialized facilities such as drop towers, sounding rockets, and space-based laboratories. Here we realize synthetic microgravity for quantum degenerate gases using optically engineered force landscapes that compensate Earth's gravity to the milli-g level while maintaining continuous confinement of the atomic ensemble. These force landscapes are generated by dynamically painted optical dipole potentials and calibrated in situ through Bloch oscillations in a vertical optical lattice, enabling precise control of the residual acceleration. We use this capability to demonstrate matter-wave beam splitting with arm separations of several hundred microns. We further implement a Bloch-band atom interferometer in which interaction-induced dephasing is strongly suppressed through controlled three-dimensional expansion in the synthetic microgravity potential. This reduction of mean-field effects restores near-$\sqrt{N}$ scaling of interferometric sensitivity for large quantum degenerate ensembles. Our results establish a versatile platform for realizing synthetic microgravity with trapped quantum gases in terrestrial laboratories, bringing the advantages of microgravity experiments to continuously operating systems and opening new opportunities for quantum sensing, matter-wave interferometry, and precision measurements.

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

When Top-1 Fails: Calibrating LoRA Monitors for Masked Diffusion LMs

Discrete diffusion language model (DLM) fine-tuning inherits inexpensive diagnostics from denoising-time confidence monitors, but their PEFT-training meaning is untested. We test top-1 argmax concentration as a collapse warning. Across 816 LoRA/PEFT configurations from three DLM families, the warning fires for every configuration while logs record 0/816 actual collapses at the 200 step horizon, giving zero precision. The cause is pre-equilibrium saturation: top-1 concentration is already high before optimization and quickly becomes insensitive to final training stability. We then evaluate max LoRA gradient norm, a parameter-side signal that samples gradient routing rather than token concentration. On a pooled held-out LLaDA-family split, a train-optimized threshold identifies top-decile final-loss configurations with precision 0.68 and F1=0.79, above the all-positive top-1 baseline even at the lower split-bootstrap confidence bound. Autoregressive controls and cross-family threshold failures bound the result to short-horizon DLM-LoRA inspection rather than a universal collapse detector. Workflow: drop top-1 as a PEFT alarm, log max-gradient early in training, and calibrate thresholds per DLM family before routing runs for inspection.

07.
arXiv (quant-ph) 2026-06-11

A quantum implementation of high-order power method for estimating geometric entanglement of pure states

arXiv:2405.19134v3 Announce Type: replace Abstract: Entanglement is one of the fundamental properties of a quantum state and is a crucial differentiator between classical and quantum computation. There are many ways to define entanglement and its measure, depending on the problem or application under consideration. Each of these measures may be computed or approximated by multiple methods. However, hardly any of these methods can be run on near-term quantum hardware. This work presents a quantum adaptation of the iterative high-order power method for estimating the geometric measure of entanglement of multi-qubit pure states using rank-1 tensor approximation. This method is executable on early fault-tolerant (hybrid) quantum hardware and does not depend on quantum memory. We simulate this algorithm and mitigate the effects of noise on the results of the computation using a theoretical model based on a known mitigation approach, which assumes a global depolarising noise channel.

08.
arXiv (quant-ph) 2026-06-17

Optimal Probe State for Phase Estimation Under Covariant Measurement

arXiv:2606.18169v1 Announce Type: new Abstract: We study the optimization of input states for phase estimation under covariant measurements. Building on Holevo's framework, which provides the optimal covariant measurement for a fixed input state, we further optimize over the input state itself. For a general even $2\pi$-periodic cost function with non-negative Fourier coefficients, we derive a necessary and sufficient condition for the optimal input state: Its Fock coefficients are determined, up to arbitrary phases, by the eigenvector corresponding to the largest eigenvalue of a Toeplitz matrix defined by the cost function. This characterization yields an explicit expression for the attainable lower bound of the average cost under optimal covariant measurements and shows that this bound asymptotically approaches zero in the infinite-energy limit. For the specific cost function $W(\theta,\tilde{\theta})=4\sin^2[(\theta-\tilde{\theta})/2]$, we obtain the optimal input state and the corresponding minimum average cost in closed form, demonstrating Heisenberg scaling with respect to the mean photon number.

09.
arXiv (CS.LG) 2026-06-18

Identifying Structural Biases from Causal Mechanism Shifts

arXiv:2606.18834v1 Announce Type: new Abstract: Causal discovery methods commonly assume that all data is independently and identically distributed (i.i.d.) and that there are no unmeasured variables affecting the system. In practice, these assumptions are often violated, leading to inaccurate inference. In this paper, we study how to identify hidden confounding and selection biases from causal mechanism shifts. In particular, we show that structural biases lead to dependent mechanism shifts. That is, by considering for which variables the mechanisms change given data from different environments, we can tell which variables are unbiased, which are subject to hidden confounding, and which are undergoing selection bias. We formalize this into an empirically testable criterion based on mutual information, and show under which conditions it identifies structural biases. To tell which nodes are subject to what kind of bias, we introduce the StruBI algorithm. Experiments on synthetic and real-world data show that StruBI works well in practice, accurately recovering affected variable sets and types of biases, outperforming the state-of-the-art by a wide margin.

10.
arXiv (CS.CV) 2026-06-11

NSVQ: Mitigating Codebook Collapse by Stabilizing Encoder Drift in Vector Quantization

Vector quantization is central to modern generative modeling pipelines, but large-codebook VQ models often suffer from codebook collapse. We identify encoder drift as a key driver of this failure: as the encoder moves the latent distribution, sparsely updated code vectors can lag behind, lose assignments, and increase quantization error, creating a feedback loop through the straight-through estimator. We propose NSVQ, a non-stationary-aware VQ training strategy that combines a dense non-stationary embedding loss, codebook replacement, and stage-wise encoder freezing. NSVQ first helps the codebook track encoder drift during early training, then freezes the encoder to consolidate the codebook under a fixed latent geometry, and finally reintroduces adversarial refinement. Experiments on ImageNet-1k show that NSVQ improves reconstruction quality while maintaining full codebook utilization. On ImageNet-1k at 128$\times$128 with 65,536 codes, NSVQ reduces rFID from 2.39 to 2.10 compared with SimVQ, while both methods maintain 100\% utilization. Additional latent diffusion experiments show that NSVQ also improves downstream ImageNet generation FID.

11.
arXiv (CS.AI) 2026-06-19

Latent Confounded Causal Discovery via Lie Bracket Geometry

arXiv:2606.19610v1 Announce Type: cross Abstract: Recent work on Kan-Do-Calculus (KDC) has established that the boundary between passive observation and active intervention in causal inference is a category-theoretic bi-adjunction, with interventions modeled by left Kan extensions and conditioning by right Kan extensions. This paper introduces two causal discovery algorithms under latent confounding, building on the information-geometric and categorical consequences of KDC. In smooth statistical settings, Radon-Nikodym derivatives between observational and interventional measures induce local causal vector fields; failures of these fields to close under Lie brackets become computable Frobenius residuals, which we interpret as witnesses of failed visible integrability and possible latent or unmodeled structure. Our first algorithm, BRIDGE (Bracket Residuals for Interventional Discovery and Geometric Estimation), combines an interventional density or Radon-Nikodym-ratio engine with a geometric screen that proposes a high-recall family of admissible arrows, identifies non-closing visible pairs as latent-obstruction candidates, and passes the reduced family to downstream score-based or differentiable discovery routines. The second algorithmic contribution, Spectral Kan-Do Flow Matching (SKFM), learns amortized intervention fields and factors latent curvature spectrally, exposing the direct Lie-space endpoint toward which BRIDGE points. A detailed set of experiments show that both algorithms are capable of discovering causal models with latent confounders while collapsing the super-exponential space of possible DAGs by many orders of magnitude. This paper introduces a new paradigm in causal discovery, where latent structure is inferred directly from the geometry of intervention-induced flows.

12.
arXiv (CS.AI) 2026-06-25

Domain-Specific Agents for Cherenkov Telescope Array Control Software and Gamma-Ray Data Analysis

arXiv:2510.01299v3 Announce Type: replace-cross Abstract: We present domain-adapted large language model agents designed to support Cherenkov Telescope Array operation and data analysis. The agents combine contextual knowledge with automated validation and iterative correction to produce more reliable outputs. This approach reduces manual effort, improves consistency, and helps accelerate operational and scientific workflows. The results demonstrate the potential of agentic systems as practical assistants in specialized research environments.

13.
arXiv (CS.AI) 2026-06-12

The Safety-Aware Denoiser for Text Diffusion Models

arXiv:2605.08116v2 Announce Type: replace-cross Abstract: Recent work on text diffusion models offers a promising alternative to autoregressive generation, but controlling their safety remains underexplored. Existing safety approaches are geared toward autoregressive models and typically rely on post-hoc filtering or inference-time interventions. These are inadequate for effectively addressing safety risks in text diffusion models. We propose the Safety-Aware Denoiser (SAD), a safety-guidance framework in text diffusion models. The SAD modifies the iterative denoising process such that the text sample at the final denoising step is steered toward provably safe regions of the text space. This inference-time method can integrate safety constraints into the denoiser, avoiding computationally expensive retraining of the underlying diffusion model and enabling flexible, lightweight safety guidance. We evaluate the safety of the generated text using the SAD, with respect to hazard taxonomy, memorization, and jailbreak. Experimental results show that SAD substantially reduces unsafe generations while preserving generation quality, diversity, and fluency, outperforming existing methods. These results demonstrate that our safety guidance during denoising provides an effective and scalable mechanism for enforcing safety in text diffusion models.

14.
arXiv (CS.CV) 2026-06-24

WorldOlympiad: Can Your World Model Survive a Triathlon?

We introduce WorldOlympiad, a benchmark for diagnosing video-based world models across physical faithfulness, geometric consistency, and interaction fidelity. While existing benchmarks often focus on visual quality, semantic alignment, or short-term temporal coherence, they provide limited insight into whether generated videos obey physical rules, preserve coherent 3D structure, and sustain controllable interactions over long horizons. To address this gap, WorldOlympiad decomposes world-model evaluation into three complementary dimensions. The physical track uses object segmentation and MLLM-as-judge to assess whether generated videos follow interpretable rules in mechanics, thermal phenomena, and material properties. The geometry track reconstructs generated videos with Gaussian splatting and evaluates structural consistency, cross-view coherence, and camera-trajectory alignment. The interaction track assesses whether generated rollouts follow complex action prompts and maintain smooth, coherent transitions across consecutive video chunks. WorldOlympiad further covers three major downstream scenarios, including gaming, robotics, and general real-world videos, capturing diverse challenges from interactive control and embodied manipulation to open-domain motion and camera dynamics. Together, these tracks and scenarios form a scalable and interpretable evaluation suite that exposes failure modes beyond generic video quality. Experiments on state-of-the-art models reveal substantial gaps in physical reasoning, 3D consistency, and long-horizon interaction, underscoring the need for more structured evaluation protocols for generative world models.

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

Sharp Favard length of random Cantor sets

arXiv:2512.17753v2 Announce Type: replace-cross Abstract: We show that for a large class of planar $1$-dimensional random fractals $S$, the Favard length $\operatorname{Fav}(S(r))$ of the neighborhood $S(r)$ is comparable to $\log^{-1}(1/r)$, matching a universal lower bound; up to now, this was only known in expectation for a few concrete models. In particular, we show that there exist $1$-Ahlfors regular sets with the fastest possible Favard length decay. For a wide class of planar one-dimensional "grid random fractals", including fractal percolation and its Ahlfors-regular variants, we further show that $\operatorname{Fav}(S(r))/\log(1/r)$ converges almost surely, and we identify the limit explicitly. Furthermore, we prove that for some $1$-dimensional Ahlfors-regular random fractals $S$, the Favard length of $S(r)$ decays instead like $\log\log(1/r)/\log(1/r)$, showing that the $1/\log(1/r)$ decay is not universal among random fractals, as might be expected from previous results.

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

T2D-Bench: Evidence-Gated Evaluation of LLM Outputs for Type 2 Diabetes Using a Multi-Layer Clinical-Lifestyle Knowledge Graph

arXiv:2606.24145v1 Announce Type: new Abstract: Large language models (LLMs) can produce clinically fluent recommendations for type 2 diabetes while failing to satisfy guideline constraints or explicitly justify lifestyle-related glycemic claims. We present T2D-Bench, a reproducible benchmark and evidence-gated evaluation framework for testing whether LLM outputs satisfy explicit, graph-checkable evidence requirements. T2D-Bench is built on a multi-layer clinical-lifestyle knowledge graph that combines a biomedical spine (UMLS, DrugBank, SIDER), computable ADA Standards of Care rules, and lifestyle knowledge connected through a mechanistic bridge to glycemic laboratory effects. Across 100 structured vignettes spanning diagnosis, medication safety, and adversarial lifestyle conflicts, baseline outputs failed benchmark-defined evidence-path checks in 35% of cases for GPT-4o-mini and 33% for GPT-4o. The evidence gate detects unsupported omissions and uses constrained revision to bring outputs into verifier-level compliance with benchmark-defined evidence requirements. These results show that computable evidence constraints can make unsupported clinical omissions explicit, measurable, and correctable in diabetes-focused LLM outputs.

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

Tinker Tales: A Tangible Dialogue System for Child-AI Co-Creative Storytelling

arXiv:2602.04109v2 Announce Type: replace-cross Abstract: Conversational AI agents are increasingly explored as creative partners, yet how conversation design shapes child-AI dialogue in co-creative settings remains underexplored. We present Tinker Tales, a tangible dialogue system for child-AI collaborative storytelling, in which educational frameworks (narrative development and social-emotional learning) are instantiated as conversation design, shaping how the agent engages children across four narrative stages. The system combines a physical storytelling board, NFC-embedded toys, and a mobile app mediating multimodal interaction through tangible manipulation and voice-based dialogue. We conducted a home-based user study with 10 children (ages 6-8) across two conversation design conditions varying in how the agent structured elaboration, with and without educational scaffolding. Our findings show that prompt framing shapes the form and consistency of children's narrative contributions, structuring how they participate in co-creative dialogue with AI.

18.
arXiv (quant-ph) 2026-06-16

Programmable Gauge-Field Textures with Ultracold Atoms in Momentum Space

arXiv:2606.15124v1 Announce Type: cross Abstract: Synthetic gauge fields with ultracold atoms offer a route to quantum matter in which electromagnetic environments can be designed rather than merely imposed. While the Harper-Hofstadter model has been realized in several cold-atom systems, existing implementations are largely limited to spatially uniform magnetic fluxes. Here we experimentally realize a highly programmable two-dimensional momentum-state lattice of ultracold atoms with local control over the Peierls phase pattern, enabling direct implementation of Harper-Hofstadter Hamiltonians with tunable and spatially structured synthetic gauge fields. We observe a crossover from ballistic to strongly flux-modified bulk dynamics with suppressed transport. By introducing a synthetic electric field through site-dependent energy gradients, we further demonstrate Hall-type transverse drift arising from the interplay between electric and magnetic fields. In addition, we engineer a synthetic flux domain wall separating regions with opposite magnetic fluxes and observe anisotropic propagation guided along the interface. These results move cold-atom gauge-field engineering from uniform magnetic backgrounds toward designer gauge textures, providing an experimental setting for transport across programmable topological interfaces.

19.
arXiv (CS.AI) 2026-06-15

Closing the Reflection Gap: A Free Calibration Bonus for Agentic RL

作者:

arXiv:2606.14211v1 Announce Type: new Abstract: LLMs are increasingly deployed as agents that interact with external environments and observe feedback such as execution results, error messages, and tool outputs. A well-functioning agent should be able to leverage this feedback to accurately assess its own performance. Yet we find a persistent reflection gap: LLM agents tend to mis-assess their own outputs after observing concrete environment feedback – even for questions they correctly answered – and standard RL barely helps due to a credit-assignment mismatch. To close this gap, we propose RefGRPO, a simple yet effective fix that augments standard RL algorithms with two key ingredients: a free calibration bonus computed by contrasting the agent's own reflection with the actual outcome (requiring no additional reward model, LLM judge, or external annotation), and a dynamic schedule on its coefficient. Compared to standard RL baselines, our method simultaneously improves reflection calibration (e.g., reduces underconfidence rate $44.4\% \to 7.7\%$) and task accuracy (e.g., $75.1\% \to 76.5\%$) on text-to-SQL across five benchmarks. The resulting calibrated reflection turns the agent into its own verifier grounded in environment feedback, which further enables (i) better self-improvement that uses reflections as pseudo-rewards without outcome supervision, and (ii) more effective test-time selective prediction by committing only to rollouts flagged as correct.

20.
arXiv (CS.CL) 2026-06-19

Segment-Level Mandarin Chinese Speech-Based Cognitive Impairment Detection via an Autoencoder with Contrastive Learning

\noindentBackground and Objective: Speech has emerged as a low-cost and non-invasive digital biomarker with considerable potential for cognitive impairment detection. However, limited labeled data and cross-dataset variability remain major challenges for robust speech-based screening systems. \par\noindentMethods: We developed a segment-level representation learning framework for speech-based cognitive impairment detection. Speech recordings were divided into short segments and converted into spectrogram representations. To improve robustness under limited-data conditions, offline and online augmentation strategies were combined with autoencoder-based representation learning and contrastive objectives to enhance discriminative latent representations. \par\noindentResults: Experiments conducted on four independent Mandarin Chinese speech datasets demonstrated stable and competitive performance in both binary and three-class classification tasks, with particularly notable improvements in the clinically challenging three-class setting. Ablation studies further supported the effectiveness of the proposed framework. \par\noindentConclusions: The findings suggest that segment-level speech representation learning may provide a scalable and practical approach for cognitive impairment screening in resource-constrained clinical settings.

21.
arXiv (CS.CV) 2026-06-24

CrossFusion: A Multi-Scale Cross-Attention Convolutional Fusion Model for Cancer Survival Prediction

Cancer survival prediction from whole slide images (WSIs) is a challenging task in computational pathology due to the large size, irregular shape, and high granularity of the WSIs. These characteristics make it difficult to capture the full spectrum of patterns, from subtle cellular abnormalities to complex tissue interactions, which are crucial for accurate prognosis. To address this, we propose CrossFusion, a novel multi-scale feature integration framework that extracts and fuses information from patches across different magnification levels. By effectively modeling both scale-specific patterns and their interactions, CrossFusion generates a rich feature set that enhances survival prediction accuracy. We validate our approach across six cancer types from public datasets, demonstrating significant improvements over existing state-of-the-art methods. Moreover, when coupled with domain-specific feature extraction backbones, our method shows further gains in prognostic performance compared to general-purpose backbones. The source code is available at: https://github.com/RustinS/CrossFusion

22.
arXiv (CS.CV) 2026-06-17

Structure-Aware Text Recognition for Ancient Greek Critical Editions

Recent advances in visual language models (VLMs) have transformed end-to-end document understanding. However, their ability to interpret the complex layout semantics of historical scholarly texts remains limited. This paper investigates structure-aware text recognition for Ancient Greek critical editions, which have dense reference hierarchies and extensive marginal annotations. We introduce two novel resources: (i) a large-scale synthetic corpus of 185,000 page images generated from TEI/XML sources with controlled typographic and layout variation, and (ii) a curated benchmark of real scanned editions spanning more than a century of editorial and typographic practices. Using these datasets, we evaluate three state-of-the-art VLMs under both zero-shot and fine-tuning regimes. Our experiments reveal substantial limitations in current VLM architectures when confronted with highly structured historical documents. In zero-shot settings, most models significantly underperform compared to established off-the-shelf software. Nevertheless, the Qwen3VL-8B model achieves state-of-the-art performance, reaching a median Character Error Rate of 1.0\% on real scans. These results highlight both the current shortcomings and the future potential of VLMs for structure-aware recognition of complex scholarly documents.

23.
arXiv (CS.CL) 2026-06-25

Constituency Structure over Eojeol in Korean Treebanks

The design of Korean constituency treebanks raises a central representational question concerning the choice of terminal units. Although Korean words are morphologically complex, treating morphemes as constituency terminals can obscure the distinction between word-internal morphology and phrase-level syntactic structure, and can create mismatches with eojeol-based dependency resources. This paper argues for an eojeol-based constituency representation, with morphological segmentation and fine-grained POS information encoded in a separate, non-constituent layer. A comparative analysis shows that, under explicit normalization assumptions, the Sejong, Penn Korean, and KAIST treebanks can be compared over a shared eojeol-based constituency backbone. Building on this result, we outline an eojeol-based annotation scheme that preserves interpretable constituency, supports cross-treebank comparison and constituency-dependency alignment, and provides a surface-form terminal layer for future end-to-end Korean constituency parsing.

24.
arXiv (quant-ph) 2026-06-24

Quantum Metric Bound State of Light

arXiv:2606.22479v2 Announce Type: replace-cross Abstract: The spatial confinement of defect-induced bound states is conventionally governed by the effective mass in dispersive bands. More recently, Compact Localized States (CLSs) arising from exact destructive interference have been utilized to achieve confinement in flat bands. However, CLSs rely on pristine lattice symmetries and fine-tuned defect profiles. The introduction of a generic local impurity inevitably breaks these strict phase-matching conditions, resulting in extensive bound states whose fundamental length scale has remained an open question. Here, we establish a third regime of confinement: the quantum metric bound state. We provide a rigorous mathematical proof demonstrating that in the absence of kinetic energy and CLS protection, the exponential decay length of these states is lower-bounded by the quantum metric of the unperturbed flat band. We demonstrate the tightness of this geometric limit by constructing a family of highly tunable flat-band generators, and we verify its universality across diverse realistic architectures. Ultimately, this classification establishes the independently measurable quantum metric as a predictive design principle for engineering confined modes in synthetic wave platforms.

25.
arXiv (math.PR) 2026-06-16

A Machine-Checked Itô Calculus for Brownian Motion

arXiv:2606.15089v1 Announce Type: cross Abstract: We present a machine-checked development of the $L^2$ Itô calculus of Brownian motion on a bounded time interval $[0,T]$, formalized in Lean 4 on top of Mathlib and the BrownianMotion package. The development contains: the construction of the Itô integral as an isometry of Hilbert spaces, from a predictable-rectangle $\pi$-system through the density of simple adapted processes; the Itô integral as a process, proved to be an $L^2$-continuous martingale through a single structural identity (the integral at time $t$ is the conditional-expectation projection of its terminal value onto $\mathcal{F}t$), from which adaptedness, the martingale property, the contraction bound, and both the terminal and the time-indexed Itô isometries follow as corollaries; and Itô's formula for $C^3$ functions with bounded derivatives, including its time-dependent form $df = f_x,dB + (f_t + \tfrac12 f{xx}),dt$, obtained by a discrete-to-continuous argument through weighted quadratic variation and explicit $L^2$ remainder bounds. To our knowledge this includes the first machine-checked proof of Itô's formula, and the first machine-checked construction of the Itô integral as a martingale-valued process, in any proof assistant. We are deliberate about the boundary: the theory is the $L^2$ theory on $[0,T]$ with bounded-derivative integrand classes; localization to the unrestricted $C^2$ formula, integrators beyond Brownian motion, and pathwise statements are out of scope, and we say precisely why and where. The development is roughly 7,200 lines of Lean across 22 modules; every theorem is sorry-free, the axioms of each headline result are pinned to Mathlib's classical defaults by a build-enforced gate, and the whole is reproducible from a pinned toolchain.