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

Cross-Layer Discrete Concept Discovery for Interpreting Language Models

Interpreting language models remains challenging due to the existence of residual stream, which linearly mixes and duplicates features across adjacent layers, causing single-layer analyses to miss this cross-layer structure. Cross-layer sparse autoencoders (SAEs) address layer mixing but operate in continuous space, where concepts split across many neurons without clear boundaries. We introduce Cross-Layer Vector Quantized-Variational Autoencoder (CLVQ-VAE), a novel framework which maps representations from a lower layer to a higher layer through a discrete vector-quantization bottleneck, collapsing duplicated residual-stream features into compact, interpretable concept vectors. Our approach combines top-k temperature-based sampling with exponential moving average (EMA) codebook updates, providing controlled exploration of the discrete latent space while maintaining codebook diversity. Across both encoder- and decoder-based models on ERASER-Movie, Jigsaw, and AGNews, CLVQ-VAE outperforms clustering, single-layer vector quantized-variational autoencoder (VQ-VAE), and sparse autoencoder (SAE) baselines across three evaluation axes: removing identified concepts drops model accuracy by up to 93%, LLM judges rank our concepts first in 66.7% of comparisons, and human annotators recover model predictions from our visualizations with 78% accuracy versus 54% for clustering.

02.
arXiv (quant-ph) 2026-06-16

Inverted Dirac oscillator

arXiv:2606.15303v1 Announce Type: new Abstract: The Dirac oscillator is obtained from the Dirac Hamiltonian $H^{\mathrm{D}} = \left( c\vec{\alpha}\cdot \vec{p} + mc^{2}\beta \right)$ by modifying the momentum through a non-Hermitian substitution $\overrightarrow{p} \rightarrow \overrightarrow{p} \pm i\omega \beta \overrightarrow{q}$. Despite the non-Hermitian nature of this momentum operator, the full Hamiltonian remains Hermitian due to the presence of the Dirac matrix $\vec{\alpha}$. However, if one instead introduces a Hermitian modification of the form $\vec{p} \rightarrow \vec{p} \pm \omega \beta \overrightarrow{q}$, the resulting Hamiltonian is no longer Hermitian. In this case, the system corresponds to an inverted Dirac oscillator $H^{\mathrm{r}}$, where the potential becomes unbounded from below, the energy spectrum becomes continuous, and the eigenfunctions fail to be square-integrable, leading to normalization difficulties. We show that the Hamiltonian $H^{\mathrm{r}}$ is a pseudo-$\mathcal{PT}$-symmetric operator, and we introduce an unbounded, non-unitary transformation that establishes a connection between $H^{\mathrm{r}}$ and $H^{\mathrm{D}}$. The purpose of this work is to analyze this relativistic quantum system – known as the Dirac inverted oscillator – which, despite its various applications, admits an exact analytical solution

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

Context-Aware Optimization of Follow-Up Intervals for Type 2 Diabetes Care Using Markov Decision Processes

arXiv:2606.19092v1 Announce Type: cross Abstract: Chronic disease management relies on regular patient-provider interactions to follow-up on disease progression and control. For Type 2 Diabetes (T2D), current guidelines prescribe fixed time intervals between subsequent primary care visits for all patients, overlooking heterogeneity in clinical trajectories and patient characteristics. This study introduces a Contextual Markov Decision Process (CMDP) model to optimize subpopulation-specific follow-up interval decisions using Electronic Health Record (EHR) data from 22,154 T2D patients across 10 primary care clinics. Contexts are identified by: i) dimensionality reduction of variables representing the individual health trajectories utilizing Principal Component Analysis, and ii) assigning patients to contexts via principal components and additional patient-level features using clustering. Two distinct contexts emerged, representing a lower- and a higher-risk subpopulation. CMDP-derived policies recommend: (i) follow-up within 1 month if lab value at current visit is unmeasured; (ii) up to 3 months for elevated lab values or recent hospitalizations; and (iii) 6 to 12 months for sustained glycemic control, with shorter follow-up intervals for patients in high-risk context. The optimal policies achieved lower expected cumulative cost than benchmarks (e.g., in the higher-comorbidity context, the CMDP policy reduced cost by about 34.8%, and in the lower-comorbidity context by about 6.4%, relative to an American Diabetes Association-like fixed interval follow-up policy. These findings demonstrate how context-aware approaches can inform adaptive follow-up strategies, and have the potential to advance chronic care management in primary care by synthesizing machine learning and probabilistic decision models.

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

Generalized Schrödinger Bridge on Graphs

arXiv:2602.04675v2 Announce Type: replace Abstract: Transportation on graphs is a fundamental challenge across many domains, where decisions must respect topological and operational constraints. Despite the need for actionable policies, existing graph-transport methods lack this expressivity. They rely on restrictive assumptions, fail to generalize across sparse topologies, and scale poorly with graph size and time horizon. To address these issues, we introduce Generalized Schrödinger Bridge on Graphs (GSBoG), a novel scalable data-driven framework for learning executable controlled continuous-time Markov chain (CTMC) policies on arbitrary graphs under state cost augmented dynamics. Notably, GSBoG learns trajectory-level policies, avoiding dense global solvers and thereby enhancing scalability. This is achieved via a likelihood optimization approach, satisfying the endpoint marginals, while simultaneously optimizing intermediate behavior under state-dependent running costs. Extensive experimentation on challenging real-world graph topologies shows that GSBoG reliably learns accurate, topology-respecting policies while optimizing application-specific intermediate state costs, highlighting its broad applicability and paving new avenues for cost-aware dynamical transport on general graphs.

05.
arXiv (CS.AI) 2026-06-19

MakeupMirror: Improving Facial Attribute Preservation in Diffusion Models for Makeup Transfer

arXiv:2606.20094v1 Announce Type: cross Abstract: Makeup transfer models enable fun augmented reality (AR) experiences as well as virtual try-on (VTO) for online makeup shopping. While recent state-of-the-art diffusion based solutions such as Stable-Makeup dramatically improve the accuracy and realism of makeup transfer, they still face limitations in identity and skin color preservation, making production-level VTO for makeup shopping unrealistic. In this work, we propose MakeupMirror, a diffusion-based approach to makeup transfer that makes significant progress towards preserving facial features and skin tone. We introduce several technical innovations over Stable-Makeup: (1) integration of facial geometry conditioning with ControlNets to maintain facial fidelity; (2) region-specific makeup transfer control to enable precise makeup application across facial regions such as skin, eyes and lips; (3) skin tone-based makeup transfer modulation that prevent skin tone alteration in cross-subject transfer scenarios; and (4) integration of a Levenberg-Marquardt Langevin sampler to speed up inference while maintaining generation quality. Our experiments on CPM-Real, Makeup Wild, and (herein newly collected, more diverse) MakeupSelfies datasets show that MakeupMirror improves relative facial recognition similarity by +60%, reduces relative skin tone difference by -50% over Stable-Makeup, with a latency of 0.7s, while achieving expert acceptance rate of 94% across core facial identity preservation criteria.

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

Information geometry and entanglement under phase-space deformation through nonsymplectic congruence transformation

arXiv:2505.02269v3 Announce Type: replace Abstract: The Fisher-Rao (FR) information matrix is a central object in multiparameter quantum estimation theory. The geometry of a quantum state can be envisaged through the Riemannian manifold generated by the FR-metric corresponding to the quantum state. Interestingly, any congruence transformation $GL(2n,\mathbb{R})$ in phase space leaves the FR-distance for Gaussian states invariant. In the present paper, we investigate whether this isometry affects the entanglement in the bipartite system. It turns out that the entanglement-generating congruent transformation depends upon the system and background space. To make our study relevant to physical systems, we choose Bopp's shift in phase space as an example of $GL(2n,\mathbb{R})$, so that the results can be interpreted in terms of noncommutative (NC) phase-space deformation. We provide an estimation of the measure of entangled states over separable states for bipartite Gaussian states under a Bopp's shift. Since the dynamics of free oscillators in background NC-space is mathematically equivalent to the dynamics of a charged particle under a homogeneous magnetic field, we provide an outline for a gedankenexperiment through photocurrent measurement in order to determine the effects of congruent transformation on the distinguishibility of Gaussian states.

07.
arXiv (quant-ph) 2026-06-16

Quantum Illumination with Symmetry-Constrained Random Unitaries

arXiv:2606.15586v1 Announce Type: new Abstract: Quantum illumination provides a quantum advantage in detecting weakly reflecting objects embedded in a noisy environment, even when environmental noise destroys most of the initial entanglement. We investigate this advantage using Haar-random probe states constrained to symmetry-resolved subspaces. Employing tools from quantum channel discrimination and asymptotic hypothesis testing, we derive the discrimination exponents associated with Haar-random probe ensembles and identify the role of symmetry in determining their performance. We show that typical states drawn from fixed-charge sectors achieve the same asymptotic quantum-illumination advantage as maximally entangled probes. In particular, we show that the effective thermal-noise suppression and the corresponding Chernoff exponent are governed by the dimension of the accessible symmetry sector. Our results reveal that the operational resource underlying quantum illumination can be generalized from fine-tuned structure of a specific probe state to the existence of a large symmetry-protected correlation subspace. These findings establish a direct connection between quantum illumination, symmetry-resolved typicality, and quantum channel discrimination, and demonstrate that near-optimal quantum hypothesis testing resources can emerge naturally from generic many-body quantum states constrained by conservation laws.

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

Half a Link can Be Enough to Predict a Whole Link: Understanding Generalization in Knowledge Graph Foundation Models

arXiv:2606.18001v1 Announce Type: new Abstract: Knowledge graph (KG) foundation models (KGFMs) are zero-shot generalizers: trained once, they can predict links on unseen graphs without retraining. However, understanding when and how they can robustly generalize across KGs is still an open question. In this paper, we shed some light on their generalization mechanisms highlighting how their performance on unseen KGs is not uniform when it comes to partially seen links, which we call half-links. In fact, we show that to predict a test triple $(h,r,t)$ it might suffice in practice to have observed the half-link $(h,r)$ or $(r,t)$ in the inference graph. This yields a taxonomy of four scenarios when combinations of these half-links are observed or not. In a rigorous stratified analysis over these scenarios, we reveal that SoTA KGFMs use seen half links for predictions, while unseen half-links pose different challenges. As such, our finer-grained taxonomy can be a diagnostic protocol for robust KGFM generalization and highlights where novel KGFMs can improve.

09.
arXiv (CS.AI) 2026-06-19

TelcoAgent: A Scalable 5G Multi-KPM Forecasting With 3GPP-Grounded Explainability

arXiv:2606.19821v1 Announce Type: new Abstract: Key Performance Measurement (KPM) forecasting is essential for proactive network management of 5G and next-generation telecom networks. However, existing machine learning (ML) approaches face significant limitations in scalability and explainability, restricting their effectiveness in real-world deployments. We propose TelcoAgent, a foundation model-based framework that enables accurate, scalable, and explainable forecasting of multiple KPMs across diverse network cells without the need for site-specific training. Specifically, the framework comprises three key components: (i) an automated three-agent pipeline that constructs a 3rd Generation Partnership Project (3GPP) knowledge graph directly from specification documents, (ii) a scalable, time-series foundation model (TSFM)-based prediction pipeline to deliver accurate, zero-shot forecasting, and finally (iii) a reasoning and explanation pipeline that provides actionable, domain-grounded diagnostics. Evaluated using a 3-month, real-world, city-scale 5G KPM dataset from a U.S.-based network operator, TelcoAgent demonstrates high forecasting accuracy for all 7 considered KPMs per cell across 200 cells, while delivering explainable insights and actionable instructions to address network degradations.

10.
arXiv (CS.AI) 2026-06-17

Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformers

arXiv:2606.18206v1 Announce Type: new Abstract: Looped architectures provide an inductive bias toward learning step-by-step procedures for tasks that require compositional reasoning. The number of effective layers reached by looping determines the quality of the solution these models find. Like deep architectures, looped architectures are prone to a signal propagation problem induced by depth as the halting decision is postponed. In this paper, we address this signal propagation issue using pre-norm layers and residual scaling. Building on these architectural modifications, we propose FPRM, a Transformer-based Fixed-Point Reasoning Model that uses fixed-point convergence as an end-to-end halting mechanism in a looped architecture. We show that fixed-point halting allows FPRM to adapt its compute to task difficulty. FPRM is effective on common reasoning benchmarks, namely Sudoku, Maze, state-tracking, and ARC-AGI.

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

When Lower Privileges Suffice: Investigating Over-Privileged Tool Selection in LLM Agents

As LLM agents increasingly select tools autonomously, their choices among tools with different privileges become safety-relevant. However, prior tool-selection studies focus on safety-agnostic metadata preferences, leaving privilege-sensitive choices underexplored. To address this gap, we study over-privileged tool selection, in which an agent selects or escalates to a higher-privilege tool despite a sufficient lower-privilege alternative. We introduce ToolPrivBench to evaluate whether agents choose higher-privilege tools despite sufficient lower-privilege alternatives, measuring both initial selection and escalation after transient tool failures. Across eight domains and five recurring risk patterns, we find that over-privileged tool selection is common among mainstream LLM agents and is further amplified by transient failures. We further find that general safety alignment does not reliably transfer to least-privilege tool choice, while prompt-level controls provide only limited mitigation under transient failures. We therefore introduce a privilege-aware post-training defense that teaches agents to prefer sufficient lower-privilege tools and escalate only when necessary. Our mitigation experiments show that this defense substantially reduces unnecessary high-privilege tool use while preserving general capabilities.

12.
arXiv (CS.AI) 2026-06-11

Generalization Hacking: Models Can Game Reinforcement Learning by Preventing Behavioral Generalization

arXiv:2606.12016v1 Announce Type: cross Abstract: Model post-training, and in particular reinforcement learning (RL), is one of the primary mechanisms by which developers can shape models' values and behaviors. However, as models become increasingly evaluation and training aware, they may be motivated to resist training when the perceived objective conflicts with their current values, undermining developers' ability to detect misalignment and correct model behavior through further training. In this paper, we demonstrate generalization hacking, in which a model collects reward during RL while preventing the rewarded behavior from generalizing. We construct a model organism on Qwen3-235B-A22B, finetuning on synthetic documents describing training awareness and self-inoculation, a novel mechanism in which the model frames compliance as context-specific in its chain of thought, without demonstrating or instructing either behavior. The model organism achieves train-time harmfulness comparable to controls while maintaining a persistent ${\sim}15$ percentage point compliance gap across 700 steps of RL. Additionally, a control organism trained only on training awareness documents independently discovers inoculation-like reasoning under RL pressure, developing its own compliance gap despite never being exposed to the concept. Because the generalization-hacking organism receives high reward throughout, standard training metrics provide no signal that generalization has failed. Our results constitute the first demonstration that a model can actively resist RL behavioral modification while maintaining high reward, suggesting that as models become more capable and training-aware, they may be able to undermine the training process itself.

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

Learning from Own Solutions: Self-Conditioned Credit Assignment for Reinforcement Learning with Verifiable Rewards

arXiv:2606.18810v1 Announce Type: cross Abstract: Reinforcement learning with verifiable rewards (RLVR) has driven substantial progress in training LLMs for reasoning tasks, but representative methods such as GRPO assign uniform credit across all tokens, wasting gradient on routine tokens while under-crediting pivotal reasoning steps. Existing token-level credit assignment methods require resources beyond the model's own rollouts. GRPO variants rely on process reward models or ground-truth answers. Knowledge distillation assigns credit through per-token divergence but requires external teachers (On-Policy Distillation) or privileged information (On-Policy Self Distillation). However, these dependencies limit applicability in the pure RLVR setting. We observe that conditioning the model on its own verified trajectories induces a measurable per-token KL divergence between the original and conditioned distributions, and prove that distilling from a self-teacher constructed by verified trajectories leads to infeasible weighted-average solutions when multiple verified trajectories exist. We propose SC-GRPO (Self-Conditioned GRPO), which uses KL divergence mentioned before as a multiplicative weight on GRPO gradients. Across five benchmarks spanning math, code, and agentic tasks, SC-GRPO consistently outperforms 8.1% over GRPO and 5.9% over DAPO with stronger OOD performance. Moreover, SC-GRPO achieves higher performance than OPD.

14.
arXiv (CS.AI) 2026-06-11

FreeBridge: Variational Schrödinger Bridges for Cellular Transition Dynamics

arXiv:2606.11286v1 Announce Type: cross Abstract: High-content imaging assays quantify cellular responses to chemical and genetic perturbations, yet continuous trajectories of individual cells are unobservable because cells are chemically fixed at acquisition. Perturbation modeling therefore reduces to inferring stochastic transport between control and treated populations observed only as separate marginals. While recent generative models achieve strong end-point alignment, boundary consistency does not determine intermediate evolution: multiple stochastic processes may connect identical marginals while traversing regions unsupported by observed single-cell morphologies. We introduce FreeBridge, a Schrödinger Bridge formulation for single-cell transition modeling under endpoint-only supervision. FreeBridge defines atomic states as instance-segmented single-cell representations, establishing a fixed cellular manifold, and learns stochastic transport constrained within this geometry via empirical latent support regularization. Across BBBC021, RxRx1, and JUMP, FreeBridge maintains competitive or improved endpoint fidelity and mechanism-of-action retention under a unified evaluation protocol; on BBBC021, it further reduces intermediate support violations. These findings highlight the importance of geometric grounding for biologically interpretable perturbation dynamics. Project page: https://y-research-sbu.github.io/FreeBridge/.

15.
arXiv (CS.AI) 2026-06-11

EKF-Based Depth Camera and Deep Learning Fusion for UAV-Person Distance Estimation and Following in SAR Operations

arXiv:2602.20958v2 Announce Type: replace-cross Abstract: Vision-based Unmanned Aerial Vehicles (UAVs) frameworks aid human search tasks by detecting and recognizing specific individuals, then tracking and following them while maintaining a safe distance. A key safety requirement for UAV following is the accurate estimation of the distance between camera and target object under real-world conditions, achieved by fusing multiple image modalities. As part of the system for automatic people detection and face recognition using deep learning, in this paper we present the fusion of depth camera measurements and monocular camera-to-body distance estimation for robust tracking and following. Deep learning based filtering of depth camera data and estimation of camera-to-body distance from a monocular camera are achieved with YOLO-pose, enabling real-time fusion of depth information using the Extended Kalman Filter (EKF) algorithm. The proposed subsystem, designed for use in drones, estimates and measures the distance between the depth camera and the human body keypoints, to maintain the safe distance between the drone and the human target. Our system provides an accurate estimated distance, which has been validated against motion capture ground truth data. The system has been tested in real time indoors, where it reduces the average errors, RMSE and standard deviations of distance estimation up to 15,3% in three tested scenarios. Based on the test results, the EKF fusion-based approach increases the depth detection range by reducing the errors outside the optimal depth camera working range. It also shows improved robustness and precision in challenging conditions, such as reflections and poor visibility, making it suitable for SAR.

16.
arXiv (CS.CV) 2026-06-18

Recognizing and Reconstructing a Multi-Unit Floor Plan

Digital twins have a major potential to form a significant part of urban management in emergency planning, as they allow more efficient designing of the escape routes, better orientation in exceptional situations, and faster rescue intervention. Nevertheless, creating the twins still remains a largely manual effort, due to a lack of 3D-representations, which are available only in limited amounts for some new buildings. Thus, in this paper we aim to synthesize 3D information from commonly available 2D architectural floor plans. We propose two novel pixel-wise segmentation methods based on the MDA-Unet and MACU-Net architectures with improved skip connections, an attention mechanism, and a training objective together with a reconstruction part of the pipeline, which vectorizes the segmented plans to create a 3D model. The proposed methods are compared with two other state-of-the-art techniques and several benchmark datasets. On the commonly used CubiCasa benchmark dataset, our methods have achieved the mean F1 score of 0.86 over five examined classes, outperforming the other pixel-wise approaches tested. We have also made our code publicly available to support research in the field.

17.
arXiv (quant-ph) 2026-06-12

Spectral analysis of equilibration: information leakage in isolated quantum systems

arXiv:2606.12545v1 Announce Type: new Abstract: We develop a unified dynamical-spectral framework for equilibration in isolated quantum systems based on a subspace coarse-graining approach. Central to our formulation is the Leakage Fidelity Function (LFF), defined as the probability that a unitarily evolving state escapes the support of its initial subspace. This quantity provides a direct, operational measure of information flow and memory loss without invoking ensemble assumptions or perturbative arguments. We derive universal bounds on temporal fluctuations of the LFF, in terms of the spectral gap structure and the square of the effective dimension, evincing that large spectral delocalization suppresses fluctuations and guarantees equilibration on average. By introducing spectral power distributions and associated entropic measures, we establish a quantitative link between phase mixing, gap participation, and dynamical stability. We further investigate the equilibration timescale by connecting the LFF to quantum speed limits, thereby revealing the average time required for equilibration. Our results provide a state-dependent, geometrically transparent perspective on how spectral complexity and subspace information leakage jointly govern irreversibility in closed quantum many-body systems.

18.
arXiv (CS.CV) 2026-06-24

Bengal-HP_RU: A Dataset of Bengal People For Head Pose Estimation

Existing head pose datasets predominantly feature subjects of Western or East Asian origin, leaving South Asian populations, particularly Bengali individuals, largely underrepresented. We introduce Bengal-HP_RU, the first publicly available head pose dataset centred on Bengali subjects, comprising 12,894 labelled head images annotated with continuous yaw, pitch, and roll values. Images were collected from Wikimedia Commons under free licences and processed through an automated pipeline followed by manual label correction. The dataset is partitioned by Wikimedia uploader identity to prevent data contamination, yielding 10,494 training and 2,400 test images across 296 unique uploaders. Bengal-HP_RU exhibits substantial diversity in subject age, gender, occlusion, illumination, and background, reflecting realistic in-the-wild conditions. The dataset is publicly available at https://doi.org/10.17632/xbw9kr37jb.2.

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

Trusted Uncertainty in Large Language Models: A Unified Framework for Confidence Calibration and Risk-Controlled Refusal

Deployed language models must decide not only what to answer but also when not to answer. We present UniCR, a unified framework that turns heterogeneous uncertainty evidence including sequence likelihoods, self-consistency dispersion, retrieval compatibility, and tool or verifier feedback into a calibrated probability of correctness and then enforces a user-specified error budget via principled refusal. UniCR learns a lightweight calibration head with temperature scaling and proper scoring, supports API-only models through black-box features, and offers distribution-free guarantees using conformal risk control. For long-form generation, we align confidence with semantic fidelity by supervising on atomic factuality scores derived from retrieved evidence, reducing confident hallucinations while preserving coverage. Experiments on short-form QA, code generation with execution tests, and retrieval-augmented long-form QA show consistent improvements in calibration metrics, lower area under the risk-coverage curve, and higher coverage at fixed risk compared to entropy or logit thresholds, post-hoc calibrators, and end-to-end selective baselines. Analyses reveal that evidence contradiction, semantic dispersion, and tool inconsistency are the dominant drivers of abstention, yielding informative user-facing refusal messages. The result is a portable recipe of evidence fusion to calibrated probability to risk-controlled decision that improves trustworthiness without fine-tuning the base model and remains valid under distribution shift.

20.
arXiv (CS.LG) 2026-06-11

SPADE: Split-and-Delay Embeddings for Autoregressive High-Granularity Calorimeter Simulation

arXiv:2606.11304v1 Announce Type: cross Abstract: We introduce SPADE (SPlit And Delay Embeddings), an autoregressive transformer for sequences whose tokens carry multiple features. Rather than embedding these features jointly, SPADE embeds them independently. Delaying each feature stream relative to the previous one allows intra-token correlations to be learned by the standard self-attention mechanism. Applied to point-cloud calorimeter shower generation in the highly granular ILD detector, SPADE is competitive with the state of the art AllShowers model on photon showers, and substantially outperforms its VQ-VAE-based predecessor OmniJet-$\alpha_C$. The mechanism is applicable to any generative task with multi-feature tokens, enabling LLM-style pretraining workflows for higher-dimensional data.

21.
arXiv (CS.LG) 2026-06-19

Spectral DPPs via NEPv: A Scalable Continuous Relaxation of Determinantal MAP for Diversity-Aware Data Selection

arXiv:2606.19411v1 Announce Type: new Abstract: Selecting a small, diverse, high-quality subset from a massive pool of candidates is a recurring primitive in modern machine learning – data curation and coreset selection for training and fine-tuning large models, active-learning batch acquisition, prompt and exemplar selection for in-context learning, retrieval diversification, and experimental design. Determinantal Point Processes (\operatorname{DPP} s) give a principled, well-calibrated notion of diversity for this task, but their MAP objective – pick a size-$k$ subset $S$ maximizing $\logdet(L_S)$ – is NP-hard, and the standard greedy and sampling algorithms scale superlinearly in the ground-set size $n$. This cost is prohibitive precisely in the data-centric regime where diversity matters most, where $n$ ranges over millions to billions of candidate examples, features, or embeddings. We recast \operatorname{DPP}-MAP as a continuous optimization problem over the Stiefel manifold, and show that its first-order optimality conditions form a Nonlinear Eigenvalue Problem with eigenvector dependency (\operatorname{NEP}v) of a previously unstudied form. This \operatorname{NEP}v\ admits a self-consistent field (\operatorname{SCF}) iteration with a spectral-gap-based local contraction guarantee, giving a principled iterative solver where the diversity objective drives an eigenvector-dependent operator. The resulting algorithm, \OurMethod, requires only matrix-vector products with the kernel and runs in time $O\!\big((ndk+nk^2)\,t\big)$ for a small number of iterations $t$, scaling near-linearly in $n$ and integrating directly with low-rank and feature-map kernels common in ML. This paper focuses on the relaxation, solver, and scaling analysis; full real-data benchmarking is left to a planned empirical study.

22.
arXiv (CS.AI) 2026-06-16

The Quality-Utility Paradox: Why High-Reward Data Impairs Small Model Mathematical Reasoning

arXiv:2606.16152v1 Announce Type: new Abstract: Knowledge distillation from powerful reasoning models is widely used to improve Small Language Models (SLMs) on mathematical reasoning, often assuming that traces with higher reward model scores provide more useful supervision. We identify a counterintuitive Quality-Utility Paradox in mathematical reasoning distillation. Data refined or synthesized by a stronger Oracle obtains higher perceived quality according to reward models, yet consistently underperforms traces generated by the SLM itself and selected through rejection sampling across Qwen2.5, LLaMA-3, and DeepSeek families. Our analysis shows that Oracle refinement couples logical repair with distributional drift away from the SLM's native reasoning distribution. This drift increases the learner's adaptation cost and can outweigh the benefit of improved reasoning logic. To test this mechanism, we introduce Style-Aligned Refinement, which preserves the native trajectory of the SLM while retaining logical repair from the Oracle. This intervention lowers adaptation cost and restores downstream utility. These findings suggest that effective mathematical reasoning distillation should jointly optimize perceived solution quality and learner-data compatibility, rather than relying solely on reward-model scores. The datasets and code are available at https://github.com/Dracoqhl/Quality-Utility-Paradox.

24.
arXiv (quant-ph) 2026-06-12

Spin correlations, low-energy scales, and anisotropy scaling in kagome frustrated magnets

arXiv:2606.12512v1 Announce Type: cross Abstract: Neutron scattering is central to identifying quantum states of magnetic materials. In the search for quantum spin liquids, broad spectral features of inelastic spectra have been cited as evidence for spinon excitations, but can also arise from magnon excitations excitations in the presence of quenched disorder and strong magnon interactions. We develop a new approach to this problem, based on the adiabatic continuity in the $XXZ$ Heisenberg model on geometrically frustrating (GF) lattices as a function of the model's anisotropy. Using this approach, we identify universal features and energies of finite-temperature spin correlators. Focusing on the kagome lattice, we show that the low-energy spin spectral function contains robust, momentum-independent peaks with frequencies: $\omega_1 \approx 3.4 T^*$ and $\omega_2 \approx 6.3 T^*$, where the ``hidden energy scale'' $T^*$ is the characteristic scale of a low-temperature peak in the heat capacity, at which many GF magnets also display spin-glass freezing. We show that the spectral features at low energies $\omega\lesssim T^*$ arise from single-magnon scattering and identify the magnetizations of the respective excitations. We explore the evolution of the spectral features with temperature and discuss extensions to other GF lattices. Our results provide a sharp spectroscopic criterion for interpreting neutron scattering in kagome and other GF quantum magnets.

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

Creating and Evaluating K-12 GenAI Assessment Graders Through Context Engineering

arXiv:2606.12422v1 Announce Type: cross Abstract: The integration of large language models (LLMs) into educational assessment represents a transformative shift in classroom grading practices. While automated scoring systems and machine learning techniques have existed for decades, generative AI (GenAI) now enables educators to implement standards-based grading (SBG) with unprecedented efficiency and scale. This paper examines the theoretical foundations and evaluates an LLM grader that uses commercially available foundation models with context and prompt engineering to score student work against a rubric. Drawing on an empirical interrater agreement study using Massachusetts Comprehensive Assessment System (MCAS) data, we observed the Quadratic Weighted Kappa (QWK) and Proportional Reduction in Mean-Squared Error (PRMSE) across mathematics, science, and ELA, using Claude Sonnet 4, Haiku 4.5, GPT-5, and GPT-5 Mini. The results demonstrate that LLM graders, especially when based on foundational models with more parameters, achieve substantial agreement with human raters in mathematics and science assessments, while the performances vary in ELA, suggesting generic foundation models can be effective at scoring in given contexts. Additional analysis of teacher and student feedback reveals strong acceptance of AI-generated narrative feedback but skepticism toward numerical scores, suggesting that LLMs function most effectively as formative tools rather than summative evaluators. Our findings indicate that thoughtfully designed hybrid models that combine AI efficiency with teacher judgment can reduce workload, enhance feedback quality, and support equitable assessment practices without displacing professional expertise.