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01.
arXiv (CS.CL) 2026-06-16

From Affect Prediction to Affect Forecasting: Evidence for Distinct Information Sources in Longitudinal Text

Modeling dimensional affect in longitudinal text requires distinguishing current affect estimation from future affective change forecasting. Existing approaches often treat each text as an independent observation and apply similar assumptions to both tasks, without testing whether they rely on different information sources. This paper investigates that distinction using longitudinal self-reported ecological essays and feeling-word entries. We propose the Trait–State Affective Prediction (TSAP) framework and its temporal extension E-TSAP for per-text valence and arousal prediction, evaluated on a held-out prediction test set of 1,737 entries from 91 users. We further propose the Affective Change Forecaster Hybrid (ACF-Hybrid) for next-step affective change forecasting, evaluated on a held-out forecasting test set of 46 users. For prediction, E-TSAP achieves composite Pearson correlations of 0.670 for valence and 0.449 for arousal. For forecasting, textual representations perform worse than compact numeric trajectory baselines: the text-inclusive model achieves only r=0.316 for valence and r=0.284 for arousal, whereas a simple prior-state baseline reaches r=0.615 and r=0.670, respectively. ACF-Hybrid, using dimension-specific numeric trajectory features, achieves r=0.659 for valence and $r=0.658$ for arousal. These results show that textual semantics support current affect prediction, whereas future affective change is better captured through prior numeric trajectory dynamics.

02.
arXiv (CS.CV) 2026-06-16

Learning Sparse Latent Predictive Foundation Model for Multimodal Neuroimaging

Brain MRIs are routinely acquired as multiple complementary sequences with unique contrast weighting, including T1-weighed imaging (T1w) anatomic and fluid-sensitive T2-weighted (T2w) contrasts. However, methods for learning unified representations across the multitude of MRI contrast mechanisms at health-system scale are lacking. In this study, we introduce Neuro-JEPA, a sparse multimodal neuroimaging foundation model that combines a latent predictive objective with a Mixture-of-Experts architecture to encode brain MRI across core T1w, T2w, and fluid-suppressed FLAIR imaging (FLAIR). We further provide a systematic methodological study of architectural, masking, objective, and sparsity design choices beneficial for robust neuroimaging multimodal representation learning. Neuro-JEPA was pretrained on 1,551,862 scans from 428,647 studies after modality-specific preprocessing with data curation across three core structural brain MRI sequences. We evaluated the learned representations across clinical and research settings, including 25 tasks from three health systems: NYU Langone, NYU Long Island, and Massachusetts General Hospital, and 22 tasks from 12 public datasets, covering unimodal, multimodal and cross-domain evaluation configurations. Across these benchmarks, existing neuroimaging foundation models showed inconsistent gains over a simple convolutional neural network (CNN) baseline, whereas Neuro-JEPA achieved stronger and more consistent performance across all evaluated settings. These results establish a scalable methodological framework for multimodal neuroimaging representation learning and highlight the need for foundation model evaluation protocols that include simple baselines, clinically heterogeneous cohorts and controlled multimodal comparisons.

03.
arXiv (quant-ph) 2026-06-11

Robust Mixed-State Cluster States and Spurious Topological Entanglement Negativity

arXiv:2504.16165v2 Announce Type: replace Abstract: We investigate 1D and 2D cluster states under local decoherence to assess the robustness of their mixed-state subsystem symmetry-protected topological (SSPT) order. By exactly computing fidelity correlators via dimensional reduction of effective statistical mechanics models, we pinpoint the critical error rate for strong-to-weak spontaneous breaking of strong subsystem symmetry. Without resorting to the replica trick, we demonstrate that mixed-state SSPT order remains remarkably robust up to the maximal decoherence rate when noise respects strong subsystem symmetry. Furthermore, we propose that the mixed-state SSPT order can be detected by a constant correction to the area-law scaling of entanglement negativity, termed spurious topological entanglement negativity. This also highlights that topological entanglement negativity, a widely used diagnostic for mixed-state topological order, is generally not invariant under finite-depth quantum channels.

04.
arXiv (CS.LG) 2026-06-25

LLM Program Optimization via Retrieval Augmented Search

arXiv:2501.18916v2 Announce Type: replace Abstract: Recent work has demonstrated the potential of large language models (LLMs) for program optimization, a key challenge in programming languages. We propose a blackbox adaptation method called Retrieval Augmented Search (RAS) that performs beam search over candidate optimizations; at each step, it retrieves in-context examples from a given training dataset of slow-fast program pairs to guide the LLM. Critically, we find that performing contextual retrieval based on an LLM-generated natural language description significantly outperforms retrieval based on the source code. We also propose AEGIS, a method for improving interpretability by decomposing training examples into ''atomic edits'' that are significantly more incremental in nature. We show that RAS performs up to 2.06$\times$ better than prior state-of-the-art blackbox adaptation strategies on optimizing C++ programs, and that AEGIS performs up to 1.37$\times$ better while making significantly smaller edits. We also show that using RAS improves the mean runtime percentile of Python programs by 10.27 compared to baselines.

05.
arXiv (CS.CL) 2026-06-16

Prior over Evidence: Stereotype-Driven Diagnosis in LLM-Based L2 Pronunciation Feedback

Large language models are increasingly deployed for written pronunciation feedback in second-language (L2) English learning, under the assumption that their diagnoses are grounded in the supplied speech evidence rather than in priors from pretraining. This assumption is tested on 1,800 L2-Arctic utterances spanning six L1 backgrounds, three audio-capable LLMs, four pronunciation dimensions, and five evidence conditions ranging from a text-only baseline to numeric acoustic features and raw audio. Each (utterance x model x condition x dimension) cell is scored on three metrics: Rating Accuracy (RA) against gold labels, Evidence Coherence (EC) assessing internal consistency without ground truth, and Grounded Correctness (GC) evaluated against gold evidence. Results show three findings across models. First, rating accuracy and grounded reasoning decouple: 39.6% of judged cells contain internally coherent reasoning that supports a wrong rating, against only 15.8% where the reasoning supports a correct rating. Second, phoneme-level feedback converges to a fixed inventory of L2-English difficulty phones that recurs across all six L1 backgrounds and all evidence conditions. Third, acoustic evidence improves the rating only when the supplied feature directly probes the target dimension: textualised F0 range raises pitch-variation grounding from (0.18-0.19) to (0.45-0.62) across all three models, while stress and phoneme correctness, which require target-to-realisation alignment, remain ungrounded. The same audio waveform without textualised F0 values does not reproduce this improvement. These findings indicate that current general-purpose LLMs are more reliable as verbalisers of externally computed pronunciation evidence than as standalone diagnostic engines.

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

Thermodynamic Signatures of Reasoning: Free-Energy and Spectral-Form-Factor Diagnostics for Hallucination Detection in Large Language Models

作者:

Hallucination detection in large language models (LLMs) is deployment-critical, and recent work shows that the spectrum of attention-derived graph Laplacians carries strong signal about reasoning quality. Prior spectral diagnostics, however, summarize the Laplacian spectrum by a handful of eigenvalues or hand-picked scalars, leaving most of its structure unused. We propose Free-Energy Signatures (Fes), a spectral descriptor that treats each layer's attention Laplacian as a Hamiltonian and extracts its thermodynamic potentials partition function, free energy, spectral entropy, heat capacity together with the random-matrix-theory (RMT) spectral form factor. We prove three results: (i)~Lipschitz stability of Fes under attention perturbation; (ii)~an expressiveness result showing that Fes enriches finite spectral summaries and approximates moment-derived spectral functionals under explicit regularity and grid-resolution assumptions; and (iii)~a finite-sample PAC bound on the AUROC of a training-free detector built from Fes. Empirically, across six open-weight LLMs and six benchmarks, a lightweight probe on Fes descriptors achieves the strongest aggregate AUROC among attention-spectral baselines, improving over LapEig by $+6.5$ AUROC points and over GoR-4 by $+2.4$ points on average, while requiring no update to the underlying LLM. In the fully unsupervised setting, an RMT-deviation score achieves mean AUROC $0.71$, providing a label-free but weaker detector. A complementary RMT analysis shows that correct generations exhibit more Wigner-Dyson like spectral statistics, whereas hallucinations exhibit more Poisson-like statistics. The anonymized code and config are provided in the supplementary material.

07.
arXiv (CS.CV) 2026-06-16

Null-Space Diffusion Distillation Unlocks Speed, Fidelity and Realism in Lensless Imaging

Lensless imaging reconstructs scenes from highly multiplexed measurements, resulting in a severely ill-posed inverse problem. In this work, we identify a fundamental trade-off between measurement consistency, perceptual quality, and inference speed across lensless reconstruction paradigms. Traditional methods favor consistency but produce perceptually degraded results, supervised approaches achieve high-quality reconstructions with fast inference but may violate physical constraints, and diffusion-prior methods achieve high perceptual quality and consistency–particularly when structured constraints such as range-null decomposition are used–but remain slow due to iterative sampling. Motivated by this observation, we propose Null-Space Diffusion Distillation (NSDD), a single-pass reconstruction model that distills structured diffusion-prior inference into an efficient feed-forward network. NSDD learns to produce high-quality reconstructions that preserve measurement consistency while avoiding costly iterative sampling. Experimental results demonstrate that NSDD achieves perceptual quality and consistency competitive with diffusion-prior methods, while providing significantly faster inference and offering a favorable balance across all three objectives. Furthermore, ablation experiments show that distilling the range–null decomposition improves reconstruction quality and robustness over unstructured full-reconstruction distillation, including on unseen real scenes. These results highlight the potential of structure-aware distillation for efficient lensless imaging. Code is available at github.com/JRCSAVSN/NullSpaceDiffusionDistillation.

08.
arXiv (CS.AI) 2026-06-19

Sensorimotor World Models: Perception for Action via Inverse Dynamics

arXiv:2606.20104v1 Announce Type: cross Abstract: Perception for action suggests that representations of the world should be shaped not by visual fidelity alone, but by their relevance for actions. At the same time, latent JEPA-style world models advocate learning compact predictive states from high-dimensional observations to facilitate the prediction of future states, but end-to-end training of these models is nontrivial because representations may collapse if our only goal is to construct a latent state that is easy to predict. We introduce a sensorimotor world model (SMWM): a latent world model trained end-to-end with inverse dynamics regularization. This single regularizer addresses both issues: it prevents representation collapse and induces action-aligned representations. By forcing latent states to preserve information about the action underlying a transition, it biases the model toward the controllable degrees of freedom of the environment while discarding uncontrollable distractors. This yields stable latent world models trained from offline, reward-free trajectories, without frozen encoders, exponential moving averages, or complex latent regularizers. Empirically, SMWM learns compact, interpretable latent spaces and enables competitive planning performance across simple 2D and 3D control tasks.

09.
arXiv (math.PR) 2026-06-15

A random approach to the multibonacci sequence

arXiv:2606.14294v1 Announce Type: cross Abstract: This paper presents a random approach to the multibonacci sequence. We generalise the model introduced by Benjamin, Levin, Mahlburg, and Quinn, which is based on a random tiling method using dominoes and squares that leads to the Fibonacci sequence, and which was extended to the tribonacci case in a previous work by the authors. Our approach employs tiling with linear $k$-ominoes, $k=1,\ldots,s$, combined with specific colouring, to generate a weighted multibonacci sequence. For a natural random variable~$X$ defined by this model, we establish the distribution of $X$ in terms of multibonacci numbers and compute $\mathbb{E}[X] = 2^{s+1}-3$.

10.
arXiv (CS.CV) 2026-06-16

Lesion-DDPM: Lesion-Enhanced 3D Diffusion for MS MRI Synthesis

3D FLAIR MRI is widely recommended as one of the standard MRI sequences for brain imaging in multiple sclerosis (MS), but publicly available MS datasets remain relatively small and vary across scanners, acquisition protocols, and lesion patterns. This scarcity and variability hinder the development of robust neuroimaging machine learning models and are particularly challenging for generative models that aim to synthesize images while preserving small, sparse lesions. We propose Lesion-DDPM, a 3D conditional diffusion framework for lesion-aware FLAIR synthesis that incorporates multi-level anatomical mask injection together with a lesion-weighted reconstruction loss to emphasize lesion voxels while maintaining global brain structure. Using a curated subset of the MSLesSeg dataset, we compare Lesion-DDPM with representative state-of-the-art GAN- and diffusion-based models, assessing both image-generation metrics and downstream 3D U-Net segmentation. In our experiments, Lesion-DDPM achieved the lowest lesion-region reconstruction error among all methods. In a downstream 3D U-Net lesion segmentation task, a model trained only on Lesion-DDPM-generated scans and evaluated on real MRIs reached a Dice score of 0.616 compared with 0.569 for the best competing synthetic dataset. When Lesion-DDPM images were added to the real training set, the Dice score further increased to 0.685.

11.
arXiv (CS.CV) 2026-06-25

CoGeoAD: Hierarchical Color-Geometric Fusion with Multi-View Attention for Zero-Shot 3D Anomaly Detection

Zero-shot 3D anomaly detection is essential for industrial quality inspection, where labeled anomaly samples are scarce. Meanwhile, existing methods lack an effective mechanism to fuse complementary 2D color images with 3D geometric structures, limiting their ability to detect both surface and structural defects in a unified framework. To address these issues, we propose CoGeoAD, a unified CLIP-based framework that fuses color and geometric features by constructing pixel-aligned paired multi-view images. The framework introduces a Data-Driven Multi-View Attention (MVA) mechanism to adaptively aggregate 3D features and a Multi-Stage Color-Geometric Fusion (MS-CGF) module to hierarchically integrate multi-level features from both modalities. Extensive experiments on the MVTec3D-AD and Eyecandies benchmarks demonstrate that CoGeoAD achieves state-of-the-art performance, effectively capturing both structural and textural anomalies in complex industrial scenarios. our source code is available at https://github.com/kingdomShu/CoGeoAD.

12.
arXiv (CS.CV) 2026-06-24

MATCH: Flow Matching for Multi-View Anomaly Detection

Detecting anomalies in industrial objects is an important topic for increasing production efficiency. More complex objects often require the analysis of several view points, which has led to the field of multi-view anomaly detection. We present MATCH, the first multi-view anomaly detection method based on Flow Matching (FM). With the ODE formulation of Flow Matching, we can estimate likelihoods and thereby derive an anomaly score to detect anomalies in multi-view image data at object, image, and pixel-level. The architectural flexibility of FM models allows us to efficiently transform features of different spatial sizes to the normal distribution. We evaluate thoroughly on the already established Real-IAD data set and are also the first to provide a comprehensive evaluation of popular anomaly detection methods for the MANTA-Tiny data set. MATCH achieves state-of-the-art performance in both anomaly detection and segmentation, all while running on consumer-level hardware. By omitting the costly divergence term needed for likelihood estimation, we ensure that MATCH is usable in real-time production scenarios. Lastly, several ablation studies are conducted to validate the methodological choices.

13.
arXiv (CS.CL) 2026-06-24

Business as Rulesual: A Benchmark and Framework for Business Rule Flow Modeling with LLMs

Extracting structured procedural knowledge from unstructured business documents is a critical yet unresolved bottleneck in process automation. While prior work has focused on extracting linear action flows from instructional texts, such as recipes, it has insufficiently addressed the complex logical structures, including conditional branching and parallel execution, that are pervasive in real-world regulatory and administrative documents. Furthermore, existing benchmarks are limited by simplistic schemas and shallow logical dependencies, restricting progress toward logic-aware large language models.To bridge this Logic Gap, we introduce BREX, a carefully curated benchmark comprising 409 real-world business documents and 2,855 expert-annotated rules. Unlike prior datasets centered on narrow service scenarios, BREX spans over 30 vertical domains, covering scientific, industrial, administrative, and financial regulations. We further propose ExIde, a structure-aware reasoning framework that investigates five distinct prompting strategies, ranging from implicit semantic alignment to executable grounding via pseudo-code generation. This enables explicit modeling of rule dependencies and provides an out-of-the-box framework for different business customers without finetuning their own large language models. We benchmark ExIde using 13 state-of-the-art large language models. Our extensive evaluation reveals that executable grounding serves as a superior inductive bias, significantly outperforming standard prompts in rule extraction. In addition, reasoning-optimized models demonstrate a distinct advantage in tracing long-range and non-linear rule dependencies compared to standard instruction-tuned models.

14.
arXiv (CS.CV) 2026-06-25

ReaDy-Go: Real-to-Sim Dynamic 3D Gaussian Splatting Simulation for Environment-Specific Visual Navigation with Moving Obstacles

Visual navigation models often struggle in real-world dynamic environments due to limited robustness to the sim-to-real gap and the difficulty of training policies tailored to target deployment environments (e.g., households, restaurants, and factories). Although real-to-sim navigation simulation using 3D Gaussian Splatting (GS) can mitigate these challenges, prior GS-based works have considered only static scenes or non-photorealistic human obstacles built from simulator assets, despite the importance of safe navigation in dynamic environments. To address these issues, we propose ReaDy-Go, a novel real-to-sim simulation pipeline that synthesizes photorealistic dynamic scenarios in target environments by augmenting a reconstructed static GS scene with dynamic human GS obstacles, and trains navigation policies using the generated datasets. The pipeline provides three key contributions: (1) a dynamic GS simulator that integrates static scene GS with a human animation module, enabling the insertion of animatable human GS avatars and the synthesis of plausible human motions from 2D trajectories, (2) a navigation dataset generation framework that leverages the simulator along with a robot expert planner designed for dynamic GS representations and a human planner, and (3) robust navigation policies to both the sim-to-real gap and moving obstacles. The proposed simulator generates thousands of photorealistic navigation scenarios with animatable human GS avatars from arbitrary viewpoints. ReaDy-Go outperforms baselines across target environments in both simulation and real-world experiments, demonstrating improved navigation performance even after sim-to-real transfer and in the presence of moving obstacles. Moreover, zero-shot sim-to-real deployment in an unseen environment indicates its generalization potential. Project page: https://syeon-yoo.github.io/ready-go-site/.

15.
arXiv (CS.AI) 2026-06-24

Red-Teaming the Agentic Red-Team

arXiv:2606.24496v1 Announce Type: cross Abstract: The use of agentic systems to perform offensive security operations has moved from a theoretical possibility to a commoditized capability. However, while the community has focused on creating more and more capable agents, less attention has been allocated to assessing the security of those systems. In this work, we present the first in-depth security analysis of the most widely used agentic systems for offensive security operations. We show that most of these tools share common design flaws that enable an active adversary to exfiltrate API keys, establish persistent footholds, and fully compromise the operator's machine, even when the agent operates inside a sandboxed container. To support our analysis, we introduce a full cyber kill chain for such agentic systems, capturing the progression from initial LLM manipulation to lateral movement, persistence, guardrail bypass, and sandbox escape. Building on our security analysis, we derive a robust architecture for agentic offensive-security tools and propose actionable, broadly applicable design principles that mitigate the disclosed attack paths at the architectural level.

16.
arXiv (CS.CL) 2026-06-11

When is Your LLM Steerable?

Activation steering offers a lightweight approach to control language models' behavior at inference time, but whether it succeeds or fails heavily depends on the prompt, concept, model, and steering configuration. Finding the regime and boundaries of successful steering typically requires expensive grid searches and post-hoc evaluation of full autoregressive rollouts. In this work, we investigate whether steerability can be predicted from the model's internal states at the beginning of the generation process, e.g., after generating the first few tokens, and how to leverage such a predictor to improve steering success rate. To this end, we first introduce ASTEER, a testbed including 1.4M steered generations, spanning 150 concepts with each steering success/failure labeled. Leveraging this testbed, we analyze the model's early decoding dynamics by extracting features that compare hidden states before and after steering across layers and initial decoding steps. These features help us understand how steering's effects propagate along layers and token positions, which provide key information for steerability prediction. We then train a Gradient Boosting Decision Trees (GBDT) classifier on these features to predict whether an intervention will under-steer, succeed, or over-steer without requiring full rollout. Our predictor achieves around 0.7 macro-F1 score on unseen concepts, demonstrating that early hidden states encode substantial, structured information about eventual steering efficacy. We further leverage this steerability predictor as guidance for steering strength searching, achieving near-optimal performance with a small fraction of decoding cost.

17.
arXiv (CS.CL) 2026-06-24

Privacy-Preserving RAG via Multi-Agent Semantic Rewriting: Achieving Confidentiality Without Compromising Contextual Fidelity

Retrieval-Augmented Generation enhances large language models by incorporating external knowledge, but deploying it in sensitive scenarios risks privacy leakage via malicious prompts. To address this, we propose a multi-agent framework that sanitizes retrieved content through semantic rewriting. By employing three specialized agents for privacy extraction, semantic analysis, and reconstruction, our approach collaboratively removes sensitive identifiers while preserving the semantic core. We evaluate the framework on the ChatDoctor and Wiki-PII datasets across six large language models. Experimental results demonstrate a significant reduction in privacy leakage under targeted attacks. For instance, we reduced targeted information exposure in LLaMA-3-8B from 144 instances in the baseline to just 1. Furthermore, we maintain strong contextual fidelity with a BLEU-1 score of 0.122, outperforming the existing SAGE method's 0.117. Finally, the framework operates as an asynchronous preprocessing module, introducing no additional latency to online inference, as all rewriting is executed as a one-time offline preprocessing step. To promote reproducibility, the source code of this work is publicly available at https://github.com/foursoils/Privacy-Preserving-RAG.

18.
arXiv (CS.LG) 2026-06-11

RePAIR: Predictive Self-Supervised Representation Learning in Chess

arXiv:2606.11860v1 Announce Type: new Abstract: In this paper, we introduce Representation Prediction via Autoencoding using Iterative Refinement (RePAIR) - a novel self-supervised representation learning architecture that synthesizes Masked Autoencoders (MAE), Joint Embedding Predictive Architectures (JEPA), and Bidirectional Encoder Representations from Transformers (BERT). We demonstrate how it can be used to encode objects in sequential data like consecutive chess positions into compact yet meaningful representations. The basic principle of the architecture is to mask large portions of a sequence of latent states, similar to BERT and MAE. Then, we apply a lightweight Predictor to the latent representations that repairs gaps in the sequence in a lower-dimensional embedding space akin to JEPA. Our experiments in the domain of chess show that the Encoder refines the board representations such that meaningful chess concepts emerge clustered in the latent space. Furthermore, reconstructions of the masked board states show that the model is able to reason about the piece movements without relying on costly reinforcement learning methods. Lastly, we find that the resulting representation space allows for quick and intuitive dissections of chess games by observing the game path trajectories in this semantically rich space.

19.
arXiv (quant-ph) 2026-06-12

A Robust Strontium Tweezer Apparatus for Quantum Computing

arXiv:2601.16564v2 Announce Type: replace-cross Abstract: Neutral atoms for quantum computing applications show promise in terms of scalability and connectivity. We demonstrate the realization of a versatile apparatus capable of stochastically loading a 5x5 array of optical tweezers with single $^{88}$Sr atoms featuring flexible magnetic field control and excellent optical access. A custom-designed oven, spin-flip Zeeman slower, and deflection stage produce a controlled flux of Sr directed to the science chamber. In the science chamber, featuring a vacuum pressure of $3 \times 10^{-11}$ mbar, the Sr is cooled using two laser cooling stages, resulting in $\sim 3 \times 10^5$ atoms at a temperature of 5(1) $\mu$K. The optical tweezers feature a $1/e^2$ waist of 0.81(2) $\mu$m, and loaded atoms can be imaged with a fidelity of $\sim 0.997$ and a survival probability of $0.99^{+0.01}_{-0.02}$. The atomic array presented here forms the core of a full-stack quantum computing processor targeted for quantum chemistry computational problems.

20.
arXiv (CS.CV) 2026-06-16

Disentangling Hallucinations: Orthogonal Semantic Projection for Robust Interpretability

As Vision-Language Models are increasingly deployed in safety-critical applications, the trustworthiness of their explanations becomes crucial. Explainable AI (XAI) methods for Vision-Language Models often suffer from semantic hallucination, where attribution maps highlight prominent image regions even when prompted with incorrect text descriptions (e.g., highlighting a dog when prompted ``cat''). Although this problem is widespread, a formal mathematical analysis of XAI methods and CLIP embeddings is largely missing in the literature. We demonstrate that this phenomenon is not specific to a single architecture but is a fundamental consequence of Linear Semantic Leakage in high-dimensional embedding spaces. We propose a unified theoretical framework, Linear Semantic Attribution (LSA), which generalizes across discriminative methods. We introduce OSP, a geometric intervention that utilizes the residual property of OMP to disentangle unique semantic signals from shared concepts. We prove theoretically and demonstrate empirically that OSP minimizes hallucination by orthogonalizing the query vector against distractor concepts, rendering the attribution model blind to shared features while preserving fidelity for correct prompts. Our code is available at: https://github.com/emirhanbilgic/Orthogonal-Semantic-Projection

21.
arXiv (CS.LG) 2026-06-11

Bernstein-Schur Kernels: Random Features by Sketched Modulation and Radial Randomization

arXiv:2606.11255v1 Announce Type: new Abstract: Bernstein–Schur kernels are products of a finite-feature kernel (one with an explicit finite-dimensional feature map) and a completely monotone shift-invariant kernel: nonstationary kernels that fall between the shift-invariant and dot-product templates random features usually exploit, so in general neither Bochner sampling nor polynomial sketching applies to the full kernel directly. We give one random-feature construction for the whole class that randomizes both factors: it sketches the finite modulation and randomizes the completely monotone radial factor, sampling the latter's one-dimensional Bernstein–Widder scale and then applying Gaussian random Fourier features (whose frequency is still $d$-dimensional). The feature dimension is then $Dm$, set by the sketch size $m$ and the radial-draw count $D$, free of the $O(d^2)$ size of the exact modulation feature. Keeping the modulation \emph{exact is the analyzable limit ($m\to\infty$): there we prove unbiasedness, an exact variance for the recommended flat estimator, an expected matrix-Bernstein operator-norm bound (with a matching high-probability tail) controlled by the top eigenvalues of the kernel and modulation Gram matrices together with an intrinsic dimension rather than the crude $N\max_{ij}$ entrywise route, and a deterministic relative-spectral kernel-ridge stability result. By conditioning on the sketch, the doubly-randomized estimator inherits the same intrinsic-dimension operator-norm guarantee plus a single additive sketch term, tunable by $m$ independently of $D$. The motivating instance is the biased $yat$-kernel $k_{yat,b}(w,x)=(w^\top x+b)^2/(\|w-x\|^2+\varepsilon)$, $b\ge0$, whose family span contains the inverse-multiquadric kernel by finite differences in $b$; for it the radial mixture is the IMQ spectral sampler, and one frequency per scale is variance-optimal at a fixed radial-feature budget.

22.
arXiv (math.PR) 2026-06-18

On the Singular Control of a Diffusion and its Running Infimum or Supremum

arXiv:2501.17577v2 Announce Type: replace-cross Abstract: We study a class of singular stochastic control problems for a one-dimensional diffusion $X$ in which the performance criterion to be optimised depends explicitly on the running infimum $I$ (or supremum $S$) of the controlled process. We introduce two novel integral operators that are consistent with the Hamilton-Jacobi-Bellman equation for the resulting two-dimensional singular control problems. The first operator involves integrals where the integrator is the control process of the two-dimensional process $(X,I)$ or $(X,S)$; the second operator concerns integrals where the integrator is the running infimum or supremum process itself. Using these definitions, we prove a general verification theorem for problems involving two-dimensional state-dependent running costs, costs of controlling the process, costs of increasing the running infimum (or supremum) and exit times. Finally, we apply our results to explicitly solve an optimal dividend problem in which the manager's time-preferences depend on the company's historical worst performance.

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

Scalable anomaly detection via a univariate Christoffel function

arXiv:2606.12483v1 Announce Type: new Abstract: Anomaly detection plays a critical role in identifying unusual patterns across domains such as fraud detection, network intrusion, and system fault diagnosis. Recently, Christoffel function-based methods, rooted in polynomial optimization, have emerged as promising alternatives to deep learning due to their strong mathematical foundations and computational frugality. However, their practical applicability is hindered by the need to invert a matrix whose size grows exponentially with the data dimension, rendering the method intractable even for moderate-dimensional datasets. This paper addresses the dimensionality limitations of Christoffel function-based anomaly detection while preserving its key theoretical properties, i.e., the on-off support dichotomy behavior and the accurate support shape capture. We introduce UCF, a univariate Christoffel function which is based on the squared distance between the query point and the support points. Extensive experiments on the ADBench benchmark demonstrate that UCF consistently outperforms 14 state-of-the-art baselines in terms of Average Precision. By resolving the scalability bottleneck of the Christoffel Function, this work expands the toolkit of anomaly detection methods with a robust, theoretically grounded, and universally applicable approach.

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

PosterForest: Hierarchical Multi-Agent Collaboration for Scientific Poster Generation

arXiv:2508.21720v3 Announce Type: replace Abstract: Automating scientific poster generation requires hierarchical document understanding and coherent content-layout planning. Existing methods often rely on flat summarization or optimize content and layout separately. As a result, they often suffer from information loss, weak logical flow, and poor visual balance. We present PosterForest, a training-free framework for scientific poster generation. Our method introduces the Poster Tree, a structured intermediate representation that captures document hierarchy and visual-textual semantics across multiple levels. Building on this representation, content and layout agents perform hierarchical reasoning and recursive refinement, progressively optimizing the poster from global organization to local composition. This joint optimization improves semantic coherence, logical flow, and visual harmony. Experiments show that PosterForest outperforms prior methods in both automatic and human evaluations, without additional training or domain-specific supervision.

25.
arXiv (math.PR) 2026-06-19

Power-law hypothesis and (un)fairness of PageRank on undirected multi-type PAMs

arXiv:2606.19583v1 Announce Type: new Abstract: The preferential attachment model (PAM) describes the sequential growth of a network based on the "rich-get-richer" principle. Several versions of it have become established for modeling, e.g., citation networks, capturing a power-law degree distribution. Directed versions of the preferential attachment model where the edges are directed from the new to the old vertices have been the subject of extensive research. They have been shown to exhibit remarkable properties such as heavier tails for the limiting graph-normalized PageRank than for the in-degrees. By contrast, for the undirected version, we recently showed that PageRank has similar tails as the degree. In the present paper, we discuss the PageRank asymptotics for a multi-type version of the undirected PAM (here vertices have different colors), complementing previous results of Antunes, Bhamidi, Banerjee and Pipiras on the asymptotics of PageRank on similar directed multi-type or colored PAMs. Our studies are motivated by the aim to go beyond the rigid rule of edge orientation in directed preferential attachment models. As the main result, for the case of a finite set of colors, we show that the power-law hypothesis for PageRank is fulfilled also for the colored undirected PAM, where, by contrast to the directed case, the power-law exponent is color-dependent for some choices of the initial color distribution and the attractiveness function. For the specific case of a two-type model, we discuss implications of our results on fairness in sampling underrepresented nodes from the network.