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01.
arXiv (math.PR) 2026-06-19

Finite-Sample Bounds for Expected Signature Estimation under Weak Dependence

arXiv:2605.20541v2 Announce Type: replace-cross Abstract: The expected signature uniquely determines the law of a random rough path under a moment-growth condition, yet finite-sample bounds for estimating its truncations from a single long dependent trajectory remain unavailable. We study a strictly stationary stochastic process equipped with a geometric rough-path lift, observed in non-overlapping blocks of equally-spaced samples, and prove a non-asymptotic mean-squared error (MSE) bound for the block-averaging estimator of its truncated expected signature. Under moment and stationarity assumptions together with a direct covariance-decay condition on block signatures – strictly weaker than $\alpha$-mixing and applicable to long-range-dependent processes – the error separates into a discretization term and a fluctuation term, with rates determined respectively by path regularity and dependence strength. A levelwise rough-factorial variance analysis keeps finite-truncation constants explicit and yields an optimal allocation rule under a fixed observation budget. We verify the assumptions for independent-coordinate fractional Ornstein–Uhlenbeck processes in three regimes: short-range (Hurst $1/41/2$. Monte Carlo experiments show empirical slopes steeper than the guaranteed upper-bound rates.

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

UtVAA: Ultra-tiny Vision Transformer with Affix Attention for Mobile Image Classification

Vision Transformers (ViTs) have demonstrated strong representation capability in image classification. However, their quadratic self-attention complexity and large parameter counts limit deployment on resource-constrained mobile and edge devices. This paper introduces UtVAA, an ultra-tiny Vision Transformer architecture designed for efficient visual recognition under strict computational budgets. It incorporates a novel Affix Attention block that combines depthwise-pointwise local feature extraction, linear self-attention, coordinate attention for spatial dependency modelling, and a lightweight ternary fusion strategy to integrate local and global representations. In addition, Dilated Bottleneck blocks expand the receptive field using dilated depthwise separable convolutions while maintaining low FLOPs and stable optimisation through residual connections. UtVAA is implemented in scalable Tiny, Medium, and Large variants, with the smallest model containing 204.67K parameters and 53.95M FLOPs. Experimental results on CIFAR-10, CIFAR-100, PlantVillage-Tomato and SLIF-Tomato datasets show that UtVAA achieves competitive accuracy within a sub-million-parameter regime. Overall, the results demonstrate that transformer-based vision models can be redesigned into ultra-tiny architectures without significant loss in discriminative performance, making UtVAA suitable for mobile and edge deployment. Code is available at https://github.com/romiyal/UtVAA

03.
arXiv (CS.AI) 2026-06-16

The Missing Knowledge Layer in Cognitive Architectures for AI Agents

arXiv:2604.11364v2 Announce Type: replace Abstract: The two most influential cognitive architecture frameworks for AI agents, CoALA [21] and JEPA [12], both lack an explicit Knowledge layer with its own persistence semantics. This gap produces a category error: systems apply cognitive decay to factual claims, or treat facts and experiences with identical update mechanics. We survey persistence semantics across existing memory systems and identify eight convergence points, from Karpathy's LLM Knowledge Base [10] to the BEAM benchmark's near-zero contradiction-resolution scores [22], all pointing to related architectural gaps. We propose a four-layer decom position (Knowledge, Memory, Wisdom, Intelligence) where each layer has fundamentally different persistence semantics: indefinite supersession, Ebbinghaus decay, evidence-gated revision, and ephemeral inference respectively. Companion implementations in Python and Rust demonstrate the architectural separation is feasible. We borrow terminology from cognitive science as a useful analogy (the Knowledge/Memory distinction echoes Tulving's trichotomy), but our layers are engineering constructs justified by persistence-semantics requirements, not by neural architecture. We argue that these distinctions demand distinct persistence semantics in engineering implementations, and that no current framework or system provides this.

04.
arXiv (CS.AI) 2026-06-18

Robust Regularized Policy Iteration under Transition Uncertainty

arXiv:2603.09344v3 Announce Type: replace Abstract: Offline reinforcement learning (RL) enables data-efficient and safe policy learning without online exploration, but its performance often degrades under distribution shift. The learned policy may visit out-of-distribution state-action pairs where value estimates and learned dynamics are unreliable. To address policy-induced extrapolation and transition uncertainty in a unified framework, we formulate offline RL as robust policy optimization, treating the transition kernel as a decision variable within an uncertainty set and optimizing the policy against the worst-case dynamics. We propose Robust Regularized Policy Iteration (RRPI), which replaces the intractable max-min bilevel objective with a tractable KL-regularized surrogate and derives an efficient policy iteration procedure based on a robust regularized Bellman operator. We provide theoretical guarantees by showing that the proposed operator is a $\gamma$-contraction and that iteratively updating the surrogate yields monotonic improvement of the original robust objective with convergence. Experiments on D4RL benchmarks demonstrate that RRPI achieves strong average performance, outperforming recent baselines including percentile-based methods on the majority of environments while remaining competitive on the rest. Moreover, RRPI exhibits robust performance by aligning lower $Q$-values with high epistemic uncertainty, which prevents the policy from executing unreliable out-of-distribution actions.

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

EQPO: Equitable Group Relative Policy Optimization for Clinical Reasoning

arXiv:2510.19893v2 Announce Type: replace Abstract: Medical AI systems demonstrated impressive diagnostic performance, yet they routinely show uneven accuracy across demographic groups, disadvantaging underrepresented populations. Although multimodal reasoning foundation models have pushed clinical diagnosis forward, reinforcement learning-based post-training tends to absorb and magnify the biases present in majority-dominated training corpora. We propose Equitable Group Relative Policy Optimization (EQPO), a hierarchical reinforcement learning method that encourages balanced learning across heterogeneous clinical populations by adaptively reweighting samples according to subgroup representation, task difficulty, and data source. As demographic annotations are frequently missing in real-world clinical data, EQPO additionally applies unsupervised clustering to recover latent subpopulations when they are unavailable. On 7 diagnostic benchmarks covering 5 modalities (X-ray, CT, dermoscopy, mammography, ultrasound), EQPO reduces F1 standard deviation by 43.9% and the maximum cross-group F1 gap by 42.7% on QoQ-Med3-8B over vanilla GRPO, and narrows predictive parity gaps by 27.2% on MedGemma-4B over bias-mitigated RL baselines while raising F1 by 12.5% even without any demographic labels. Examining the training trajectory shows that EQPO steadily improves fairness over the course of optimization, in contrast to baseline methods whose fairness degrades as training proceeds, and the discovered implicit groups remain stable and align with masked demographic attributes. We further release EquiMedGemma-4B and EquiQoQ-Med3-8B, equitability-aware clinical VLLMs that attain state-of-the-art accuracy with markedly smaller demographic gaps.

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

Bootstrapped Monitoring: Leveraging Transparent Reasoning to Oversee Stronger AI Agents

arXiv:2606.11998v1 Announce Type: new Abstract: Trusted monitoring is a cornerstone of AI control. However, as frontier models grow more capable, the increasing capabilities gap between trusted and untrusted models may render trusted models unreliable monitors. We introduce bootstrapped monitoring, a protocol that addresses this by inserting a stronger, intermediate untrusted model with transparent chain-of-thought reasoning into the oversight chain. The untrusted monitor ($U_m$) evaluates the agent's actions, while a weaker trusted model ($T$) oversees $U_m$'s reasoning to detect collusion. We evaluate bootstrapped monitoring on multi-turn software engineering tasks (BashArena) across multiple agents and monitors. Bootstrapped monitoring substantially improves catch rates over trusted-only monitoring, even when the untrusted monitor actively colludes with the agent, provided we have access to its raw chain-of-thought. Our results suggest that bootstrapped monitoring can extend the useful lifetime of trusted models in control as AI capabilities advance.

07.
arXiv (CS.AI) 2026-06-15

Silent Failures in Federated Personalization of Foundation Models

arXiv:2606.00947v2 Announce Type: replace-cross Abstract: Foundation models are increasingly personalized on decentralized private data through federated learning and are now deployed at scale under growing regulatory requirements for post-market monitoring. We argue that this convergence creates a distinct and under-recognized class of trustworthiness failures, which we term "Silent Failures." These include amplified bias, fairness collapse, and alignment erosion that may remain difficult to detect because federated learning's privacy constraints limit visibility into model behavior. A landscape analysis of existing benchmarks reveals a structural divide. Federated benchmarks evaluate system performance but provide limited insight into model behavior, whereas centralized trustworthiness benchmarks assess behavior but require model access incompatible with federated privacy. We introduce a taxonomy of six silent failure modes arising from the interaction of foundation model personalization, dataset shift, and core federated constraints. Our analysis shows that privacy-preserving training alone is insufficient for trustworthy deployment. We conclude with a research agenda for privacy-preserving behavioral evaluation and propose that silent failures become a standard diagnostic category for trustworthy federated artificial intelligence.

08.
arXiv (CS.LG) 2026-06-16

Formalizing and Mitigating Structural Distortion in LLM Attention for Zero-Shot Graph Reasoning

arXiv:2606.15633v1 Announce Type: new Abstract: Large Language Models (LLMs) have shown promise for reasoning over Text-Attributed Graphs (TAGs). However, applying LLMs to graphs requires linearizing their structure into sequences, introducing distortion rooted in the graph bandwidth problem. While this distortion has been shown to degrade performance, it is often attributed to prompt design or model scale, leaving the underlying mechanism unclear. In this work, we show how rotary positional embeddings turn graph linearization into bandwidth-dependent attention decay, suppressing attention between graph-adjacent nodes that are forced far apart in the serialized sequence. This shifts the focus of LLM-based graph reasoning from prompt engineering and scaling toward correcting attention misalignment. Motivated by this analysis, we propose Graph-aligned Language Attention (GaLA), a lightweight, inference-time modification for LLMs. GaLA biases attention toward graph-adjacent nodes while preserving the LLM's sequential inductive biases. Across TAG benchmarks, GaLA improves performance with negligible overhead, demonstrating that distortion is a correctable bottleneck in LLM-based graph reasoning.

09.
arXiv (quant-ph) 2026-06-16

Finite-Dimensional Type I von Neumann Algebras in PyTorch: A GPU-Accelerated Framework for Random Block-Diagonal Operators

arXiv:2606.15882v1 Announce Type: cross Abstract: We present \texttt{torch\_vn\_algebra}, an open-source Python library built on PyTorch for numerical experiments with finite-dimensional Type I von Neumann algebras (direct sums of matrix algebras). The library provides: $\bullet$ a compact batched tensor representation $(B,C,k_{\max},k_{\max})$ that handles both Monte Carlo samples and multiple direct summands; $\bullet$ lazy evaluation of operators to avoid unnecessary memory allocation; $\bullet$ generation of random operators with arbitrary eigenvalue distributions (user-provided samplers) and various unitary ensembles (Haar, $\mathrm{SU}(n)$, COE, CSE, diagonal phases); $\bullet$ functional calculus via SVD (absolute value, square root, inverse, entropy) and a hybrid method for extreme eigenvalues (exact diagonalisation for $k_{\max}\le256$, otherwise power iteration); $\bullet$ three trace functionals (blunt, normalised subspace trace, and the von Neumann tracial state); $\bullet$ GPU-accelerated batched linear algebra for moderate-scale Monte Carlo studies (e.g., $2\times10^4$ samples of $100\times100$ operators). The library is validated against analytical expectations (Haar moments, trace properties). Performance benchmarks on a Tesla P100 GPU are presented and discussed. Limitations and future work are outlined. The code is open-source.

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

Lighting-aware Unified Model for Instance Segmentation

Foundation models like the Segment Anything Model (SAM) demonstrate impressive zero-shot generalization but frequently degrade under diverse real-world illumination, particularly for instance segmentation. In this work, we address this limitation by developing Lighting Convolutional-Attention (\lca{)}, an adapter module that enhances segmentation robustness without fine-tuning the heavy backbone. \lca{} employs a dual-branch architecture to process RGB features alongside contrast maps, enabling physically motivated sensitivity to structural changes rather than illumination artifacts. We optimize \lca{} through a pairwise training strategy, introducing a targeted loss term that explicitly penalizes discrepancies between clean images and their corresponding illumination variants. To evaluate and support this architecture, we conduct a comprehensive empirical study across multiple existing benchmarks and present a novel Unity-based synthetic dataset specifically designed to accurately replicate complex real-world lighting conditions. Extensive experimental results demonstrate that our approach successfully bridges the domain gap, delivering superior lighting-robust segmentation.

11.
arXiv (CS.LG) 2026-06-17

From Theory to Application: A Practical Introduction to Neural Operators in Scientific Computing

arXiv:2503.05598v2 Announce Type: replace-cross Abstract: This review examines neural operator architectures for learning solution operators of parametric partial differential equations (PDEs), with an emphasis on conceptual clarity and practical implementation. The work analyzes key models, including DeepONet, PCANet, and the Fourier Neural Operator, highlighting their underlying representations, computational structures, and comparative performance. These architectures are demonstrated on three canonical PDE problems: the Poisson equation, a linear elasticity problem, and a hyperelasticity problem. To make the presentation self-contained, key foundational topics are introduced, including finite-dimensional representations of function spaces, singular-value decomposition, and sampling from infinite-dimensional function spaces. Beyond forward modeling, the review discusses the use of neural operators as surrogate models within a Bayesian inverse-problem framework, including prior specification, forward-map approximation, and posterior computation. The performance of the three neural-operator architectures is evaluated on in-distribution samples, out-of-distribution samples, and Bayesian inference tasks. The review also discusses challenges related to prediction accuracy and generalization, outlining emerging strategies such as residual-based error correction and multi-level training. The review concludes by positioning neural operators within broader scientific-computing workflows and by identifying directions for reliable, scalable operator learning.

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

Peak-Based Nuclide Identification in HPGe $\gamma$-Spectrometry with Machine Learning and SHAP

arXiv:2606.14874v1 Announce Type: cross Abstract: High-purity germanium gamma spectra often require time-consuming analyses from subject matter experts. Photopeaks within these spectra are carefully fitted and numerical methods are employed to assist with nuclide identification (NID) and quantification. Amending the list of nuclides identified by analysis software can be nontrivial. When many samples need to be analyzed, it is therefore challenging to make timely and correct decisions. Supervised machine-learning-based NID can serve as an expert-informed, automated tool to improve the initial set of radionuclides suggested to an analyst and more effectively drive subsequent quantification. To that end, we implemented machine learning models that map photopeaks carefully fitted by analysts to NID results for experimental spectra containing various isotopic combinations drawn from a set of 65 isotopes. The best model achieved an F1 score of 0.97, markedly surpassing the F1 score of 0.84 achieved by traditional software when compared using a nuclide library comprising the same 65 isotopes assessed by the models. Finally, we illustrated the most important input features for model predictions using Shapley Additive Explanations. These explanations revealed that the models use physically relevant photopeaks when making predictions for the isotopes in our nuclide library.

13.
arXiv (CS.CL) 2026-06-15

Be My Tutor: On-Policy Co-Distillation for Mutual LLM Improvement via Peer Feedback

We study multi-domain LLM training in which two models, each stronger in a different domain, co-evolve by tutoring each other through on-policy feedback. Unlike one-way distillation or single-model fine-tuning, our goal is mutual Pareto improvement: each model improves across domains without losing its original strength. To this end, we propose On-Policy Co-Distillation (OPCoD), where each student's self-distillation is conditioned on its own correct rollout and feedback from its peer. To make feedback exchange effective, OPCoD uses cognizance-based gating to decide when to give feedback and feedback anchoring to ground feedback in the problem. On Science Q\&A tasks, OPCoD consistently outperforms baselines and achieves Pareto improvement across all evaluated domain pairs and students.

14.
arXiv (CS.CV) 2026-06-19

Benchmarking Vision Foundation Models for Domain-Generalizable Face Anti-Spoofing

Face Anti-Spoofing (FAS) remains challenging due to the requirement for robust domain generalization across unseen environments. While recent trends leverage Vision-Language Models (VLMs) for semantic supervision, these multimodal approaches often demand prohibitive computational resources and exhibit high inference latency. Furthermore, their efficacy is inherently limited by the quality of the underlying visual features. This paper revisits the potential of vision-only foundation models to establish a highly efficient and robust baseline for FAS. We conduct a systematic benchmarking of 15 pre-trained models, such as supervised CNNs, supervised ViTs, and self-supervised ViTs, under severe cross-domain scenarios including the MICO and Limited Source Domains (LSD) protocols. Our comprehensive analysis reveals that self-supervised vision models, particularly DINOv2 with Registers, significantly suppress attention artifacts and capture critical, fine-grained spoofing cues. Combined with Face Anti-Spoofing Data Augmentation (FAS-Aug), Patch-wise Data Augmentation (PDA) and Attention-weighted Patch Loss (APL), our proposed vision-only baseline achieves state-of-the-art performance in the MICO protocol. This baseline outperforms existing methods under the data-constrained LSD protocol while maintaining superior computational efficiency. This work provides a definitive vision-only baseline for FAS, demonstrating that optimized self-supervised vision transformers can serve as a backbone for both vision-only and future multimodal FAS systems. The project page is available at: https://gsisaoki.github.io/FAS-VFMbenchmark-CVPRW2026/ .

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

Multi-task Learning is Not Enough: Representational Entanglement in Dual-output Second Language Speech Recognition

Second-language (L2) speech recognition often requires transcriptions of pronunciations and intended meanings. Multi-task learning (MTL) is a natural approach because it assumes that shared representations benefit both outputs. However, this paper shows that this assumption does not hold across Korean and English. MTL improves meaning but degrades surface transcription, especially in English, where the degradation scales with surface-meaning divergence measured by Levenshtein edit distance. Encoder analysis links these patterns to encoder-level entanglement, with Korean preserving distinct task representations while English produces nearly identical ones. Cross-task decoder analysis shows that the meaning dual-output decoder adapts with a unique representation, while the surface dual-output decoder remains constrained by the encoder. These findings motivate the design of MTL frameworks that mitigate encoder-level entanglement to reduce surface degradation in dual-output L2 automatic speech recognition.

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

IVIE: A Neuro-symbolic Approach to Incremental and Validated Generation of Interactive Fiction Worlds

Computational creativity in Interactive Fiction faces a fundamental tension: Large Language Models (LLM) may produce creative narratives but struggle with world coherence, while symbolic systems ensure consistency but lack creative flexibility. We present IVIE (Incremental & Validated Interactive Experiences), a neuro-symbolic approach to generating complete and playable interactive fiction worlds from scratch. Building upon PAYADOR's neuro-symbolic framework, IVIE implements a four-stage incremental generation pipeline that delegates creative decisions–setting and character creation, puzzle design–to LLMs while grounding the world state through symbolic validation. The system generates worlds with interconnected locations, functional items, non-player characters, and coherent puzzles, all structured around a central goal-oriented architecture. Human evaluation shows the approach generates immersive, thematically coherent worlds with high player engagement. Results seem to indicate that the neuro-symbolic approach successfully balances flexibility with narrative coherence: symbolic validation grounds LLM generation without eliminating generative freedom. However, challenges remain: LLM inconsistencies occasionally bypass puzzle constraints, and objective validation gaps allow some structurally impossible goals. We identify key design considerations for future neurosymbolic interactive storytelling systems, particularly regarding LLM capabilities and their limitations.

17.
arXiv (math.PR) 2026-06-18

Stability of Khintchine-type inequalities via log-monotonicity

arXiv:2606.19313v1 Announce Type: new Abstract: We investigate Khintchine-type inequalities for the weighted sums $S=\sum_ka_kX_k$ of independent copies of a symmetric random variable $X$. We show how log-monotonicity of the sequence $r_k(X)=k! \mathbb{E}[X^{2k}]/(2k)!$ implies sharp comparisons between the $L_p$ and $L_2$ norms of $S$ for every even integer $p\geq 2$, extending classic Khintchine-type inequalities and yielding new results in the log-convex setting. We also investigate the stability of our inequalities. Our first stability inequality sharpens the classic inequality by a deviation of the coefficient vector from the coordinate extremizers, while the second quantifies deviation from the Gaussian limit. Our results recover recent stability inequalities for random signs and apply to a broad class of distributions, including type-$\mathscr{L}$ random variables, ultra sub-Gaussian random variables and Gaussian mixtures.

18.
arXiv (CS.CL) 2026-06-12

Marginal Alignment Does Not Guarantee Joint-Distribution Fidelity: An Official-Reference Audit of Nemotron-Personas-Korea with Cross-Locale Replication

Authors:

Synthetic persona datasets cite alignment with official demographics as a basis for trust, yet downstream users consume them as joint structures across age, sex, region, occupation, education, name, and institutional status. Marginal alignment does not imply that these joints are preserved. We propose the Independence-Assumption Footprint (IAF), an audit primitive that operates on the attribute combinations a dataset card itself documents as treated independently. For each such combination, IAF compares the synthetic joint against an external official or institutional reference, using direct joint tables where available and rule-implied checks otherwise. Applied to NVIDIA Nemotron-Personas-Korea (one million Korean synthetic personas), IAF finds that NPK aligns with KOSIS marginals while three joints fail. The major-by-occupation distribution against the KEIS graduate universe carries a large conditional mismatch. The age profile of military service is institutionally inconsistent. Female representation in male-dominated occupations is substantially over-flattened toward parity, with the strict screening verdict mapping-dependent and age-robust under direct standardisation. A transferability demonstration across six further NPK locales finds locale-dependent rather than universal diagnostics, with reference-taxonomy cardinality confounding cross-locale flag counts. For synthetic personas used as silicon samples, marginal claims must therefore be paired with disclosure-anchored joint audits before reuse. The released audit artefacts (reference manifests, occupational crosswalks, derived metrics, reproducibility scripts) instantiate this protocol on the NPK family and are released for retargeting at other synthetic persona resources.

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

SciHorizon-GENE: Benchmarking LLM for Life Sciences Inference from Gene Knowledge to Functional Understanding

Large language models (LLMs) have shown growing promise in biomedical research, particularly for knowledge-driven interpretation tasks. However, their ability to reliably reason from gene-level knowledge to functional understanding, a core requirement for knowledge-enhanced cell atlas interpretation, remains largely underexplored. To address this gap, we introduce SciHorizon-GENE, a large-scale gene-centric benchmark constructed from authoritative biological databases. The benchmark integrates curated knowledge for over 190K human genes and comprises more than 540K questions covering diverse gene-to-function reasoning scenarios relevant to cell type annotation, functional interpretation, and mechanism-oriented analysis. Motivated by behavioral patterns observed in preliminary examinations, SciHorizon-GENE evaluates LLMs along four biologically critical perspectives: research attention sensitivity, hallucination tendency, answer completeness, and literature influence, explicitly targeting failure modes that limit the safe adoption of LLMs in biological interpretation pipelines. We systematically evaluate a wide range of state-of-the-art general-purpose and biomedical LLMs, revealing substantial heterogeneity in gene-level reasoning capabilities and persistent challenges in generating faithful, complete, and literature-grounded functional interpretations. Our benchmark establishes a systematic foundation for analyzing LLM behavior at the gene scale and offers insights for model selection and development, with direct relevance to knowledge-enhanced biological interpretation.

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

Triangular Consistency as a Universal Constraint for Learning Optical Flow

arXiv:2606.19938v1 Announce Type: cross Abstract: We propose triangular consistency as a first-principled constraint for optical flow, which is agnostic to network architecture, supervision type, and dataset, and applies to both image-pair and multi-frame settings. This simple but powerful constraint is to compose two flows to induce a third flow and enforce consistency among the three. The composed flows may arise from (i) image pairs, yielding cycle consistency; (ii) multiple video frames, producing longer-range motion through temporal chaining; or (iii) image pairs combined with controlled synthetic transformations, which becomes data augmentation. This triangular consistency introduces negligible computational overhead and requires no additional annotations. Since it is derived directly from the geometry of optical flow, it does not rely on model-specific assumptions and serves as a ``universal'' plug-and-play component for optical flow training. Experiments show consistent improvement across supervised, unsupervised, and transfer learning settings.

21.
arXiv (quant-ph) 2026-06-11

Bound State Solutions of the Relativistic Finite-difference Equation for the Ring-shaped Quesne Oscillator Potential

arXiv:2606.12082v1 Announce Type: new Abstract: We solve exactly the relativistic finite-difference equation for the quantum three-dimensional ring-shaped Quesne oscillator potential. Our investigation is based on a finite-difference version of relativistic quantum mechanics. So-called relativistic configurational r-space is a key concept here. We show that the radial wavefunctions and angular wavefunctions are expressed through the continuous dual Hahn polynomials and Jacobi polynomials, respectively. A discrete energy spectrum has been found. The radial wave functions and energy spectrum have the correct nonrelativistic limit. We also build a dynamical symmetry group SU (1, 1) for the radial part of the equation of motion, which allows us to find the energy spectrum purely algebraically.

22.
arXiv (CS.CV) 2026-06-19

Shape of Thought: Progressive Object Assembly via Visual Chain-of-Thought

Multimodal models for text-to-image generation have achieved strong visual fidelity, yet they remain brittle under compositional structural constraints, notably generative numeracy, attribute binding, and part-level relations. To address these challenges, we propose Shape-of-Thought (SoT), a visual CoT framework for process-supervised progressive shape assembly in the rendered 2D domain, without external engines at inference time. SoT trains a unified multimodal autoregressive model to generate interleaved textual plans and rendered intermediate states, helping the model capture shape-assembly logic without producing explicit geometric representations. Unlike text-only CoT, each decision is grounded in a rendered state, making counts, attachments, topology, and intermediate part-addition errors inspectable across the trajectory. To support this paradigm, we introduce SoT-26K, a large-scale dataset of grounded assembly traces derived from part-based CAD hierarchies, and T2S-CompBench, a benchmark for evaluating structural integrity and trace faithfulness. Fine-tuning on SoT-26K achieves 88.4% on component numeracy and 84.8% on structural topology, outperforming direct generation by +24.2 points on component numeracy and +19.3 points on structural topology. SoT establishes a transparent testbed for rendered-domain structure-aware generation. The code is available at https://github.com/yuhuo03/Shape-of-Thought.

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

Ex-Omni: Enabling 3D Facial Animation Generation for Omni-modal Large Language Models

Omni-modal large language models (OLLMs) aim to unify multimodal understanding and generation, yet extending them to jointly produce speech and 3D facial animation remains largely unexplored despite its importance for natural human-computer interaction. A key challenge is the mismatch between the discrete semantic reasoning of LLMs and the dense temporal dynamics required for 3D facial motion. We propose Expressive Omni (Ex-Omni), an open-source model that augments OLLMs with native speech-accompanied 3D facial animation. Ex-Omni decouples semantic reasoning from temporal generation through a blendshape-aware speech unit generator and a blendshape decoder, where speech units provide temporal scaffolding and hidden speech representations carry facially relevant cues. We further introduce a unified token-as-query gated fusion (TQGF) mechanism for controlled semantic injection, as well as InstructS2SF-1200K, a dataset consisting of 1200K samples for pre-training. Extensive experiments show that Ex-Omni maintains competitive speech understanding and generation ability while achieving better audio-visual synchronization and lower face-generation latency than cascaded pipelines.

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

Beyond Correctness: Enhancing Architectural Reasoning in Code LLMs via Scalable Labeling with Agentic Judgment

arXiv:2606.14948v1 Announce Type: cross Abstract: LLMs have substantially improved software engineering yet real-world development requires architectural understanding. Such understanding is prohibitively expensive to label manually and impossible to verify through tests alone. We propose an agentic judging pipeline using a strong LLM as a scalable proxy for expert architectural evaluation, comprising two judges: the Architecture Complexity Judge (ACJ), which estimates codebase-specific architectural understanding a task demands, and the Architecture Quality Judge (AQJ), which evaluates patch conformance to repository-specific architectural conventions via source-grounded rubrics. Fine-tuning Qwen3-8B/14B/32B on 3,360 curated instances achieves resolved rates of up to 27.2% on SWE-bench Verified - up to 540% over the base model and 256% over unfiltered fine-tuning. Meanwhile, the trained models achieve strong cross-language generalization and consistent improvements in architectural patch quality.

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

Counterfactual Optimization of Baseball Pitch Sequences and Estimation of Its Impact on Season-Level Statistics

arXiv:2606.17345v1 Announce Type: cross Abstract: Although pitch sequencing is a central topic in baseball analytics, previous studies have primarily focused on optimizing the final pitch within a single plate appearance, leaving the role of preceding setup pitches and their impact on long-term season-level performance insufficiently examined. To address these issues, this study conducted counterfactual analyses using MLB Statcast data. A Transformer-based machine-learning model was trained to predict whether a target pitch would result in an in-play outcome or swing-out. Counterfactual pitch sequences were then generated by replacing either the final pitch or the preceding setup pitch with alternative pitch types and locations while keeping the surrounding contextual information fixed. Optimal counterfactual selections were defined as those that minimized the predicted in-play probability, and their expected effects on pitchers' seasonal statistics were estimated using regression models linking model outputs to season statistics. The results suggest that the optimization of both final and setup pitches may substantially influence season-level performance, including improvements of more than 1.0 in K/9. The analyses also provided several practical insights, including velocity-band-specific effective locations, the importance of pitch commands, and the expansion of pitch-selection options through middle-velocity pitches. These findings quantitatively support the strategic importance of pitch sequencing in baseball.