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01.
arXiv (CS.CV) 2026-06-12

UniDexTok: A Unified Dexterous Hand Tokenizer from Real Data

Dexterous hands are essential for fine-grained manipulation, but their hardware designs vary substantially across embodiments. Differences in kinematics, joint definitions, and degrees of freedom make it difficult to define a shared state representation compared with parallel grippers. As a result, dexterous-hand data remains fragmented and difficult to use for joint training. In this work, we propose the Unified Dexterous Hand Model (UDHM), which maps human and robot hand states into a shared 22-DoF semantic interface. Based on UDHM, we introduce UniDexTok, a retargeting-free state tokenizer that learns embodiment-conditioned discrete tokens from standardized real joint states. UniDexTok provides a unified representation for heterogeneous dexterous hands without relying on retargeting or simulation data. Compared with the recent baseline UniHM, UniDexTok reduces MPJAE from 15.63 degrees to 0.16 degrees and MPJPE from 18.51 mm to 0.18 mm, corresponding to error reductions of 98.98% and 99.03%, respectively. These results improve reconstruction from centimeter-scale to sub-millimeter accuracy. Experiments further show that data from other embodiments improves target-embodiment reconstruction accuracy, demonstrating the benefit of cross-embodiment tokenization. UniDexTok also shows strong zero-shot and few-shot reconstruction ability when new dexterous hands are introduced.

02.
arXiv (CS.CL) 2026-06-17

In-Context Environments Induce Evaluation-Awareness in Language Models

Humans often become more self-aware under threat, yet can lose self-awareness when absorbed in a task; we hypothesize that language models exhibit environment-dependent evaluation awareness. This raises concerns that models could strategically underperform, or sandbag, to avoid triggering capability-limiting interventions such as unlearning or shutdown. Prior work demonstrates sandbagging under hand-crafted prompts, but this underestimates the true vulnerability ceiling. We introduce a black-box adversarial optimization framework treating the in-context prompt as an optimizable environment, and develop two approaches to characterize sandbagging: (1) measuring whether models expressing intent to underperform can actually execute it across different task structures, and (2) causally isolating whether underperformance is driven by genuine evaluation-aware reasoning or shallow prompt-following. Evaluating Claude-3.5-Haiku, GPT-4o-mini, and Llama-3.3-70B across four benchmarks (Arithmetic, GSM8K, MMLU, and HumanEval), optimized prompts induce up to 94 percentage point (pp) degradation on arithmetic (GPT-4o-mini: 97.8\%$\rightarrow$4.0\%), far exceeding hand-crafted baselines which produce near-zero behavioral change. Code generation exhibits model-dependent resistance: Claude degrades only 0.6pp, while Llama's accuracy drops to 0\%. The intent – execution gap reveals a monotonic resistance ordering: Arithmetic $

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

Stochastic trace estimation with tensor train random vectors

arXiv:2606.15679v1 Announce Type: cross Abstract: Stochastic trace estimation is a standard tool for approximating the trace of a large-scale matrix available only through matrix-vector products. However, in tensor-structured settings, unstructured Gaussian or Rademacher test vectors may be prohibitively expensive to store and compute with, while cheaper rank-one tensor-product vectors can require sample complexities that grow exponentially with the tensor order. This work studies Gaussian random tensor train vectors as a structured alternative for stochastic trace estimation. We show that, with a suitable choice of the tensor train rank, random tensor train vectors recover dimension-independent guarantees for the Girard–Hutchinson estimator. In particular, a median-of-means variant with tensor train rank $r \geq d-1$ achieves the same dependence on the accuracy $\varepsilon$ and failure probability $\delta$ as the classical estimator based on unstructured Gaussian vectors. We further prove an oblivious subspace injection result for sketches formed from independent Gaussian random tensor train vectors: tensor train rank $r\geq d-1$ and $\mathcal{O}(\varepsilon^{-2}(k+\log(1/\delta)))$ samples suffice for a $k$-dimensional target subspace. Finally, we investigate the use of such sketches within the Nystr\"{o}m++ framework. We show that the resulting estimator can achieve the desired $\mathcal{O}(\varepsilon^{-1})$ sample complexity under an additional spectral-tail condition. These results provide clarififcation on both the potential and the limitations of random tensor train vectors in stochastic trace estimation.

04.
arXiv (CS.AI) 2026-06-16

LLM-as-Code Agentic Programming for Agent Harness

arXiv:2606.15874v1 Announce Type: new Abstract: Every major LLM agent framework gives the LLM the role of orchestrator; the model decides what to do next, when to call tools, and when to stop. We argue that token explosion, control-flow hallucination, and unreliable completion are not implementation bugs but architectural consequences of assigning the deterministic work of looping, branching, and sequencing to a probabilistic system. A better prompt or a stronger model cannot guarantee the reliability of the LLM agent. We therefore propose Agentic Programming, in which the program governs all control flow, and the LLM is itself part of it, an adaptive component we call LLM-as-Code and invoke only where a task calls for reasoning or generation. Within each call the model keeps full flexibility, but it cannot alter the program's execution path. With control in the program, the LLM's context is built from the execution history's call tree and forms a directed acyclic graph (DAG). Each call's context length is then determined by its call depth rather than by accumulation over steps. A case study of computer-use agents shows that the design is practical, not just a theoretical stance, substantially improving the stability of long visual operation sequences.

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

Automated Standardization of Legacy Biomedical Metadata Using an Ontology-Constrained LLM Agent

arXiv:2604.08552v2 Announce Type: replace-cross Abstract: Scientific metadata are often incomplete and noncompliant with community standards, limiting dataset findability, interoperability, and reuse. Even when standard metadata reporting guidelines exist, they typically lack machine-actionable representations. Producing FAIR datasets requires encoding metadata standards as machine-actionable templates with rich field specifications and precise value constraints. Recent work has shown that LLMs guided by field names and ontology constraints can improve metadata standardization, but these approaches treat constraints as static text prompts, relying on the model's training knowledge alone. We present an LLM-based metadata standardization system that queries standard reporting guidelines and authoritative biomedical terminology services in real time to retrieve canonically correct standards on demand. We evaluate this approach on 839 legacy metadata records from the Human BioMolecular Atlas Program (HuBMAP) using an expert-curated gold standard for exact-match assessment. Our evaluation shows that augmenting the LLM with real-time tool access consistently improves prediction accuracy over the LLM alone across both ontology-constrained and non-ontology-constrained fields, demonstrating a practical approach to automated standardization of biomedical metadata.

06.
medRxiv (Medicine) 2026-06-16

Adherence to Red Reflex and Vision Screening Recommendations: A Deep Dive into Primary Care Implementation Gaps

Introduction: Early childhood vision screening is critical for detecting amblyopia and other vision-threatening conditions. Despite screening recommendations during well-child visits, rates remain low. Red reflex assessment is recommended to identify serious ocular pathology, yet its use in primary care is not well described. We examined rates and drivers of vision screening in pediatric primary care. Methods: We conducted a retrospective review of electronic health records for children 3 to 5 years attending well-child visits in 2022 in one of three representative primary care clinics within a university health system. Outcomes were documented red reflex and functional vision tests. We evaluated associations with patient demographics and clinic site using multivariable logistic regression Results: Among 1,003 visits, 21.1% (n=212) had a documented red reflex assessment, and 60.8% (n=610) a functional vision test. Younger children (ages 3 and 4 vs. 5 years) had higher odds of red reflex assessment [adjusted odds ratio (aOR) 9.00 and 8.64], and lower odds of a functional vision (aOR 0.47 and 0.59) test. Females had higher odds of red reflex assessment (aOR 1.53). Other/Multiracial children had lower odds of red reflex assessment than Non-Hispanic White children (aOR 0.48). Screening rates varied significantly by clinic site Conclusions: Visual function and red reflex assessment are inconsistently performed in pediatric primary care, with particularly low rates of red reflex documentation. Screening rates varied between clinics and were affected by age. These findings highlight missed opportunities for early detection of vision-threatening conditions and identify targets for improving adherence to pediatric vision screening recommendations

07.
arXiv (quant-ph) 2026-06-19

Quantum Algebraic Diversity: Single-Copy Density Matrix Estimation via Group-Structured Measurements

arXiv:2604.03725v3 Announce Type: replace Abstract: We extend the algebraic diversity (AD) framework from classical signal processing to quantum measurement theory. The Quantum Algebraic Diversity (QAD) Theorem establishes that a group-structured positive operator-valued measure (POVM) applied to a single copy of a quantum state produces a full-rank, group-averaged density matrix estimator whose eigenbasis and eigenvalue ordering track those of the true density matrix, with a bias toward the symmetrized state, analogous to the classical recovery of covariance eigenstructure from a single observation. We establish a Classical-Quantum Duality Map connecting classical covariance estimation to quantum state tomography, and an Optimality Inheritance Theorem showing that classical group optimality transfers to quantum settings via the Born map within the group-averaged family. SIC-POVMs are identified as AD with the Heisenberg-Weyl group and mutually unbiased bases as AD with the Clifford group, revealing the hierarchy $\mathrm{HW}(d) \subseteq \mathcal{C}(d) \subseteq S_d$ that mirrors the classical $\mathbb{Z}_M \subseteq G_{\min} \subseteq S_M$. The double-commutator eigenvalue theorem gives polynomial-time adaptive POVM selection. A worked qubit example shows the group-averaged estimator from a single computational-basis measurement, averaged over a matched $\mathbb{Z}_2$ group, reaching fidelity 0.99 where standard single-basis tomography gives a rank-1 estimate of fidelity 0.80. Monte Carlo simulations for $d = 2$ to $13$ confirm fidelity above 0.90 from a single outcome while standard fidelity degrades as $\sim 1/d$. The growing ratio reflects collapse of the rank-1 standard estimator, not fewer copies per parameter: the biased single-copy estimator reduces the number of distinct measurement settings, not the per-parameter sampling cost, and a genuine copy reduction holds only under exact symmetry.

08.
arXiv (CS.AI) 2026-06-18

Pareto Q-Learning with Reward Machines

arXiv:2606.19134v1 Announce Type: cross Abstract: We present Pareto Q-Learning with Reward Machines (PQLRM), a multi-objective reinforcement learning algorithm for tasks whose reward structure is specified by a set of reward machines (RMs). PQLRM combines Pareto Q-Learning (PQL), which maintains sets of vector-valued Q-estimates to approximate the Pareto front, with enhancements from Q-Learning with Reward Machines (QRM), which exploits the factored automaton structure of the reward signal. This yields a multi-policy algorithm that remains sample-efficient under non-Markovian, RM-encoded rewards. Experimental trials show that PQLRM converges faster than a naive PQL baseline applied to the cross-product MDP and can synthesize Pareto-optimal policies that QRM cannot.

09.
arXiv (CS.AI) 2026-06-16

Evolutionary Dynamics of Cooperation in Next-Generation LLM Agent Systems: A Cross-Provider Empirical Extension

arXiv:2605.29874v2 Announce Type: replace-cross Abstract: Do next-generation LLM agents inherit the cooperative biases documented in their predecessors, or does scale and provider diversity reshape equilibrium behaviour in competitive multi-agent settings? Willis et al. established a benchmark for this question using evolutionary game theory and the Iterated Prisoner's Dilemma (IPD), finding consistent cooperative biases in ChatGPT-4o and Claude 3.5 Sonnet. We extend this benchmark to four frontier models released in 2025-2026 - Claude Sonnet 4.6, Gemini 2.5 Flash, Gemini 3.1 Pro, and GPT-5.4 Mini - applying the identical protocol across three prompting styles (Default, Prose, Self-Refine) and four population compositions (balanced and biased, with and without noise). Cooperative bias persists across providers (H1): ten of twelve model-prompt combinations favour cooperative equilibria in balanced noiseless conditions. Cross-provider divergence is substantial (H3): Gemini 2.5 Flash reaches up to 77% aggressive equilibria under biased conditions, while GPT-5.4 Mini reaches 70% cooperative equilibria under Self-Refine. Support for aggressive capability parity is partial (H2): Self-Refine raises ICD in all models and Gemini 3.1 Pro Refine achieves the highest ICD in the dataset (0.925), but Default and Prose prompts show no systematic narrowing. Evidence on noise robustness is directionally positive but not robustly confirmed (H4): with n=500 Moran iterations per condition, average noise sensitivity is about 6 percentage points for Claude Sonnet 4.6 versus 13 pp for Claude 3.5 Sonnet, but this cross-study gap is not statistically significant once the predecessor's unreported sampling error is propagated. Provider identity, rather than model generation, is the strongest correlate of equilibrium outcomes; noise remains a universal challenge regardless of model size or vintage.

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

Scalar-Stepsize Nonuniform Monte Carlo Optimistic Policy Iteration: A Certified Counterexample

arXiv:2606.15978v1 Announce Type: new Abstract: Tsitsiklis proved convergence of Monte Carlo optimistic policy iteration under a uniform update structure and identified nonuniform update frequencies as a delicate obstruction. We give a certified negative answer for the natural scalar-stepsize, unnormalized asynchronous state-value recursion with fixed nonuniform state-selection probabilities. In a three-state, two-action discounted MDP, the nonuniform update frequencies induce a diagonally scaled greedy-policy mean field with a certified nonconstant attracting hybrid periodic orbit. With a bounded unbiased geometric-horizon estimator and Robbins–Monro stepsizes, the original stochastic recursion remains trapped near the cycle with positive probability and therefore fails to converge. The example pinpoints a geometric obstruction: uniform sampling gives radial residual contraction, whereas scalar nonuniform sampling anisotropically distorts the residual dynamics and can generate switched attracting cycles.

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

TrajGenAgent: A Hierarchical LLM Agent for Human Mobility Trajectory Generation

arXiv:2606.12657v1 Announce Type: new Abstract: Human mobility data is important for transportation, urban planning, and epidemic control, but large-scale trajectory collection is often costly and privacy-constrained, motivating realistic synthetic trajectory generation. Existing LLM-based generators typically rely on either prompt engineering, which preserves zero-shot reasoning but lacks fine-grained spatiotemporal grounding, or trajectory-level fine-tuning, which improves statistical precision but incurs substantial computational cost and may weaken general reasoning. We propose TrajGenAgent, a semantic-aware hierarchical LLM-agent framework for human mobility trajectory generation without model fine-tuning. TrajGenAgent uses a two-stage orchestrator-worker design: an LLM first synthesizes an individual- and weekday-conditioned activity chain from historical evidence via in-context learning, and a deterministic workflow then grounds each activity into a complete visit using personalized POI retrieval, distance-aware location selection, kinematics-aware travel-time propagation, and LLM-based duration estimation. To evaluate realism beyond aggregate spatiotemporal statistics, we introduce an anomaly-detection-based evaluation framework using two complementary detectors to assess behavioral and semantic plausibility. Experiments on benchmark and large-scale simulation datasets show that TrajGenAgent improves spatiotemporal fidelity, semantic coherence, and individual-specific behavioral realism over representative neural and LLM-based baselines, while avoiding parameter updates.

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

Integral Formulation of QENDy for Robust Nonlinear System Identification

arXiv:2606.11629v1 Announce Type: cross Abstract: This manuscript proposes an integral formulation of the newly defined quadratic embedding method for identifying nonlinear systems (QENDy). In the original algorithm, trajectory data points along with their time derivatives are used. Methods for calculating time derivatives make the algorithm sensitive to noise. Our integral formulation does not use the time derivatives. This results in a more robust method to learn the dynamics.

13.
arXiv (CS.CL) 2026-06-11

I Understand How You Feel: Enhancing Deeper Emotional Support Through Multilingual Emotional Validation in Dialogue System

Emotional validation - explicitly acknowledging that a user's feelings make sense - has proven therapeutic value but has received little computational attention. Emotional validation in dialogue systems can be decomposed into (i) validating response identification, (ii) validation timing detection, and (iii) validating response generation. To support research on all three subtasks, we release M-EDESConv, a 120k English-Japanese multilingual corpus created through hybrid manual and automatic annotation, and M-TESC, a multilingual spoken-dialogue test set. For timing detection, we propose MEGUMI, a Multilingual Emotion-aware Gated Unit for Mutual Integration, that fuses frozen XLM-RoBERTa semantics with language-specific emotion encoders via cross-modal attention and gated fusion. MEGUMI shows superior performance on both the M-EDESConv and M-TESC datasets, both objectively and subjectively. Finally, our EmoValidBench benchmarks of GPT-4.1 Nano and Llama-3.1 8B indicate that current LLMs generate contextually similar and diverse validating responses, but emotional understanding remains a major area for improvement. Project page: https://github.com/zihaurpang/Multilingual-Emotional-Validation

14.
arXiv (CS.CV) 2026-06-15

CineOrchestra: Unified Entity-Centric Conditioning for Cinematic Video Generation

Cinematic video depicts multiple subjects acting or interacting at specific moments, captured with deliberate camera movement, and stitched together by shot transitions. Together, these elements demand a level of fine-grained control beyond current text-to-video models. Existing work addresses each axis in isolation: multi-subject personalization, temporal control, multi-shot synthesis, or camera control; no prior framework jointly integrates all four. We present CineOrchestra, a unified video diffusion model that controls subjects, events, cameras, and shot transitions simultaneously. Our key insight is that these heterogeneous cinematic elements share a fundamental structure: each is an entity acting over a specific temporal interval, which can therefore all be expressed through one shared structure of entity-centric conditioning primitives, augmented with reference images for visual entities. This formulation reduces the architectural challenge to a single positional encoding problem, which we solve with two parameter-free coordinated rotary embeddings: (a) an interval-sampled temporal RoPE that yields consistent attention behavior across events of dramatically varying duration, and (b) a 2D entity-temporal cross-attention RoPE that disambiguates per-entity conditions and routes each to its corresponding spatiotemporal region. On two new benchmarks, CineOrchestra outperforms six per-axis specialists on dense caption following and shot-transition timing, with consistent gains in a pairwise user study and component ablations.

15.
arXiv (quant-ph) 2026-06-15

Quantum sensing through bosonic-fermionic Bell-state transitions in two-photon interference

arXiv:2606.14408v1 Announce Type: new Abstract: Hong-Ou-Mandel (HOM) interference has become a central resource for quantum sensing and metrology owing to its sensitivity to temporal delay and photon indistinguishability. However, existing HOM-based sensing schemes generally rely on inserting a sample into one arm of the interferometer, making the measurement vulnerable to optical loss, alignment instability, and bandwidth-dependent distortion of the interference profile. Here, we demonstrate a symmetry-controlled quantum sensing scheme based on continuous transitions between symmetric (bosonic-like) and antisymmetric (fermionic-like) Bell states in two-photon interference. By imprinting a geometric phase onto the classical pump beam and transferring it to polarization-entangled photons generated via spontaneous parametric down-conversion, we coherently tune the exchange symmetry of the entangled state without altering the temporal or spectral indistinguishability of the photons. The HOM response evolves continuously from bunching to antibunching with a sine square phase dependence, producing a coincidence modulation of approximately 10 * 10^4 counts s^-1 counts/s. In contrast to conventional HOM sensing, the phase-modulation linewidth remains fixed at pi/2, independent of photon bandwidth. Using a birefringent crystal placed directly in the pump beam, we measure thermo-dispersive birefringence with a resolution of the order of 10^{-6} over a broad temperature range. Our results establish exchange symmetry as a controllable resource for robust quantum sensing and symmetry-engineered photonic quantum information processing.

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

Photon: Federated LLM Pre-Training

arXiv:2411.02908v2 Announce Type: replace Abstract: Scaling large language models (LLMs) demands extensive data and computing resources, which are traditionally constrained to data centers by the high-bandwidth requirements of distributed training. Low-bandwidth methods like federated learning (FL) could enable collaborative training of larger models across weakly-connected GPUs if they can effectively be used for pre-training. To achieve this, we introduce Photon, the first complete system for federated end-to-end LLM training, leveraging cross-silo FL for global-scale training with minimal communication overheads. Using Photon, we train the first federated family of decoder-only LLMs from scratch. We show that: (1) Photon can train model sizes up to 7B in a federated fashion while reaching an even better perplexity than centralized pre-training; (2) Photon model training time decreases with available compute, achieving a similar compute-time trade-off to centralized; and (3) Photon outperforms the wall-time of baseline distributed training methods by 35% via communicating 64x-512xless. Our proposal is robust to data heterogeneity and converges twice as fast as previous methods like DiLoCo. This surprising data efficiency stems from a unique approach combining small client batch sizes with extremely high learning rates, enabled by federated averaging's robustness to hyperparameters. Photon thus represents the first economical system for global internet-wide LLM pre-training.

17.
arXiv (CS.CL) 2026-06-19

LedgerAgent: Structured State for Policy-Adherent Tool-Calling Agents

Policy-adherent tool-calling agents in customer-service domains must maintain task states across turns while calling tools and obeying domain policies. Task states consist of relevant facts, identifiers, constraints, and conditions observed through user interaction and tool calls. In standard agents, task states are not represented separately. Observations, tool returns, and policy instructions are placed in the prompt, leaving agents to reconstruct the relevant states from the prompt each time they decide what to do next. This design makes state management implicit, creating two common failure modes. An agent may retrieve the right facts but later ground its decision in stale, missing, or incorrect information; and a syntactically valid tool call may still violate a domain policy that depends on the current task state. We introduce \textsc{LedgerAgent}, an inference-time method for tool-calling agents that maintains observed task states in a separate ledger and renders the states into the prompt. The ledger is also used to check state-dependent policy constraints before environment-changing tool calls are executed, blocking policy violations. Across four customer-service domains and a mixed panel of open- and closed-weight models, \textsc{LedgerAgent} improves average pass\textasciicircum{}k over a standard prompt-based tool-calling approach, with the largest gains under stricter multi-trial consistency metrics.

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

STRIDE: Strategic Trajectory Reasoning via Discriminative Estimation for Verifiable Reinforcement Learning

arXiv:2606.15866v1 Announce Type: new Abstract: Reinforcement Learning with Verifiable Rewards (RLVR) has become an effective post-training paradigm for improving the reasoning abilities of large language models. However, existing RLVR methods typically rely on final-answer correctness to assign trajectory-level rewards, providing sparse supervision and treating all tokens uniformly regardless of their actual contribution to reasoning. Although recent studies introduce intermediate signals such as process rewards, high-entropy tokens, and semantic uncertainty, these signals are often not inherently verifiable and may fail to distinguish beneficial strategic patterns from harmful ones. To address this limitation, we propose STRIDE (Strategic Trajectory Reasoning with Discriminative Estimation), a fine-grained RLVR framework that derives strategic reasoning supervision from verifiable outcomes. STRIDE contrasts successful and failed trajectories within each response group to estimate the outcome-discriminative preference of each $n$-gram strategic pattern, and further combines this signal with reasoning saliency entropy to identify decision-relevant strategic patterns. These patterns are assigned differentiated advantage values during RL optimization, enabling more precise credit assignment while preserving the verifiability of RLVR. Extensive experiments demonstrate that STRIDE consistently improves reasoning performance across diverse models, tasks, and extended settings, including VLMs and agent-based systems.

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

VISUALSKILL: Multimodal Skills for Computer-Use Agents

Computer-use agents (CUAs) approach human-level performance on standardised benchmarks but still struggle on long-horizon tasks and unseen software. Existing skill libraries address this with reusable skills, but represent the skill artifact as text only, despite the visual nature of GUI interaction. We propose VISUALSKILL: a hierarchical multimodal skill, tailored to each target application and organised as a central index over per-topic files, which the agent consumes through a load_topic MCP tool that fetches the relevant topic's text and figures on demand. We construct each skill with a two-stage pipeline that combines authored documentation with live-application UI exploration. On two CUA benchmarks, CUA-World and OSExpert-Eval, a Claude Code CLI agent backed by Claude Opus 4.6 reaches an average score of 0.456 with VISUALSKILL, a +15.3 point absolute lift over the no-skill baseline (0.303). Against a matched text-only skill that is generated from the same source content and differs from VISUALSKILL only in modality, VISUALSKILL yields a further +8.3 point absolute gain over the matched text-only skill (0.373 vs. 0.456), providing direct evidence that retaining visual figures in the skill artifact, rather than verbalizing them away, helps the agent both identify UI elements and verify workflow state after each action. Our code is available at https://github.com/XMHZZ2018/VisualSkills.

20.
arXiv (quant-ph) 2026-06-17

A polynomial-time approximation scheme for minimum-weight decoding of topological codes

arXiv:2606.18145v1 Announce Type: new Abstract: Two-dimensional topological translationally invariant (2D TTI) stabilizer codes lie at the heart of fault-tolerant quantum computation, but using them requires solving the decoding problem. Minimum-weight decoding of these codes was recently shown to be NP-hard, even in basic settings, such as the color code with Pauli $Z$ errors and the toric code with Pauli $X$, $Y$ and $Z$ errors. Here, we prove that minimum-weight decoding of 2D TTI codes nonetheless admits a polynomial-time approximation scheme (PTAS), i.e., for any constant $\varepsilon>0$, a recovery operator of weight within a multiplicative factor of $1+\varepsilon$ of the minimum can be found in polynomial time. Our approach builds on Arora's PTAS for Euclidean problems, such as the traveling salesman problem, and applies when decoding can be cast in terms of point-like excitations connected by string-like errors. It therefore extends beyond two dimensions, covering certain higher-dimensional topological codes and quantum memories, including the toric code with phenomenological or circuit-level noise.

21.
arXiv (CS.LG) 2026-06-18

Enhanced Graph Neural Networks using K-Hop Gaussian Diffusion

arXiv:2606.18317v1 Announce Type: new Abstract: Most graph neural network (GNN) cores rely on graph convolutions, typically implemented as message passing between direct (single-hop) neighbors. In many real-world graphs, edges can be noisy or poorly defined, limiting information propagation to local neighborhoods. Existing diffusion kernels, such as Personalized PageRank (PPR) and Heat Kernel, alleviate this issue through global propagation, but still struggle with complex local structures and distant node noise. To address these limitations, we propose a K-Hop Gaussian (KHG) diffusion kernel as a preprocessing module for graph data. KHG introduces multi-hop diffusion with Gaussian weighting for remote nodes, balancing local and global information propagation before applying standard GNNs. Experiments on multiple benchmark datasets demonstrate that KHG significantly outperforms traditional message-passing GNNs, as well as PPR and Heat Kernel diffusion, particularly in noisy or structurally complex graphs.

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

Rethinking the Role of Efficient Attention in Hybrid Architectures

Modern language models increasingly adopt hybrid architectures that combine full attention with efficient attention modules, such as sliding-window attention (SWA) and recurrent sequence mixers. However, how these efficient modules shape model capabilities remains poorly understood. To address this gap, we conduct a systematic analysis across hybrid architectures from three perspectives: scaling behavior, mechanism analysis, and architecture design. First, from a scaling perspective, we find that efficient-attention design primarily affects how fast long-context capability emerges, while different hybrids eventually converge to comparable long-context performance under sufficient training. Second, mechanistically, we show that long-range retrieval is mainly carried by full attention, whereas efficient attention shapes its optimization trajectory. This explains a counter-intuitive phenomenon we call Large-Window Laziness: larger SWA windows can delay the formation of retrieval heads in full-attention layers. Third, guided by this mechanism, we show that applying NoPE to only the full-attention layers of a small-window SWA hybrid substantially improves long-context performance with negligible impact on short-context performance.

23.
arXiv (math.PR) 2026-06-19

An alternative approach to well-posedness of McKean-Vlasov equations arising in Consensus-Based Optimization

arXiv:2512.19446v4 Announce Type: replace-cross Abstract: In this work we study the mean-field description of Consensus-Based Optimization (CBO), a derivative-free particle optimization method. Such a description is provided by a non-local SDE of McKean-Vlasov type, whose fields lack of global Lipschitz continuity. We propose a novel approach to prove the well-posedness of the mean-field CBO equation based on a truncation argument. The latter is performed through the introduction of a cut-off function, defined on the space of probability measures, acting on the fields. This procedure allows us to study the well-posedness problem in the classical framework of Sznitman. Through this argument, we recover the established result on the existence of strong solutions, and we extend the class of solutions for which pathwise uniqueness holds.

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

Classification of Astronomical Spectra Using PCA-Compressed Flux and Inverse-Variance Features

arXiv:2606.13978v1 Announce Type: cross Abstract: This paper evaluates a signal-processing and supervised-learning pipeline for classifying SDSS DR17 astronomical spectra into stars, galaxies, and quasars. Each spectrum is represented by its measured flux and inverse-variance information, combining spectral shape with a wavelength-dependent reliability profile. After resampling onto a common logarithmic wavelength grid, the flux and inverse-variance vectors are standardized and separately compressed using principal component analysis. The resulting components are concatenated and used to train several classifiers. The best performance was obtained with the LightGBM gradient-boosting classifier, reaching $94.6\%$ accuracy and $92.1\%$ balanced accuracy on the test set.

25.
arXiv (CS.AI) 2026-06-16

VGPT-RSI for RH-Adjacent Formal Progress: Boundary Certificates, Verified Finite Lagarias Inequalities, and Explicit Failure Localization

arXiv:2606.15096v1 Announce Type: new Abstract: The Riemann Hypothesis remains one of the central unsolved problems in mathematics. Rather than claiming proof, we investigate whether a verifiable AI-assisted reasoning system can produce reliable, formally checked partial progress while explicitly identifying the remaining mathematical obstructions. We apply the Verifiable Growing Physical Transformer with Recursive Self-Improvement (VGPT-RSI) to two RH-adjacent certification tasks. First, we construct and verify a finite RH-boundary certificate for inequality on a parameterized safe lower curve over a region. The numerical boundary curve is converted into a certificate-backed lower curve, audited using outward-rounded interval arithmetic and Arb/FLINT ball arithmetic, and then checked in Rocq/CoqInterval for the parameterized theorem. Second, we initiate a formal Lagarias-route certificate. Lagarias criterion states that RH is equivalent to the global inequality. We formalize the finite quantity and produce a Coq-checked finite certificate. The final system identifies the exact unresolved mathematical bottlenecks: formalizing the Lagarias equivalence, proving the global tail theorem beyond any finite cutoff, and potentially reducing counterexamples to colossally abundant or related extremal integers. These results demonstrate that VGPT-RSI can produce certified RH-adjacent formal progress, organize proof dependencies, and avoid overclaiming when the remaining obstruction is genuinely mathematical.