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

Detecting Functional Memorization in Code Language Models

Large language models (LLMs) are increasingly used to generate code at scale. Meanwhile, prior work has investigated whether training data may be recoverable from model outputs, by auditing the textual overlap between training examples and model generations. Code, however, can be functionally equivalent while textually dissimilar. In this work, we study functional memorization: extraction of functional logic beyond what verbatim metrics detect. We construct a counterfactual setup for Olmo-3-32B, comparing a midtrained model (exposed to target code) against a pretrained reference (not exposed). We prompt both models with Python function signatures and measure both textual and functional similarity (i.e., LLM-as-a-judge, execution-based). Our results show clear evidence of functional memorization, highlighting the need for auditing metrics that go beyond textual overlap.

02.
arXiv (CS.AI) 2026-06-15

TRACE: Trajectory-Routed Causal Memory for Delayed-Evidence Visuomotor Imitation

arXiv:2606.14551v1 Announce Type: cross Abstract: Robots under autonomous operation may require decisions based on evidence that is no longer visible. We study delayed-evidence tasks, where an early cue disappears before a later decision point, so visually similar observations can require different actions. In these settings, the current observation is not a sufficient state for control. We introduce TRAjectory-routed Causal Evidence (TRACE), a memory framework for visuomotor imitation policies. TRACE stores task-relevant visual and robot-state evidence, such as object identity, target choice, or route-dependent state, in a fixed-size latent memory that remains bounded over long episodes. Instead of indexing memory by raw time or manually provided task labels, TRACE uses path signatures: compact, order-sensitive features of the executed robot-state trajectory. These signatures do not store the visual cue itself; rather, they provide trajectory-conditioned keys for writing and retrieving the evidence stored when the cue was visible. When the robot later reaches an ambiguous observation, the policy conditions on TRACE memory to recover the missing context and choose the correct branch. TRACE attaches through lightweight adapters to policies, without changing the policy backbone, action head, or imitation objective. Across real-world long-horizon manipulation tasks with visually ambiguous branch points, TRACE improves branch selection and task success over alternative baselines, including short-history and recurrent memory. Project page: https://jeong-zju.github.io/trace

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

Sumi: Open Uniform Diffusion Language Model from Scratch

Diffusion models have become a promising alternative to autoregressive models. Among these, uniform diffusion language models (UDLMs) permit any token to be updated at any step, in principle enabling more flexible generation. However, no UDLM has yet been pretrained from scratch at both large parameter scale and large token budget. Both autoregressive modeling and masked diffusion modeling already have capable models at scale that the community can study and build on; uniform diffusion has none. A scratch-pretrained UDLM at scale would provide a clean reference point for studying scaling behavior, generation dynamics, controllability, and trade-offs against established autoregressive and masked diffusion models. To this end, we introduce Sumi ("ink" in Japanese), a fully open 7B uniform diffusion language model pretrained from scratch on 1.5T tokens. Sumi performs competitively with autoregressive models trained at comparable token budgets on knowledge, reasoning, and coding benchmarks, while under-performing on commonsense benchmarks, where our education-heavy data mixture is a likely contributor. We release our model weights, checkpoints, and full training recipe, including a complete specification of the data mixture over publicly available corpora. We hope this release enables the community to study native uniform diffusion at scale and catalyzes work on its as-yet poorly understood aspects.

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

RSRCC: A Remote Sensing Regional Change Comprehension Benchmark Constructed via Retrieval-Augmented Best-of-N Ranking

Traditional change detection identifies where changes occur, but does not explain what changed in natural language. Existing remote sensing change captioning datasets typically describe overall image-level differences, leaving fine-grained localized semantic reasoning largely unexplored. To close this gap, we present RSRCC, a new benchmark for remote sensing change question-answering containing 126k questions, split into 87k training, 17.1k validation, and 22k test instances. Unlike prior datasets, RSRCC is built around localized, change-specific questions that require reasoning about a particular semantic change. To the best of our knowledge, this is the first remote sensing change question-answering benchmark designed explicitly for such fine-grained reasoning-based supervision. To construct RSRCC, we introduce a hierarchical semi-supervised curation pipeline that uses Best-of-N ranking as a critical final ambiguity-resolution stage. First, candidate change regions are extracted from semantic segmentation masks, then initially screened using an image-text embedding model, and finally validated through retrieval-augmented vision-language curation with Best-of-N ranking. This process enables scalable filtering of noisy and ambiguous candidates while preserving semantically meaningful changes. The dataset is available at https://huggingface.co/datasets/google/RSRCC.

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

Exploding and vanishing gradients in deep neural networks: the effect of residual connections

arXiv:2606.17013v1 Announce Type: cross Abstract: The well known phenomenon of exploding and vanishing gradients in deep neural networks is analyzed using multiplicative ergodic theory. The effect of adding a residual connection is explained in this context. Specifically, a characterization of Liapunov exponents due to Furstenberg and Kifer is exploited in order to make a precise statement about the Liapunov spectrum and the effect of residual connections on it.

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

Confidence Calibration for Multimodal LLMs: An Empirical Study through Medical VQA

arXiv:2606.19950v1 Announce Type: cross Abstract: Multimodal Large Language Models (MLLMs) show great potential in medical tasks, but their elicited confidence often misaligns with actual accuracy, potentially leading to misdiagnosis or overlooking correct advice. This study presents the first comprehensive analysis of the relationship between accuracy and confidence in medical MLLMs. It proposes a novel method that combines Multi-Strategy Fusion-Based Interrogation (MS-FBI) with auxiliary expert LLM assessment, aiming to improve confidence calibration in Medical Visual Question Answering (VQA). Experiments demonstrate that our method reduces the Expected Calibration Error (ECE) by an average of 40\% across three Medical VQA datasets, significantly enhancing MLLMs' reliability. The findings highlight the importance of domain-specific calibration for MLLMs in healthcare, offering a more trustworthy solution for AI-assisted diagnosis.

07.
arXiv (quant-ph) 2026-06-15

Merged amplitude encoding for Chebyshev quantum Kolmogorov–Arnold networks: trading qubits for circuit executions

arXiv:2603.02818v3 Announce Type: replace Abstract: Quantum Kolmogorov–Arnold networks based on Chebyshev polynomials (CCQKAN) evaluate each edge activation function as a quantum inner product, creating a trade-off between qubit count and the number of circuit executions per forward pass. We introduce merged amplitude encoding, a technique that packs the element-wise products of all $n$ input-edge vectors for a given output node into a single amplitude state, reducing circuit executions by a factor of $n$ at a cost of only 1–2 additional qubits relative to the sequential baseline. The merged and original circuits compute the same mathematical quantity exactly; the open question is whether they remain equally trainable within a gradient-based optimization loop. We address this question through numerical experiments on 10 network configurations under ideal, finite-shot, and noisy simulation conditions, comparing original, parameter-transferred, and independently initialized merged circuits over 16 random seeds. Wilcoxon signed-rank tests show no significant difference between the independently initialized merged circuit and the original ($p > 0.05$ in 28 of 30 comparisons), while parameter transfer yields significantly lower loss under ideal conditions ($p < 0.001$ in 9 of 10 configurations). On 10-class digit classification with the $8\times8$ MNIST dataset using a one-vs-all strategy, original and merged circuits achieve comparable test accuracies of 53–78\% with no significant difference in any configuration. These results provide empirical evidence that merged amplitude encoding preserves trainability under the simulation conditions tested.

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

Phantoms and Disclosures: a Causal Framework for Auditing Synthetic Data

arXiv:2606.16952v1 Announce Type: cross Abstract: The rapid adoption of generative AI and Large Language Models (LLMs) has spurred interest in synthetic data as a privacy-preserving alternative to sensitive real-world datasets. However, generating high-utility synthetic data often carries the risk of memorizing and regurgitating private information from the training corpus. In this work, we present a customizable empirical auditing framework designed to detect and explain such data disclosures. Our framework introduces a mechanism to distinguish between "true disclosures"-where the system directly reproduces a user's information-and "phantom disclosures''-where the system incidentally generates a user's data. By partitioning input data into training and holdout sets and applying rigorous statistical hypothesis testing, we determine if observed disclosures are consistent with strict privacy baselines, such as zero-learning or specific Differential Privacy (DP) bounds. Crucially, this approach requires no model access, no canary insertion, and no reference model training -only the synthetic output and a held-out control set. We demonstrate that this framework effectively functions as a membership inference attack, providing empirical lower bounds on privacy leakage that are tighter than prior data-based auditing methods. Our approach is model-agnostic, applies to any synthetic data generation mechanism, and requires orders of magnitude fewer computational resources than shadow-model or canary-based alternatives.

09.
bioRxiv (Bioinfo) 2026-06-17

Posterior-calibrated multimodal motor states reveal longitudinal and imaging-associated heterogeneity in Parkinson's disease

Parkinson's disease (PD) motor heterogeneity is commonly summarized by hard subtype labels, although clinical states vary longitudinally, severity can dominate unsupervised structure, and model uncertainty is rarely calibrated. We developed a posterior and refit-stability calibrated multimodal motor state framework that assigns probabilistic MDS-UPDRS-III motor states, aggregates them at the patient level, separates global burden from residual tremor-axial profile, and tests whether imaging can recover the resulting posterior distribution. In 29,366 aligned PPMI motor-posterior visits spanning 4,773 participant identifiers, patient-level state families were stable on average (modal-family fraction 0.925; 95% CI 0.921 - 0.930), but 25.5% of patients transitioned state over follow-up (95% CI 24.1 - 26.7%). PD-only cohort definitions produced smaller denominators and are reported as sensitivity cohorts with rerun calibration and imaging-posterior checks. Severity and covariates explained substantial motor-domain variance, especially bradykinesia (rsecond=0.850), but residual profile modeling retained five active components across total-severity, principal-component, leave-one-domain, non-target-burden, and clinical-only severity axes. Refit-stability calibration with 250 patient-blocked bootstrap refits showed high nominal posterior confidence (0.989) but lower empirical label consistency (0.849), quantifying overconfidence rather than hiding it. Patient-held-out temporal modeling predicted future axial burden (best XGBoost rsecond=0.605) and future state transition (XGBoost AUC=0.830; 95% CI 0.822 - 0.837). DaTSCAN plus FreeSurfer ROI features predicted patient-level soft motor posterior vectors (RF jsd=0.209; 95% CI 0.199 - 0.220; macro-AUROC=0.692), while severity/demographic-adjusted imaging features further improved soft posterior recovery (jsd=0.188). BioFIND transfer reproduced clinically meaningful endpoint gradients after state assignment in 225 external patients, supporting external face validity rather than definitive transportability. These results support PD motor phenotypic states as calibrated, dynamic, clinically interpretable profiles with convergent imaging associations, not as definitive biological subtypes.

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

DragMesh-2: Physically Plausible Dexterous Hand-Object Interaction with Articulated Objects

Dexterous interaction with articulated objects is important for household, assistive, and humanoid manipulation, where multi-finger hands can provide compliant contact patterns beyond parallel-jaw grasping. However, articulated-object manipulation differs from static-object manipulation: the target part cannot be directly actuated, and its motion must emerge through sustained physical hand–handle contact. This makes the transition from object-centric articulated generation to hand-driven dexterous hand–object interaction non-trivial, since geometric trajectory replay or open-loop execution does not model the contact dynamics required to move the articulated part. Moreover, policies trained only for task completion under fixed dynamics can overfit nominal contact loads, especially without tactile or force feedback, and may degrade when the contact load changes. To address these challenges, we present DragMesh-2, a contact-driven framework for dexterous interaction with articulated objects that extends articulated interaction from object-centric generation to hand-driven dexterous hand–object interaction, where articulated motion must arise through physical contact. We further propose PICA, a physically informed contact-aware training mechanism that injects physical signals into policy learning without tactile or force feedback, improving robustness and task success under changing contact loads. Finally, we conduct systematic evaluation across multiple damping conditions and articulated-object categories to study robustness under contact-load variation, and provide a pure-geometry dexterous interaction resource to support future loco-manipulation and humanoid hand–object interaction research. Across seven GAPartNet objects, DragMesh-2 achieves stronger robustness under contact-load variation than the compared methods while maintaining high task success across damping conditions.

11.
medRxiv (Medicine) 2026-06-15

Active commuting, anxiety symptoms and mental wellbeing: a dose-response study

Climate change draws attention to the planetary health perspective in sport and exercise sciences, that is, to physical activity that supports both human wellbeing and environmental sustainability. Active commuting is a sustainable form of physical activity with well-established somatic health benefits. However, more knowledge is needed on its relationship with mental health. We examined dose-response associations between active commuting, anxiety symptoms, and mental wellbeing among Finnish adults, and whether green commuting environment moderates these relationships. We used data from the cross-sectional Environment and Health Survey collected in June-September 2023 in the ten largest cities in Finland. Employed participants with data on anxiety symptoms (Generalized Anxiety Disorder-7, GAD-7), mental wellbeing (World Health Organization-Five Well-Being Index, WHO-5), commuting profile over a year (mode, frequency, distance, and perceived greenness along the commute route), and sociodemographic and lifestyle factors were included (n=1,672; mean age 45.3 years; 53.8% women). Active commuting was defined as travelling the entire commute by walking or cycling (including e-biking) that was converted into approximated annual km/week and MET-h/week. We used linear and logistic regression with restricted cubic splines to evaluate dose-response associations, adjusted for key covariates. The role of perceived greenness was tested using an active commuting x commute greenness interaction term. We found no dose-response relationships between active commuting and anxiety symptoms or mental wellbeing in any of the models. No effect modification by commute greenness was observed. More research on how active commuting may support planetary health from a mental health perspective is needed.

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

RouteJudge: An Open Platform for Reproducible and Preference-Aware LLM Routing

arXiv:2606.18774v1 Announce Type: new Abstract: We present RouteJudge, an online pairwise preference evaluation framework for LLM routing systems, with a public platform available at https://routejudge.cn. Different from model-level response evaluation, RouteJudge focuses on router-level decision quality. For each user query, multiple routing strategies independently recommend candidate models under the same model pool and budget constraints. The selected model responses are then presented to users through anonymous pairwise comparisons, and the resulting user preferences are attributed back to the routing strategies behind the compared responses. Each evaluation record stores the query, routing decisions, model responses, preference labels, cost, latency, and task metadata, enabling preference-aware, cost-aware, and task-conditioned analysis of LLM routers. To support the continuous expansion of routing methods in RouteJudge, we further release ORBIT (Optimal Routing and Budgeted Inference Toolbox), a modular and extensible toolbox that standardizes the end-to-end workflow of LLM routing. ORBIT provides unified interfaces for benchmark loading, query representation, router implementation, budget-aware evaluation, and method comparison, allowing researchers to develop and evaluate routing algorithms under consistent protocols. It also serves as the submission and integration layer for RouteJudge: researchers can implement routing methods within ORBIT, validate them on existing routing benchmarks, and submit compatible routers for online preference-based evaluation. The code of ORBIT is available at https://github.com/AIGNLAI/LAMDA-ORBIT.

13.
arXiv (CS.CL) 2026-06-17

Translating the Untranslatable: An Operationalizable Ontology for Untranslatability

Untranslatability, cases where meaning cannot be directly preserved across languages, is well-studied in linguistics but underexplored in NLP. As machine translation (MT) systems improve on standard benchmarks, their limitations increasingly concentrate in such cases, where translation cannot be reduced to one-to-one equivalence. We introduce a structured ontology of untranslatability along with a taxonomy of compensation strategies, which are specific techniques to convey meaning under these untranslatable circumstances. We operationalize this framework into a multilingual dataset of untranslatable sentences paired with strategy-based translations, enabling controlled analysis of translation behavior. Initial human preference studies suggest that translation quality depends on the strategy used, with consistent preferences for outputs that include explanatory context, known as the Annotation compensation strategy. Our framework and dataset provide a foundation for studying and modeling strategy-informed machine translation.

14.
arXiv (quant-ph) 2026-06-15

Tantalum as a base material for superconducting integrated circuits

arXiv:2606.13750v1 Announce Type: new Abstract: The performance of superconducting integrated circuits for quantum applications is fundamentally limited by material-related losses. Tantalum, as an emerging material for next-generation quantum circuits, has attracted considerable attention in recent years after demonstrating breakthrough performance in both superconducting microwave resonators and qubits. Concurrently, a growing body of work is devoted to the operation of tantalum-based circuits and related fabrication techniques. This interest is further stimulated by tantalum thin films polymorphism resulting in a variety of its crystalline structure, superconducting properties, coherence, etc. Furthermore, tantalum circuits exhibit distinctive features in cryogenic experiments, which have not been observed in aluminum- or niobium-based ones. In this review, we summarize the recent research of tantalum thin films growth and phase selection mechanisms on various substrates, key aspects of fabrication and performance of superconducting circuit, including a material first-principles theoretical study. In conclusion, we address a number of open issues, including the role of \b{eta}-phase impurities, the effect of hydrofluoric acid solutions on chain characteristics, and the anomalous behavior of {\alpha}-tantalum chains at cryogenic temperatures.

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

Towards Data-free and Training-free Compression for Speech Foundation Models Using Parameter Clustering

arXiv:2606.11836v1 Announce Type: cross Abstract: This paper presents a novel data-free and training-free compression approach for speech foundation models using channelwise clustering via k-means. More fine-grained, mixed sparsity pruning by layer-level varying number of parameter clusters is also explored. Experiments conducted on the LibriSpeech dataset suggest that when operating with pruning sparsity of 50% on HuBERT-large, consistent WER reductions of 27.73%/18.61% absolute (34.37%/21.91% relative) over the magnitude-based pruning were obtained on the test-clean and test-other subsets before fine-tuning and 0.19%/0.79% absolute (3.36%/4.62% relative) after fine-tuning with only 3 epochs. Similar WER reductions of 2.86%/5.02% absolute (59.21%/55.29% relative) were observed against magnitudebased pruning on Whisper-large-v3 at 10% sparsity, all with no significant WER increase relative to the uncompressed baseline.

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

On-Demand Coherent Mapping of Telecom Optical States onto Erbium Hyperfine Spins

arXiv:2606.15009v1 Announce Type: new Abstract: Optical quantum memories operating directly at telecom wavelengths are a key enabling technology for long-distance quantum networks, yet on-demand storage onto long-lived ground-state spins in this spectral region has remained elusive due to the challenge of coherently transferring optical excitations to hyperfine spin states. Here we demonstrate spin-wave storage in $^{167}$Er$^{3+}$:Y$_2$SiO$_5$ at 0.8 K and 1.1 T, establishing the core operational primitive required for on-demand telecom quantum memories. Using classical optical control pulses, we coherently transfer collective optical excitations to erbium hyperfine states with transfer efficiency exceeding 12%, enabling on-demand retrieval. We measure a hyperfine population lifetime of 25 s and demonstrate spin-wave storage for up to 25 $\mu$s. By identifying hyperfine inhomogeneous broadening as the dominant present limitation, our measurements define a clear pathway toward second-scale storage through improved spectral tailoring and dynamical decoupling. The results highlight the application of erbium-based solid-state memories for scalable fiber-compatible quantum repeater architectures.

17.
arXiv (CS.LG) 2026-06-16

Asymptotically Optimal Sequential Testing with Markovian Data

arXiv:2602.17587v3 Announce Type: replace-cross Abstract: We study one-sided and $\alpha$-correct sequential hypothesis testing for data generated by an ergodic, finite-state Markov chain. The null hypothesis is that the unknown transition matrix belongs to a prescribed set $P$ of stochastic matrices, and the alternative corresponds to a disjoint set $Q$. We establish a non-asymptotic instance-dependent lower bound on the expected stopping time of any valid sequential test under the alternative, which is asymptotically tight. Our novel analysis improves the existing lower bounds, which are either asymptotic or provably sub-optimal in this setting. Our lower bound incorporates both the stationary distribution and the transition structure induced by the unknown Markov chain. We further propose an optimal test whose expected stopping time matches this lower bound asymptotically as $\alpha \to 0$. We illustrate the usefulness of our framework through applications to sequential detection of model misspecification in Markov Chain Monte Carlo and to testing structural properties, such as the linearity of transition dynamics, in Markov decision processes. Our findings yield a sharp and general characterization of optimal sequential testing procedures under Markovian dependence.

18.
medRxiv (Medicine) 2026-06-17

Brain age gap correlates with DTI-derived microstructural abnormalities in multiple sclerosis.

Background: Brain age gap (BAG) is increased in multiple sclerosis (MS), but whether it reflects microstructural pathology beyond conventional atrophy remains unclear. Objective: To test whether BAG is elevated in MS and correlates with conventional and diffusion tensor imaging (DTI) abnormalities relative to healthy controls. Methods: A case-control study of 43 people with MS and 18 healthy controls was performed. BAG was estimated from T1-weighted MRI using brainageR. Controls were used as MRI reference distributions. MRI values were expressed as deviation z-scores and correlated with BAG within MS. Conventional MRI and DTI domains were analysed using age/sex-adjusted partial correlations with domain-wise Benjamini-Hochberg FDR correction, where appropriate. Results: BAG was higher in MS than controls (4.79 vs -2.58 years; p

19.
bioRxiv (Bioinfo) 2026-06-15

oxo-flow: compiled, memory-safe bioinformatics workflow orchestration

Authors:

Bioinformatics analyses depend on workflow engines to coordinate dozens of computational tools across complex dependency chains. The most widely adopted engines-Snakemake, Nextflow, the Common Workflow Language (CWL), and the Workflow Description Language (WDL)-run on interpreted or just-in-time (JIT) compiled language runtimes, incurring hundreds of milliseconds of startup latency and providing no compile-time safety guarantees from the host language. We developed oxo-flow, a workflow engine written in Rust that compiles to a single native binary. On an Apple M5 processor, oxo-flow parses, validates, and dry-runs a production-scale workflow in roughly 22 milliseconds-before Snakemake or Nextflow have finished loading their runtime environments. Peak memory usage is 16 megabytes, representing six- to seven-fold reductions relative to Snakemake and Nextflow. Dry-run latency is essentially independent of workflow size: a hundred-fold increase in rule count adds approximately 0.4 milliseconds. oxo-flow integrates 31 command-line tools, a REST interface with 60 endpoints, an embedded web application, and native cluster submission into a single 10-megabyte binary. It provides per-rule environment isolation across seven backends, checkpoint-based fault tolerance with cryptographic output verification, and a formal installation and operational qualification protocol for regulated laboratory environments. Ten curated workflows and three demonstration pipeline repositories are available. oxo-flow is freely available under Apache License 2.0 at https://github.com/Traitome/oxo-flow.

20.
arXiv (CS.LG) 2026-06-17

Learning Survival Models with Right-Censored Reporting Delays

arXiv:2510.04421v3 Announce Type: replace-cross Abstract: Survival analysis provides statistical methods to model the time until an event occurs. Reporting delays arise when event times are not observed at their occurrence but are only revealed upon reporting. This issue is particularly critical for timely risk evaluation when the observation window is short due to administrative censoring. In this study, we incorporate right-censored reporting delays by jointly modeling parametric hazards for the event and reporting processes. We then construct a consistent estimator for the model parameters and develop a Monte Carlo expectation-maximization algorithm to compute it. To address the challenges posed by administrative censoring, we leverage these findings and propose a transfer-learning procedure. Experimental results demonstrate that our method improves the accuracy of timely risk evaluation under administrative censoring.

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

Time-Frequency Grid States for Reconstruction and Correction of Channel-Induced Distortion in Entangled Photons

arXiv:2606.12216v1 Announce Type: new Abstract: Characterization of time-frequency (TF) quantum states requires reliable reconstruction of their TF distributions. However, imperfect transmission or measurement channels can distort reconstructed joint spectral intensities (JSIs), especially when the underlying perturbation mechanism is unknown. Here, we experimentally demonstrate a reconstruction and correction framework that uses a TF grid state as an intrinsic frequency-domain reference. By analyzing the displacement of the grid points, a Gaussian process regression model is employed to reconstruct a correction mapping for the nonlinear coordinate deformation without assuming a prior physical model of the distortion. The learned mapping reduces the residual coordinate deviation of the TF grid state by approximately a factor of 11 and, when applied to an independent frequency-entangled test state, improves the Gaussian-shape fidelity from 76.2\% to 90.0\%. These results establish TF grid states as practical metrological resources for diagnosing and correcting distortions in TF quantum systems, providing a pathway toward distortion-resilient quantum communication and high-dimensional quantum information processing.

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

Functions of Bounded Variation and Point Processes

arXiv:2606.08304v2 Announce Type: replace-cross Abstract: We investigate the relationship between the analytical properties of functions of bounded variation and the statistical behavior of hyperuniform point processes. We establish several characterization formulas for the jump part of the gradient of a bounded variation function, extending and unifying previous results by Beretti–Gennaioli and Dávila. In particular, we provide new expressions for the $L^2$-jump of the gradient using both difference quotients and Fourier transform methods. Furthermore, we connect these analytic structures to the theory of hyperuniform point processes. By analyzing the variance of linear statistics associated with bounded variation functions, we provide asymptotic estimates that depend on the specific classification of the hyperuniformity of the point process. The results show how the regularity and jump discontinuities of a function dictate the growth rate of fluctuations in point processes. Finally, we introduce an averaged quadratic BMO-type oscillation functional over translated and rotated cube partitions, similar to the one recently studied by Ambrosio et al., and prove, using results from point process, that it converges to an explicit dimensional constant times the $L^2-$jump, giving in particular a further new characterization of the perimeter of a set.

23.
arXiv (CS.CL) 2026-06-16

Multi-Turn Reflective Masking Elicits Reasoning in Mask Diffusion Models

While reasoning on autoregressive (AR) models is often performed by chain-of-thought reasoning and reflection, their refinement of previous outputs still relies on fully sequential generation, even when only local edits are needed. In contrast, the masking mechanism in Mask Diffusion Models (MDMs) naturally supports explicit local edits on previous outputs, allowing selective refinement without discarding previous answers and generating another from scratch. While this property more closely aligns with how humans correct mistakes by iterative local refinement, existing MDMs do not support multi-turn masking and denoising. We propose Reflective Masking (RM), which elicits such an intrinsic reasoning capability in MDMs via lightweight post-training. RM provides a native test-time scaling, where an MDM iteratively revisits and revises its prior outputs based on evolving context. To exploit insights from previous turns like AR reasoning, we further introduce History Reference, a parameter-free mechanism that leverages intermediate denoising states during revision. Our approach requires no architectural changes and is easily applicable to existing MDMs. Across diverse tasks and modalities, including text generation, Sudoku, and image editing, Reflective Masking consistently outperforms standard masking-based baselines and demonstrates strong generality, positioning RM as a fundamental primitive for reasoning on MDMs.

24.
arXiv (CS.CL) 2026-06-19

Think Again or Think Longer? Selective Verification for Budget-Aware Reasoning

Test-time reasoning is increasingly used as a serving-time control knob, but extra reasoning is not uniformly valuable: it can repair failed attempts, waste compute on already-correct answers, or introduce harmful answer changes. We study this as a deployment allocation problem rather than a new-verifier problem. We introduce \sevra, Selective Verification for Reasoning Allocation, a serving-layer controller that decides whether to preserve a frozen solver's initial answer or invoke active verification. Using a frozen Qwen3-4B solver, we log intervention outcomes and train recoverability-aware gates from serving-visible attempt state. On \mathfive, selective verification reaches 76.3\% accuracy, compared with 75.5\% for always verifying, while reducing post-generation tokens by 26.8\% and harmful flips from 2.2\% to 1.0\%. However, an 8,192-token initial solve reaches 76.0\% accuracy with 28\% fewer total model tokens, showing that selective recovery is useful but not the best tested cost frontier. In frozen transfer to \gsm, the selective policy verifies only 3.0\% of examples, improves accuracy from 93.4\% to 94.5\%, and reduces verification tokens by 91.2\% relative to always verifying; again, a longer initial solve matches its accuracy with fewer realized tokens. On CommonsenseQA, always-on verification hurts, while Self-Consistency@5 improves accuracy at about five times the realized token cost. The resulting deployment rule is: tune the initial budget first, then use selective recovery when explicit checks, bounded retries, auditability, or regression-risk control matter.

25.
arXiv (quant-ph) 2026-06-12

Geometric Algebra Quantum Gate Decomposition

arXiv:2606.12480v1 Announce Type: new Abstract: Quantum gates are usually described through matrix and tensor-product formalisms that often obscure their geometric structure. In this work, we formulate the Pauli and Clifford groups within the complex Geometric Algebra (GA) framework. We show that the Pauli group is naturally identified with the group of blades up to a global phase, thereby providing a geometric interpretation of Pauli operators and their commutation relations in terms of oriented subspaces. We further prove that Clifford operators are generated by products of {\pi}/4-Pauli rotors and introduce a greedy Pauli rotor decomposition algorithm whose empirical behavior suggests unexpectedly compact decompositions for Clifford operators. Finally, we show that Clifford+T universality admits a natural geometric interpretation through {\pi}/8-rotors within this framework.