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

Prediction of Runtime Parameters of Parallel Chemistry Applications via Active and Generative Learning

arXiv:2606.16226v1 Announce Type: new Abstract: In this work, we develop two main Machine Learning based approaches to predict the runtime parameters of highly scalable parallel chemistry computations.These approaches employ active and generative learning together with the empirically determined gradient boosted regression tree models chosen among a rich suite of machine learning models. When evaluated on Coupled-Cluster with Singles and Doubles computations, our models achieve a mean absolute error percentage (MAPE) as low as 0.023 and a coefficient of determination as high as 99.9%. Furthermore, when combined with active learning to mitigate the lack of large amounts of training data, our models score a MAPE about 0.2 with 20-25% of the original dataset.

02.
arXiv (math.PR) 2026-06-19

A Cycle Walk for Sampling Measures on Spanning Forests for Redistricting

arXiv:2509.08629v2 Announce Type: replace-cross Abstract: We introduce the Cycle Walk, a new Markov chain Monte Carlo method for sampling distributions on balanced graph partitions, motivated by applications in political redistricting. The method operates on spanning forests and combines two types of updates: local "cycle" moves within districts and global moves that exchange population between adjacent districts while preserving balance constraints. This construction enables efficient Metropolis–Hastings correction while allowing proposals at multiple spatial scales. We show that the Cycle Walk naturally interpolates between existing approaches based on local updates and a class of global update methods derived from recombination (RECOM). Through a range of numerical experiments on synthetic graphs and real-world precinct data, we demonstrate that the Cycle Walk exhibits improved empirical convergence diagnostics for distributions that place weaker weight on spanning-tree counts, a regime that is challenging for existing methods. In particular, the algorithm remains effective when incorporating alternative compactness measures that more closely reflect policy-relevant criteria. These results suggest that the Cycle Walk provides a flexible and computationally efficient framework for sampling from a broader class of redistricting distributions than previously accessible with MCMC techniques.

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

Dynamically Optimal Unraveling Schemes for Simulating Lindblad Equations

arXiv:2509.19887v2 Announce Type: replace Abstract: Stochastic unraveling schemes are powerful computational tools for simulating Lindblad equations, offering significant reductions in memory requirements. However, this advantage is accompanied by increased stochastic uncertainty, and the question of optimal unraveling remains open. In this work, we investigate unraveling schemes driven by Brownian motion or Poisson processes and present a comprehensive parametric characterization of these approaches. For the case of a single Lindblad operator and one noise term, this parametric family provides a complete description for unraveling scheme with pathwise norm-preservation. We further analytically derive dynamically optimal quantum state diffusion (DO-QSD) and dynamically optimal quantum jump process (DO-QJP) that minimize the growth rate of the variance of an observable locally in time. Compared to jump process ansatz, DO-QSD offers two notable advantages: firstly, the variance for DO-QSD can be rigorously shown not to exceed that of any jump-process ansatz locally in time; secondly, it has very simple expressions. Numerical results demonstrate that the proposed DO-QSD scheme may achieve substantial reductions in the variance of observables and the resulting simulation error.

04.
arXiv (quant-ph) 2026-06-12

Kubo-Martin-Schwinger conditions for non-Hermitian systems

arXiv:2606.13251v1 Announce Type: new Abstract: We investigate the extension of the Kubo–Martin–Schwinger (KMS) thermal equilibrium condition to non-Hermitian Hamiltonians with real spectra and biorthogonal eigensystems, providing a systematic analysis through three complementary routes. Our central result is a thermodynamic characterisation of quasi-Hermiticity: for $H \in M_d(\mathbb{C})$ diagonalisable with real spectrum, the biorthogonal Gibbs functional $\omega_{\rm{bi}}(A) = Z_{\rm{bi}}^{-1} \sum_n e^{-\beta E_n}\langle\phi_n|A|\psi_n\rangle$ satisfies $\omega_{\rm{bi}}(A^\dag A) \geq 0$ for all $A$ if and only if $H$ is quasi-Hermitian. The proof constructs the metric $\eta$ directly from the eigenprojectors of $\omega_{\rm{bi}}$ via the Riesz representation theorem, with no prior choice of $\eta$, providing a metric-free certificate of quasi-Hermiticity outside the Mostafazadeh–Scholtz framework. Under the full quasi-Hermitian hypothesis, we prove that the $\eta$-Gibbs state $\omega_\eta(A) = Z_\eta^{-1}\, \rm{Tr}[\eta e^{-\beta H}A]$ satisfies all three analytic KMS conditions, using the Hadamard three-line theorem and Bari's theorem on Riesz bases. The result is non-trivial: the transported state $\hat\omega(X) = \rm{Tr}[e^{-\beta h}X\eta]/Z_\eta$ differs from the Gibbs state of the isospectral Hermitian partner $h = \eta^{1/2}H\eta^{-1/2}$ whenever $[\eta,h]\neq 0$, so the KMS property cannot be deduced from the Hermitian theory by similarity. The gap between this result and the full Haag–Hugenholtz–Winnink $C^*$-algebraic framework is identified. Failure modes at exceptional points and for complex spectra are analysed, and the relation to the Fagnola–Umanità quantum detailed balance condition for open systems is discussed.

05.
bioRxiv (Bioinfo) 2026-06-23

biomeStat: Using Agentic AI for Scalable Genomic Epidemiology Demonstrated Through End-to-End Analysis of 1,000 Asian Dengue Virus Genomes

Genomic epidemiology workflows typically require expert curation of multiple specialized tools, extensive manual parameter tuning, and access to heterogeneous compute infrastructure. While standard generative AI models often hallucinate in complex biological domains, we introduce biomeStat: an autonomous AI agent that functions as a strict deterministic orchestrator. By automatically writing code to execute established bioinformatics tools in sandboxed environments, biomeStat dynamically provisions compute resources (CPU and GPU) and guarantees reproducibility, making it immediately useful for scientists without requiring command-line expertise. To demonstrate the platform, we performed a fully autonomous genomic epidemiology and structural analysis of 1,000 Dengue virus (DENV) genomes sampled from 16 Asian countries between 2000 and 2025. The agent seamlessly orchestrated phylogenetic reconstruction (IQ-TREE, TreeTime), Bayesian phylodynamics (BEAST2 via NVIDIA H200 GPU), selection pressure analysis (HyPhy), and structural mapping (PyMOL). The analysis was completed in under 24 hours of wall-clock time, revealing endemic stability (R_e ~1.0) and identifying 1,869 candidate immune escape sites structurally colocalized with B-cell and T-cell epitopes. Furthermore, the agent validated 176 highly conserved drug target residues across the viral replication complex, confirming that resistance-associated positions for emerging antivirals JNJ-1802 and NITD-688 remain absolutely conserved across all four serotypes. By bridging the gap between natural language intent and deterministic computational execution, biomeStat reduces weeks of expert effort into a single-session analysis with full methodological transparency.

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

Geometry-Aware Superpixel Graph Transformer with Metadata for Skin Lesion Classification

Automated skin cancer classification from dermoscopic images remains challenging due to heterogeneous lesion structure, strong intra-class variability, and subtle visual differences between benign and malignant cases. Existing CNN/ViT pipelines typically rely on global or patch-level features and often combine patient metadata via late fusion, which limits spatially grounded multimodal reasoning. We present a novel region-based graph learning framework that explicitly models lesions as graphs of spatially coherent superpixel regions represented as frozen CNN features. To capture fine-grained lesion arrangements, we encode inter-regional geometry as edge attributes and introduce a dedicated metadata context node connected to all regions, providing structured integration of demographic/clinical variables within the same relational space. Node representations are updated using our edge-aware graph transformer followed by attention-driven propagation, and a final graph-level embedding for benign-malignant classification. Experiments on four public benchmarks demonstrate that explicit region-level relational modeling and graph-native multimodal fusion yield consistent gains over the state-of-the-art. Consequently, we establish a new graph-centric perspective in which CNN features are modeled as relational nodes and improved through contextual integration, yielding more expressive and robust classifications.

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

Text-Driven Fusion for Infrared and Visible Images: Achieving Image Scene Adaptation on Hyperbolic Space

Infrared and visible image fusion aims to integrate complementary modalities, while existing Euclidean methods impose rigid distance metrics that distort multi-modal interactions and parent-to-child semantic hierarchies. To overcome these limitations, we introduce a text-driven fusion framework empowered by hyperbolic manifold learning. During training, BLIP-extracted text prompts serve as topological anchors within the hyperbolic space, guiding vision-attribute alignment through hyperbolic embeddings that naturally accommodate varying semantic granularities. By exploiting the exponential volume growth dictated by the Poincaré ball's negative curvature, this approach seamlessly embeds hierarchical trees to encode coarse-to-fine semantics without metric saturation, while the vast peripheral space prevents texture distortion during cross-modal fusion. At inference, the fusion process autonomously adapts to input content using the learned text-attribute priors, completely eliminating the need for textual input. Experimental results show our method outperforms state-of-the-art approaches on benchmark datasets, with code available at https://github.com/Shaoyun2023/TEDFusion.

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

Information Gap and Feasibility-Aware Inference in Binomial Logistic Mixtures

arXiv:2606.15665v1 Announce Type: cross Abstract: This paper studies the information gap between mixture detection and label recovery in binomial logistic mixtures. Standard likelihood-based criteria such as the Bayesian information criterion (BIC) can detect the presence of two components, but this does not guarantee that the corresponding labels are recoverable. We show that this gap is intrinsic to binomial logistic mixtures with a fixed number of trials: observed-data evidence for mixture structure and per-observation information for label recovery have different local orders in the component separation, and only the former accumulates with the sample size. As a result, there exists a detectable-but-unrecoverable regime in which BIC selects two components while the posterior labels remain essentially uninformative. To address this issue, we propose two feasibility-aware inference procedures: a recoverability-aware BIC with a posterior-entropy penalty and an entropy-regularized estimator that mitigates the tendency of the maximum likelihood estimator to produce overly separated components and overly concentrated posterior responsibilities. Numerical experiments confirm the predicted gap and demonstrate that the proposed methods avoid misleading component selections and improve the calibration of posterior label probabilities.

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

Meta Flow Maps enable scalable reward alignment

arXiv:2601.14430v2 Announce Type: replace-cross Abstract: Controlling generative models is computationally expensive. This is because optimal alignment with a reward function–whether via inference-time steering or fine-tuning–requires estimating the value function. This task demands access to the conditional posterior $p_{1|t}(x_1|x_t)$, the distribution of clean data $x_1$ consistent with an intermediate state $x_t$, a requirement that typically compels methods to resort to costly trajectory simulations. To address this bottleneck, we introduce Meta Flow Maps (MFMs), a framework extending consistency models and flow maps into the stochastic regime. MFMs are trained to perform stochastic one-step posterior sampling, generating arbitrarily many i.i.d. draws of clean data $x_1$ from any intermediate state. Crucially, these samples provide a differentiable reparametrization that unlocks efficient value function estimation. We leverage this capability to solve bottlenecks in both paradigms: enabling inference-time steering without inner rollouts, and facilitating unbiased, off-policy fine-tuning to general rewards. Empirically, our single-particle steered-MFM sampler outperforms a Best-of-1000 baseline on ImageNet across multiple rewards at a fraction of the compute.

10.
arXiv (quant-ph) 2026-06-17

Projected logical ensembles in surface codes via the random-matrix theory of quantum dots

arXiv:2606.17140v1 Announce Type: new Abstract: Measurements underpin active quantum error correction (QEC) and have been recognized as a source of novel measurement-induced many-body phenomena. Here, we study the statistical properties of post-measurement logical states arising in QEC on topological codes subject to deterministic transversal unitary gates. Upon syndrome extraction followed by maximum-likelihood decoding, a Born-weighted ensemble arises which we dub the "projected logical ensemble" (PLE). Focusing on surface codes subject to uniform single-qubit Pauli-$X$ rotations, we characterize the measurement-induced randomness of the PLE. To this end, we show that for a code with a single logical qubit, the PLE is isomorphic to an ensemble of scattering matrices describing mesoscopic quantum dots obtained from a 2D Majorana network model with suitable boundary conditions. We uncover regimes where these quantum dots are chaotic such that their scattering matrices are well-described by random matrix theory. In these regimes, the PLE approaches a universal ensemble that is maximally random up to symmetry and decoder-induced constraints. The symmetry constraints, set by stabilizer and logical operator weights, realize Altland-Zirnbauer classes D or DIII, which we both illustrate. Our results establish a fundamental connection between emergent universality concepts in mesoscopic physics, quantum many-body systems, and QEC.

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

Visuals Lie, Consistency Speaks: Disentangling Spatial Attention from Reliability in Vision-Language Models

Multimodal Foundation Models are increasingly used as reasoning agents, making reliability, knowing when a model may hallucinate, critical. A common intuition, which we call the Attention-Confidence Assumption, holds that reliability follows from "structural" visual perception: tight attention on relevant regions should signal a trustworthy answer, while scattered attention signals confusion. We challenge this through the VLM Reliability Probe (VRP), a systematic cross-family study of reliability signals in contemporary Vision-Language Models (VLMs). We introduce structural-attention metrics, cluster counts (C_k) and spatial entropy (H_s), to quantify the visual encoder's gaze, and track its evolution (Delta H_s) across layers. This reveals a "Symbolic Detachment": models often "Early Lock" visual features only to diffuse attention later, severing early perception from final generation. Contrary to the grounding hypothesis, we find a "Cluster Failure": spatial attention has near-zero correlation (R approx 0.001) with accuracy. Instead, reliability is a phenomenon of generation dynamics and internal-state distributions. Self-Consistency, the agreement rate across sampled reasoning paths, is the dominant predictor of truth (R = 0.429). Scaling causal interventions exposes a sharp architectural divergence: LLaVA locks its prediction in a fragile late-stage bottleneck, whereas PaliGemma and Qwen2-VL distribute reliability globally, staying resilient even when ~50% or more of their most predictive layer is destroyed. For current VLMs, reliability signals are detached from visual grounding maps and are best inferred from generation-time dynamics and hidden-state probes.

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

DriveReward: A Comprehensive Dataset and Generative Vision-Language Reward Model for Autonomous Driving

Reward models play a pivotal role in reinforcement learning (RL) and multi-modal trajectory selection for autonomous driving. However, acquiring such rewards typically relies on hand-crafted rule-based objectives or perception ground truth, which hinders generalization for data-scaling. While Vision-Language Models (VLMs) have demonstrated feasibility as reward models in other domains, their effectiveness in driving tasks remains underexplored. In this work, we bridge this gap by (1) introducing DriveReward, a reasoning trajectory evaluation dataset rigorously labeled via temporally-grounded visual guidance, and augmented with counterfactual driving behaviors., (2) alongside a specialized Vision-Language Reward Model. To address the scarcity of failure cases in conventional datasets, we propose a counterfactual data annotation scheme to construct cases encompassing diverse driving styles and erroneous behaviors. Evaluations on our proposed benchmark reveal that even leading open-source and proprietary VLMs fail to excel across all tasks, highlighting significant room for improvement in existing models. Building on these findings, we subsequently tailor a specialized 1B reward model that outperforms larger VLMs on task-specific reward alignment. Finally, we validate our reward model's effectiveness by integrating it into RL finetuning and multi-modal trajectory scoring across multiple baselines, achieving performance comparable to rule-based reward calculations in both open-loop and closed-loop evaluation.

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

The Silent Cost of Artificial Intelligence Assistance: A Theory of Autonomy Surrender, the Recovery Mechanism, and the Restoration of Human Agency

arXiv:2606.13962v1 Announce Type: cross Abstract: The integration of artificial intelligence into human decision-making environments has introduced a previously undertheorized cost: the gradual surrender of human autonomy in exchange for access to information and computational assistance. Building on the Human Identity and Autonomy Gap (HIAG) framework, this paper advances a theoretical model of autonomy surrender as a measurable, cumulative process driven by cognitive bandwidth depletion. The model proposes three interacting mechanisms: the silent cost of AI assistance, in which autonomy is transferred incrementally and without awareness; the surrender threshold, beyond which reclaiming autonomous function becomes cognitively and psychologically difficult; and the recovery mechanism, which establishes the design obligation and the ethical responsibility accompanying deliberate human re-assumption of control. The paper argues that human re-entry into the decision loop is not a passive option but an active cognitive event requiring intentional bandwidth restoration. The design of AI systems must incorporate structured re-entry pathways, here termed recovery mechanisms, that preserve human agency while appropriately distributing responsibility. The model further predicts a terminal state, here termed preference inversion, in which functional dependence on AI assistance is experienced not as a deficit but as a preference, transforming the restoration of autonomy from a design problem into a cultural and political one. Implications are drawn for AI system design, governance frameworks, and human factors research.

14.
arXiv (CS.CV) 2026-06-16

Pixel-TTS: Image based Text Rendering for Robust Text-to-Speech

Recent advances in pixel-based text modeling show that representing text as images enables models to exploit visual cues for language understanding. Grounding text in its visual form allows structurally similar characters with different Unicode encodings to produce similar embeddings, benefiting cross-lingual and zero-shot scenarios. Conventional text-based approaches treat each character independently, limiting generalization to unseen characters and requiring embedding expansion during cross-lingual adaptation. We propose Pixel-TTS, the first framework for visually grounded speech synthesis. It renders text as images and projects them through a 2D convolutional layer to generate embeddings. This design eliminates embedding matrix expansion during fine-tuning while improving robustness to unseen characters and orthographic variations. Extensive experiments show Pixel-TTS achieves competitive performance with strong baselines, faster convergence and robust zero-shot generalization.

15.
arXiv (CS.AI) 2026-06-12

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems

arXiv:2509.03340v4 Announce Type: replace-cross Abstract: Bifurcation phenomena in nonlinear dynamical systems often lead to multiple coexisting stable solutions, particularly in the presence of symmetry breaking. Deterministic machine learning models are unable to capture this multiplicity, averaging over solutions and failing to represent lower-symmetry outcomes. In this work, we formalize the use of generative AI, specifically flow matching, as a principled way to model the full probability distribution over bifurcation outcomes. Our approach builds on existing techniques by combining flow matching with equivariant architectures and an optimal-transport-based coupling mechanism. We generalize equivariant flow matching to a symmetric coupling strategy that aligns predicted and target outputs under group actions, allowing accurate learning in equivariant settings. We validate our approach on a range of systems, from simple conceptual systems to physical problems such as buckling beams and the Allen–Cahn equation. The results demonstrate that the approach accurately captures multimodal distributions and symmetry-breaking bifurcations. Moreover, our results demonstrate that flow matching significantly outperforms non-probabilistic and variational methods. This offers a principled and scalable solution for modeling multistability in high-dimensional systems.

16.
arXiv (math.PR) 2026-06-11

Hilbert space embeddings of independence tests and interaction measures of several variables

arXiv:2411.08653v2 Announce Type: replace-cross Abstract: We present a unified theoretical framework for kernel-based measures of dependence on product spaces. Building on the ideas underlying distance covariance, distance multivariance, and the Hilbert-Schmidt Independence Criterion (HSIC), we define a new family of kernels on an $n$-fold Cartesian product, termed positive definite independent of order $k$ (PDI$_{k}$ kernels). These kernels extend the concepts of positive definite and conditionally negative definite kernels to higher orders and provide the foundation for generalized independence and interaction tests, such as the generalized Lancaster interaction of order $k$ ($\Lambda_{k}^{n}$), and the Streitberg interaction ($\Sigma$). Our analysis focuses on the continuous setting, where we prove a Kernel Mean Embedding Theorem for PDI$_{k}$ kernels and establish the corresponding integrability restrictions. Based on these results, we characterize how the Kronecker products of PDI kernels behave.

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

Beyond Uniform Forgetting: A Study of Sequential Direct Preference Optimization Across Preference Settings

Aligning language models with human preferences often requires optimising multiple behavioural objectives. A practical approach is to apply these objectives sequentially using preference optimisation methods such as Direct Preference Optimisation (DPO), but it remains unclear whether later training uniformly degrades preferences learned earlier or whether the effect depends on the relationship between objectives. We study sequential DPO across four preference settings covering distributional conflict, multi-attribute interaction, strong safety signal, and compatible response-quality objectives. Using Llama-3.1-8B-Instruct with LoRA adapters, we evaluate all objectives after every stage with a fixed base-model reference. We find that sequential DPO does not produce a single forgetting pattern; preference change ranges from partial degradation to stability, pair-level redistribution, or positive transfer depending on objective relationship, signal strength, and training order. Pair-level analysis using length-normalised policy margins shows that aggregate metrics can mask heterogeneous changes across preference pairs, whereas quartile decomposition reveals that high-confidence pairs can either degrade or improve depending on the setting. Mechanistic diagnostics show that Stage~2 gradients and adapter updates are near-orthogonal to the previous objective across all settings, providing little evidence that direct gradient opposition is the primary driver. These findings suggest that future sequential alignment pipelines should account for objective compatibility and signal strength, rather than assuming that later objectives affect earlier preferences uniformly.

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

Adaptive inference and function vectors in deep transformers

arXiv:2606.16694v1 Announce Type: cross Abstract: Transformers are widely used as a general-purpose substrate for learning complex correlations between a large collection of coupled variables, but their internal mechanisms have remained mysterious. We introduce a theory of a deep transformer as a mean-field interacting system that implements distributed inference, subject to constraints on communication, locality and depth. We show that such a system can exploit internal state representations ('function vectors') to infer a latent context variable at increasingly finer scales over its layers. In an in-context regression task, the theory predicts a non-trivial relationship between non-Gaussian, hierarchical structure in the latent context variable, and transformer depth. Predictions are tested using constrained linear attention transformers and demonstrate adaptive inference in deep architectures. Feedforward blocks and depth enable transformers to implement a much richer class of in-context learning algorithms than previously described.

19.
medRxiv (Medicine) 2026-06-23

Unscreenable: The Burden, Structure, and Analytic Consequences of "Unable to Assess" Delirium Documentation in the Intensive Care Unit

Objective: To quantify the burden, structure, and downstream analytic consequences of "Unable to Assess" (UTA) delirium documentation in the intensive care unit (ICU). Design: Retrospective cross-sectional and repeated-measures study. Setting: A single US academic medical center (Medical Information Mart for Intensive Care IV [MIMIC-IV], 2008-2019). Patients: 72,944 adult ICU stays with at least 1 delirium screen. Interventions: None. Measurements and Main Results: Among 610,632 screens, 130,455 (21.4%; 95% CI, 21.0%-21.8%) were recorded as UTA, exceeding the 119,052 (19.5%) scored positive. The UTA fraction rose from 2.0% at a Richmond Agitation-Sedation Scale (RASS) score of 0 to 97.8% at RASS -4; 22.0% of UTA screens occurred in arousable patients, where UTA was associated with mechanical ventilation (odds ratio [OR], 3.43; 95% CI, 3.17-3.71) and non-English primary language (OR, 3.74; 95% CI, 3.43-4.08). Building the delirium label three ways from the same patients shifted prevalence modestly (32.1% to 30.8%) and prediction (area under the curve, 0.737 to 0.719) but most affected the delirium-mortality association: in a baseline-adjusted model the OR was 4.12 (95% CI, 3.88-4.36) under complete-case handling and fell to 2.16 (95% CI, 2.06-2.27) when UTA was recoded as negative. UTA was recoverable from the observed clinical state (area under the curve, 0.95). Conclusions: In this ICU cohort, Unable to Assess was the most common recorded delirium result other than Negative, exceeding positive screens; recoding it as negative roughly halved the apparent delirium-mortality association by relabeling deeply sedated, high-mortality patients. Delirium datasets should preserve and report UTA, whose concentration among arousable non-English-speaking patients is a measurable equity target.

20.
arXiv (quant-ph) 2026-06-11

The Simplified Stabilizer ZX-Calculus is Minimal

arXiv:2606.12383v1 Announce Type: new Abstract: The stabilizer fragment of the ZX calculus is amongst the most important fragments of the theory. The closely related Clifford+T fragment is approximately universal (arXiv:1705.11151). Additionally, the stabilizer calculus can be described by a small collection of rewrites, most of which have been shown to be necessary (arXiv:1709.08903). However, two rules, describing the red/green compact-structure coincidence and the important bialgebra law, had not been shown to be necessary. We present a countermodel-style argument showing that both of these rules are individually necessary relative to the connectivity meta-rule of Backens–Perdrix–Wang (arXiv:1709.08903), and hence establish that the rule set presented in arXiv:1709.08903 has no redundant rewrite rule.

21.
arXiv (quant-ph) 2026-06-24

Auxiliary Schmidt Rank as a Resource for Photonic Bell Measurements

arXiv:2606.24591v1 Announce Type: new Abstract: In quantum communication and fusion-based quantum computation, photonic Bell measurements are fundamentally limited when only passive linear optics is employed. While for qubits, some Bell states can be unambiguously identified with static beam splitters and no extra photons or entanglement, additional auxiliary photons or at least additional auxiliary degrees of freedom with a certain level of additional entanglement are needed to approach or attain a complete, deterministic Bell measurement. Here, we prove an exact resource threshold when the same two photons carry system qudits of dimension $d$ and a fixed auxiliary entangled state $\Phi$, possibly distributed over several additional degrees of freedom, with total Schmidt rank $r_\Phi$. We show that a single conclusive Bell-label functional can occur for $r_\Phi\geqslant\lceil d/2\rceil$, but deterministic discrimination of all $d^2$ Bell-state labels requires $r_\Phi\geqslant d$. A maximally entangled rank-$d$ auxiliary state achieves the bound by local Bell-basis sorting between each photon's system and auxiliary degrees of freedom. Thus, the auxiliary Schmidt rank is a certified resource for ancilla-photon-free, embedded photonic Bell measurements.

22.
arXiv (CS.AI) 2026-06-17

Beyond the Sampled Token: Preserving Candidate Support in RLVR

arXiv:2510.14807v3 Announce Type: replace Abstract: We revisit exploration collapse in reinforcement learning with verifiable rewards (RLVR), from the perspective of the candidate distribution for next-token prediction. We formally show that as probability concentrates on the top-$1$ candidate, the expected number of distinct responses collapses to one regardless of the sampling budget $K$. This theoretical implication is further verified by our empirical tracking of top-$N$ candidate probabilities during training, where the top-$1$ candidate progressively dominates while plausible alternatives are suppressed. These findings suggest a key desideratum for effective exploration: preserving non-negligible probability mass on the top-$N$ candidates. To this end, we propose Candidate-aware Support Preservation (CaSP), with two complementary designs. Specifically, CaSP redistributes positive gradients among top-$N$ candidates for correct responses, and applies a stronger penalty to the top-$1$ candidate for incorrect responses. Unlike many exploration-oriented methods that improve pass@$K$ at the cost of pass@1, CaSP improves pass@$K$ across the full $K$ spectrum. These gains generalize to 6 math, 2 logical-reasoning, and 2 coding benchmarks, and scales to 32B-parameter models and sampling budgets up to $K=1024$, positioning it as a principled, candidate-level approach for RLVR exploration.

23.
arXiv (CS.CV) 2026-06-18

FlowObject: Flow Steering for Bridging Generative Priors and Reconstruction Fidelity

Recovering complete 3D representations of objects from few casual image captures remains a significant challenge. Recent 3D generative models, particularly those based on Flow-Matching (FM), can synthesize high-quality textured assets; however, they often suffer from ''synthetic bias'' where learned priors override observational evidence, alongside a lack of alignment with the observed instance. Conversely, optimization-based methods like 3D Gaussian Splatting (3DGS) provide high fidelity on visible surfaces but fail to reason about unobserved geometry. In this paper, we present FlowObject, a framework that reformulates sparse-view 3D reconstruction as a training-free, guided inverse problem. Our approach applies a dual-space guidance strategy to steer the Ordinary Differential Equation (ODE) trajectory of a flow-matching model, enabling the completion of unseen regions through learned generative priors while enforcing strict consistency with real-world observations. By integrating a 3DGS refinement stage, FlowObject further bridges the gap between ''synthetic-looking'' generative outputs and photorealistic reconstructions. Comprehensive benchmarks on synthetic and real-world datasets demonstrate that current state-of-the-art methods often struggle to achieve geometric completeness and observational consistency simultaneously, especially under severe occlusions. In contrast, our method significantly outperforms state-of-the-art generative models and optimization-based frameworks in both geometric completeness and view-dependent appearance fidelity.

24.
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.

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

Pushing the Boundaries of Natural Reasoning: Interleaved Bonus from Formal-Logic Verification

arXiv:2601.22642v2 Announce Type: replace Abstract: Large Language Models (LLMs) show remarkable capabilities, yet their stochastic next-token prediction creates logical inconsistencies and reward hacking that formal symbolic systems avoid. To bridge this gap, we introduce a formal logic verification-guided framework that dynamically interleaves formal symbolic verification with the natural language generation process, providing real-time feedback to detect and rectify errors as they occur. Distinguished from previous neuro-symbolic methods limited by passive post-hoc validation, our approach actively penalizes intermediate fallacies during the reasoning chain. We operationalize this framework via a novel two-stage training pipeline that synergizes formal logic verification-guided supervised fine-tuning and policy optimization. Extensive evaluation on six benchmarks spanning mathematical, logical, and general reasoning demonstrates that our 7B and 14B models outperform state-of-the-art baselines by average margins of 10.4% and 14.2%, respectively. These results validate that formal verification can serve as a scalable mechanism to significantly push the performance boundaries of advanced LLM reasoning.