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arXiv2026

Quantum Fidelity Landscape-Guided Prior Calibration for Single-Circuit QGAN Image Generation

Quantum Generative Adversarial Networks (QGANs) have emerged as representative generative models in the Noisy Intermediate-Scale Quantum (NISQ) era and have attracted increasing attention in quantum machine learning. However, most existing QGAN methods rely on patch-based decomposition strategies, which weaken the global consistency of generated images and increase quantum resource overhead. In this work, we investigate a simpler approach: pixel-level, end-to-end image generation using a single-quantum-circuit QGAN. By analyzing the structural matching relationship between the quantum prior and the target data distribution in Hilbert space, we provide a new theoretical perspective for understanding the training behavior of naive end-to-end QGANs. Specifically, we introduce the Quantum Fidelity Landscape (QFL), defined as the pairwise-fidelity structure induced by an ensemble of quantum states and preserved under shared unitary transformations of the quantum generation process. We show that, under a fixed Lipschitz readout, this invariant imposes a one-sided bound on decoded sample separation, motivating calibration of the prior-induced QFL before adversarial training. To validate this theoretical insight, we propose BasicQGAN, a QGAN framework incorporating quantum prior calibration. Before adversarial optimization, BasicQGAN aligns the prior-induced QFL with the data-induced QFL. Experimental results on small-scale grayscale image datasets show that BasicQGAN achieves stable and effective end-to-end pixel-level image generation while requiring fewer qubits and trainable parameters than representative patch-based quantum generators. Furthermore, experiments with different initial quantum-state ensembles show that QFL-calibrated ensembles achieve better generative performance.

quant-ph↗
arXiv2026

Interlayer coupling between twisted graphenes through atomically-precise barriers

Understanding and controlling interlayer coupling in van der Waals (vdW) materials is crucial for engineering novel electronic phenomena, including correlated states, topological phases, and superconductivity. Twisted bilayer graphene (TBG) offers a highly tunable platform to explore how interlayer orientation and separation influence quantum transport and moiré physics. Here, we introduce a method for achieving precise, atomic-scale control of interlayer coupling in TBG using dual-gated devices separated by ultrathin, thickness-tunable hBN spacers. This approach enables systematic control of interlayer interactions, demonstrating that the critical displacement field required for electron-hole bilayer behavior decreases as the layer separation increases at a fixed twist angle. Remarkably, at small twist angles, moiré-related side peaks persist even when layers are separated by tetralayers of hBN (approximately 1.3 nm), indicating robust interlayer band hybridization. By combining atomic-layer-precise control of interlayer coupling with independent twist angle tunability, our platform opens new avenues for discovering novel moiré physics governed by engineered interlayer coupling and moiré patterns.

cond-mat.mes-hall↗
arXiv2026

When Is Coarse Supervision Worth It? Cost-Aware Learning under Unknown Aggregation

Modern learning systems often acquire supervision at multiple resolutions, trading annotation cost against information content. We study cost-aware two-resolution learning, where expensive fine labels reveal a vector response and cheaper coarse labels reveal a scalar aggregate formed with unknown weights, while the target remains the full response. The challenge is that unknown aggregation changes which directions coarse data can identify, so the value of coarse supervision depends jointly on cost, noise, and identification. We characterize this information geometry and develop an estimate-and-track policy that learns the aggregation rule and tracks the optimal resolution mix. We derive a closed-form break-even condition for coarse supervision and prove that the online policy attains the optimal leading cumulative-risk coefficient, with a matching local asymptotic minimax lower bound. Synthetic experiments support the predicted all-fine/mixed transition, show the online learner approaching the oracle-share benchmark, and demonstrate a finite-budget gain over all-fine acquisition when coarse supervision is sufficiently favorable. Our results provide a principled way to balance information and annotation cost across supervision resolutions.

cs.LG↗
arXiv2026

JudgeProfile: Understanding and Steering Subjectivity in LLM Judges

LLM judges are inherently subjective, often favoring different responses in pairwise comparison when neither option is objectively wrong. To study this subjectivity, we introduce JudgeProfile, a framework that dissects LLM evaluation into perception (how a judge compares two responses across specific attributes like clarity, correctness, and detail) and prioritization (how much each attribute influences the final choice). We curate SubjectiveSet, a dataset of 50,013 response pairs from 17 public data sources, evaluated by 21 LLM judges across 87 attributes. We find a hidden consensus in perception: judges frequently agree on attribute judgments even when their overall choices diverge. Building on this separation, we first characterize each judge's prioritization using attribute weights estimated from its own overall choices. These weights differ across judges even when estimated from the same attribute judgments. We then learn new weights from reference labels to adapt their decisions to a target evaluation standard. Reweighting perceived attributes improves average held-out agreement with reference labels from 66.48% to 71.97%, outperforming fine-tuning and rubric prompting. Our findings show that understanding and steering the subjectivity of LLM judges requires attention not only to what they perceive, but also to how they prioritize it.

cs.AI↗
arXiv2026

LAURA: Knowledge Distillation for Interpretable Ambiguous Clause Identification in Legal Contracts

Legal contracts contain ambiguities that expose enterprises to financial and legal risks. Some ambiguities allow flexible interpretation without triggering disputes, while others lead to significant legal conflicts. This makes identification alone insufficient, and interpretable rationale analysis essential. We propose LAURA, a post-training framework for interpretable ambiguous clause identification. LAURA leverages knowledge distillation with an IRAC-Unlearning prompting technique to transfer knowledge from a teacher LLM to an open-weight student model (<=1B parameters), which is then trained using a joint objective combining classification and rationale generation losses. The framework supports both legal and non-legal stakeholders in making informed decisions about which ambiguities require further attention. Extensive experiments across 7 baselines and 7 open-weight models demonstrate that LAURA with Flan-T5 (250M) delivers state-of-the-art interpretability over all interpretable baselines while matching the identification performance of the best-performing opaque baseline.

cs.CL↗
arXiv2026

A Divide-and-Conquer Quantum-Selected Configuration Interaction for Evaluating $π$-$π$ Stacking Interaction Energies in the Benzene Dimer

Accurate evaluation of $π$--$π$ stacking interactions requires a description of electron correlation on a small energy scale. Direct variational quantum calculations of the benzene dimer with CAS(28e,20o) require 40 qubits and deep circuits. Here, we propose Divide-and-Conquer Quantum-Selected Configuration Interaction (Deep QSCI), combining the divide-and-conquer idea of Deep VQE with QSCI, and apply it to the sandwich benzene dimer. We perform QSCI for one monomer and construct a reduced local basis by applying particle-number-conserving one-electron excitations to its ground state. Using this basis and the intermonomer interaction Hamiltonian, we build and diagonalize an effective Hamiltonian of the dimer. Since the monomers have the same structure, the QSCI result is reused for both monomers and across intermolecular distances, reducing the required quantum register from 40 to 20 qubits for the monomer CAS(14e,10o). With 6-31G**, the model gives an attractive minimum of -0.91 kcal/mol at 4.0 $Å$, compared with the counterpoise-corrected CCSD(T) value of -1.14 kcal/mol. With cc-pVDZ, a large cancellation appears between the product-state interaction energy and the energy lowering by diagonalization. This may reflect insufficient consistency of the active orbitals and reduced local bases between monomers. Orbital consistency, reduced-space convergence across basis sets, and charge transfer remain key issues for quantitative accuracy. Deep QSCI thus provides a resource-efficient approach to constructing model interaction curves without repeating monomer quantum calculations at each separation.

quant-ph↗
arXiv2026

Into the danger zone: stable extrapolation in high-dimensional function and operator learning

Out-of-distribution (OOD) generalization is a central challenge in scientific machine learning. We study regression problems in which the test distribution differs from the training distribution and ask: under what assumptions on the target function or operator is stable extrapolation possible, and how far beyond the training domain can one extrapolate? Existing theory controls the test error through additive penalties measuring the discrepancy between the training and test distributions. Such guarantees show robustness to small distribution shifts, but can very pessimistic in comparison to OOD performance observed empirically. We identify classes of holomorphic functions and operators for which the OOD generalization error converges at algebraic rates even in the presence of large distribution shifts. This phenomenon stems from the increasing smoothness of higher-index coordinates, leading to what we term a `blessing of high dimensionality'. For learning with either polynomials, deep neural networks or deep neural operators, we derive explicit rates for arbitrary test measures supported on suitable domains and quantify how the admissible domain depends on the underlying regularity of the function or operator. Our extrapolation guarantees are independent of the test distribution, depending only on its support. We also present a series of numerical experiments across a range of functions and operators that support the main theoretical findings.

math.NA↗
arXiv2026

Block-Wise Variational Quantum Algorithms for PDEs with Interface Penalty Constraints

Global variational quantum algorithm (VQA) frameworks for solving partial differential equations (PDEs) often rely on a single expressive ansatz over a uniform grid, which becomes structurally inefficient when solutions exhibit spatially heterogeneous complexity such as localized singularities or thin boundary layers. A localized nonsmooth feature can degrade the convergence of the entire global quantum representation, imposing unnecessary circuit depth and amplifying the risk of vanishing gradients in barren plateaus. To overcome this limitation, we propose a block-wise VQA framework for PDEs characterized by spatially heterogeneous solution complexity. The computational domain is decomposed into locally represented quantum subproblems, where grid budgets and ansatz families are dynamically assigned based on a computable difficulty indicator. Artificial block interfaces are coupled through unified jump penalties for state values, derivatives, and physical fluxes, while adaptive reblocking tracks moving rough regions to maintain local accuracy without excessive global qubit overhead. The error analysis rigorously separates spatial discretization, ansatz expressivity, optimization convergence, finite-shot sampling noise, transfer errors from reblocking, and interface-coupling contributions. Reproducible residual-based simulations on representative elliptic, advection--diffusion, and Burgers problems demonstrate lower approximation errors and reduced peak local circuit width compared to global VQA approaches. These results substantiate block-wise quantum resource localization, confirming that high-fidelity PDE solutions can be achieved on near-term quantum devices without requiring a single globally expressive ansatz.

quant-ph↗
arXiv2026

Information-theoretic receding-horizon active learning of nonlinear dynamical systems

Accurately learning nonlinear dynamics from a finite-duration experiment requires the efficient collection of informative data. We address this challenge for stochastic controlled nonlinear dynamical systems whose state is observed along a single trajectory. Our goal is to reconstruct the unknown controlled state-increment map over a prescribed compact subset of state-input space. We construct a parametric estimator of the map using fixed nonlinear features, so that the model is nonlinear in the state and input, but linear in the unknown parameters. A Gaussian prior over the parameters yields recursive Bayesian posterior updates as data stream in, enabling online quantification of predictive uncertainty in the reconstructed dynamics over the target set. We formulate an optimal adaptive-design problem over an information state, using a prediction-oriented acquisition criterion based on the mean marginal mutual information between candidate future trajectories and the reconstructed dynamics over the target set. We then approximate the resulting adaptive-design problem by a non-myopic receding-horizon formulation, evaluate its remaining expectation using a scenario-based sample average, and solve the resulting deterministic program with the cross-entropy method, leveraging parallel candidate-scenario evaluations. Numerical experiments on a noisy multistable system demonstrate that the proposed adaptive information-seeking strategy reduces predictive uncertainty and reconstruction error more efficiently than common excitation baselines under comparable experimental constraints.

eess.SY↗
arXiv2026

Integrated assessment of tritium releases from fission and fusion energy systems and their environmental implications

Tritium is a naturally occurring radioactive isotope of hydrogen; a low-energy beta emitter with its health significance through internal exposure. The anticipated deployment of fusion energy systems is expected to increase tritium production significantly. Here we present an integrated assessment of tritium generation, release pathways, and resulting environmental concentrations across existing and emerging nuclear technologies. We first compile a comprehensive database of tritium production and releases from monitoring reports and literature. Analysis of light-water-reactor operating data shows that tritium discharge levels and release pathways are governed mainly by plant-specific strategies rather than reactor power or design parameters. This pattern reflects industry operating practices and efforts, with releases remaining well below regulatory limits. Our synthesis further indicates that FLiBe-based (Li2BeF4) systems may increase tritium production and mobility through enhanced permeation of tritiated hydrogen, although mitigation strategies are available to further limit emissions. Environmental transport modeling suggests that, under appropriate siting conditions, resulting tritium concentrations remain below regulatory thresholds. Furthermore, comparative risk analysis indicates that the associated carcinogenic impacts are expected to be lower than those from fossil-fuel-based power generation. Together, these findings demonstrate the importance of a comprehensive monitoring framework for contextualizing and managing routine effluent releases across energy systems.

physics.app-ph↗
arXiv2026

On the Capacity of DNA Labeling in the Single-Label Setting

DNA labeling has attracted increasing attention in biomedical applications, including molecular imaging, diagnostics, and genomic analysis. In a DNA labeling process, a set of DNA sequence patterns, referred to as labels, is designed according to the requirements of a specific application. For each DNA sequence, the labeling process generates an output sequence that records the positions of the labels. DNA sequences with different labeling outputs can therefore be distinguished through the labeling process. To quantify this capability, the labeling capacity is defined as the exponential growth rate of the maximum number of DNA sequences that can be distinguished through the labeling process as the sequence length tends to infinity [2]. To date, the labeling capacities of several cases in the single-label setting have been determined. In this paper, we formulate the labeling process as a deterministic channel and show that its zero-error capacity is equal to the labeling capacity. For a single label, the corresponding channel can be represented by a star graph. Thus, characterizing the labeling capacity of a single label is equivalent to determining the zero-error capacity of the corresponding star graph. We derive the zero-error capacities of all star graphs, thereby providing a complete characterization of the labeling capacities for all single-label cases. Furthermore, we develop a general method for constructing capacity-achieving codes. These results apply to labeling problems over arbitrary finite alphabets and are not restricted to the DNA alphabet. Finally, for a fixed label length, we exactly characterize the range of achievable labeling capacities and identify all single-label structures that attain the minimum and maximum capacities.

cs.IT↗
arXiv2026

Label-Permutation Symmetry and Stability in Oscillator Potts Machines

Oscillator Potts machines (OPMs) provide a physics-inspired, energy-minimization framework for solving combinatorial optimization problems described by the $q$-state Potts Hamiltonian. Although OPMs may be viewed as multistate extensions of oscillator Ising machines (OIMs), here, we show that they exhibit dynamical properties absent in the binary case. Specifically, we derive a configuration-dependent local-stability condition for a recently proposed multiharmonic OPM formulation and show that configurations with the same Potts energy need not be dynamically equivalent. In particular, for $q\geq4$, permutations of the Potts labels can alter the Jacobian spectrum and, consequently, the regularization strength required to locally stabilize a given Potts configuration. Thus, different phase encodings of the same Potts solution can exhibit different local stability properties despite having identical Potts energies.

physics.comp-ph↗
arXiv2026

Tensile minimal surfaces and thread boundary problems

Minimal surfaces bounded by cables or threads arise naturally in tensile architecture: a membrane under uniform tension takes the shape of a minimal surface, and its flexible, inextensible boundary lies along an asymptotic line of constant geodesic curvature. Such configurations have been studied experimentally since the 1960s at the Institute for Lightweight Structures in Stuttgart and more recently realized in gridshells built along networks of asymptotic and geodesic curves. Motivated by this architectural context, we construct two new families of embedded minimal surfaces bounded by finitely many asymptotic arcs of constant curvature, using the Plateau-conjugate method applied to the solution of a partially-free boundary problem for minimal disks that meet the unit sphere orthogonally along the free boundary component. For every integer $m\geq 3$ , we prove the existence of a one-parameter family of embedded minimal annuli, called tensile catenoids, whose boundary components each consist of $m$ asymptotic arcs of constant curvature that meet at cusps. As the parameter varies, the family degenerates from a planar configuration to a union of $m$ minimal disks. For every integer $k\geq 3$, we prove the existence of an embedded minimal surface with the topology of a sphere minus $k$ disks, called a tensile $k$-noid, each of whose $k$ boundary components consists of four asymptotic arcs joined by cusps. Both families are symmetric with respect to a horizontal plane and possess several vertical planes of symmetry. Embeddedness follows from showing that the fundamental piece obtained by conjugation is a graph contained in the region delimited by the planes of symmetry.

math.DG↗
arXiv2026

Multiplexed chiral and helical acoustic anomaly bulk states in an inverse-designed metamaterial

Valley and pseudospin are fundamental degrees of freedom (DOFs) in topological acoustics. However, they have so far been realized mostly in separate systems. Here, we achieve the multiplexing of valley and pseudospin DOFs in one acoustic system. An acoustic metamaterial simultaneously hosting single and double Dirac cones is inversely designed by the developed topology optimization method. Thereafter, under a hard-boundary condition, valley-locked chiral states and pseudospin-locked helical states emerge within two separate frequency windows and can be selected by tuning the operating frequency. Furthermore, their applications for multifrequency acoustic energy enhancement are experimentally demonstrated. Our work provides a strategy to modulate acoustic waves carrying distinct topological DOFs within a single integrated platform, facilitating the development of multiplexed acoustic devices with robustness.

physics.optics↗
arXiv2026

Structure-preserving upwind Lagrange multiplier schemes for solid-state dewetting with a logarithmic Flory--Huggins potential

Phase-field simulations of solid-state dewetting based on polynomial potentials may exhibit spurious bulk-diffusion coarsening, inconsistent with the surface-diffusion-dominated physics. To address this issue, we formulate a degenerate Cahn--Hilliard model with the logarithmic Flory--Huggins potential and dynamic contact line boundary conditions for the film--substrate--vapor triple junction. The logarithmic barrier confines the phase variable to its physical range and suppresses spurious coarsening at the continuum level. We develop a fully discrete, structure-preserving scheme that combines a Lagrange multiplier approach with an upwind finite-volume discretization and rigorously guarantees pointwise boundedness, mass conservation, and energy dissipation without artificial cut-offs or projections. A dimensional-splitting strategy further reduces computational cost while preserving these properties in each one-dimensional sweep. We also derive an explicit estimate of the equilibrium radius contraction caused by spontaneous film shrinking, showing that the logarithmic potential produces weaker spurious shrinkage than the polynomial potential. Numerical experiments confirm the analysis and demonstrate that, for small temperature parameters, the proposed scheme suppresses spurious coarsening and pinch-off while accurately reproducing surface-diffusion-dominated dynamics and relaxation toward equilibrium island structures.

math.NA↗
arXiv2026

T$^2$Mem: Learning Test-Time Memory for Robotics

Memory-dependent robotic manipulation requires policies to use information that is no longer available in the current observation. Retaining history alone is insufficient: memory must preserve information that supports future actions. One challenge is whether a memory-free foundation model can learn to retain and use historical information from action demonstrations alone, without external memory support. We introduce T$^2$Mem, a framework that develops this capability within a pretrained vision-language-action policy, without external reasoning models or memory-specific annotations. T$^2$Mem uses test-time training to encode observation history into compact fast weights through online self-supervised updates, avoiding repeated processing of the full history. An observation-grounded interface extracts vision-language information for memory formation and supplies retrieved context to the action expert. Action supervision shapes what the memory learns to retain and use, while alternating memory-policy learning gives each component a fixed counterpart during optimization. Across 16 RoboMME tasks, T$^2$Mem improves average success from 17.93% to 56.83% over the memory-free base policy and outperforms the recurrent-memory methods reported in the benchmark, while controlled profiling indicates at least 3x inference speedup over explicit methods. Project website: https://yzliu84.github.io/T2MEM-project/

cs.RO↗
arXiv2026

CALIBUDGET: Calibration-Guided Source Allocation for Fixed-Budget Mixed-Reasoning Adaptation

Fixed-budget adaptation from heterogeneous data sources requires deciding not only how much data to use, but how much exposure each source receives. Size-proportional rules can crowd out small sources, whereas difficulty-only rules can chase noisy estimates or allocate residual budget to nearly saturated pools. We introduce CALIBUDGET, a floor-protected, reliability-aware integer allocator that treats source exposure as an explicit adaptation variable. From small train-internal calibration splits, it combines model need, post-floor availability, and bootstrap stability, then produces exact capacity-respecting quotas without changing the model, objective, or total budget. In a controlled setting combining mathematical and commonsense data, CALIBUDGET improves CommonAvg, FragileAvg, and MacroAvg over validation-error-with-floor, the strongest matched comparator, in all three paired LLaMA-2-7B LoRA+ runs. The respective mean gains are 0.56, 0.46, and 0.41 percentage points (pp). Overall increases by 0.18 pp, whereas MathAvg decreases by 0.20 pp, exposing a coverage-retention boundary rather than a uniform gain. CALIBUDGET changes only 1.14-1.42% of the source budget but improves performance in 15 of 24 comparisons across commonsense tasks and seeds. These results suggest that small changes in source quotas can matter; example-level selection can then determine which examples fill each quota.

cs.LG↗