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

Mask-Proof: An LLM-based Automated Data Curation Pipeline on Mathematical Proofs

arXiv:2606.15258v1 Announce Type: new Abstract: Large language models (LLMs) are increasingly capable of mathematical problem solving and can even assist with research-level proofs, yet we still lack a scalable and reproducible way to measure step-level reasoning in long proofs across diverse sources. This evaluation gap limits trustworthy AI assistance in proof-certified scientific progress. Existing evaluations often emphasize final answers or rely on costly expert grading, while end-to-end proof generation remains open-ended and hard to verify automatically. We introduce Mask-Proof, a pipeline that turns real proofs into automatically checkable masked-step tasks. It masks key formula steps, provides the necessary surrounding context, and evaluates model reconstructions with an LLM-based equivalence judge using repeated votes for stability. The resulting Mask-ProofBench contains 292 curated problems across diverse research areas. Experiments with 17 models show that reasoning-enhanced models outperform standard models by 12% to 27%. Our evaluator achieves 96.8% agreement with expert annotators, enabling faithful, reproducible, and comparable measurement of step-level mathematical reasoning. Benchmark, annotations, and code are available at https://github.com/weating/Mask-Proof.

02.
arXiv (quant-ph) 2026-06-11

Super-Heisenberg Non-Equilibrium Quantum Sensing with Waveguide-Coupled Emitters

arXiv:2606.11975v1 Announce Type: new Abstract: We explore an array of quantum emitters as non-equilibrium probes, coupled to a one-dimensional photonic waveguide, aiming to estimate its properties such as wave number which encodes the waveguide frequency and dispersive characteristics. By considering transient dynamics following initial excitation, we show that the quantum Fisher information (QFI) can be significantly enhanced through careful emitter positioning. For two-emitter probes, optimal spacing stabilizes populations and coherences in the single-excitation subspace, suppressing super radiant decay and extending both the magnitude and longevity of QFI. Randomized emitter configurations also reveal that vanishing waveguide-mediated cross decay maximizes both achievable sensitivity and the temporal duration over which information about the parameter remains accessible. Extending to multipartite probes, we demonstrate that the maximum QFI and its temporal integral scale with system size, exceeding the Heisenberg limit for all positioning strategies. Our results highlight the potential of waveguide-coupled emitter arrays as versatile quantum sensors, where collective radiative dynamics can be harnessed to achieve tunable, long-lived, and enhanced precision.

03.
arXiv (CS.CV) 2026-06-12

CACR:Reinforcing Temporal Answer Grounding in Instructional Video via Candidate-Aware Causal Reasoning

The task of temporal answer grounding in instructional video (TAGV), which aims to locate precise video segments that respond to natural language queries, is increasingly important for direct video answer retrieval. This task remains challenging due to the need to comprehend semantically complex questions and to address the significant length mismatch between untrimmed videos and short target moments. Existing methods often suffer from sensitivity to irrelevant content or insufficient visual reasoning capabilities. To tackle these limitations, we propose a Candidate-Aware Causal Reasoning (CACR) framework. Our approach first employs a Visual-Language Pre-training based Candidate Selection (VBCS) algorithm to efficiently generate K candidate segments, then applies a temporal logic reasoning module enhanced by a rejection reward mechanism and optimized via Group Relative Policy Optimization (GRPO) for robust inference. Extensive experiments on six benchmarks demonstrate that our method achieves state-of-the-art performance in terms of mean Intersection-over-Union (mIoU), providing a new perspective for reasoning-based retrieval in long videos.

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

Brownian Kernel Ladders

arXiv:2606.15812v1 Announce Type: new Abstract: Constructing mathematically tractable function spaces that capture hierarchical compositional representations remains a central challenge in statistical learning theory. We introduce Brownian kernel ladders (BKLs), a recursively defined hierarchy of integral reproducing kernel Hilbert spaces generated through Brownian-kernel integral constructions. Starting from linear functionals, each layer is obtained by integrating Brownian kernels over probability measures supported on subsets of the previous layer, yielding a recursive function-space model in which depth is encoded directly through the hierarchy. Based on this framework, we define canonical BKL spaces together with an associated complexity functional. We establish several analytical and statistical properties of these spaces. In particular, we show that BKL spaces form quasi-Banach spaces, satisfy depth-dependent Hölder regularity estimates, and exhibit strict monotonicity with respect to depth. We further prove existence results for regularized empirical risk minimization and derive Gaussian complexity bounds that remain uniformly controlled with respect to both the ambient dimension and the hierarchy depth. A key ingredient of the analysis is a combinatorial proof technique based on recursive subset decompositions and Brownian-kernel threshold representations. These estimates yield excess-risk guarantees of near-parametric order for regularized empirical risk minimization over BKL spaces. Our results provide a mathematically tractable hierarchical function-space framework for studying compositional representations in deep learning.

05.
arXiv (quant-ph) 2026-06-17

An energy-based uncertainty principle and low-energy state preparation

作者:

arXiv:2603.15495v2 Announce Type: replace Abstract: Preparing low-energy states of many-body Hamiltonians is a central challenge in quantum computing, quantum complexity, and condensed matter physics. Existing approaches often get trapped in suboptimal states such as high-energy eigenstates or, more generally, low-variance states that resist further energy reduction. In this work, we explore a different perspective: instead of optimizing with respect to a single Hamiltonian, we leverage the fact that many systems admit families of Hamiltonians that share similar low-energy subspaces but differ at higher energies. We show that this redundancy can be turned into an algorithmic resource by establishing an energy-based uncertainty principle, which implies that these Hamiltonians cannot simultaneously admit low-variance states at higher energies. This suggests a simple strategy of alternating energy-lowering steps across such Hamiltonians, which we investigate numerically on several models. We also introduce a sparse variant where the uncertainty principle yields quadratically larger variance at higher energies, leading to more pronounced energy change. Overall, this work suggests a range of open questions at the interface of random matrix theory, local Hamiltonians and low-energy state preparation, aimed at understanding when such approaches are practical and how they can be analyzed rigorously.

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

Smooth time-dependent control of dipolar Bose-Einstein condensates

arXiv:2606.20507v1 Announce Type: cross Abstract: We consider protocols for control of dipolar Bose-Einstein condensates where the critical role is played by the long-range anisotropic interatomic magnetic dipole-dipole interaction. The phase diagram of such a condensate has been explored theoretically and experimentally with certain values of the interatomic scattering length corresponding to superfluid and supersolid phases, where supersolidity appears as a modulation in the ground state density. Preparation of this modulated ground state is challenging, since excitations appear as a result of a finite-time evolution required to produce qualitative changes in the wavefunction density. To solve this problem we consider the time-dependent control of a dipolar Bose-Einstein condensate using shortcuts to adiabaticity techniques, concentrating on design of the time-dependent scattering length, a parameter of the system easily tunable by contemporary experiments. The first technique is the variational approach based on the Euler-Lagrange equations for a separable ansatz describing the evolution of the superfluid state. Secondly, we study the transition from superfluid to supersolid using a direct optimization protocol. We discuss the fidelity of the developed protocols in terms of the evolution time.

07.
arXiv (quant-ph) 2026-06-12

Diffusive Dynamics of Nonstabilizerness

arXiv:2606.13606v1 Announce Type: new Abstract: Symmetries shape the quantum-information dynamics of many-body systems, but their effect on nonstabilizerness, the resource complementary to entanglement, is less understood. We compute the stabilizer Rényi entropy, a measure of nonstabilizerness, in $\mathrm{U}(1)$-symmetric one-dimensional random circuits. The disorder-averaged dynamics is captured by a four-replica tensor network, which we evaluate by $S_4$-adapted infinite time-evolving block decimation (iTEBD) directly in the thermodynamic limit. Together with a hydrodynamic argument, our results identify a diffusive universality class for the late-time approach of nonstabilizerness to its random-state value, with the stabilizer Rényi entropy gap closing as $1/t$. The same scaling is verified in an energy-conserving nonintegrable Ising chain. More broadly, our framework provides a hydrodynamic perspective on nonstabilizerness generation and offers insight into the design of approximate Haar-random states in Hamiltonian dynamics.

08.
arXiv (quant-ph) 2026-06-11

The quantum harmonic oscillator and the real Hilbert space

arXiv:2606.12060v1 Announce Type: new Abstract: The harmonic oscillator is considered within generalized frameworks using complex and quaternionic numbers. The classical oscillator is considered in terms of a complex position function, and quantum oscillators are examined in terms of complex wave functions, and in terms of quaternionic wave functions as well. Both of the quantum solutions are obtained within the real Hilbert space formalism. The results reveal the complex and quaternionic descriptions as suitable frameworks for non-stationary processes, including damped oscillations, forced oscillations, and additionally self-interacting processes that cannot be appropriately described otherwise.

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

NRITYAM: Language Models Meet Art and Heritage of Dance

Language models have become essential tools in shaping modern workflows. However, their global effectiveness hinges on a nuanced understanding of local socio-cultural contexts. To address this gap, we present NRITYAM, a comprehensive benchmark for evaluating the cultural comprehension capabilities of language models in the context of global dance traditions. NRITYAM comprises 9,260 carefully curated question-answer pairs spanning 12 languages, making it the largest dataset dedicated to evaluating cultural knowledge in dance. The dataset has been developed from the ground up through close collaboration with native dance artists and native speakers of the languages, who authored and validated culturally relevant questions specific to their regions. We evaluate a broad set of models, including large language models, small language models, multimodal large language models, and small multimodal language models. As a multilingual and multicultural benchmark, NRITYAM sets a new standard for evaluating the ability of AI systems to understand and reason about traditional performing arts. Detailed dataset samples are available at~\url{https://github.com/niladrighosh03/NRITYAM}.

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

PrologMCP: A Standardized Prolog Tool Interface for LLM Agents

arXiv:2606.14935v1 Announce Type: new Abstract: Frontier reasoning-tuned language models still fail on deductive tasks at depth, and the cost of improved performance through extended internal reasoning scales poorly. Symbolic delegation offers a complementary route: a language model translates the problem, while a solver performs the inference. However, current autoformalization pipelines for logic programming are typically bespoke integrations tied to particular tasks or agents. We introduce PrologMCP, a task-agnostic, open-source server that exposes Prolog as a stateful tool through the Model Context Protocol (MCP). Its compact tool interface, structured error reporting, and per-session isolation make the translate-run-inspect-repair loop a reusable primitive for MCP-capable agents. We evaluate a formalizer agent enhanced with PrologMCP against standard and reasoning LLMs (Claude Sonnet 4.6, GPT-4.1, and o4-mini) on two subsets of PARARULE-Plus: a general-purpose sample and a more challenging one targeting a specific failure mode of natural-language reasoning. On the general sample, the formalizer matches or exceeds reasoning LLMs (accuracy 1.00 vs.\ 1.00 / 0.998), with the largest gains over standard models (0.762 for GPT-4.1). On the challenging subset, the formalizer remains near-perfect (1.00 / 0.99) while reasoning LLMs drop to 0.95 / 0.94. These results suggest that delegating inference to Prolog via MCP is a robust and inspectable alternative to extended natural-language reasoning.

11.
arXiv (CS.CV) 2026-06-16

MambaH-Fit: Rethinking Hyper-surface Fitting-based Point Cloud Normal Estimation via State Space Modelling

We present MambaH-Fit, a state space modelling framework tailored for hyper-surface fitting-based point cloud normal estimation. Existing normal estimation methods often fall short in modelling fine-grained geometric structures, thereby limiting the accuracy of the predicted normals. Recently, state space models (SSMs), particularly Mamba, have demonstrated strong modelling capability by capturing long-range dependencies with linear complexity and inspired adaptations to point cloud processing. However, existing Mamba-based approaches primarily focus on understanding global shape structures, leaving the modelling of local, fine-grained geometric details largely under-explored. To address the issues above, we first introduce an Attention-driven Hierarchical Feature Fusion (AHFF) scheme to adaptively fuse multi-scale point cloud patch features, significantly enhancing geometric context learning in local point cloud neighbourhoods. Building upon this, we further propose Patch-wise State Space Model (PSSM) that models point cloud patches as implicit hyper-surfaces via state dynamics, enabling effective fine-grained geometric understanding for normal prediction. Extensive experiments on benchmark datasets show that our method outperforms existing ones in terms of accuracy, robustness, and flexibility. Ablation studies further validate the contribution of the proposed components.

12.
arXiv (CS.CV) 2026-06-17

Bridging Modality Disconnect in Self-Reflection via Closed-Loop Visually Grounded Verification

In the era of Vision-Language Models (VLMs), enhancing multimodal reasoning capabilities remains a critical challenge, particularly in handling ambiguous or complex visual inputs, where initial inferences often lead to hallucinations or logic errors. Existing VLMs often produce plausible yet ungrounded answers, and even when prompted to "reflect", their corrections may remain detached from the image evidence. To address this, we propose the MIRROR framework for Multimodal Iterative Reasoning via Reflection On visual Regions. By embedding visual reflection as a core mechanism, MIRROR is formulated as a closed-loop process comprising draft, critique, region-based verification, and revision, which are repeated until the output is visually grounded. To facilitate training of this model, we construct **ReflectV**, a visual reflective dataset for multi-turn supervision that explicitly contains reflection triggers, region-based verification actions, and answer revision grounded in visual evidence. Experiments on both general vision-language benchmarks and representative vision-language reasoning benchmarks show that MIRROR improves correctness and reduces visual hallucinations, demonstrating the value of training reflection as an evidence-seeking, region-aware verification process rather than a purely textual revision step.

13.
arXiv (CS.LG) 2026-06-18

Hierarchical Attention via Domain Decomposition

arXiv:2606.18525v1 Announce Type: new Abstract: We propose a hierarchical attention mechanism based on two-level overlapping Schwarz domain decomposition. The method is motivated by the observation that two-level Schwarz domain decomposition methods combine local subdomain corrections with a coarse level that communicates global, long-range information. We test its usefulness in the context of finite-dimensional operator learning using a simple, one-dimensional diffusion problem with homogeneous Dirichlet boundary conditions. Although elementary, this problem provides a controlled sequence-to-sequence setting in which the exact nonlocal solution operator is known. After discretization, learning the solution operator amounts to approximating the inverse of a symmetric positive definite matrix. As a baseline, we use a global softmax-free low-rank attention operator of the form $QK^T$. The proposed construction replaces this dense global factorization by a two-level additive structure: local low-rank attention blocks on overlapping subdomains are combined with a coarse attention block. The resulting operator has the form $$M_{\theta}^{-1} = \Phi Q_0 K_0^T \Phi^T + \sum_{i=1}^{N} R_i^T D_i^{1/2} Q_i K_i^T D_i^{1/2} R_i.$$ Here $R_i$ restricts to an overlapping subdomain, $D_i$ is a partition-of-unity weight, and $\Phi$ is a coarse interpolation (or prolongation) matrix. Numerical experiments for synthetic Fourier right-hand sides indicate that the domain-decomposition attention operator is able to train faster and can give more accurate approximations than a global low-rank attention baseline while using significantly fewer parameters.

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

Visualizing Uncertainty: Spatial Maps of Missing and Conflicting Evidence in Deep Learning

arXiv:2606.15767v1 Announce Type: cross Abstract: Understanding when and why deep neural networks are uncertain is crucial for deploying reliable machine learning systems in safety-critical domains. While existing uncertainty quantification methods provide scalar measures of model confidence, they offer limited insight into which spatial regions of an input contribute to different types of uncertainty. We propose a novel visualization framework, Uncertainty Activation Map (UAM), that combines Evidential Deep Learning (EDL) with Full-Gradient Class Activation Mapping (FullGrad) to generate interpretable spatial uncertainty activation maps. Our approach distinguishes between two fundamental types of uncertainty: vacuity, representing lack of evidence, and dissonance, capturing conflicting evidence between competing hypotheses. By leveraging the complete gradient decomposition property of FullGrad and the principled uncertainty quantification of Subjective Logic, our method produces theoretically grounded visualizations that highlight specific image regions responsible for model uncertainty. With this framework, vacuity and dissonance activation maps are generated by computing belief-weighted attributions, enabling identification of where models lack knowledge versus where they encounter ambiguous evidence. Extensive evaluations across multiple benchmark datasets demonstrate that the proposed framework effectively addresses the critical gap between uncertainty quantification and explainability, providing intuitive visual feedback to assess model reliability in complex visual recognition tasks.

15.
arXiv (CS.LG) 2026-06-18

Estimating carbon pools in the European Shelf sea environment: replacing reanalysis by model-informed machine learning?

arXiv:2508.10178v3 Announce Type: replace-cross Abstract: Shelf seas are important for the economy and the carbon cycle, but shelf sea observations for carbon pools are often sparse, or highly uncertain. An alternative can be provided by carbon reanalyses (whether assimilating proxy variables, such as chlorophyll-$a$, or directly carbon), but these are often expensive to run. We propose to use a computationally cheap ensemble of neural networks (i.e. deep ensemble) to learn the relationship between the directly observable (atmospheric, riverine and ocean) variables and marine carbon pools from a coupled physics-biogeochemistry model. The deep ensemble was trained on a North-West European Shelf (NWES) physical-biogeochemistry model free run simulation. After training, the deep ensemble was run using inputs from the NWES reanalysis instead of the free run, demonstrating that it can efficiently predict several NWES carbon pools (e.g., detritus, zooplankton, heterotrophic bacteria) in much better agreement with the reanalysis than the free run, while also providing uncertainty information. We further show that the deep ensemble performs similarly well when it is driven directly by the observations assimilated into the reanalysis, with the limitation that carbon pools can then be predicted only at the observed locations and times. We focus on explainability of the results and demonstrate potential use of the deep ensembles for future climate what-if scenarios. We suggest that model-informed machine learning presents a viable alternative to expensive reanalyses and could complement observations, wherever they are missing and/or highly uncertain.

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

DySink: Dynamic Frame Sinks for Autoregressive Long Video Generation

Autoregressive long video generation often adopts bounded-memory streaming for efficiency, typically combining local windows for short-term continuity with static early-frame sinks as long-range anchors. However, this fixed allocation keeps early frames cached even when the current visual state has substantially diverged from them, while discarding potentially more relevant intermediate history. As a result, the retained long-range context may become less adaptive and bias generation toward outdated cues; in severe cases, RoPE-induced phase re-alignment can homogenize inter-head attention and cause sink collapse, where content regresses toward sink frames. We propose DySink, a retrieval-based framework that maintains a compact memory bank and selects visually relevant historical frames as dynamic frame sinks. DySink couples adaptive retrieval with a sink anomaly gate, which detects excessive inter-head consensus over retrieved context and suppresses collapse-prone context. Experiments on minute-long videos show that DySink consistently improves dynamic degree over strong baselines while also achieving higher temporal quality. The code and model weights will be released at https://github.com/yebo0216best/DySink.

17.
arXiv (quant-ph) 2026-06-11

Fabricating fiber cavity mirror substrates compatible with high coupling efficiency

arXiv:2606.12168v1 Announce Type: cross Abstract: Fiber optical cavities offer small mode volumes and correspondingly strong light-matter interactions in an open Fabry-Perot geometry. However, existing fabrication techniques do not reliably produce substrates with surface profiles amenable to high mode matching between the cavity mode and fiber core, thereby limiting the achievable collection efficiency. Here we present a technique to fabricate fiber mirror substrates while using $in situ$ reflectometry to constrain the achievable mode matching prior to coating. By measuring the back-reflection from freshly cleaved fiber tips, we pre-select 138 fibers compatible with 96.5-99.5% mode matching, and after a single CO$_2$ laser ablation pulse, these fibers remained compatible with 95.3-99.2\%. This simple technique provides rapid feedback during each stage of substrate fabrication, greatly enhancing the yield of viable fiber mirror substrates prior to (expensive) coating runs.

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

Two Wrongs, No Right: Auditing Social-Desirability Bias in LLM Annotators for Computational Social Science

作者:

LLM annotators are increasingly used in computational social science (CSS), but it is unclear whether their alignment-shaped errors preserve the empirical conclusions a researcher would report. We audit three open-source 7B instruction-tuned models (Zephyr, Mistral-Instruct, Qwen2.5-Instruct) across six TweetEval tasks under four prompt conditions (72 cells) and find that social-desirability failures do not run in a single direction. Zephyr exhibits leniency bias, systematically under-applying harmful labels (offensive language: false benign rate 0.729, false alarm rate 0.031). Mistral and Qwen exhibit overcorrection, over-applying the same labels (Mistral hate-speech FAR = 0.604). All three models exhibit neutrality bias on abortion stance, underestimating opposition prevalence by 24 to 40 percentage points and inflating the neutral label. None of the four prompting interventions we test (neutral, safety framing, depersonalized, chain-of-thought) corrects these failures across models; safety framing can worsen stance distortion. Strikingly, Zephyr's hate-speech prevalence estimate matches the gold rate exactly while its class-conditional errors are large in both directions, an accidental cancellation that misleads aggregate validation. We translate these patterns into a three-part taxonomy with diagnostic FBR/FAR signatures and a lightweight gold-sample validation protocol. The headline for trustworthy CSS: a model that looks calibrated on aggregate metrics can still flip the substantive empirical conclusion a researcher would report.

19.
arXiv (quant-ph) 2026-06-15

New Identity for Cayley's First Hyperdeterminant with Applications to Symmetric Tensors and Entanglement

作者:

arXiv:2512.03093v3 Announce Type: replace Abstract: In this article, a new formula for computing Cayley's first hyperdeterminant in terms of the Levi-Civita symbol is given. It is then shown that this formula can be used to compute the hyperdeterminant of symmetric tensors in polynomial time with respect to their order (assuming fixed side length). Applications to quantifying the entanglement of states of bosonic quantum systems are then discussed. Additionally, in order to obtain the fast calculation of the hyperdeterminant on symmetric tensors, generalized elimination and duplication matrices are defined and their explicit formulas are derived.

20.
arXiv (CS.AI) 2026-06-12

MOSAIC: Modality-Specific Adaptation for Incremental Continual Learning in Parkinson's Disease Gait Assessment

arXiv:2606.13258v1 Announce Type: new Abstract: Gait-based Parkinson's disease assessment increasingly relies on heterogeneous sensors, but clinical systems rarely collect all modalities simultaneously. New sensors may arrive through device upgrades, protocol changes, or multi-center deployment, while historical patient data are often unavailable because of privacy and storage constraints. This modality-incremental setting faces three challenges: unreliable cross-modal distillation, modality-specific statistical shifts, and reduced plasticity after preservation. We propose MOSAIC, a compact continual learning framework. First, we identify the Toxic Teacher phenomenon and introduce Modality-Specific Warm-Up to stabilize newly learned modality representations before distillation. Second, we propose a statistics-decoupled MSBN architecture that isolates sensor statistics while maintaining a shared semantic backbone. Third, we design a curriculum-guided repulsive objective for Plasticity Recovery, preserving legacy knowledge while recovering modality-specific capacity. Experiments on three multimodal Parkinson's gait datasets show that MOSAIC improves final performance and mitigates forgetting. Project code is available at: https://github.com/minlinzeng/MOSAIC_Modality-Specific-Adaptation-for-Incremental-Continual-Learning-in-PD-Gait-Assessment.git

21.
arXiv (CS.CV) 2026-06-24

Ingredient-Level Food Image Segmentation for Nutrition Awareness

Food images often contain several visible ingredients, so assigning one dish label to an entire image hides important visual structure. This work studies ingredient-level semantic segmentation on FoodSeg103, where the model predicts an ingredient class for each pixel. Two SegFormer variants were fine-tuned and evaluated under a controlled setup: SegFormer-B0 as the smaller baseline model and SegFormer-B1 as the larger final model. Both models use ImageNet-pretrained MiT backbones with newly initialized 104-class output layers. On the held-out FoodSeg103 test split of 2,135 images, B0 achieved 0.7709 pixel accuracy and 0.2521 mean IoU, while B1 achieved 0.7929 pixel accuracy and 0.3204 mean IoU. B1 improved every saved test metric, including a +0.0683 absolute gain in mean IoU. The system also converts predicted masks into visible ingredient-area percentages, giving a simple visual composition summary of the predicted meal. This summary can serve as a first-pass nutrition-awareness cue by providing a visual alternative to detailed food tracking similar to plate-based meal guidance, but it is not a direct estimate of calories, macronutrients, food mass, volume, density, or true portion size.

22.
arXiv (CS.CL) 2026-06-12

GENIE: A Fine-Grained Measure for Novelty

Large Language Models have consistently demonstrated a lack of creativity and diversity across tasks. Prior work has focused on addressing whether models are capable of generating creative outputs. Here, we aim to consider novelty and investigate what makes model-generated content novel or not novel in a task-specific manner. We propose a fine-grained evaluation metric GENIE to measure the novelty of responses along task-specific features with respect to a population of responses. We show that unlike GENIE, holistic metrics struggle to capture the high-dimensionality of novelty and do not provide insight on which properties they target. Finally, we use GENIE to measure the effectiveness of mitigation methods that address creativity to better understand where these methods can improve novelty.

23.
arXiv (quant-ph) 2026-06-16

Fully Quantum Algorithm for the 1-dimensional linear Lattice Boltzmann Method

arXiv:2606.16514v1 Announce Type: new Abstract: A fully quantum algorithm for solving the one-dimensional linear advection-diffusion equation using the Lattice Boltzmann method as a numerical procedure is presented in this work. We start by presenting a state of the art of the current usage of quantum algorithms for solving ordinary and partial differential equations. We then describe two algorithms for the one-dimensional Lattice Boltzmann method with two degrees of freedom. The first one is an existing hybrid quantum-classical algorithm with measurements at each time step, and the second one is our improved version, viz. a fully quantum algorithm where only one measurement is needed at the end of the algorithm. The fully quantum algorithm is first executed on a quantum simulator and then compared with a classical approach. Subsequently, the fully quantum algorithm is run on a quantum system with 133 qubits to investigate the effect of noise and the depth of the circuit on the output state. We find fluctuations in the final result due to the decoherence noise of the qubits.

24.
arXiv (quant-ph) 2026-06-16

Quantum Information Geometry of Multicomponent Superconducting Fluctuation Transport

arXiv:2606.15928v1 Announce Type: cross Abstract: Quantum geometry underlies many electronic responses, but its transport signatures have so far been established mainly for pure single-particle Bloch states. Whether collective many-body fluctuations possess a measurable quantum geometry remains largely unexplored. Here we show that superconducting fluctuation transport provides a direct probe of quantum information geometry in collective many-body matter. Starting from a multicomponent time-dependent Ginzburg-Landau theory in the Gaussian fluctuation regime, we identify the equilibrium density matrix of fluctuating Cooper pairs as the static pair propagator, which defines a positive mixed-state manifold in momentum space. The geometry of this manifold is directly measurable through paraconductivity: the longitudinal paraconductivity is governed by the quantum Fisher information of superconducting fluctuation modes, while the fluctuational anomalous Hall effect is governed by the mean Uhlmann curvature, the mixed-state counterpart of Berry curvature. This correspondence further yields geometric bounds between these two transport components, with no direct analogue in normal electronic transport. Applied to chiral superconducting fluctuations in quarter-metal systems motivated by rhombohedral multilayer graphene, a symmetry-allowed Lifshitz invariant generates finite mean Uhlmann curvature and logarithmically enhances the anomalous Hall conductivity above the critical temperature. Our results establish collective superconducting fluctuations as an experimentally accessible transport probe of mixed-state quantum information geometry.

25.
arXiv (CS.LG) 2026-06-15

Lifted Schrödinger Bridges for Gaussian Mixture Endpoints: Projection Gaps and Path-Space Obstructions

arXiv:2605.24795v2 Announce Type: replace-cross Abstract: We study stochastic density control between Gaussian-mixture endpoint distributions under Brownian prior dynamics. Since the direct Schrödinger bridge between Gaussian mixtures is generally not available in closed form, we introduce a lifted path-space construction in which each trajectory is augmented with a source–target component label. Consequently, the problem decomposes into Gaussian component-to-component Schrödinger bridges with explicit marginal, drift, and cost formulas, while the mixture-level assignment reduces to a finite-dimensional entropic coupling problem with a Sinkhorn scaling form. We then analyze the projection obtained by discarding or forgetting the label. By construction, the projected law satisfies the original Gaussian-mixture endpoint constraints, but its relative entropy generally differs from the lifted relative entropy by a nonnegative conditional label-information gap. This gap reveals a path-space obstruction: the lifted optimizer cannot, in general, be identified with the direct unlabeled Schrödinger bridge after projection. We also derive the posterior-averaged Markov drift associated with the projected marginal flow, prove a kinetic-energy upper bound, and identify a common path-potential condition under which the projection gap vanishes. Several numerical illustrations showing density and shape control are recorded for a self-contained exposition.