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arXiv2026

Periodic conditional measurements on a photonic chip

Quantum measurements not only extract information but also reshape quantum evolution through measurement backaction. Here, we investigate periodic conditional measurements, in which coherent evolution is repeatedly interrupted by local measurements. We show that the bright and dark modes of the conditional evolution operator provide a unified spectral description of both the post-selected final state along no-detection trajectories and the statistics of detection events. Using a three-dimensional photonic chip, we demonstrate on-demand state engineering through dark-mode preservation and bright-mode selection, enabling the protection of topological corner states and excited-state shelving. We further observe the predicted transition of the total detection probability on an effectively infinite one-dimensional lattice and identify its microscopic origin in Floquet near-dark modes. These results establish periodic conditional measurements as a general framework for engineering conditional quantum states and manipulating event-detection statistics in monitored quantum dynamics.

quant-ph↗

arXiv2026

Ontology Refinement with Embeddings and LLMs: A Case Study on CASTON

Ontologies are widely used to represent and organize complex knowledge in domains such as biomedicine and healthcare. However, constructing reliable ontologies remains challenging, as class hierarchies, whether manually or automatically constructed, may contain subtle subsumption errors that require careful refinement. We study this problem in CASTON, a casting-domain ontology, and present a lightweight but scalable refinement workflow that combines a fine-tuned ontology embedding model with Large Language Models (LLMs). The embedding model is used to extract a limited number of candidate axioms for refinement together with possible replacement candidates, and an LLM then returns repair suggestions. In a small expert evaluation, the default configuration using a CASTON-fine-tuned OnT embedding model and Qwen3-8B produced reliable high-confidence repairs: all six high-confidence replacements were accepted by both domain experts. The implementation is available at https://github.com/HuiYang1997/OntRefine.

cs.AI↗

arXiv2026

DuET: Note-Frame Dual Encoding for Piano Performance-to-Score Transcription

Transcribing expressive piano performances into scores requires interpreting individual note timings within an underlying metrical structure. However, score attributes are associated with notes, whereas beats may occur without coincident note onsets. We introduce DuET, a Dual-Encoder Transformer that jointly learns note-level performance MIDI-to-score (PM2S) transcription and frame-level beat and downbeat tracking. Bidirectional cross-attention connects note and frame encoders, while an autoregressive decoder alternates between their representations to predict structured score attributes. We further introduce TimeRoPE and Time-Pitch Rotary Positional Encoding (TPRoPE) to establish a shared performance-time reference and explicitly encode relative temporal and pitch relationships. Evaluations on ASAP, a classical piano dataset, and our curated Gangqinpu dataset, which spans multiple genres with a focus on popular piano music, demonstrate improvements in score timing and notated duration. Compared with the strongest baseline on each dataset, DuET reduces MUSTER mean error from 6.56% to 3.64% on Gangqinpu and from 11.30% to 11.22% on ASAP. Ablations support the benefits of frame-level context, time-based positional encoding, and decoder-history masking. Code, weights, and demos are available at https://github.com/wei-zeng98/DuET.

cs.SD↗

arXiv2026

Can LLMs Tell Stories Out of Order? A Corpus and Benchmark for Nonlinear Narrative Generation

Every story has two orders: the order in which its events happen and the order in which they are told. A story is nonlinear when the two differ. We introduce a benchmark of 83 published works that measures whether language models can tell nonlinear stories. For each work, we annotate one list of events in both orders, together with a story graph of causal dependencies, character knowledge, and the questions the telling raises and resolves. Given events in chronological order, all 19 models tell them, on average, more chronologically than the published works do; asked for a specific structure, they land within the human range about half the time. We then compare a model's stories of the same events under different conditions, using both an automated judge and 71 human readers. Both prefer the chronological story a model writes by default to the nonlinear one it writes on request, which readers find harder to follow in 81% of decisive judgments. Readers also prefer stories written from the story graph to stories constrained to the published telling order (72% of decisive judgments), a difference the judge does not detect. Our results suggest that following an instruction to reorder a story is not yet the same as telling it well out of order.

cs.CL↗

arXiv2026

Limits of adaptive linear postprocessing in six-state quantum key distribution

Two-way classical communication improves the noise tolerance of quantum key distribution, but the limits of adaptive parity processing remain unclear. For the six-state protocol with equal three-basis error rate $p\in[p_*,1/2]$, where $p_*=(5-\sqrt5)/10\simeq27.64\%$, we construct a single compatible collective attack that defeats a broad class of linear postprocessing. Each public message may be an affine function of the sender's raw key, chosen adaptively from the public history. For every finite input length and every accepted transcript of positive probability, Eve's optimal probability of recovering any affine function of Alice's raw key is at least Bob's. Consequently, reliable agreement on a linear final key is incompatible with secrecy. The same conclusion holds for arbitrary publicly seeded privacy amplification after reliable recovery of a linear candidate. The proof conditions on the complete transcript, which restricts the two raw keys to affine subspaces. A local degradation of Eve's state, a known Rényi-entropy comparison, and a coset-probability inequality then give the recovery comparison. Both inequalities are proved in self-contained appendices. The result allows block splitting, regrouping, nonzero-syndrome selection, and adaptive linear reconciliation.

quant-ph↗

arXiv2026

Cross-Prompt Inference Mitigates Rare-Class Suppression in Imbalanced VLM Finetuning

When a vision-language model is finetuned on class-imbalanced data, rare-class recall can fall well below the model's own zero-shot performance. In this regime, we uncover a surprising matched-prompt penalty whereby the standard choice of reusing the descriptive finetuning prompt at inference can yield lower rare-class recall than using a different descriptive prompt. We call this inference-time strategy cross-prompt inference. We evaluate diverse VLMs across six datasets and find that cross-prompt inference consistently recovers rare-class recall, with varying trade-offs in frequent-class recall. The effect reflects a train-eval prompt interaction rather than prompt quality alone, and does not arise with non-descriptive prompt changes. It is strongest when imbalance and visual confusability produce substantial rare-class suppression, and is weak or absent when such suppression does not occur. Using Tuning Contribution (TuCo), which decomposes a model's computation into pretrained and finetuning parts, we find that cross-prompt inference reduces reliance on finetuning-induced computation and shifts the model toward its pretrained component. Reducing that finetuning contribution also substantially reduces the cross-prompt advantage. These results show that rare-class knowledge suppressed by imbalanced finetuning can remain accessible under a different inference prompt.

cs.CV↗

arXiv2026

Fixed-spinor radial solutions of a perturbed Euclidean spinorial Yamabe equation

We study the perturbed Euclidean spinorial Yamabe equation \[ D_{g_{\mathbb R^n}}ψ = \frac n2\bigl(1+\varepsilon K(x)\bigr) |ψ|^{2^*-2}ψ \qquad\text{on }\mathbb R^n,\quad n\ge2, \]where $2^*:=2n/(n-1)$, $\varepsilon>0$ is a small parameter and $K$ is a prescribed radial function. We establish a finite-dimensional reduction within a radial spinor space determined by a fixed unit spinor, reducing the problem to the analysis of a function of the dilation parameter. Under suitable assumptions on $K$, we obtain explicit existence criteria for solutions with this prescribed spinorial structure, together with a multiplicity criterion yielding solutions associated with distinct scales. These criteria are expressed in terms of the behavior of $K$ at the origin and weighted integral quantities.

math.AP↗

arXiv2026

Smale's mean value constant and admissible univalent Blaschke pairs

Let $\mathcal{P}$ be the class of polynomials $P$ of degree at least $2$ with $P(0)=0$, $P'(0)=1$, let $S(P)=\min_{P'(c)=0}|P(c)/c|$ and let $\mathcal{M}=\sup_{P\in\mathcal{P}}S(P)$ be Smale's mean value constant. Smale proved that $\mathcal{M}\le4$, observed that $\mathcal{M}\ge 1$, and asked whether $\mathcal{M}=1$. We show that $\mathcal{M}$ coincides with $$ \mathcal{B}=\sup\frac1{B(0)}, $$ the supremum running over pairs $(W,B)$ in which $W$ is a normalised univalent map of the standard unit disk $\mathbb{D}$ and $B$ is a finite Blaschke product with $B(0)>0$ such that $WB$ is locally univalent in $\mathbb{D}$. Smale's question is therefore a problem in univalent function theory. We also introduce the degree-restricted constants $\mathcal{B}_d$ for $B$ with $\mathrm{deg} B \le d$ and show that $$1.1018586788\ldots=\sqrt{\frac{8081}{6656}} \le \mathcal{B}_1 < \sqrt{\frac{7}{5}}=1.1832159566\ldots$$ This implies that $\mathcal{M}>1.1018$ and we also show that there are polynomials of arbitrarily large degree with $S(P)>1.1018$.

math.CV↗

arXiv2026

Global Well-Posedness for the 3-D Inviscid Oldroyd-B Model with Fractional Stress Diffusion

We study the 3-D incompressible inviscid Oldroyd-B model with fractional stress diffusion $(-Δ)^βτ$ and without stress damping. For $β\in (\frac{1}{2},1)$ and $s\in [2β+\frac{1}{2},\frac{5}{2}]$, we establish local well-posedness for initial data $(u_0,τ_0)$ in $H^s(\mathbb R^3)$, provided that $\|(u_0,τ_0)\|_{H^β}$ is bounded and $\|Λ^β(u_0,τ_0)\|_{H^{s-β}}$ is sufficiently small. If, in addition, $β\in(\frac{1}{2},\frac{5}{6}]$, we give a global well-posedness result. Our results complement the work of Constantin, Wu, Zhao and Zhu \cite{ConstantinWuZhaoZhu2021} by treating the Sobolev regularity $s\in[2β+\frac12,\frac{5}{2}]$, below the threshold $s>\frac52$ considered there. We also provide an $\ell^2$ alternative to the high-frequency $\ell^1$ summability condition in the framework of Wu and Zhao \cite{WuZhao2022}.

math.AP↗

arXiv2026

Multiplicative Path Weights in Networks: From Katz Connectivity to Mean First-Passage Times

Signal dispersion, stress propagation in interbank systems, and transmission probabilities in epidemic and reliability models are all captured by studying paths on directed graphs where the path weight is defined as the product of its edge weights. Connectivity in such networks is naturally quantified by aggregating these multiplicative path weights across nodes. This paper provides a comprehensive treatise on connectivity and ranking measures based on multiplicative path weights. We demonstrate how standard all-path connectivity, such as the standard Katz centrality, can be extended beyond its classical spectral threshold. In addition, we derive closed-form expressions for connectivity based on first-hit paths and introduce a new version of Katz centrality. Furthermore, for random edge weights, we derive resolvent-based expressions for the first and second moments, alongside variance bounds, under a path-indexed coupling framework. Finite irreducible Markov chains are a subclass of the models studied, and we show that the scaled matrix of first-hit path probabilities is the probability-generating function for first-passage and return times, and that differentiation yields the classical first-passage times. Numerical examples illustrate the application of our results in a variety of settings.

cs.SI↗

arXiv2026

Approach to Equilibrium in Translation-Invariant Quantum Systems: Structural Results II

We continue the development, started in [AHP 25 (2023), 715-749], of a structural theory of approach to equilibrium in translation-invariant quantum spin systems. Dynamical Steady States (DSS) are defined as w*-limit points of the time-averaged evolution of an initial state. We show that if a DSS is an equilibrium state of a sufficiently regular interaction, then the specific energy of this interaction is necessarily a constant of the motion. Two distinct mechanisms lead to this conclusion, one based on dynamical surface energies and the other on conservation of specific relative entropy. We conjecture that these properties hold for a natural class of interactions. For a DSS admitting a physical equilibrium description, the associated equilibrium states are characterized by a dynamical Gibbs variational principle: they are precisely the minimizers of the specific relative entropy from the initial state over the physical equilibrium states. The achieved minimum equals the increase of specific entropy. The structural theory also yields characterizations of approach to thermal equilibrium, based on two model-dependent questions: restoration of a sufficiently local thermodynamic description at large times and classification of the corresponding local constants of motion. Once locality is restored, the constants of motion determine the possible asymptotic equilibrium states. In particular, if finite-range locality is restored and the energy is the only finite-range constant of the motion, then every DSS is a thermal equilibrium state at the temperature fixed by energy conservation. The finite-time dynamical input underlying this theory is established in a companion paper.

math-ph↗

arXiv2026

A sharp survival threshold for branching Brownian motion in a self-generated resource environment

We study branching Brownian motion in a resource environment created by the particles themselves. Particles reproduce at rate $β$ times the resource nearby, resource is consumed at rate $c$ times the number of particles nearby, and each death returns resource mass $m$. Let $θ=βm/c$, which represents the number of births supported by resource from one corpse, assuming perfect efficiency. We prove that the population dies out almost surely if $θ\leq1$, even with perfect recycling $\left(θ=1\right)$. If $θ>1$ and the interaction kernel has finite range and is bounded below at short distances, the population survives with positive probability from every initial state with at least two particles, or with one particle and some resource. The threshold does not depend on the diffusivity, the death rate or the interaction kernel. We prove extinction for $θ\leq 1$ by showing the total mass in the system to be a supermartingale. The proof of survival rests on two estimates: a large colony grows if it consumes its corpses with little waste, and a dense colony recycles corpses efficiently. Together these imply that a large, dense colony grows with exponentially high probability, and a standard doubling and restart argument then yields survival.

math.PR↗

arXiv2026

Tool-Augmented Large Language Models for Reliable Medical Calculation from Patient Notes

Medical calculators translate raw patient observations into clinically actionable values and scores. However, applying these calculators directly to free-form patient notes requires precise variable extraction combined with the exact execution of complex formulas, scoring rules, and output conventions. Relying solely on direct large language model (LLM) prompting is unreliable in this context, as rule recall, parameter extraction, arithmetic reasoning, and formatting become entangled within a single generative step. To address these limitations, we propose a tool-augmented LLM framework for reliable medical calculation from patient notes. The framework retrieves and structures calculator specifications, generates reusable executable tools, and uses a constrained extractor to map each patient note to calculator-ready inputs. The tools then perform deterministic calculation, separating clinical language understanding from rule execution and arithmetic. Evaluated on the MedCalc-Bench dataset, our method achieves 86.73% final-answer accuracy, outperforming the one-shot prompting and supervised fine tuning-only baselines by 24.0 and 17.27 percentage points. Ablation and error analyses show that these performance gains are primarily driven by rule-grounded tool synthesis and schema-constrained extraction, whereas remaining failures are concentrated in clinical-semantic extraction and benchmark-specific output contracts. By grounding calculator logic in executable tools, the proposed approach alleviates arithmetic hallucinations and improves the computational reliability of the final clinical outputs.

cs.AI↗

arXiv2026

Difference between pair creation and anomaly matching: Nontrivial aspects of invertible symmetries and defects in $SU(N)$ models

We study the connection between the $SU(N)_{K}$ Wess-Zumino-Witten (WZW) model and $SU(N)_{K'}$ WZW models, enforcing the unbroken $\mathbb{Z}_{N}$ symmetries. The fundamental underlying structures are the (half-)integer spin simple currents in the topological quantum field theories and anomaly matching conditions in conformal field theories. For the (half-)integer spin simple current condition of the folded models $SU(N)_{K}\boxtimes_{\mathbb{Z}_{N}} \overline{SU(N)_{K'}}$ or $SU(N)_{K}\boxtimes_{\mathbb{Z}_{N}} SU(N)_{K'}$, we obtain the generalized pairing condition $K= \pm R^{2}K' (\text{mod}.N)$ with $\text{gcd}(R,N)=1$. On the other hand, the anomaly matching condition results in the weaker condition $K= \pm RUK' (\text{mod}.N)$ with $\text{gcd}(R,N)=\text{gcd}(U,N)=1$. Surprisingly, the anomaly matching without the pairing condition results in the intrinsic mismatch of the preservation law of the $\mathbb{Z}_{N}$ defects and symmetries. The pairing condition canonically relates symmetries and defects, as in category theory, whereas it is unclear whether it can be a guiding principle in prohibiting the massless renormalization group flows.

hep-th↗

arXiv2026

Determining the Threshold Excess in Top-Quark Pair Production through a Global PDF Analysis

We present an empirical determination of the threshold excess $Δ$ in top-quark pair production, taking full account of correlated uncertainties with PDFs, the top-quark mass $m_t$ and the strong coupling $α_s(m_Z)$. We extract $Δ$ from a variety of differential $t\bar{t}$ cross-section measurements by ATLAS and CMS at 8 and 13 TeV, using theoretical predictions of the $t\bar{t}$ continuum up to NNLO QCD accuracy, including an estimate of missing higher order uncertainties and NLO EW corrections. At 8 TeV we see no evidence of a significant threshold excess, but at 13 TeV obtain results above the NNLO QCD $t\bar{t}$ background at just over two $σ$ when we combine all the available measurements. We also find evidence of a strong correlation between $Δ$ and $m_t$, which must be taken into account if the uncertainty on any threshold excess is to be estimated reliably.

hep-ph↗

arXiv2026

Kolmogorov-Arnold Networks: Curse of Dimensionality and Structural Bias

Kolmogorov-Arnold networks (KANs) have a dimension-independent approximation exponent when the target admits a sufficiently smooth representation by univariate edge functions. We ask whether this favorable scaling belongs to the architecture or to the assumed target class. For arbitrary-depth standard spline-KANs, we prove a worst-case lower bound on isotropic Sobolev balls: below a dimension-independent accuracy threshold, the required number of spline coefficients grows at least exponentially with input dimension. Existing composition-matched MLP results, by contrast, show that favorable exponents on low-arity targets are not exclusive to KANs. We also revisit empirical comparisons. On four scaling-law targets, spline-KAN approximants constructed from known decompositions transfer exactly to MLPs with the cubic ReLU activation $σ(x)=(\max\{0,x\})^3$, although their full dense parameter counts are larger. In controlled ridge-profile scans, KANs have a strong advantage when each nonlinear component depends on one input coordinate. When a component couples multiple input coordinates, this advantage may narrow sharply. At tight budgets, interacting targets often favor MLPs. In the random-label test on MNIST, ReLU-MLPs fit the randomized training labels more efficiently than spline-only KANs. Together, these results locate favorable scaling in target structure and a compatible inductive bias, not a general KAN-specific escape from the curse of dimensionality.

cs.LG↗

arXiv2026

A 2D Image Feedback-Based Autonomous Endovascular Navigation Method: A Perception and Control Framework

In endovascular interventions, physicians rely on planar DSA and X-ray fluoroscopy to interpret vessel anatomy and device motion, yet converting these images into feedback for autonomous navigation remains difficult. A perception and control method is formulated for two-dimensional image feedback. Vessel masks are converted into a labeled centerline graph, and device-tip estimates are projected onto a planned path to obtain progress, deviation, and direction. A rule-based controller uses these quantities for delivery, branch selection, probing, rollback, and recovery. The method was evaluated on a physical dual-device robotic platform in 65 closed-loop runs using simulator-rendered planar images across three paths. All runs reached at least 0.95 maximum observed guidewire progress; two runs (3.1%) met the prespecified failure rule of three or more autonomous stop events. The results establish route-level performance on the tested platform; clinical image sequences and broader anatomy remain to be evaluated.

cs.RO↗

arXiv2026

FlashAttention with Statistics: Low-Overhead Attention Features for Compact Hallucination Detectors

Large language models can produce fluent answers that the supplied context does not support. A compact frozen proxy model can detect such answers by reading the context and another model's response, even from a proprietary generator. Attention-based detectors use summary statistics of the proxy's attention weights, but standard pipelines materialize the attention matrix, whose memory grows quadratically with sequence length. We compute these statistics without materializing attention, by accumulation in the FlashAttention pass, sparse lookups after it, or a second tiled pass over the scores, and classify them by this path into nearly free and costlier ones. On an H100, the statistics of five published detectors add 16% to the latency of a Qwen3-8B forward at 2K tokens, falling to 1.4% at 35K, and store 22.5 KiB per response token. On three benchmarks, probes trained on frozen Qwen3 proxies of 0.6B to 8B parameters prove strong detectors: a 4B proxy outperforms the strongest of nine zero-shot 4-9B LLM judges in F1 on two of the three, the proxies match or outperform specialized grounding checkers of up to 7B parameters, probing each proxy beats prompting it as a judge, and adding attention features significantly improves F1 in half of the 12 benchmark-proxy pairs, never significantly lowering it.

cs.AI↗