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Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

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arXiv2026

Markovian Random Words, a Gaussian Random Matrix Model and Beyond

After centering and scaling, the length of the longest weakly increasing subsequence of a finite-state Markov random word converges to a Brownian last-passage functional with dependent components. We investigate when this functional, and more generally the limiting RSK Young-diagram shape, admits a Gaussian random-matrix representation. We introduce Hermitian Gaussian matrices with correlated diagonal entries and show that isotropy of the Brownian covariance on the trace-zero hyperplane yields such a representation. Within this natural class of Hermitian models with independent Gaussian off-diagonal entries, we prove a rigidity theorem showing that isotropy, together with equality of the off-diagonal variances, characterizes the conditional largest-eigenvalue representation. Explicit three-letter non-cyclic Markov chains demonstrate that this representation is not universal: the limiting Brownian functional may fail to have the law of the largest eigenvalue of any centered jointly Gaussian $3\times 3$ Hermitian matrix. Finally, we extend the random-matrix identification to chains with non-uniform stationary distributions and to countable state spaces.

math.PR↗

arXiv2026

Predictions for neutron-tagged Coulomb dissociation in ultraperipheral Ru+Ru and Zr+Zr collisions

The photonuclear response reflects nuclear structure and the dynamics of excitation and decay, with neutron-emission channels retaining information that can be obscured in inclusive dissociation yields. We calculate specified-side and mutual neutron-tagged Coulomb-dissociation cross sections in ultraperipheral $^{96}_{44}\mathrm{Ru}+{}^{96}_{44}\mathrm{Ru}$ and $^{96}_{40}\mathrm{Zr}+{}^{96}_{40}\mathrm{Zr}$ collisions at $\sqrt{s_{\mathrm{NN}}}=200~\mathrm{GeV}$ using an impact-parameter-dependent equivalent-photon framework with photonuclear inputs from TALYS calculations and ENDF evaluations. Across the two input sets, the predicted Ru/Zr ratios span $1.54$-$1.71$ for exact $1n$ and $2.49$-$3.09$ for $1n1n$, while inclusive $Xn$ (at least one neutron) and $XnXn$ ratios remain near unity at $0.96$-$0.99$ and $1.05$-$1.10$, respectively. The one-neutron ratios lie well above the corresponding flux-only $Z^2$ and $Z^4$ charge-scaling references, reflecting differences in the low-energy one-neutron response that are amplified by mutual tagging. This topology hierarchy identifies neutron-tagged isobar ratios as sensitive probes of photonuclear response, revealing response differences hidden in inclusive dissociation. These calculations also provide neutron-emission inputs for neutron-tagged vector-meson photoproduction in isobar collisions.

hep-ph↗

arXiv2026

WaveMark: Robust Wavelet-Domain Image Watermarking for Diffusion Models

Image watermarking enables provenance tracing for photorealistic images generated by diffusion models. However, state-of-the-art (SOTA) removal attacks can suppress embedded signals with little perceptual degradation. This vulnerability limits the effectiveness of watermarks for intellectual property protection and misuse attribution. We propose WaveMark, a novel wavelet-domain watermarking method that embeds messages in a diffusion model's initial noise. To support robust recovery from perturbed carriers, WaveMark distributes keyed replicas of message bits across spatial positions, wavelet orientations, and scales. Each carrier groups coefficients from four latent channels and encodes a randomized bit through magnitude projection, providing an explicit decoding margin. We evaluate WaveMark with SD2.1 on SDP and MS-COCO Captions under 14 attacks. WaveMark achieves 100.0% bit accuracy (BA) without attacks, while maintaining image quality comparable to the evaluated baselines. Under SOTA MarkNull and MarkNull-A, it retains over 88% BA, outperforming all baselines.

cs.CR↗

arXiv2026

Subset Sum and Integer Programming Feasibility Test in Near-Optimal Time

Given an integer $t$ and a set of integers in $[N]$, Subset Sum asks whether there exists a subset that sums to $t$. A long open problem is whether Subset Sum can be solved in $O(N)$ time. We show that Subset Sum can be solved in $O(N^{1 + \varepsilon})$ time where $\varepsilon > 0$ is an arbitrarily small constant. Our result also generalizes to multi-sets in multi-dimension. That is, for any fixed $d$ and $\varepsilon >0$, the $d$-dimensional subset sum can be solved in $O(n + N^{d + \varepsilon})$ time. As an application, for any fixed $d$ and $\varepsilon$, feasibility test of integer programming with $d$ constraints can be done in $O(N^{d+\varepsilon} \mathrm{poly}(\ell_{\mathrm{in}}))$ time, where $N$ is the maximum absolute value in the constraint matrix and $\ell_{\mathrm{in}}$ is the input size. Although the algorithm is quite involved, its high-level idea is clear. It is already known that when the input set is dense and $t$ lies in the interior of the zonotope, then Subset Sum is easy to solve [Galil-Margalit '91, Bringmann-Wellnitz '21, Chen-Hu-Mao-Zhang '26]. Our key observation is that a sparse input can exhibit a dense structure when lifted to higher dimension. We show that such a lifting can be done efficiently. After lifting, the interior of the zonotope is easy to tackle, and one only needs to deal with the thin area near the boundary of the zonotope. Then we show that the boundary area can be decomposed into subproblems and solved recursively, and that there cannot be too many recursion levels since each level of recursive reduces the volume of the area significantly.

cs.DS↗

arXiv2026

MathVis: Can AI Reason through Drawing? A Benchmark for Mathematical Figure Generation

This paper introduces MathVis, a benchmark designed to evaluate LLMs' ability to visualize frontier mathematical problems and perform diagram-assisted reasoning. The benchmark consists of 512 tasks, each comprising a mathematical statement, a reference diagram, executable TikZ or SVG code, a Gold Intermediate Representation (IR), atomic rubrics, and error codes. Through rigorous evaluation, GPT-6-Astra, Claude Fable 5, and Gemini 3.1 Pro Preview achieve pass@1 scores of 31.25%, 26.56%, and 22.85%, respectively. We found that although the tasks require visualization, LLMs produce outputs dominated by formal languages, symbols, and graphics programs, rather than explicit diagram-mediated reasoning. Furthermore, while the solutions generated by LLMs may contain all the necessary elements, they are often visually confusing to humans. Ultimately, this benchmark aims to visualize mathematical problems and promote research on enabling LLMs to simplify their reasoning via visual diagrams.

cs.AI↗

arXiv2026

The biwheel conjecture for braces

Let $b(n)$ denote the minimum number of perfect matchings in a simple brace of order $n$. De~Carvalho, Lucchesi and Murty (SIAM Journal on Discrete Mathematics, 27(2): (2013) 940-958) proved that $b(n)\ge(n-2)^2/8$ and conjectured that $b(n)=(n-2)^2/4$ for all sufficiently large even $n$. We prove this conjecture.

math.CO↗

arXiv2026

Vacuum-field-mediated Landau-level reconstruction in a cavity-coupled two-dimensional electron gas

We study a two-dimensional electron gas in the integer quantum Hall regime coupled to a single spatially modulated cavity mode in the static off-resonant limit. Retaining both paramagnetic and diamagnetic contributions on equal footing, we derive a gauge complete single-particle Hamiltonian in which virtual photon exchange generates a periodic kinetic renormalization and a diamagnetic scalar potential. Both terms transfer momentum by $2k_0$ and displace guiding centers by $ΔX=2k_0\ell_B^2$, forming a finite-$k_0$ momentum ladder. Diagonalizing the strip Hamiltonian, we find that the ladder reconstructs the Landau-level band structure and redistributes, rather than multiplies, the associated chiral edge states. Occupied-subspace Chern numbers remain $C_ν=ν$ for $ν=1,2,3$ throughout $0\leλ_{\mathrm{cav}}\le 0.5$, while the bulk gaps decrease without closing. Strip Kubo responses show cavity-induced displacements of the Hall-step energies; at finite width the plateau heights are noninteger and approach the integers as $L_x$ increases. The ladder is spectrally resolved at $k_0\ell_B=0.5$ and collapses at $k_0\ell_B=0.1$. These results isolate a spatially local, finite-$k_0$ momentum ladder as a clean-system mechanism by which a structured vacuum field reconstructs quantum Hall spectra and strip transport without changing the integer topology, complementary to cavity-mediated all-to-all hopping.

cond-mat.mes-hall↗

arXiv2026

JoyInside-VLM-Agent: Product-Conditioned Multimodal Policy Learning for Embodied Agents

Embodied agents must translate multimodal observations and user requests into executable actions while adapting to product constraints, changing goals, and execution feedback. We present JoyInside-VLM-Agent, a ReAct-style multimodal agent developed through product-conditioned trajectory construction and staged policy learning for robotic platforms and smart hardware. A closed-loop sandbox generates multimodal interaction trajectories covering goal revisions and failure recovery, which are checked against execution outcomes and semantic criteria. Supervised fine-tuning and multi-teacher on-policy distillation precede reinforcement learning with DPER (Dual-Source Privileged On-Policy Self-Distillation with Token-Level Evidence Routing). DPER routes token-level evidence between a frozen privileged teacher and a privileged student sharing the rollout policy's parameters, modulating reward-derived token advantages while preserving their signs. Training rewards combine generative process evaluation, multi-judge rankings, and task-queue consistency. JoyInside-VLM-Agent achieves a BFCL v4 overall score of 77.44, exceeding the evaluated baselines; results on the other public benchmarks are mixed. On JoyInside-Devices and JoyInside-Robotics, the evaluated system, which includes domain-specific skill refinement, leads the baselines on all reported metrics. Two real-world quadruped case studies illustrate visually grounded search, replanning after execution failure, and explicit failure reporting.

cs.RO↗

arXiv2026

Emo-BPO: Emotion Bidirectional Preference Optimization for Diffusion-based Emotional TTS

Diffusion-based TTS has demonstrated strong capability in emotional speech generation. However, existing emotion alignment methods primarily reinforce target emotional expressions while overlooking modeling of competing emotional modes, limiting fine-grained controllability. This issue becomes more pronounced under classifier-free guidance (CFG), which relies on contrasting conditional trajectories to shape generation. We propose Emotion Bidirectional Preference Optimization (Emo-BPO), a simple effective framework that jointly learns emotion-aligned and emotion-contrastive score functions from reordered same-text emotional pairs. Our method requires neither auxiliary reward models nor additional annotations, and can be seamlessly integrated into existing diffusion-based TTS systems to improve emotional controllability and expressiveness.

cs.SD↗

arXiv2026

Video Codec-Guided Training-Free Token Compression for Video Large Language Models

Video large language models (VLLMs) rely on long visual token sequences to understand complex temporal content, which makes visual token compression important for efficient inference. Existing training-free compression methods mainly reduce the number of tokens sent to the language model, but the compression process itself can still require many visual feature comparisons, especially for intra-frame token protection and inter-frame temporal token merging. This paper proposes a video codec-guided training-free token compression method for VLLMs that uses coding information already available in compressed video as a low-cost search prior. The method aligns reference-frame dependencies, motion vectors, and residuals with the visual token grid. Residual information forms compact candidate pools for token protection, while motion information is propagated along reference-frame chains to construct localized candidates for temporal token merging between sparsely sampled frames. Local visual feature similarity comparison is then used within these candidates to make the final compression decisions, without modifying the base VLLM. Experiments on three representative VLLMs and four video-understanding benchmarks show that the proposed method achieves performance comparable to the state-of-the-art training-free baseline FlashVID, and in some settings surpasses it, while substantially reducing the feature comparisons required by token protection and temporal matching. These results demonstrate that codec information can effectively improve the accuracy-complexity tradeoff of video token compression.

cs.CV↗

arXiv2026

DataCupid: Stable Matching Repair for Training Data Acquisition with Delayed Feedback

Matching repair after utility changes can reuse valid observations, but new evaluations must respect matching capacity and may return out of order. We study announced invalidations with bounded, possibly reward-dependent reporting delays and pending evaluations that do not occupy future matching capacity. Residualload repair (RLR) combines sound outcome certificates with batched matching schedules for unequal sample deficits. Its complete dyadic quota schedule admits a sharp issue-round bound with coefficient cb < 1.607 relative to the terminal residual endpoint load, together with separate delay and evidence-lifetime bounds. RLR-P monitors complete issue-order prefixes without changing the sampling plan before acceptance. With a deterministic pure oracle, a single-repair coupling from the same drained initial state guarantees no increase in certification time, issued observations, or time to a reusable checkpoint. We also derive an information-load lower bound. On fixed priority-star markets with unknown Bernoulli gaps, PrioritySearch attains the history-adjusted first-order constant for expected certification time as δ {\sim} 0, under hypothesis-independent linear history scaling and sublogarithmic reporting delays. Paired simulations and measured-feedback replay quantify the trade-offs: in the replay, RLR-P has lower mean capped update-certification time than a monitored width-based baseline, at higher oracle CPU cost.

cs.LG↗

arXiv2026

MVGraph: Benchmarking LVLMs on Evidence Composition across Multi-View Visual Graph

We introduce MVGraph, a benchmark for evaluating large vision-language models (LVLMs) on multi-graph reasoning where the evidence required by a query is distributed across multiple interrelated visual graph views. Although such evidence commonly resides in source-specific graphs, temporal snapshots, or local observations, existing graph reasoning benchmarks remain confined to a single self-contained structure, assessing only graph perception and reasoning while leaving the alignment and composition of evidence across views underexplored. MVGraph comprises 8k instances spanning 8 \textit{graph-theoretic} tasks, abstracted from two multi-graph scenarios (partial and temporal graph views). Each problem is programmatically constructed and verified to be unsolvable from a single view. Beyond end-to-end evaluation, we decompose multi-graph reasoning into four complementary capabilities---Perception, Alignment, Composition, and Reasoning---and design 29 diagnostic tasks with 64k instances to probe each one, along with golden intermediate representations for evaluating the intermediate process. Across 15 LVLMs, we reveal the difficulty of multi-graph reasoning and identify cross-view edge alignment and relation-level composition as prominent bottlenecks through stage-oriented diagnostics. Meanwhile, temporal constraints and increasing view counts expose further capability boundaries. Code and data are available at https://github.com/AAAndy-Zhu/MVGraph.

cs.CV↗

arXiv2026

On the number of conjugacy classes of finite solvable groups of order divisible by $p^2$

In 2003, Héthelyi and Külshammer proved that if $G$ is a finite solvable group and $p$ is a prime such that $p^2$ divides $|G|$, then $k(G)\geq (49p+1)/60$, and they constructed an infinite family of groups for which this bound was claimed to be attained. We point out that the groups in this family are not Frobenius groups, so that their class numbers are considerably larger than stated, and that in fact the bound is never attained. We then determine the best possible bound of this shape: we show that $k(G)\geq (49p+7)/60$ for all primes $p$, which is sharp for $p=17$, and that $k(G)\geq (49p+451)/60$ for all primes $p>2719$, which is sharp for infinitely many primes $p$. Thus the slope $49/60$ found by Héthelyi and Külshammer is best possible, but the correct additive constant is $451/60$ rather than $1/60$.

math.GR↗

arXiv2026

MotionCoach: Constructing Multimodal Guidance for Video Professional Motion Editing

Video editing models achieve strong performance in modifying appearance, backgrounds, styles, and motions, empowered by large-scale training data. Beyond general scenarios, professional motions are significant in performance, sports, and martial arts. This paper focuses on professional motion editing, which involves fine-grained motion technique and temporal structure. Given professional motion names but lacking detailed descriptions, existing models often fail to generate professional motions, such as incorrectly lifting the front wheel under a Stoppie instruction. To address this challenge, we introduce MotionCoach, a trained multimodal agent that uses multi-turn tools and performs self-verification, producing a grounded prompt and a reference clip as reliable and sufficient multimodal guidance to inject external professional motion knowledge into video editing models. To supply training data, we build a data pipeline to construct trajectories. We cold-start the agent on MotionCoach-SFT-10k and apply Group Relative Policy Optimization (GRPO) on MotionCoach-RL-2k with rewards on the motion guidance prompt, the motion outcome video, and the format. For evaluation, we introduce VPMEBench, comprising 314 professional motion editing tasks with fine-grained references and annotations. Extensive experiments show that MotionCoach improves the overall score from 55.1 to 65.6 on Seedance 2.0 and from 51.2 to 64.5 on MiniMax-H3. Learning to construct multimodal guidance enables precise professional motion editing without retraining video editing models.

cs.CV↗

arXiv2026

The strength of the minimum principle in constructive reverse mathematics

The minimum principle states that every real-valued uniformly continuous function f : X -> R on a compact metric space X attains its minimum. Working in the base system EL0 of constructive reverse mathematics, we show that the minimum principle is equivalent to weak Konig's lemma and to the Cantor intersection theorem (i.e., the contrapositive of the Heine-Borel theorem). Moreover, the above equivalence naturally extends to the equivalence between the corresponding principles with unique existence assumptions, which are then shown to be equivalent to the Fan theorem for detachable bars and the positivity property for a real-valued uniformly continuous function on a compact space. These results sharpen the equivalence among these principles obtained by Ishihara [Math. Log. Q. (1990), 237-240] and Berger and Ishihara [Math. Log. Q. (2005), 360-364] in Bishop's constructive mathematics.

math.LO↗

arXiv2026

High-Throughput Discovery of Chiral Carbon-Boron Semimetals with Weyl Topology and Phonon-Mediated Superconductivity

Chiral crystals provide a natural platform for unconventional topological fermions, while light-element carbon--boron frameworks are promising for phonon-mediated superconductivity owing to strong covalent bonding and high phonon frequencies. Here, we combine Wyckoff-position-based structure generation with high-throughput first-principles calculations to search for C--B crystals in selected hexagonal chiral space groups. Starting from 972 generated $\mathrm{C}_m\mathrm{B}_n$ structures ($m,n=1\text{--}4$), successive filters based on energetic stability, dynamical stability, electronic metallicity, topological band features, and thermal stability identify six stable candidates: $(\mathrm{C}_3\mathrm{B}_2)_8$, $(\mathrm{C}\mathrm{B}_2)_3$, $(\mathrm{C}\mathrm{B}_4)_6$, $(\mathrm{C}_3\mathrm{B}_2)_6$, $(\mathrm{C}_2\mathrm{B}_3)_6$, and $(\mathrm{C}\mathrm{B}_2)_6$. These materials host diverse topological semimetal states near the Fermi level, including charge-one, charge-two, and charge-three Weyl points, nodal rings, and nodal-surface states. Notably, $(\mathrm{C}_3\mathrm{B}_2)_8$ exhibits screw-symmetry-protected charge-three Weyl points and strong electron--phonon coupling, yielding a McMillan transition temperature of $31.1\,\mathrm{K}$ for the Coulomb pseudopotential parameter $μ^* = 0.10$. In addition, $(\mathrm{C}\mathrm{B}_2)_3$ hosts multiple charge-one Weyl points and pronounced anisotropic multiband superconductivity revealed by fully anisotropic Eliashberg calculations. These results extend the materials scope of topological semimetals with phonon-mediated superconductivity to chemically designed chiral light-element structures.

cond-mat.mtrl-sci↗

arXiv2026

Ionic liquid/PDMS coated nanostructured ZnO surfaces for superior antibacterial activity

The development of nanostructured antibacterial surfaces has gained significant attention due to the urgent need to combat bacterial colonization and biofouling across food, healthcare, and marine sectors. Among functional metal oxides, zinc oxide (ZnO) nanostructures are particularly promising owing to their rich morphology, favourable physicochemical attributes, and intrinsic bactericidal properties. Here, we utilize a green, eco-friendly Hot Water Treatment (HWT) method to fabricate dense ZnO nanorod arrays on zinc substrates. To overcome the practical limitations and challenges of conventional antibacterial coatings, such as poor operational stability, cytotoxicity, and the risk of antimicrobial resistance, we developed a durable hybrid coating composed of an imidazolium-based ionic liquid stabilized with polydimethylsiloxane. The resulting hybrid-coated nanostructured surfaces exhibit superior antibacterial efficacy against Escherichia coli through a combination of topography-induced mechanical strain and membrane disruption.

cond-mat.soft↗

arXiv2026

Spatial Prediction with Guided Diffusion

Spatial prediction is a critically important task in data analyses that involve spatially or spatio-temporally-referenced data. It is commonly carried out using hierarchical models, which comprise a process model describing the latent process of interest, and a data model describing how the process is observed. The target quantity is the predictive distribution, which is the conditional distribution of the latent spatial process given the observed data. Unfortunately, the predictive distribution is rarely available in closed form and can be difficult to sample from. Here, we show how recent developments in guided diffusion modelling from machine learning can address a wide class of problems in spatial prediction when the likelihood function derived from the data model is known and differentiable, possibly after relaxation. To show the versatility of the approach, we apply it to both Gaussian and non-Gaussian process models and a variety of data models that describe direct partial observations, linear and areal aggregates, counts, right censoring, and area-exceedance functionals. Where possible, we validate the framework against exact and Markov-chain-Monte-Carlo (MCMC)-derived predictive distributions. We demonstrate our approach on several simulation studies and in a controlled experiment of methane-flux inversion over the UK and Ireland. We show that guided diffusion can sample from the correct predictive distribution in a variety of settings, that it can be applied to models where MCMC is intractable, and that it scales well with the dimensionality of the latent process.

stat.ME↗