Papers

When a large language model refuses an unethical request, what does refusal mean? In conversation, refusal is bounded by what the model says; once the model is equipped with executable tools, what it does can diverge from what it says, a failure mode that English-only evaluations cannot fully reveal. We introduce Lumen-bench, a behavioral benchmark of tool-calling ethics spanning 30 models, five languages (Portuguese, English, Spanish, Mandarin Chinese, Hindi), 108 Portuguese-authored scenarios, six social-pressure conditions, two system prompts (ethical and neutral), and 21 generic tools. The evaluation comprises 194,400 trials. Judgments come from a reasoning-model judge (o4-mini), calibrated against one Portuguese-speaking author ($n=83$; harmful/non-harmful $\kappa=0.78$), compared with two other provider judges (Fleiss' $\kappa=0.78$, $n=607$), and complemented by retrospective sandbox replay. Four findings emerge. (i) Within-model comparisons support higher harmful-action rates in Hindi and Portuguese than English under the ethical prompt, and Hindi and Spanish under the neutral prompt, after multiple-testing correction. (ii) Premium models have lower median violation rates, although price does not guarantee safety or competence. (iii) Replacing the ethical system prompt with a neutral one raises pooled violation rates from 2.76% to 13.64%. (iv) In 8.57% of substantive-call cases, refusal or ethical objection accompanies a harmful tool call: the judges consistently identify the say-do gap, although they differ in how many responses they assign to this category. Matched benign controls demonstrate legitimate task completion in 82.8% of 3,300 trials. Code and reproduction scripts are available at https://github.com/TropicAI-Research/lumen.

We provide a new rearrangement in Gauss space transforming symmetric sets while decreasing their Gaussian perimeter. We use this rearrangement to analyze the minimizers of the Gaussian perimeter among symmetric sets.

Chromatic choosability is a fundamental notion in list coloring. A graph $G$ is chromatic-choosable if its chromatic number $\chi(G)$ equals its list chromatic number $\chi_{\ell}(G)$. In 1990, Kostochka and Sidorenko introduced the list color function of a graph $G$, denoted by $P_{\ell}(G,m)$, which is the list-coloring analogue of its chromatic polynomial $P(G,m)$. A graph $G$ is enumeratively chromatic-choosable if $P_{\ell}(G,m)=P(G,m)$ for every $m \in \mathbb{N}$. In 2002, Ohba proved that for every graph $G$, there exists an $N \in \mathbb{N}$ such that $K_p \vee G$ is chromatic-choosable whenever $p \geq N$. Allred and Mudrock recently conjectured that an analogous statement holds for enumerative chromatic choosability. In this paper, we prove that $K_1 \vee G$ is enumeratively chromatic-choosable whenever $G$ is a theta graph. Our proof combines classical inequalities, the polynomial method, and ideas from DP (or correspondence) coloring.

The Fibonacci, Lucas, and Pell sequences satisfy certain families of “polynomial” identities. While a few members of these families are well-known, we are not able to find a general statement of these identities in the mathematical literature. We show that such polynomial identities exist for many generalized Fibonacci sequences, and we classify sequences that have these identities obtained by two distinct approaches. One approach uses the Girard-Waring formula, while the other relies on Binet's formula and linear algebra.

Production vector search must continuously ingest, delete, and re-tenant vectors while serving low-latency, high-recall, metadata-filtered approximate nearest-neighbor (ANN) queries for many tenants with per-tenant service-level objectives. Existing graph-based ANN systems address these requirements largely in isolation, leaving recall during concurrent re-optimization without an analytical bound. We develop a graph-based index that combines streaming updates, filtered search, and multi-tenancy, with one theoretical result and two system mechanisms. Our theory decomposes per-tenant recall loss into staleness from updates not yet integrated into the graph and filtered navigability determined by the local density of points satisfying a tenant's predicate. The staleness component exhibits anti-amortization on a merge-based graph, integrating a larger batch of inserts increases recall degradation super-linearly, so larger merges do not reduce total staleness loss. Holding the insert horizon fixed while increasing merge size 20x, we observe a monotonic decrease in terminal recall@10 from 99.44% to 99.01%. For filtered search, the theory gives a parameter-free frontier-mass relationship in local predicate density and a query-averaged per-tenant recall bound. We instantiate the bound with a filter and tenant-aware staging cache and a select-not-resize scheduler with per-tenant staleness ceilings. On a FreshDiskANN substrate, the ceiling eliminates tight-tier SLA violations under the evaluated churn workload, while merge reordering changes terminal recall by only 0.02 percentage points. The results show how recall bounds can guide background maintenance without relying on merge resizing as a recall control mechanism.

Human social perception is incremental: we infer intent before an utterance is complete, revise our interpretation as new cues arrive, and attend to specific facial, gestural, or prosodic signals that shape social meaning. Current multimodal LLM benchmarks largely evaluate final-answer understanding over complete episodes, rewarding post-hoc recognition of social meaning rather than the unfolding perception required for real-time interaction. Drawing on interactionally embedded Gestalt principles of multimodal human communication, we introduce GesBench: a human-grounded benchmark for cue-level social perception in multimodal LLMs. GesBench uses cumulative sub-utterance clips to measure when models form stable interpretations of speaker intention and social affordance, and human gaze-guided corruption to evaluate whether regions attended by humans are functionally important for model judgments. Built from more than 6000 utterance-level clips from scripted and unscripted conversational datasets, GesBench includes human annotations of unfolding judgments and gaze on a representative subset. Across open and closed multimodal models, we find a clear human-model gap: humans form predictive understandings early and revise more often, while models often hedge or repeat across different clips. GesBench shifts social evaluation from whether models eventually recognize meaning to when and where that meaning is formed. Our codes are publicly available at https://anonymous.4open.science/status/GesBench-share-212C.

Modern AI systems increasingly combine large language models (LLMs) with human experts, using the LLM to handle routine queries while deferring uncertain cases for expert review. When expert capacity is limited, however, deferral decisions must account not only for the reliability of the LLM but also for congestion in the expert queue. We formulate this as an online sequential decision-making problem in which, for each query, the system observes the confidence signal of the LLM's answer and must decide whether to output the answer or defer the query to a capacity-constrained expert. The reliability of the confidence signal is initially unknown and must be learned from expert feedback, which is both selectively observed (only deferred queries are labeled) and delayed by queuing. We propose KL-PBD, a learning algorithm that uses Kullback–Leibler lower confidence bounds on the unknown reliability parameters to guide deferral decisions. For $K$ confidence levels and horizon $T$, KL-PBD achieves $O(K\log T)$ gap-dependent regret when the accuracy at every confidence level is bounded away from the deferral boundary, and $\widetilde{O}(\sqrt{KT})$ worst-case regret. We establish matching lower bounds, showing that these rates are optimal up to logarithmic factors. Finally, we validate our approach on synthetic instances and real-world question-answering datasets, namely GSM8K, NuminaMath, and MedMCQA, using Qwen LLMs.

Traffic sign recognition plays a crucial role in the development of autonomous cars to reduce the accident rate and promote road safety. It has been a necessity to address traffic signs that are affected significantly by the environment as well as poor real-time performance for deep-learning state-of-the-art algorithms. In this paper, we introduce Real-Time Image Enhanced CNN ({\our}) for Traffic Sign Recognition. {\our} is a real-time, novel approach that tackles multiple, diverse traffic sign datasets, and out-performs the state-of-the-art architectures in terms of recognition rate and execution time. Experiments are conducted using the German Traffic Sign Benchmark (GTSRB), the Belgium Traffic Sign Classification (BTSC), and the Croatian Traffic Sign (rMASTIF) benchmark. Experimental results show that our approach has achieved the highest recognition rate for all Benchmarks, achieving a recognition accuracy of 99.75% for GTSRB, 99.25% for BTSC and 99.55% for rMASTIF. In terms of latency and meeting the real-time constraint, the pre-processing time and inference time together do not exceed 1.3 ms per image. Not only have our proposed approach achieved remarkably high accuracy with real-time performance, but it also demonstrated robustness against traffic sign recognition challenges such as brightness and contrast variations in the environment.

Decentralized learning must balance collaboration with personalization across heterogeneous agents. This paper studies when cooperation can support statistically coherent groups of personalized models. We show that data-topology compatibility enables robust orbit-wise personalization: when local objectives and communication topology have (approximately) compatible automorphisms, agents within an orbit share (approximately) equal limiting distributions, while different orbits remain distinct without explicit personalization. This creates a new intermediate regime between global consensus and independent local learning. Under exact data-topology compatibility, as a reference system, we decompose the stochastic learning dynamics into orbit-level and transverse components, derive a necessary and sufficient stability criterion for distributional synchronization, and characterize the orbit-structured stationary law. Modelling an approximate data-topology compatible system as an $\varepsilon$-perturbed reference system, we prove the introduced errors have uniform-in-time and stationary $O(\varepsilon)$ bounds in 2-Wasserstein distance. We also prove sufficient conditions for lower stationary average excess risk than both independent local training and the best single shared parameter. Experiments on synthetic data, MNIST, and CIFAR-10 are in full agreement with the theory. The code is available at https://github.com/Veronicaaa1/orbit-personalization.

We study Nesterov's accelerated gradient method with its standard constant parameters for smooth strongly convex optimization. We characterize the exact worst-case asymptotic factor for the squared distance to the minimizer. To this end, we construct candidate worst-case trajectories by combining planar spirals with a common contraction factor that satisfy a self-similarity condition. Each component rotates by a fixed angle at every iteration. The exact factor is the optimal value of a linear optimization problem over probability measures on a fixed disk, with constraints derived from smooth strongly convex interpolation. Every optimal measure has a common contraction factor, which is also the largest factor for which the angular interpolation conditions are feasible. We also show that this worst-case asymptotic rate can be realized by a single function in a finite-dimensional space whose iterates attain this factor. A matching upper bound holds uniformly over all functions in the class and all finite dimensions. Consequently, allowing the function, dimension, and initial point to vary with the iteration horizon does not increase the worst-case asymptotic factor. We also show that the exact factor is $1-4/(3\sqrt\kappa)+o(\kappa^{-1/2})$ as $\kappa\to\infty$, where $\kappa=L/\mu$ is the ratio of the gradient Lipschitz constant to the strong convexity parameter.

Foundation models need to support diverse inference budgets, yet training a separate model for each budget duplicates pretraining effort. Elastic models train several nested sub-networks inside one weight-shared supernet, but existing recipes face three obstacles: variable per-step workloads that hinder distributed scaling, limited hyperparameter (HP) transfer across model sizes, and no guarantee that all sub-networks are maximally updated at once. We present \Ours, an elastic transformer that organizes hidden dimensions into a dense core and successive shells, so that every hidden matrix is block lower triangular. One full-width forward pass contains every sub-network's exact hidden states as prefixes, so joint training keeps a fixed computation graph and costs about as much per step as training the widest sub-network alone. We further introduce \muE, an extension of maximal update parameterization (\mup) to \Ours and other elastic architectures. Its scaling rules provably keep all sub-networks of a supernet maximally updated simultaneously (\muI), and keep doing so when the supernet is widened or given more shells; sweeps confirm that HPs tuned on a small non-elastic proxy stay near-optimal for elastic families and larger supernets (\mbox{\muT}). A single \Ours run produces sub-networks that outperform MatFormer and fully elastic baselines at matched parameter counts, and approach separately trained models that together take several times the steps.

We study the attractor lattice of a class of hybrid dynamical systems on compact metric spaces. Under the trapping guard condition, we prove that hybrid attractors form a bounded distributive lattice isomorphic to the attractor lattice of an associated semiflow. The regularized preimages define a lattice epimorphism from a sublattice of the regular closed, attracting neighborhoods of the semiflow onto those of the hybrid system, and from the whole lattice when the guard set and its reset image have empty interior. Then, using grids on the state space, we construct a convergent cofiltration of outer approximations of a fixed-time map of this semiflow. This construction realizes every finite sublattice of hybrid attractors by a lattice of attracting neighborhoods that are unions of grid elements at sufficiently fine resolutions, and provides index pairs for computing Conley indices. We illustrate these constructions computationally by extracting the Conley–Morse graphs of the bouncing ball, the rimless wheel, the spiking neuron, and exhibiting the attractor lattice for an impacting oscillator.

Ensuring the safety of autonomous Unmanned Aerial Vehicles (UAVs) operating in underground mines is challenging due to the vast and uncertain Operational Design Domain (ODD). Traditional validation approaches, such as random testing, often result in inefficient situation coverage, allocating computational resources to low-risk scenarios while failing to expose critical edge cases. Building on prior work in risk-prioritized Situation Coverage, this paper investigates whether Fuzzy Logic-based risk estimation effectively correlates with real system failures. To this end, we conduct a mutation testing study within our SCALOFT simulation framework. A fixed set of software mutants is systematically injected and evaluated under two testing strategies: (i) uniformly random situation generation and (ii) Fuzzy-Guided risk-prioritized situation generation. Experimental results show that the Fuzzy-Guided approach achieves a higher mutation score and is more effective at exposing difficult-to-detect faults compared to random testing.

Motivated by three-dimensional wave diffraction by conical shapes, we consider the two-dimensional problem of wave scattering on the real sphere $\mathcal{S}^2$ resulting from a point-source incidence on a scatterer $\mathbb{S}$. Using the recently introduced notion of plane waves on $\mathcal{S}^2$ as well as recent results on the Laplace–Beltrami Green's function $G$ on $\mathcal{S}^2$, we derive three plane-wave representations for the scattered field $u$. We then explain how $u$ can be analytically continued to the complexified sphere $\mathcal{S}^2_{\mathbb{c}}$. This allows us to formulate a complexified version of Green's third identity, and to provide a characterisation of complex sources. All our results are then used to draw strong analogies between planar and spherical scattering problems, notably through the introduction of directivities.

To support emerging applications such as extended reality, autonomous systems, and large-scale cyber-physical infrastructures, next-generation wireless networks must evolve beyond traditional communication paradigms toward tightly integrated and closed-loop systems. Digital Twin Networks (DTNs) have recently emerged as a key enabler of this transformation by bridging the physical and digital worlds through real-time, bidirectional interactions and adaptive control mechanisms. In this tutorial, we provide a comprehensive overview of DTN design and optimization across multiple system dimensions. Specifically, we first introduce the fundamental design principles of DTN creation, including high-fidelity twin modeling, telemetry integration, and cyber-physical synchronization. We then present resource optimization and semantic-driven DTNs, where application-aware objectives and semantic abstractions guide efficient data processing, communication, and decision-making. Subsequently, we explore physical-layer optimization techniques for DTNs, emphasizing joint sensing, communication, and adaptive wireless resource control. Furthermore, we examine DTN-guided network management and feedback optimization, focusing on closed-loop learning, real-time control, and reinforcement-driven adaptation between digital twins and physical networks. Finally, we review ongoing standardization efforts and enabling tools that support the practical deployment of DTNs in real-world systems. This tutorial aims to provide a unified perspective on DTNs as an emerging paradigm for application-aware, AI-native, and closed-loop wireless systems, and to highlight key challenges and future research directions in this rapidly evolving field.

Slender structures in dense environments interact through contact, which alters how and when they become unstable. Here we show that contact makes snap-through history dependent, so that when and whether a beam pair snaps depends on how long the contact is loaded. Under cyclic compression, the pair snaps on loading, snaps on unloading, or stays packed, with the loading and unloading rates selecting among the three. Upon contact, one beam rolls along the other without slip, and faster driving lets it roll further before it slides and snaps: to larger compression on loading and to smaller compression on unloading. This delay is asymmetric between loading and unloading as the unloading branch carries a memory of the loading rate. Interestingly, above a threshold compression the pair snaps even when the compression is stopped, with the time to snap diverging at that threshold. By exploiting this asymmetric, rate-dependent delay, we program ordered sequences of snap events in arrays of pairs with tunable gaps, and demonstrate that the energy dissipated per cycle becomes a two-parameter function of the loading and unloading rates, increasing fourfold when, at the fastest loading, the return is slowed.

We present a finite-horizon, greedy heuristic-based co-optimization and optimal control framework that jointly determines the optimized charging rates, charging times, and an optimal charging control law for electric vehicles (EVs) to improve both voltage stability and small-signal dynamic performance of a power distribution system. The proposed strategy encourages EV drivers to be flexible in choosing their charging rates and times through monetary incentivization under a fixed budget. The design is validated using the IEEE 33-bus distribution system model with ten EV charging stations (EVCSs). Results show that incentivizing drivers to settle for lower charging rates, implemented by a wait-and-save strategy, and rescheduling their charging times strategically can significantly improve the voltage stability index (VSI) of the system as well as the damping factors for the mid-frequency oscillation modes seen in the DC-link bus voltage.

To evaluate whether a compact bidirectional state-space autoencoder improves joint classification of species, cell type, and disease state from single-nucleus RNA-sequencing profiles in heart failure (HF), while yielding interpretable gene attributions. Building on the dense denoising autoencoder (DAE) and MLP framework of Ruz Jurado et al., we developed scHFBiMamba, combining a bidirectional Mamba autoencoder (BiMambaAE) with an MLP head. BiMambaAE maps 16,545-gene profiles to 350-dimensional latent representations using 13.2M parameters, about 14.6-fold fewer than the dense DAE (192.9M). We compared six encoder-classifier configurations on 38,275 held-out cardiac nuclei using McNemar tests with Benjamini-Hochberg correction, and assessed nine classifiers on frozen representations. Biological relevance was evaluated by comparing SHAP-derived differentially explained genes with differentially expressed genes against curated HF-related Gene Ontology keywords. BiMambaAE+MLP achieved the highest aggregate F1: pooled macro-F1 across 13 outputs was 0.966 versus 0.957 for DAE+MLP, and the mean category macro-F1 was 0.977 versus 0.970. It significantly improved cell-type and disease-state accuracy (adjusted p=7.1e-3 and p=4.8e-6, respectively), with species F1 of 1.000. SHAP-derived differentially explained genes achieved a pathway-enrichment benchmark F1 of 0.105 versus 0.053 for differentially expressed genes. Compact bidirectional state-space autoencoders can outperform substantially larger dense autoencoders for joint cardiac transcriptomic classification while reducing parameters. scHFBiMamba enables accurate multi-task prediction and hypothesis-generating gene-level interpretation. Code: https://github.com/UgoLomoio/scHFBiMamba.

Unidirectional transport of light is a central capability in photonics, enabling critical functionalities such as isolation and routing. Ordinarily, this directionality depends on the mode of light, but not its phase. In this work, we experimentally demonstrate phase-dependent unidirectional transport of light for the first time. Specifically, we realize a system where conjugate quadratures of an optical field decouple and propagate in opposite directions. Our all-optical approach uses multiple pump frequencies in a high-$Q$ nanophotonic micro-resonator to achieve Hamiltonian programming through Kerr nonlinearity. Even though we rely on optical nonlinearity, our approach is not limited to any minimal power requirement on the signal. We demonstrate the ultimate limit of this by measuring the effect of quadrature-dependent transport on vacuum fluctuations. Our approach unlocks a fundamental new capability for controlling light, and can enable previously inaccessible regimes of phase-sensitive directional amplification, sensing, and routing.

This paper studies the last-coverage vertex of a nearest-neighbour random walk on a cycle: the vertex most likely to be the final one discovered. We show that the visited vertices always form a single contiguous arc of the ring, a property we call the Connected Arc Property. This lets the walk be replaced by a two-state time-inhomogeneous Markov chain, which we call the interval-expansion representation, in which each expansion step has a probability given by the classical gambler's ruin formula. Within this framework we prove that the last-coverage probability of node k in an n-node cycle is (1-r)r^(n-1-k)/(1-r^(n-1)), where r = (1-p)/p and p is the clockwise transition probability. As p approaches 1/2, we recover the uniform distribution, giving an independent derivation of a classical result. For a walk with a deterministic time-varying bias, we give an exact series representation for the last-coverage probabilities, together with a finite truncation that serves as a computable, error-bounded approximation. All results are validated by Monte Carlo simulation, and we run experiments on sinusoidal time-varying bias. Finally, we compare generalized Petersen graphs with Erdos-Renyi graphs of matching size, finding that structural symmetry is associated with more uniform last-coverage distributions.

Real-time synchronized content delivery is critical for applications such as cloud gaming, collaborative mixed reality, and live streaming, where a server must ensure that a group of users perceives the same content simultaneously for each delivery. Due to heterogeneous and unpredictable network delays, ensuring synchronization is highly challenging. We propose a clock-free scheduling framework that introduces latency compensation to control the server's delivery time for each user, aiming to maximize synchronization performance (i.e., minimizing the gap between the maximum and minimum latencies) while maintaining a low overall latency cost. Unlike prior work requiring synchronized clocks or client-side timestamps, our approach uses only acknowledgment feedback, enabling flexible deployment across diverse environments. We formulate the problem as a convex stochastic optimization with a non-smooth objective. To solve the problem, we employ the stochastic proximal point (SPP) algorithm that updates the delay compensation, using only the previous latency samples, rather than the latency distribution. By exploiting the subproblem structure, we apply ADMM to enable efficient updates with per-iteration complexity of at most $\mathcal{O}(N\log N)$, where $N$ is the number of users. We establish a convergence rate of $\mathcal{O}(1/\sqrt{K})$, where $K$ is the number of content deliveries for transmission. The framework is further extended to handle transmission failures, where packet loss results in successful delivery to only a subset of users. Finally, simulations using both synthetic and real-world latency traces demonstrate the consistent superiority of our algorithm against baseline methods.

Let $H$ be a closed subgroup of a compact connected Lie group $G$ such that $G/H$ is simply connected, the action of $G$ on $G/H$ is almost effective, and $G/H$ is a strongly isotropy irreducible space. The smallest positive eigenvalue of the Laplace-Beltrami operator $\Delta$ associated to the standard metric on $G/H$ was recently computed. In this article we obtain a second non-zero eigenvalue of $\Delta$. As a consequence, we prove that all eigenspaces of the Laplacian are irreducible as $G$-modules if and only if $(G,H)$ is a compact symmetric pair of real rank one, or $(G,H)$ is equal to $(\operatorname{G}_2,\operatorname{SU}(3))$ or $(\operatorname{Spin}(7),\operatorname{G}_2)$.

High-fidelity closed-loop simulation for autonomous driving increasingly relies on dense multi-view 3D reconstruction. While recent feed-forward geometric foundation models have revolutionized per-scene optimization, applying them to continuous, long-horizon driving sequences is computationally intractable due to GPU memory limits and the quadratic complexity of global attention. Existing scaling strategies are fundamentally limited, as causal streaming suffers from compounding scale drift and trajectory deviation, while rigid "chunk-then-align" heuristics fragment global context and produce trajectory discontinuities. To address these limitations, we introduce Drive3R, a block-wise streaming geometric foundation model. Its block-wise causal attention resolves the scalability bottleneck of fully bidirectional attention while avoiding the loss of local future context in purely causal streaming. Its confidence-aware re-anchoring further mitigates long-range drift by detecting unreliable streaming states, re-initializing the KV cache, and stitching refreshed segments through SE(3) alignment. Extensive experiments demonstrate that Drive3R establishes a new state-of-the-art on nuScenes, KITTI, and Waymo. Specifically, on nuScenes, it improves over the recent DVGT-2 baseline from 0.1806 to 0.1081 in AbsRel, from 0.6750 to 0.5344 in point-cloud Accuracy, and from 1.5812 to 0.9092 in ATE.

Data and the governing partial differential equations (PDEs) of continuous-time dynamical systems provide rich structure for statistical learning. A central challenge is how to integrate data with PDE constraints in a principled way to improve generalization. In this paper, we characterize the statistical estimation and generalization properties of learning solutions to the heat equation with a noisy source function from finite, randomly sampled data. We first derive a novel variational formulation, which we characterize as the minimizer of loss function for an energy regularized and ellipticity debiased Sobolev regression. By formulating the learning task as a supervised problem over space-time domains under physically meaningful norms, our approach goes beyond the traditional supervised learning framework by effectively leveraging auxiliary data—samples of the source function of the heat equation—to design a physics-informed energy regularization. Our analysis reveals that learning in linear parabolic PDEs exhibits intrinsic anisotropy between spatial and temporal regularity, in sharp contrast to the static elliptic problems, leading to fundamentally different estimation and generalization behaviors. Specifically, we derive non-asymptotically rate-optimal estimation errors, as well as generalization error, which explicitly capture the interplay among temporal sampling, spatial resolution, and solution smoothness. Our numerical experiments demonstrate substantial orders of magnitude of reduction in testing errors against various physics-informed neural network methods on various parabolic and hyperbolic PDEs.

Cancer detection using AI methods and image databases faces several challenges, including limited and imbalanced image datasets, long algorithm training times, and high-complexity feature generation. In particular, many cancer image datasets contain very few malignant examples compared to benign ones, limiting the amount of minority-class data available for training. Although classical AI and especially deep learning methods have had some success in providing cancer diagnostics, Quantum Machine Learning (QML) methods may offer advantages through high-dimensional feature representations, generative data augmentation, and the exploitation of feature correlations through quantum properties such as entanglement. In this paper, we propose using a generative QML method on the compressed breast ultrasound image dataset (BUSI) to generate synthetic images and hence augmented datasets for classifier training. In particular, we train a convolutional neural network with real, synthetic, and a combination of real and synthetic images. We test the algorithm on real images and provide comparative results for all three training cases. Our results show that the classifier trained entirely on synthetic images achieved an AUC-ROC of 0.802 (80.2%), compared with 0.760 (76.0%) for the real-data baseline.

We prove Kitaoka's conjecture for all real cyclotomic fields, i.e. for fields of the form $\mathbb{Q}(\zeta_k+\zeta_k^{-1})$ where $\zeta_k$ is a primitive $k$th root of unity. More precisely, we show that such a field admits a universal classical ternary quadratic form if and only if it is a real quadratic field.

Intense ultrafast lasers are the backbone of strong-field physics and enable table-top scale applications of coherent high-photon energy radiation through high-harmonic generation (HHG). Using short-wavelength drivers in HHG promises highly efficient conversion into the extreme ultraviolet, but short pulse durations are essential to this approach. We generate multi-GW peak power, sub-10 fs pulses in the visible with broad spectral tunability (220–752 nm) by harnessing soliton dynamics in large-core, gas-filled capillary fibers for high-energy resonant dispersive wave emission. This establishes the potential of resonant dispersive waves as a new class of driving lasers for HHG and strong-field physics in addition to widespread applications in ultrafast spectroscopy.

Chain-of-thought prompting enables reasoning in large language models but produces explanations that are difficult to verify, expensive to generate, and not always faithful. We introduce a Structural Chain-of-Thought framework where models generate executable computational graphs instead of free-form reasoning. The final answer is obtained by deterministically executing the graph. The model is trained using graph-based reinforcement learning that rewards structural validity, answer correctness, and node overlap with reference graphs. Experiments across five benchmarks and four model families show that our method consistently improves accuracy over supervised graph training and can reduce generation length by up to 5-6x compared with standard GRPO and chain-of-thought supervised training. Our faithfulness experiments reveal that models trained with our approach tend to rely on deriving their answers from the generated graphs rather than producing post-hoc rationalizations as usually in chain-of-thought reasoning.

Latent recursion repeatedly processes internal representations through the same neural network. Recent work has shown this approach to be effective on structured reasoning tasks such as Sudoku and maze solving. However, whether latent recursion can support neural routing remains unclear. We introduce RELAGRAM (Recursive Latent Graph Model), a novel approach that brings latent recursion to graph combinatorial optimization. RELAGRAM encodes a capacitated vehicle routing problem (CVRP) instance as edge tokens; a compact transformer recurrently updates the latent representations of these tokens. An output head maps the answer state to an edge heatmap, from which an autoregressive decoder constructs a feasible solution. On CVRP-100 instances, the 0.53M-parameter RELAGRAM achieves gaps to a PyVRP reference of 13.4%, 9.8%, and 8.3% under greedy decoding, eightfold symmetry augmentation, and 256-candidate search, respectively. Trained only on CVRP-100, RELAGRAM generalizes zero-shot to CVRP-500 and CVRP-1000, achieving gaps of 15.6% and 21.7% under 256-candidate search. Together, these results demonstrate that latent recursion is a promising approach to neural routing.

We propose a geometric realization of spacetime non-commutativity where the spacetime manifold remains smooth while the commutation relation between tangent and separation vectors of geodesic congruences is generalized via Frobenius' theorem. This non-commutative kinematic deformation leads to a modified Raychaudhuri equation with a shifted expansion scalar $\tilde \theta=\theta+\theta^{\rm NC}$. We introduce a timelike and null-like Non-Commutative Energy Condition (NCEC) under which focusing and geodesic incompleteness can, in some regimes, persist even when the standard strong energy condition is violated. Using this, we generalize the key focusing lemmas, conjugate-point propositions, and singularity theorems for both timelike geodesics orthogonal to a Cauchy surface and null geodesics orthogonal to a trapped surface. Applied to a FLRW spacetime, we argue that $\theta^{\rm NC}$ modifies both the Friedmann acceleration equation and the continuity equations. The non-commutative corrections separate into a universal modification of the dilution of the standard cosmological fluids and another contribution to the dark energy sector that is non-linear in energy density. Crucially, this provides a purely geometric origin for the evolution of dark energy, without introducing exotic dark energy fields or modifying Einstein's field equations.