Papers

For each positive integer $N$, let $p_i$ be the $i$-th prime for $i\in\{1,\ldots,N\}$, and set $$ \Phi_N=\left\{\prod_{i=1}^{N}p_i^{a_i}:a_i\in\{0,1,\ldots,N-1\}\right\}. $$ Write $f(N)$ for the largest cardinality of a subset of $\Phi_N$ containing no two distinct legs of an integral right triangle. We prove $$ N^{N-1}(\log\log\log N)\ll f(N). $$

Advances in generative AI have made it possible to produce music that is nearly indistinguishable from human compositions, raising the question of whether such works can be reliably distinguished from human compositions. We present MUSEBENCH, a large-scale benchmark for AI-generated music detection and artifact analysis, comprising over 361K tracks. The dataset includes human compositions, stylistically matched music generated by ten state-of-the-art open-source and commercial models, such as Suno and Udio, as well as human-AI co-creations and variants processed with adversarial perturbations, compression, and acoustic post-processing. Using MUSEBENCH, we benchmark 11 automated detectors and evaluate their accuracy, generalization, and robustness, under default, out-of-domain, and transformed-variant experiment settings. We further conduct a comprehensive artifact analysis through acoustic feature inspection, identifying recurring signatures such as non-idiomatic harmonic progressions, upsampling induced spectral periodicities, and violations of physical performance constraints. Our findings reveal key strengths and vulnerabilities of existing detectors and provide practical insights for building more reliable AI music detection systems.

Synthetic-aperture imaging (SAI) removes occluders such as foliage by integrating many views of a scene along a camera path. It has so far been used mainly with frame cameras. We ask whether an event camera has advantages for SAI, and answer the question in simulation, where both sensors see exactly the same scene and the same camera movement. A densely rendered Blender sequence is turned into frames with an EMVA~1288 noise model of an industrial global-shutter camera, and into an event stream with the v2e simulator parameterized like a Sony IMX636. The frames are integrated with the existing airborne optical sectioning renderer. For the events we add a new integration path that projects every single event onto the focal plane at its own interpolated pose, so no events have to be binned into frames. We compare the two sensors in three main runs and an additional dark high-speed test. In a bright scene at 25,m/s the frame camera records only three images on the path and cannot remove the occluder, while the event camera reconstructs the target, even after an event-rate controller drops most of its events to fit the camera link. At the same speed in a 5,lux scene the event camera no longer resolves the target either. In a 5,lux scene at 5,m/s both sensors reconstruct the target at similar quality. We also compare the data one traversal of the aperture costs. At high speed the capped event stream still shows the target at the same data volume as the three frames. At 1,m/s we compare both cameras at two matched data budgets, and there the event camera has no advantage over the frame camera in reconstruction quality. The data rate of the event camera depends on the scene and is highest exactly in the fast bright scenes where it is needed most.

We study the finite basis problem for flat semirings of the form $S(W)$, where $W$ is a nonempty set of nonempty words, possibly infinite. We prove that $S(W)$ is finitely based if and only if the strict interior of every word in $W$ is linear; here the strict interior of a word is obtained by deleting its first and last letters. This completely resolves an open problem raised by Jackson et al.~(J. Algebra 611: 211–245, 2022).

Interlayer excitons (IXs) in transition metal dichalcogenide bilayers possess unique dipolar properties, providing a path for exploring correlated many-body phases, electrically tunable dipole-dipole interactions, and long-range exciton transport. However, the large electron-hole separation underlying their dipolar character also results in a significantly reduced oscillator strength, limiting their direct optical interaction with light, and thus the direct probing of their dynamics and many-body interactions. Here, we show that by using Purcell engineering of critical coupling, a weak interlayer transition can absorb as strongly as the dominant intralayer transition, despite its much smaller intrinsic oscillator strength. Using this approach, in an open cavity architecture we demonstrate an order of magnitude IX absorption modulation in bilayer and trilayer MoS2, with doubling of the IX to A-exciton interaction strength weight from ~23% to ~53%. Furthermore, we demonstrate that in a tailored closed cavity architecture, the IX enhancement can reach beyond an order of magnitude, from ~5% to ~83% excitonic absorption, enabling IX absorption similar to intralayer excitons. An analytical description of the interaction is obtained via a closed-form transmission-line model which separates the excitonic and photonic contributions to the optical response, revealing how cavity architecture can be designed towards critical coupling. Our findings establish Purcell engineering of critical coupling as a general route to controlling and enhancing weak excitonic transitions.

For quandle rings, Bardakov–Passi–Singh and Elhamdadi–Nunez–Singh respectively formulated an analogue of Kaplansky's zero divisor conjecture and a weakened analogue of Kaplansky's idempotent conjecture involving the augmentation map. In this note, we verify these conjectures for medial quandles. The latter holds for a larger class of quandles; we characterize integral domains over which the statement holds for this class. We also characterize integral domains of characteristic 0 over which the statement holds for a given finite Alexander quandle.

Homogeneous turbulent flows exhibit recurring multiscale structures across spatially separated regions, suggesting that a single flow realization may contain sufficient information to learn representations of unresolved scales. We investigate this hypothesis through an extreme super-resolution framework in which a wide-activation deep super-resolution (WDSR) network is trained exclusively on overlapping patches extracted from a single high-resolution turbulent realization. Previously unseen flow fields are reconstructed through patchwise prediction followed by Hann-window-weighted overlap-add assembly. The framework is evaluated for two-dimensional homogeneous isotropic turbulence at super-resolution factors of x32 and x64, representing severe spatial under-resolution. Despite the limited training data, the proposed approach reconstructs coherent vortical structures and recovers fine-scale features more accurately than conventional interpolation. Spectral and statistical analyses further demonstrate improved recovery of high-wavenumber energy content and multiscale flow characteristics. To assess the effectiveness of exploiting internal spatial information, we compare the proposed framework against WDSR models trained on 1, 25, 50, and 100 complete high-resolution snapshots without patch extraction. This comparison distinguishes the benefits of localized learning from those associated with increasing the number of training realizations. The results demonstrate that exploiting spatial redundancy within a single turbulent realization enables accurate reconstruction of previously unseen flow fields, even under extreme spatial under-resolution. These findings establish single-realization patch-based learning as a promising data-efficient approach for turbulent super-resolution when high-resolution training data are scarce.

Proton therapy enables highly conformal tumour irradiation by exploiting the Bragg peak. Clinical precision relies on detector systems that provide linearity, spatial resolution, radiation hardness, and, for ultra-high-dose-rate (FLASH) therapy, high dynamic range with sufficient temporal response. No compact all-in-one solution currently fulfils all these requirements. Here, we present pixelated gallium nitride (GaN) arrays as a multifunctional platform. These detectors exhibit high linearity (proton currents from 70 to 1700 pA cm-2) and signal uniformity below 2% across 128 pixels. To probe GaN radiation hardness, we applied cumulative doses up to 6.7 MGy at energies from 25 MeV down to the Bragg-peak regime. Locally deposited dose dictates long-term signal loss, yet devices preserve linearity and spatial response. We demonstrate 0.25 mm effective spatial resolution, validated against radiochromic film. Proton radiography resolves fine tissue structures, with the dose extrapolated to 7 mGy per 1 ms frame in a prospective single-shot configuration. Energy-dependent responses match GATE/Geant4 simulations, and wedge measurements enable Bragg-peak tracking with an energy resolution below 10 keV in an optimised geometry. Real-time ms-scale beam monitoring enables live dose verification.These results establish GaN pixel detectors as a scalable and radiation-hard platform, enabling dosimetry, beam monitoring and energy verification in one device.

Orthogonal transforms have emerged as an effective tool for low-bit quantization of large language models (LLMs), as they reshape activation distributions without changing the underlying model function. Existing approaches typically rely either on fixed data-agnostic transforms, such as Hadamard rotations, or on calibration-time optimization of learned rotations. We study rotation selection from first principles and show that maximizing covariance leads to spectral alignment and provides a principled criterion for constructing quantization-friendly orthogonal transforms. Based on this insight, we propose SpectrumQuant, a closed-form rotation method that estimates activation covariance from calibration data and uses it to construct a covariance-aware orthogonal transform for post-training quantization. Our formulation characterizes quantization-friendly rotations as compositions of alignment and mixing components, while recovering Hadamard matrices as a special case. Interestingly, a class of butterfly matrices belongs to this category. In the realm of LLM quantization, SpectrumQuant bridges the gap between data-agnostic structured rotations and learned rotations, providing an effective and efficient data-aware alternative for post-training quantization. Experiments on Llama and Mistral models show that SpectrumQuant is competitive with state-of-the-art rotation strategies while requiring less than one-third of the GPU memory and significantly less time than learned rotations approaches like SpinQuant and DartQuant.

We show that purely continuous microscopic diffusions can homogenize to a Markov process with genuine jumps. Consider a multiscale diffusion with time-dependent generator $\mathcal{L}_{0}+r_{t}^{\epsilon}\mathcal{L}_{1}$ driven by a regenerative random environment. When the integrated activity over a regeneration cycle has a regularly varying tail of index $\beta\in(0,1)$, the cumulative operational clock converges to a $\beta$-stable subordinator, compressing finite activity-driven diffusion into vanishingly short physical time intervals. To overcome the noncommutativity of $\mathcal{L}_0$ and $\mathcal{L}_1$, we develop an extended-time parametrization paired with Khasminskii-type time discretization, establishing finite-dimensional convergence and strong semigroup convergence on $C_{0}(\mathbb{R}^{d})$ toward a jump process with nonlocal generator $\overline{\mathcal{L}}=\mathcal{L}_{0}-\kappa(-\mathcal{L}_{1})^{\beta}$. Under uniform ellipticity of $\mathcal{L}_{1}$, the fractional power $(-\mathcal{L}_{1})^{\beta}$ is identified as a $2\beta$-stable-like nonlocal operator. We also clarify physical-time path-topology obstructions and apply the framework to Poisson resetting pulses, Ornstein–Uhlenbeck diffusions, and multiscale stochastic volatility.

String theory is widely regarded as the only plausible candidate for a consistent UV-complete theory of quantum gravity. Cosmological observations suggest that our universe is undergoing accelerated expansion, pointing towards the presence of a small positive cosmological constant. Since de Sitter space is the maximally symmetric solution of Einstein's equations with a positive cosmological constant, understanding whether four-dimensional de Sitter space can be realized within string theory has become one of the central questions. Following a series of works that realize de Sitter space as an excited state—namely, as a Glauber–Sudarshan (GS) state in type IIB string theory—our goal has been to extend such a construction to heterotic string theories. Realizing de Sitter space as an excited state over a time-independent supersymmetric Minkowski background provides a mechanism for evading the vacuum-based no-go theorems that obstruct de Sitter solutions in string theory. Starting from a generic M-theory configuration, we obtain four-dimensional de Sitter space in the late-time limit of flat-slicing coordinates in both heterotic $SO(32)$ and heterotic $E_8 \times E_8$ theories through appropriate dynamical duality sequences. The corresponding GS state is constructed by evaluating the expectation value of the metric operator in M-theory using path-integral techniques. We analyse the conditions required for the existence of a well-defined effective field theory description of the setup and find that these conditions are equivalent to satisfying the null energy condition in a 3+1-dimensional FLRW cosmology. Furthermore, the de Sitter GS states are found to lie well within the temporal bound imposed by the Trans-Planckian Censorship Conjecture, rendering them as transient states. In the case of $E_8\times E_8$ theory, we also investigate implications arising from axion cosmology.

Our previous work established the mapping cone Chern character on the even-degree side, using the powers of the mapping cone curvature associated with the given mapping cone connection. In this paper, we carry out the odd-degree version using a trivial mapping cone connection and an automorphism on a trivial complex vector bundle. This version is based on the related odd-degree transgression.

Given a family of $N$ i.i.d. Gaussian points in a $d$-dimensional normed space, what is the probability that some linear transformation maps it to the unit sphere? The case of a Euclidean space is known as the ellipsoid fitting problem and has recently attracted major attention. We initiate a study of this fitting problem in a general normed space, both asymptotically and in a fixed dimension. We specifically focus on the space $\ell_\infty^d$, where a combinatorial reformulation allows us to show that $cd^2/\log d$ points can be fitted with high probability. We illustrate that the geometry of the normed space is reflected in the fitting problem by showing that in dimension $2$, the spaces $\ell_2^2$ and $\ell_\infty^2$ are characterized by having extremal fittability properties.

The GUEST (Gravitational Universe Exploration with Satellite Tracking) mission aims at detecting gravitational waves in the yet almost unexplored $\mu$Hz frequency range through high-precision orbital tracking. The unprecedented scientific objectives of this experiment demand equally advanced optical solutions: the highly eccentric orbit imposes dual measurement regimes; a low-velocity, long-range scenario at apogee and a high-velocity, short-range scenario at perigee. The substantial disparity between these conditions is addressed through a novel optical architecture incorporating two distinct types of Corner-Cube Retroreflectors (CCRs) with 1" and 2" apertures (CCR1 and CCR2, respectively). The proposed layout has been designed to ensure isotropy and homogeneity of the optical response while maintaining efficient packing over the spherical surface of the spacecraft. The resulting Optical Cross-Section (OCS) has been evaluated using a custom reduced-order model, which captures the behavior of individual CCRs under varying illumination conditions. This model has been calibrated by reconstructing the optical response of the LARES-2 satellite and has enabled a detailed assessment of the contributions of each CCR type along the GUEST orbit. Finally, sensitivity analyses have been conducted to investigate the impact of key design parameters, including the ratio between CCR types, laser wavelength, spacecraft diameter, Dihedral Angle Offsets (DAOs), and mechanical configurations.

In this note, we provide a deterministic algorithm that computes the $(\min, +)$-Matrix Product $C = A * B$ of two $N \times N$ matrices $A$ and $B$ with polynomially bounded integer entries in $\tilde{O}(N^{2.9964})$ time, improving upon the exponent of $O(N^{2.9995})$ time obtained in the recent breakthrough by Anthropic (Alman and Vassilevska Williams, 2026). Our algorithm uses a phased approach first proposed by Bringmann, Grandoni, Saha, and Vassilevska Williams in 2016. The phased approach produces an approximation $\tilde{C}$ of $C$ in truly subcubic time such that the number of remaining triples $(i,k,j): A_{i,k}+B_{k,j} < \tilde{C}(i,j)$ is truly subcubic. This provided strong evidence that a truly subcubic $(\min, +)$-Matrix Product and therefore, a truly subcubic algorithm for All Pairs Shortest Paths (APSP) may exist. However, to find the remaining triples in subcubic time, a sparse certificate is needed whose construction was not known. We use the thin matrix product theorem of the recent breakthrough to provide such a certificate. This gives a simple modular subcubic algorithm for APSP.

A single low Earth orbit (LEO) satellite offers almost no spatial degrees of freedom. Its two polarizations, however, can be exploited to carry a second layer to a handset, which 5G New Radio (NR) non-terrestrial networks do not use yet. The gain of this layer in downlink spectral efficiency (SE) is mapped over the footprint of a satellite at 330 km altitude above Munich transmitting at 2 GHz. The channel is modeled as a cascade of Jones factors for the phased-array payload, Faraday rotation, a dual-polarized land mobile satellite (LMS) channel with a line of sight, and a standardized handset antenna element at three attitudes. For a handset with boresight pointing to zenith, ideal precoding selects rank 2 with a probability of at least 0.95 within about 340 km of the nadir point at a reference signal-to-noise ratio (SNR) of 6 dB. With closed-loop precoding, such a handset on the nadir track is in rank 2 during 99% of a pass. At 13 dB, rank selection with closed-loop precoding raises the mean SE over the footprint by 49%, and upright handsets gain about 31%. Their gain is limited to the positions where they face the satellite, since the element gain is low behind the handset. At 3 dB, these gains fall to 15% and 7%.

Visual structures are often characterized by directional geometry, local oscillation, and spatial–frequency coupling. To overcome the limitations of conventional spatial convolutions mainly operating on fixed Euclidean coordinates, this article develops the learnable linear canonical transform (LLCT) framework that learns parameters within the linear canonical transform (LCT) family. The framework treats the LCT family as parameterized analytical views spanning spatial, Fourier, and intermediate linear canonical representations. The framework has the following two complementary modes. The Linear Canonical Riesz Transform (LCRT) mode combines learned linear canonical coordinates with regularized Riesz-type directional responses at sites chosen for geometric and local-structural refinement. The learnable LCT mode provides the integrated responses for latent feature sites. We establish the parameter stability of the LCT representation under admissible perturbations of the canonical matrices. Both modes use chirp multiplication and the fast Fourier transform (FFT) to preserve feature dimensions and support automatic differentiation. Experiments on crack segmentation and single-image deraining evaluate the above two modes with multiple backbones. On four segmentation backbones, the full LCRT mode gives the highest reported point estimates of F1 and IoU for the crack class among the tested variants. The learnable LCT mode gives higher values in 30 of 32 paired PSNR and SSIM measurements across four deraining backbones and four datasets. In ablation studies, the full model has the highest reported PSNR and SSIM among five tested configurations.

An agent can improve its behavior within an unresolved problem by changing how it acts and which experience it retains. We propose MMLA-RSI, a recursive self-improvement scheme with two implementations in Memory-Mediated Learning Architecture: Reasoning-Time Training (RTT) changes the policy state $\Phi$, while Reasoning-Time Memory Adaptation (RTMA) changes authoritative memory $M$. Each route also makes its adaptation method an object of improvement. A current numerical updater trains the policy proposing its successor; a current memory manager chooses the records available to the process proposing its successor. An independently admitted successor takes over the same role in the next generation. We give bounded executable rule languages, shared task/proposal interfaces, and one algorithm for either route or their composition. The RTT instance changes scalar schedules in a clipped-momentum update. The RTMA instance chooses NULL or a complete-row write with possible eviction. A fixed interpreter, trusted committer, and independent evaluator bound what can change. State versions, read closures, and conditional properties describe causal execution, accepted transitions, and finite work. Existing numerical-component studies motivate the construction. In four-candidate program selection, retaining LARC feedback updates reduces expected error by 24.65 and 36.65 percentage points for two trained initializations. In chronological continuous-integration replay, feedback binding is positive while retention increases loss. Completed SQL studies improve substantially over an unadapted substrate but do not establish the required additional online benefit. These results characterize their declared components. The two recursive routes and their joint realization are specified here; their beneficial recursive chains and discovery efficiency remain to be evaluated.

Large language models increasingly generate multiple retrieval actions jointly, while downstream systems often provide only one reward for the resulting set. Broadcasting this reward provides a valid score-function gradient estimator for the expected set-level objective, but does not determine a coalition-dependent within-set attribution. We introduce CASI (Credit Assignment via Set Intervention for Agentic Retrieval), which constructs the missing counterfactual information through snapshot-grounded set intervention: generate and retrieve once, hold replayable snapshot components fixed, and evaluate alternative subsets under common conditions. Shapley aggregation converts these marginals into within-set credit, which bounded zero-sum advantage shaping incorporates into policy optimization. For m >= 4, singleton, leave-one-out, and full-set endpoints do not generally determine the Shapley allocation; under additive set values, extra coalition evaluations are redundant. In a five-action sponsored-search setting, exhaustive auction replay over 1,200 requests reveals substantial coalition dependence. Under the training-time evaluator, CASI achieves the highest median cosine similarity to a replay-defined Shapley reference among evaluated credit rules; under a sensitivity backend, CASI does not outperform Singleton. Across five independent training runs, CASI-trained policies achieve higher held-out auction-replay set value than Singleton- or Broadcast-trained policies. In a randomized seven-day production A/B test on 10% of traffic, the CASI-trained policy yields an observed 3.51% lift in the primary advertiser-value metric over production control.

Reliable medical reasoning requires LLMs to dynamically access external biomedical evidence to improve factual trustworthiness and reasoning accuracy. However, indiscriminate retrieval can introduce noise and latency, raising a critical retrieval-timing problem: at each reasoning step, the system must decide whether the model's internal knowledge is reliable or external evidence is needed. We propose PUlSE, a lightweight probing method that uses the model's internal representations as intrinsic signals for step-level retrieval control. Our posterior trajectory analysis reveals that erroneous steps exhibit substantially higher inter-layer volatility than correct ones, suggesting unstable internal knowledge. Based on this finding, PUlSE trains a compact probe on inter-layer geometric features to detect factual errors upon step completion, and uses it as an adaptive trigger for retrieval and step regeneration. Across four medical benchmarks, PUlSE-timed retrieval matches exhaustive per-step retrieval in accuracy while reducing retrieval calls by 72%, and can transfer to an unseen legal domain, indicating potential domain-agnostic generality. Overall, our study provides an initial step toward shifting retrieval-trigger design from surface-level confidence estimates to internal activation dynamics for adaptive access.

The quark-gluon plasma (QGP) formed in relativistic heavy-ion collisions at RHIC and the LHC thermalizes from an out-of-equilibrium state of strong classical gluon fields known as the glasma. Jets and heavy quarks, produced in the initial scatterings, traverse these pre-equilibrium fields, but the glasma stage is neglected in phenomenology, which may bias the extracted QGP transport coefficients. This thesis studies its impact on jet and heavy quark transport. The glasma is described in the Color Glass Condensate framework by solving the classical Yang-Mills equations on a real-time lattice. The fields initially form longitudinal electric and magnetic flux tubes whose transverse correlation length is set by the saturation scale $Q_s$. Probes are studied with both classical transport equations and quantum evolution in the light-front Hamiltonian approach. The transport coefficients for jets and heavy quarks are much larger than in the QGP and anisotropic between transverse and longitudinal directions. The azimuthal decorrelation of back-to-back $c\bar{c}$ pairs in the glasma is comparable to that from the QGP, making $D\bar{D}$ angular correlations a potentially measurable glasma signature. The glasma also modifies the nuclear modification factor $R_{AA}$, though the effect is moderate compared to the nuclear parton distribution contribution. A systematic gauge-invariance analysis shows that the distinction between kinetic and canonical momenta is essential when comparing classical and quantum results, and that Coulomb gauge fixing largely reduces gauge artifacts. Finally, the eikonal quantum evolution of a high-energy quark is studied with time-dependent Basis Light-Front Quantization. The resulting momentum broadening agrees with the classical estimates and lays the groundwork for including quantum radiation.

This work proposes a multi-target tracking solution that reasons over combinations of sensor-level tracks to perform distributed multiple hypothesis tracking (MHT) in an asynchronous multi-sensor network. This approach handles clustered target tracking and allows for efficient information pedigree summarization for distributed data fusion (DDF). By decomposing the association problem into partitioned hypothesis sets and fusing across sensor track combinations, the method reduces combinatorial complexity compared to traditional MHT approaches. Evaluation on a satellite constellation-based tracking scenario demonstrates improved estimation accuracy and data association quality compared to a reference target tracker with global nearest neighbor association.

Anisotropic magnetorheological elastomers are magnetoactive smart materials whose complex magneto-mechanical behavior is strongly influenced by their underlying microstructure. Efficient and accurate multiscale simulations of these materials rely on small unit cells that reproduce the behavior of the real material. In this work, we present a framework for the generation and validation of such two-dimensional representative volume elements (RVEs) from a given microstructure image, assuming circular particles. The cells are generated through an optimization procedure where the two-point correlation function serves as a differentiable descriptor, while a minimum inter-particle distance is enforced as a constraint. To assess the equivalence of the generated cells, we compare their effective magneto-mechanical response with those of the reference microstructure. We demonstrate that the generated cells reproduce the reference response with high accuracy, also with substantially fewer particles. Consequently, the computational cost of subsequent multiscale simulations is reduced.

Conditional generative models are increasingly used for scientific prediction beyond the direct training support. Yet scientific questions often concern whether one intervention changes the effect of another. Such interactions can be of primary interest while explaining little of the total variation, allowing models to appear accurate overall without recovering the relevant scientific effect. It remains unclear how these models learn interactions and when these successfully extrapolate to unseen conditions. We therefore study interaction recovery in flow-matching models using a physiological time-series simulator, drug dose-response data, combinatorial cell perturbations, and molecular conformer generations, where we separate recovery from hallucinated interaction structure. In the controlled setting, individual effects are learned much earlier than interactions and models hallucinate interactions where none exist. Across settings, we find qualitatively different generalization problems, with successful prediction depending on whether condition structure continues from observed to held-out targets. When it does, interactions are recoverable. If not, models can generate plausible responses while missing the interaction. We furthermore find that hallucinations increase as targets become less identifiable, and that successful interaction recovery in output space can fail under nonlinear readouts. Finally, we show that aggregate fidelity metrics can conceal whether models learn and extrapolate interactions.

Galaxy interactions are ubiquitous in the Universe and represent a primary pathway for galaxy growth. Close passages of dwarf galaxies can induce large-scale vertical oscillations in stellar disks, a phenomenon first identified in the Milky Way within the past decade. Here, we use recent red clump distance maps of the Large Magellanic Cloud (LMC) to show that its stellar periphery is vertically offset from the central disk plane by $\sim$1.2 kpc at radii of $\sim$8.5 kpc and exhibits an S-shaped warp reaching $\sim$3.6 kpc at $\sim$11.5 kpc. We compare these observations to an $N$-body simulation of the LMC-Small Magellanic Cloud (SMC) system, in which a direct collision between the Clouds excites vertical oscillations in the outer LMC disk with amplitudes of $\sim$1~kpc and a period of $\sim$600~Myr. The simulated disk best matches the observed vertical structure $\sim$260~Myr after the collision, although this timing depends on the adopted LMC model. At that time, the simulation reproduces the sign and radial onset of the observed offset and the orientation of the warp, but underpredicts the amplitude of the warp by a factor of $\sim$4-5. These results support a collision-driven origin for the large-scale vertical structure of the LMC disk and demonstrate that dwarf–dwarf interactions can reshape stellar disks on galactic scales.

The Platonic Representation Hypothesis (PRH) holds that increasingly capable models converge toward a common representation. However, recent studies have shown different views on aligning representations via their neighborhoods, spanning trees, and distances. We show that these views can differ because the alignment criteria behind them sit at different points of one lattice, and we formalize this explanation as the Lattice Representation Hypothesis (LRH). Under the LRH, the convergence claimed by the PRH is agreement at the top of the lattice, whereas its evidence comes from neighbor overlap, a criterion near the bottom. The Aristotelian Representation Hypothesis (ARH) restricts convergence to local neighborhoods because calibration keeps the growth of neighbor overlap with model size but largely removes that of centered kernel alignment. We show that this removal can come from calibrating a maximum over layers, so global convergence remains open. Back into Plato's Cave (BPC) infers coarse shared structure from the collapse of neighbor overlap on larger evaluation sets, whereas we trace it at least partly to a fixed number of neighbors covering shorter distances. We show that the spanning-tree overlap used by Structure over Geometry (SOG) mostly repeats one-nearest-neighbor overlap. The LRH also extends to independently trained models, whose training procedure and objective decide the criteria met reliably across runs. We prove this claim for the training procedure in a linear autoencoder and for the objective in a finite contrastive Gibbs model. Experiments on dozens of pretrained vision and language models and thousands of runs of both theoretical models support these conclusions. We hope this work paves the way toward a general theory of representation hypotheses, with a framework to analyze them and compare their evidence. Project page: https://eethanshi.github.io/LRH

A central goal in solving a polynomial eigenvalue problem is to compute eigenpairs that are exact for a nearby polynomial, with each coefficient perturbation bounded by a modest multiple of unit roundoff times that coefficient's norm. A backward stable eigensolver for a linearization does not automatically provide this coefficientwise relative guarantee. Scaling can improve accuracy, but a single scaling may not work across a widely spread spectrum. We construct a family of scaled companion linearizations that covers the nonzero complex plane. Each linearization is paired with a region and an eigenvector recovery rule for which the backward-error amplification factor is bounded at exact pencil eigenvectors, independently of coefficient norm disparities. Tropical roots guide the construction, and their multiplicities reduce the number of required solves. These results provide a basis for coefficientwise relative backward stability across the spectrum.

High-quality data is essential for improving instruction tuning in threat intelligence analysis. However, existing methods for generating cybersecurity instruction data lack reliable quality assessment mechanisms, and gradient influence-based data selection methods primarily focus on single-sample matching, failing to cover diverse and complex security capabilities. To address these issues, we propose CTI-TDS, a Targeted Data Selection method for instruction tuning in Cyber Threat Intelligence analysis. Specifically, we first filter high-quality CTI instructions by integrating instruction style consistency and security knowledge verification. Furthermore, we formulate gradient influence as a distribution alignment problem, learning a gradient subspace of target tasks and applying entropic regularized optimal transport to optimize distribution matching between training samples and target tasks, enabling diversity-aware data selection. We conduct extensive experiments on CTIBench across multiple large language models. Experimental results demonstrate that when fine-tuning with only a small set of high-value instruction data, CTI-TDS outperforms existing data selection methods and achieves competitive performance on threat intelligence analysis tasks.

AI-powered image editing increasingly allows users to express high-level editing intentions, yet how these intentions are translated into concrete editing actions often remains difficult to understand. We present Atelier, a semantic image editing tool that uses image semantics and user intent to determine which editing controls to surface and how to initialize them. Guided by a formative study with eight image-editing practitioners, Atelier composes context-specific, directly manipulable controls that users can refine rather than committing AI interpretations directly to finished edits. In a within-subjects study with 12 practitioners, participants preferred AI-composed controls, described them as supporting creative exploration, and actively refined AI proposals. However, experiences of control were mixed, and interviews highlighted limited insight into why particular controls and values were proposed. Our findings suggest that making AI interpretations actionable through manipulable controls can support exploration and refinement, but actionability alone does not make those interpretations transparent to all users.

A generative site-specific beam prediction (Beam-STeP) method is proposed. Spatial priors from site-specific propagation and mobility information are jointly exploited with temporal priors from historical beam observations for beam prediction. To address the beam prediction ambiguity from multimodal spatio-temporal priors, the generative model is adopted, where a history-conditioned diffusion model is proposed to learn the multimodal conditional distribution of future beamforming vectors. Multiple beam candidates are sampled from the distribution using a denoising diffusion implicit model (DDIM). The candidate with the highest received power is then selected for transmission. Simulation results across three urban scenarios demonstrate that: i) Beam-STeP generally achieves higher normalized beamforming gains than the baselines under the same probing budget, particularly as beam prediction progresses; ii) site-specific propagation and mobility priors improve recursive beam prediction performance; and iii) DDIM sampling enables a flexible gain-latency trade-off.