Papers

We study horizon-brightened acceleration radiation for a neutral scalar field in separable Kerr-like rotating metrics with nonlinear-electrodynamic mass profiles. The principal branch has $M=0$ and $\mu=3$, with finite but direction-dependent central curvature limits. An analytic extremal charge–spin parametrization fixes the black hole domain. At a simple outer horizon, the scalar equation reduces to local conformal quantum mechanics with corotating energy $\epsh=\omega-m\OmH$. For an isolated outgoing channel we derive the first finite-gap correction in proper time, including the radial Frobenius coefficient, angular variation, geodesic terms, and switching slope. This replaces a coordinate-dependent trajectory-phase multiplier by a protocol-defined detailed-balance affinity. Direct integration of the outgoing scalar equation and an equatorial infalling trajectory validates the expansion for an explicitly specified finite gate; a solvable logarithmic-mode limit separates switching from geometric contributions. We also analyze forced equatorial circular atoms and show that co-rotating and counter-rotating ultra-relativistic motion yields a mode-dependent orbital response rather than the infalling Hawking affinity. We identify the shrinking near-extremal radial scale and quantify the effect of an unselected second radial branch, without asserting a uniform extremal limit. Random atomic injection gives a selected-mode master equation and a nonnegative population entropy-production identity. A direct first-law integrability test shows why horizon-area bookkeeping remains conditional for this off-shell metric. Independently converged Chebyshev scalar quasinormal frequencies validate the WKB results and probe the exterior geometry beyond the leading horizon data. The calculation distinguishes branch-resolved horizon thermality, finite detector protocol, and exterior scalar dynamics.

Understanding exoplanet physical properties is crucial for characterising their atmospheres and internal composition. Precise planetary masses are essential for constraining bulk densities and interiors, particularly in young systems hosting planets within or near the radius valley, where atmospheric mass loss may strongly shape their evolution. Here we revise the masses of the three transiting planets orbiting K2-233, a young ($\sim 400$ Myr) active K-type star. We combine 70 HARPS-N observations from the GAPS/ArMS Large Programme with 124 archival HARPS observations, K2 light curves, and TESS photometry obtained during our radial-velocity monitoring. We explore several Multi-GP configurations to mitigate the strong stellar activity and find that the inferred planetary masses depend significantly on the adopted activity-modelling strategy, yielding several physically viable solutions rather than a uniquely preferred one. We model the long-term atmospheric evolution of K2-233 d and find significant atmospheric mass loss. Depending on its internal composition and atmospheric properties, the planet is expected to evolve towards either a low-mass sub-Neptune retaining a thin envelope ($R_p \sim 1.71$-$1.84\ R_{\oplus}$) or a bare-core super-Earth ($R_p \sim 1.95\ R_{\oplus}$) on Gyr timescales. Our interior-structure models suggest that K2-233 b and c are likely iron-dominated, while K2-233 d retains a substantial H/He atmosphere.

We give an elementary, straightforward proof of Ovenhouse's interpretation of the denominator and the numerator of a (right) q-deformed rational in terms of weighted lattice paths on a ”snake graph”, and we give an analogous result for the left q-deformed rational introduced by Bapat, Becker, and Licata. The key ingredient is a simple formula for the q-deformation of the matrix of the composition of two homographies of the form z $\rightarrow$ a + 1/z.

Recent advances in generative image models have made many manipulated images highly realistic, raising the need for detectors that are not only accurate but also able to provide visual evidence for their decisions. In this paper, we present our solution to the Explainable Deepfake Detection Challenge [2] on the XPlainVerse dataset [1], where systems are required to predict whether an image is real or fake and generate both complex and simple explanations grounded in visible forensic cues. Our method follows a modular detection-and-explanation design. For the real/fake decision, we build a multi-backbone detector that combines several DINOv3 models with Mesorch manipulation-localization features, bringing together pretrained visual representations, DCT-aware cues, and multi-scale forensic information. To inject explanation evidence into the detector, we use a Grounding-DINO-based pseudo-mask generation pipeline that converts local artifact descriptions from training explanations into weak patch- level supervision for an Artifact Evidence Map. We further introduce a local patch-level contrastive objective that separates artifact and authenticity evidence in the detector feature space without requiring paired images or pixel-level manipulation masks. For language output, we use class-conditional Qwen3-VL models to generate complex explanations for fake and real predictions, followed by a GRPO-optimized text simplification model. The proposed methods were trained and evaluated on the challenge subset of XPlainVerse. On the full test split, our submission achieves 0.9349 detection accuracy, 0.5571 explanation score, and a 0.7456 final challenge score.

In statistical models for categorical responses, including binary, nominal and ordinal responses, a phenomenon called “separation” may occur which can render maximum likelihood estimate nonexistent and/or nonunique. Based on Sablica et al. (2026)'s general characterization of separation phenomena via structure vectors, in this article we discuss computational, numerical and practical aspects of separation phenomena in different software packages, including consequences, remedies and ways of diagnosing them. We further introduce the R package divoRce which provides the most comprehensive software suite to diagnose separation in existence. It allows to check for separation, to distinguish between types of separation, characterize the recession cone and identify variables and observations contributing to separation for almost any categorical response model in the literature, including models with baseline-category link, cumulative link, adjacent-category link and sequential link specifications. Diagnostics are based on methods for computational geometry and linear programming and can be done in floating-point or rational arithmetic with different solvers. The functionality is easily extendible by wrappers and S3 methods to accommodate implementations in third-party packages or of new categorical response models. We discuss our implementation in detail and show our software in action in a wide range of applications. We recommend to incorporate our checks for separation and existence of the MLE as a diagnostic routine in every categorical data analysis both in third-party software implementations and as part of a standard model diagnostic workflow.

Spin logic devices provide a promising route toward ultralow-power and nonvolatile information processing. In this work, we demonstrate field-free spin-orbit torque-induced asymmetric magnetization switching in in-plane anisotropy (IMA) and perpendicular magnetic anisotropy heterostructures, characterized by different critical switching currents under opposite current polarities. Combined experiments and macrospin simulations reveal that the asymmetric switching originates from an in-plane effective field Hy , which breaks the Myz mirror symmetry of the system. By controlling the magnetization direction of the IMA layer, both the switching polarity and bias direction can be tuned. Building on four distinct types of asymmetric switching behaviors, we realize a reconfigurable spin logic operation within a single Hall-bar device. These results clarify the physical origin of asymmetric magnetization switching and demonstrate an approach for realizing reconfigurable spin logic devices.

We study entropy realization for continuous actions of infinite countable amenable groups. We introduce an approximate product property for amenable group actions that permits a small proportion of tracing mistakes on prescribed pairwise disjoint, sufficiently invariant finite sets. We prove that this property implies entropy-denseness and almost entropy-approximability of every invariant measure. The construction combines zero-entropy exact tilings with a finite-block estimate for the complexity of tracing mistakes. Under asymptotic entropy expansiveness, almost entropy-approximability upgrades to entropy-approximability. For every $0\leq\alpha<h(X,G)$, ergodic measures of entropy $\alpha$ then form a residual subset of the invariant measures whose entropy is at least $\alpha$. In particular, the set of ergodic measure entropies equals $[0,h(X,G)]$.37A35, 37B40, 37B05

The fully kinetic modeling of mesothermal plasma flows presents significant challenges in the description of boundary conditions for the electrons and the electromagnetic field. Due to their higher mobility compared to ions, electrons extend downstream of the ions, which hinders the implementation of the outflow boundary conditions during transient states. Although the electron drift velocity, $u_e$, is usually neglected as $u_e \simeq u_i < v_{th,e}$, where $u_i$ is the bulk velocity of the ions and $v_{th,e}$ is the thermal velocity of the electrons, we will show how accounting for it, both at the injection of particles and at the outflow boundary condition, is of great importance to achieve quasi-neutrality of charge and current densities. A new partial reflection model for electrons is presented to represent quasi-steady and transitory states. Additionally, we will show how we can employ Ampere-Maxwell's law to better represent the transitory electric field at the outflow boundary compared to the classical `zero-field' Neumann boundary without requiring any numerical parameters. With these new boundary conditions, we improve the quasi-steady and transitory descriptions of expanding mesothermal plasmas.

Data reuploading—repeatedly encoding classical inputs at multiple layers of a parameterized quantum circuit—is a central mechanism for enhancing the expressivity of quantum neural networks (QNNs). Building on the Fourier-theoretic framework of Schuld et al.~\cite{schuld2021fourier}, we study the frequency spectrum of the general multivariate, $R$-reupload architecture (QDR). (i) We make explicit that the accessible frequencies form the set $K_R=S^{(R)}-S^{(R)}$, which equals the $R$-fold sumset $T^{(R)}$ of the difference set $T=S-S$ of the encoding spectrum, and we characterise it exactly: $K_R=\{k\in\mathcal L:\ \ell_T(k)\le R\}$, where $\mathcal L=\mathrm{span}_{\mathbb Z}(T)$ is an integer lattice and $\ell_T$ is word length in $T$. (ii) We show that the directions of the spectrum stabilise already at $R=1$ (the real span of $K_R$ equals that of $\mathcal L$), whereas the spectrum itself never saturates: the maximal frequency grows linearly in $R$ and the number of frequencies grows polynomially, as $\Theta(R^{m})$ with $m=\mathrm{rank}\,\mathcal L$. (iii) Using the spectrum size, we give a Rademacher-complexity bound on the capacity of QDRs of order $\sqrt{|K_R|/n}$. (iv) We report experiments on function approximation and classification with train/test splits, several seeds and parameter-matched classical baselines. The simulated spectra match the theory exactly. A single-qubit QDR beats a matched MLP on several smooth or periodic univariate targets and on the spiral task, but it is clearly worse on multivariate regression ($d\ge4$), where it is highly sensitive to the input-encoding scale; it beats the MLP only on equations with $d\le3$ inputs.

Traffic flow modeling is essential for understanding and predicting the collective dynamics of vehicles on road networks. Cellular automata provide a simple, interpretable yet powerful framework for representing these dynamics via local interaction rules, while retaining the ability to reproduce complex macroscopic traffic phenomena. However, learning local transition rules from data while preserving physically meaningful constraints remains challenging, particularly for stochastic models. In this work, we propose a physics-informed neural cellular automaton (PI-NCA) for data-driven traffic flow modeling. Building on the standard neural cellular automaton (NCA), we design a neural architecture that is physically consistent with the road topology and guarantees conservation of the total number of vehicles, thereby constraining the learned transition rules to physically admissible dynamics. We further extend this framework to stochastic dynamics by parameterizing probabilistic transition rules while preserving the same physics-informed constraints. We evaluate the proposed models on multiple traffic scenarios generated by the well-established Nagel-Schreckenberg and Kerner-Klenov-Wolf cellular automata. The results demonstrate that the PI-NCA successfully learns the dynamics of both traffic models and consistently outperforms a standard NCA, while the stochastic extension captures probabilistic transition rules without compromising the imposed physical constraints.

In this note, for every topological colored nonsymmetric operad with CW spaces in each arity we construct a homotopy isomorphism with a CW homotopy operad (i.e. all higher homotopies are cellular with respect to the product structure and CW structure on cubes) not changing its objects. By using the two-sided bar construction, we rectify this to a homotopy isomorphism with a strict CW operad. This applies more generally to topological algebras over colored operads in sets. In the case of diagrams of finite CW complexes over finite posets, the resulting diagram consists of finite CW spaces enhancing the Quillen adjunction between simplicial sets and topological spaces. As a byproduct, we produce an embedding of topological homotopy algebras over operads into the presheaf category over the branch resolution for the category of $P$-trees generalizing the known case of topological operads.

An essential control of AI agents is their ability to manage runtime. This ability requires a sense of time-awareness, to predict and estimate wall-clock time and to control their own actions. Prior work has focused on time-awareness, but duration-following and control in native agent harnesses remain unexplored. We present AgentTime, a benchmark for testing whether agents can work for a requested duration, predict their runtime, and estimate elapsed time afterward. It comprises 222 tasks from 18 sources spanning coding, computer use, agentic work, and automated research. Duration-following experiments append a single instruction specifying how long to work, with requests ranging from about a minute to multiple days. Accuracy on these instructions varies substantially: Fable 5.1 in Claude Code deviates from requested runtimes by a typical factor of 2.9$\times$, compared with only 1.2$\times$ for GPT-6 Astra in Codex. However, matching the requested runtime does not, by itself, establish continued work on the task. Among 158 reviewed Astra runs with classifiable transcripts, 14 explicitly slept after appearing to finish. In forecasting experiments, predictions tend to overestimate natural runtimes. In retrospective experiments, removing temporal information more than doubles deviation for Sol and Astra and nearly doubles it for Fable. An agent's ability to complete a task does not guarantee that it can control its own time or work for the whole requested duration. For agents to run reliably, safely, and autonomously over long horizons, we require the evaluation of both.

Reinforcement learning (RL) fine-tuning improves vision-language-action (VLA) policies through closed-loop experience, yet generalization beyond the fine-tuning distribution remains limited. Our analysis reveals a selective reshaping of exploration: RL contracts behavior globally, yet diversifies successful trajectories, elicits success with fewer rollouts, and covers more of the latent task-valid solution space than supervised fine-tuning. Broader successful-mode coverage may provide alternative strategies under distribution shifts. Inspired by this, we introduce DRIVE (Diversity-driven RL fIne-tuning for VLA gEneralization), which turns successful-behavior diversity into an explicit RL objective. DRIVE groups rollouts under matched task conditions, compares their trajectories with temporal alignment, and derives a success-conditioned intrinsic reward from relative behavioral diversity. This design encourages broader coverage of feasible solutions without rewarding diverse failures or superficial timing differences. Across LIBERO-Plus, ManiSkill3, and RoboTwin 2.0, DRIVE improves the average out-of-domain (OOD) performance over vanilla RL fine-tuning by 5.3 points on $\pi_0$ and 2.0 points on $\pi_{0.5}$. On a dual-arm AgileX PiPER-X platform, DRIVE further increases average OOD success from 64.1% to 73.3% (+9.2 points), demonstrating gains that persist under physical deployment.

Guy Brousseau began developing the theory of situations in the 1960s, with the ambition of building an experimental epistemology of mathematics. Over the decades, the theory has been structured, consolidated and extended, drawing on the contributions of numerous researchers. It is now recognized as one of the ”genuine ground theories” in mathematics education. In this chapter, we will describe the foundations and reasons for the existence of this theory, its systemic approach to teaching and learning issues, its current architecture, which articulates a theory of mathematical situations and a theory of didactic situations, and its key concepts, as well as its functions, particularly its predictive and explanatory functions. We will illustrate this presentation with an example in geometry that also highlights the role played by the didactic engineering methodology in this theory and related work.

Large vision-language models (LVLMs) are increasingly deployed in safety-critical applications, yet they remain vulnerable to backdoor attacks. Defending against such attacks remains costly, as existing methods require either extensive retraining on clean data or per-query intervention at inference time. To address this limitation, we propose OrthoPurify, a more efficient method to purify backdoored model weights via one-step orthogonal projection. Specifically, through structural analysis of backdoor weight updates, we find that the backdoor is encoded by diverting a small number of weight update directions from task adaptation to backdoor shortcut encoding, a phenomenon we term direction hijacking. However, identifying these hijacked directions requires a benign reference model, which is typically inaccessible to the defender. We show that a pseudo-benign model, obtained by fine-tuning the pretrained weights on only a small set of clean samples, provides a sufficient approximation, as the dominant update directions stabilize within the first few gradient steps. OrthoPurify uses this pseudo-benign reference to isolate the hijacked directions and removes them through a single projection on the weight update. Extensive experiments show that OrthoPurify reduces the attack success rate to near zero while preserving the original performance across diverse benchmarks, without retraining the backdoored model or introducing inference-time overhead. Our code is publicly available at https://github.com/womeimingzi/OrthoPurify.

Joint-embedding predictive architectures (JEPAs) predict masked or future observations in representation space, offering a natural source of predictive latents for vision-language-action (VLA) models. Yet making these latents useful across pretraining, policy learning, and deployment requires addressing three failures: mismatch with embodiment-specific control, interference with action learning, and teacher miscalibration under distribution shifts. We introduce Juno, a unified framework built around one action-conditioned JEPA that serves as a control-aligned representation backbone, a predictive teacher, and an adaptable dynamics model. During pretraining, we train it on embodiment-matched trajectories and use a dynamic CLS loss to transfer motion-weighted patch dynamics to a compact global state. During policy learning, we fuse current-frame JEPA patches into VLA perception and use a decoupled reasoning branch with separate transformation parameters to distill future latent states for action generation. During deployment, we adapt the world model on all observed transitions, including failed rollouts, freeze the adapted teacher, and re-align the policy on verified executions using LoRA adapters and a trainable action head, without expert corrections or task rewards. On SimplerEnv, Juno raises average success from $60.9\%$ to $68.5\%$ over Qwen3GR00T, the strongest baseline, and test-time adaptation further reaches $72.7\%$; on a real robot, it retains $70\%$–$75\%$ success under background, height, and object shifts where the base policy collapses to $0\%$.

We prove that the combinatorial type of a slice of the cube by a hyperplane is completely determined by its graph, within the class of cube slices. We also show that such a result cannot extend to slices of arbitrary simple polytopes by constructing a simple polytope that has two combinatorially distinct slices with isomorphic graphs.

A holographic superconductor whose scalar mass depends on the gauge field strength, $M(\Fsq)$, reproduces a superconducting dome for a suitable $M$, and recovering that $M$ from a given dome has so far taken days for a single training run. We propose a new way of training this model, with which an inversion takes from about ten minutes to an hour. Training needs the gradient of the condition that fixes the critical temperature, which the earlier method obtains by finite differences, repeating the bulk integrations for every training parameter. Here that condition is obtained, without any fit, from two integrations started at the horizon and at the boundary, and its derivative with respect to $M$ is an integral over the same two solutions, so the gradient needs no integration of its own. We use the speed to study the part of $M$ that a dome cannot determine, on the interval between the value $\Fsq$ takes at the horizon for the lowest doping and $\Fsq=0$, at which $M$ is the scalar mass $M(0)$ that fixes the dimension of the dual operator. We hold the scalar mass at several values, which we call pinned masses, retrain everything else at each, and find that the reconstructions agree wherever the horizons of the dome reach, including the minima of $M$, and differ only on that interval. A rule that keeps the reconstruction with the simplest closed form recovers both the scalar mass and the mass function of a test dome. On Gaussian and double-Gaussian domes and on the measured phase diagrams of YBa$_{2}$Cu$_{3}$O$_{y}$ and 2M-WS$_{2}$, however, the pinned mass it keeps rests on ties or on narrow margins, so for these targets the scalar mass is left open. The dome thus constrains $M$ where its horizons reach, and fixing the dimension of the dual operator needs a second observable.

Artificial intelligence supports building operations in several forms, each with its own barrier. Expert rules must be tuned for every system, supervised models need labeled data that buildings rarely record, and language models return free text that requires human-in-the-loop checking, since their stated confidence is unreliable. A newer kind of pretrained model, here called a decision model, returns a probability for every allowed answer, so one model could serve many decisions without training. This study answers three open questions for fault diagnosis in heating, ventilation, and air-conditioning systems: which decisions such a model can make, what input it needs, and whether its probabilities hold when conditions change. On 128 fault days from four public datasets of real equipment, faults are graded by the reasoning their diagnosis demands, with data given raw, as physical features, or with Brick topology. The decision model Jev, open language models, and a supervised model face nine tests that change season, control configuration, or building. Given physical features, Jev and the larger open model diagnosed faults whose evidence one feature carries, but not faults that need operating context. Under shift they kept their accuracy and calibration, while the supervised model lost 0.33 macro-F1 yet led or tied within a building. Their probabilities still needed correction, and detection was weak. The study maps which faults a decision model can diagnose and from what input, and supports a division of work in which code computes the physics and the model ranks candidate faults for an operator.

We investigate anomalous heat transport in the one-dimensional $\beta$-Fermi–Pasta–Ulam–Tsingou chain in the weakly anharmonic regime using large-scale equilibrium molecular dynamics. By resolving the heat current into phonon-mode contributions, we show that its long-time autocorrelation is controlled by diagonal mode correlations, whose decay is quantitatively determined by the corresponding phonon damping rates. Extrapolation to the thermodynamic limit gives $\Gamma_k \propto (\beta T)^{4/3} k^{5/3}$, with a subleading $k^2$ correction. The latter produces an extended pre-asymptotic regime, $C(t) \sim t^{-4/5}$, before the asymptotic decay $C(t) \sim t^{-3/5}$ is reached, leading to $\kappa(N) \sim N^{2/5} + O(N^{1/5})$. At weak anharmonicity, off-diagonal mode correlations persist up to a characteristic time $\tau_{\mathrm{od}} \sim (\beta T)^{-2}$, while increasingly large systems are required to resolve the long-wavelength phonon contribution. Weak anharmonicity therefore does not introduce a distinct asymptotic transport mechanism, but shifts the onset of the phonon-dominated regime to progressively longer times and larger length scales.

Large language model (LLM) agents interact with external resources to complete complex user tasks, exposing them to indirect prompt injection (IPI), where malicious instructions redirect agents toward attacker-intended tasks. Since IPI is difficult to defend against in real-world environments, post-incident tracing is essential for locating the injection source and reconstructing the attack chain. However, existing tracing methods primarily capture explicit control-flow and data-flow dependencies, overlooking the implicit relationships among tool calls driven by the malicious instruction. These tool calls may lack explicit dependencies and be interleaved with legitimate operations, making complete attack-chain reconstruction difficult. In this paper, we present AgentTracer, an intent-aware tracing framework that treats IPI as task intent drift. AgentTracer recovers implicit decision dependencies among tool calls to construct an Intent-Driven Execution Graph that connects dispersed tool calls by task intent. It combines the user request with an operation knowledge base to construct a user intent authorization space and identify intent-drift tool calls. Starting from an anomalous tool call under audit, AgentTracer performs target-based pruning and backward tracing to reconstruct the attack chain and locate the injection source and injection point. To evaluate AgentTracer in the presence of noise from normal tasks, we combine execution logs constructed from successful IPI attacks in AgentDyn and InjecAgent with normal execution logs containing 1,800 user requests and 9,000 background tool calls without IPI. In end-to-end experiments, AgentTracer achieves 94.17 percent injection-point accuracy and 93.56 percent path precision. Comparative experiments show that AgentTracer improves injection-point accuracy over existing methods by 18 to 54 percent.

We describe the Itgan systems for the three ASR subtasks of NADI 2026, namely robust country-level ASR (1.1), mixed-dialect ASR (1.2), and Tunisian code-switched ASR (1.3). All three share one recipe, Whisper adapted with LoRA on consumer GPUs, and each was carried by a different addition to it. On 1.1, where the dialect label is given at test time, per-dialect specialists continued from a pooled adapter gave the largest gain, and the submitted system reached 57.1% country-average WER. A post-evaluation linear probe on frozen encoder features routes utterances without the label and recovers 44% of what oracle routing gives. On 1.2 the choice of base model mattered more than adapter capacity, and system combination helped only once we added a decorrelated member, reaching 46.7% WER. On 1.3 our system placed second at 14.49% WER with the lowest CER among the leading submissions, 5.38%. Its last 0.60 WER points came without further training, mostly from an exact weight-space average of independently trained runs, with ROVER voting adding the remainder. Every comparison carries a paired-bootstrap test, and we report eight directions that did not work.

Astropauses can be defined via magnetic or fluid separatrices. For the boundary layer between the stellar wind and the local interstellar medium, two separatrices can occur, the magnetopause and the hydropause. The question is whether they are identical. To address this, we investigate under which conditions the null points of the magnetic and velocity field, which define the corresponding separatrices, coincide spatially. We analysed the case of a non-monotonous pressure distribution driving stationary counterstreaming ideal HD flows and demonstrate that the existence of an extremum of the pressure in the 3D case together with a non-degeneracy condition on the velocity field implies that this point is also a stagnation point. Turning to ideal MHD and considering the regularity of all fields, we formulated the momentum equations, revealing their quasi-linearity. This allowed us to prove the occurrence of null points by examining the rank of the Jacobians of the vector fields. We found that for a given null point of either the velocity or the magnetic field at the pressure extremum, the pendant vector field has a co-located null if the Jacobian of this field is non-singular. We extended the analysis to resistive MHD and further to MHD with general non-ideal terms and proved that if at least one of the first-order momentum equations is ideal, the stagnation point and the magnetic null point are co-located. Even for general fluid theory, the two null points co-locate as long as the curl of the generalised non-ideal terms is zero at one of them or can be represented by a linear operator in the magnetic and velocity field. In general, it is not excluded that the velocity and magnetic nulls are dislocated. However, this would require specific properties of the curl of the non-ideal term, which would reduce the probability of a relaxed quasi-stationary configuration.

We give an $n^{0.3+\varepsilon}$-approximation algorithm for the Steiner $k$-Forest problem, for any constant $\varepsilon>0$. As a function of $n$, this improves over the $O(\min\{\sqrt{n},\sqrt{k}\})$-approximation of Gupta et al. [ESA'07, TALG'10] which has stood for nearly two decades for the general case, as well as the later $n^{0.448}$-approximation of Dinitz et. al [APPROX-RANDOM'14, TALG'17] for the uniform weight case. On the other hand, we show that, due to lower bounds on the Densest $k$-Subgraph problem, the $O(\sqrt k)$-approximation for Steiner $k$-Forest likely cannot be improved. Specifically, we show that for any sufficiently small $\varepsilon>0$, an $O(k^{1/2-\varepsilon})$-approximation for Steiner $k$-Forest would surpass known degree-$n^{\Omega(\varepsilon^2)}$ Sum-of-Squares integrality gaps for Densest k-Subgraph and refute the corresponding dense-versus-random conjecture.

Quantum executions sharing a provenance record can produce different output distributions. We ask which execution details to retain, and at what precision, to guarantee agreement within a declared Hellinger tolerance. Under a specified channel model, we combine independent stochastic mechanisms and coherent rotation differences to certify recording precision without output simulation or explicit dependence on register dimension. For four-qubit quantum approximate optimization at depth one, a 13-bit comparison record suffices at tolerance 0.05 over a declared continuous noise range, uniformly in programmed angles for each fixed task. Pairwise separation constraints characterize sufficient field sets on finite context classes, exposing omissions that pass individually but fail jointly. Separately, six-qubit hardware measurements over six tested contexts certify minimum label counts of two for raw outputs and one after a fixed decoder, at tolerance 0.15 with 97% simultaneous confidence under stationary independent shots. Execution records thereby carry checkable agreement guarantees.

Reversible Jump Markov Chain Monte Carlo (RJMCMC) is a principled framework for Bayesian model comparison, but its practical use is often limited due to the difficulty of designing between-model proposals that reach regions of high posterior probability. In addition, its inherently sequential nature limits efficient use of modern GPU architectures. We address both challenges by introducing Anchored Reversible Jump Sequential Monte Carlo. Our approach combines RJMCMC with Sequential Monte Carlo (SMC) to explore the model space in parallel. Importantly, the particle population enables effective between-model proposals without problem-specific knowledge: particles are used to construct kernel density approximations of the target distributions within each model, which are then used to generate trans-dimensional proposals. Numerical experiments show that the proposed method is computationally efficient and competitive with state-of-the-art RJMCMC approaches, demonstrating its potential for scalable Bayesian model comparison.

Sample complexity is a widely used metric in sequential decision-making problems, defined as the number of suboptimal decisions during the interaction between the agent and an environment. We study the sample complexity of stochastic multi-armed bandit problems and introduce the expected sample complexity performance measure, analyzing it in a novel framework called approximately correct in expectation (ACE). We show that ACE guarantees imply almost sure convergence to the optimal expected reward, in contrast to high-probability guarantees found in other frameworks, and also show how to convert ACE guarantees into explicit expected regret bounds. We further show that, in contrast to existing measures, deterministic algorithms cannot obtain favorable ACE bounds, and analyze stochastic algorithms in two settings: when the allowed suboptimality level $\epsilon$ is known to the algorithm and when it is unknown. In the former, we devise an explore-then-$\epsilon$-greedy algorithm, and in the latter, we analyze the expected sample complexity of Thompson sampling. Finally, we establish nearly matching lower bounds for both settings, showing that the algorithms are tight in $\epsilon$ and proving a performance separation between the two regimes.

Visual generative models are trained to capture the probability distributions of natural images, yet whether their native priors reflect the regularities governing human perception of image naturalness remains an open question. Here, we probe these priors through native prediction errors across 25 open image and video generators. Because raw single-image losses are dominated by scene content and visual complexity, we evaluate directional loss differences using content-preserving, paired relational interventions that selectively disrupt facial configurations or physical illumination consistency while limiting changes in low-level image statistics. Across both domains, these loss differences reproduce human-like selective sensitivities and tolerances, capturing the classic Thatcher effect on faces and shape-dependent responses to illumination inconsistencies. Notably, these loss differences reliably track continuous gradations of human naturalness judgments across individual stimulus pairs (peaking at $r = .84$ on faces and $.64$ on physical scenes) and retain unique human-aligned signals even after controlling for feature distances from frozen vision encoders and standard image quality metrics. We also find that while overall sensitivity to these violations broadly covaries with human alignment across models, the two systematically decouple along denoising schedules, with alignment peaking earlier than sensitivity, revealing that human-like naturalness judgments dissociate from generic violation detection. Together, these findings demonstrate that learning visual distributions yields generative loss landscapes that capture distinct aspects of human naturalness perception.

Knowledge graph embedding (KGE) models encode the entities and relations of a knowledge graph into a low-dimensional latent space, enabling tasks such as classification or link prediction. Most KGE models follow an autoencoder architecture, in which an encoder projects the knowledge graph into the latent space and a decoder reconstruct it. Combining both encoder and decoder components is increasingly needed, yet existing libraries rarely support complete autoencoders, are often unmaintained, rely on undocumented default hyperparameters, and produce results that cannot be compared across libraries. Here we present KGATE (Knowledge Graph Autoencoder Training Environment), a modular Python library built on PyTorch Geometric and TorchKGE. KGATE lets users assemble initializers, encoders, decoders, losses, negative samplers, and evaluation metrics as building blocks, or plug in their own block. KGATE includes a preprocessing procedure that controls data leakage, a builtin training pipeline, and reproducibility by design. Benchmarks against six existing KGE libraries show that KGATE training time is comparable with the fastest libraries while offering a broader set of features.

We report on an exhaustive census of all 1,006,700,565 connected graphs on $11$ vertices to find the minimal examples of graphs whose independence complexes are Cohen-Macaulay but not shellable, or shellable but not vertex decomposable. In particular, there are exactly two graphs $G$ where ${\rm Ind}(G)$ is Cohen-Macaulay but not shellable, when the characteristic is not two, and exactly six graphs where ${\rm Ind}(G)$ is shellable but not vertex decomposable.