Papers

We study gradient-type dynamics for weak stochastic control through the laws of controlled diffusions on path space. Although the objective is generally nonconvex in the drift, a uniformly convex running cost induces a strictly convex functional of the corresponding path law and hence a natural Bregman geometry. We construct the associated implicit proximal scheme and prove its well-posedness and convergence to a continuous-time mirror flow. When the mirror cost coincides with the running cost and the law-dependent potential is linear, the flow becomes affine in centered entropy coordinates. This yields a variational construction of the resulting Newton flow, uniform stability estimates, and exponential convergence to the optimizer. For a general uniformly convex mirror cost and a nonlinear convex potential of the law, we construct the natural-gradient flow globally in learning time using BMO estimates for quadratic BSDEs, and establish quantitative convergence and a first-order discretization error. We further analyze interacting finite-particle approximations, proving exponential convergence to the finite-particle optimum and an O(1/N) normalized discrepancy from the mean-field optimum. In the Markovian setting, reflection coupling yields uniform spatial regularity and exponential convergence of the feedback controls on Rd, including for nonquadratic state-dependent Hamiltonians.

We supplement McMule, a Monte Carlo framework that provides QED corrections up to next-to-next-to-leading order (NNLO) in the fine structure constant $\alpha$, with the inelastic two-photon exchange (TPE) contribution, based on the data-driven dispersive calculation of Tomalak, Pasquini and Vanderhaeghen, which we extend to the $Q^2\rightarrow 0$ limit that enables applications in the low-$Q^2$ region relevant for upcoming low-energy experiments. We present results for two experimental settings: the future MAGIX@MESA experiment and the ISR@MAMI measurement. For MAGIX@MESA kinematics, the inelastic TPE is small, comparable to the proton-side NLO corrections and subdominant to both the leptonic radiative corrections and the full NNLO QED corrections once a 1 MeV photon-energy cut is applied. For the ISR@MAMI kinematics, NNLO QED corrections modify the radiative tail below the elastic peak at the 10% level.

We discuss the perturbative stability of warped anti-de Sitter (WAdS$_3$) spaces in three-dimensional gauged supergravity. To this end, we first derive the analogue of the Breitenlohner-Freedman bound for a single scalar field on such a curved background. We then apply this analysis to the half-maximal $D=3$ gauged supergravity obtained from the compactification of the $D=6$, $\mathcal{N}=(1,1)$ supergravity on S$^3$. Families of three-dimensional configurations, uplifting to spaces of the form $\mathrm{WAdS}_3 \times \mathrm{WS}^3$, are found by turning on appropriate vector and scalar fields, supporting the AdS$_3$ and S$^3$ warpings, respectively. Finally, we show that the spectra of scalar fluctuations satisfy the stability criteria for each solution.

Photonic lanterns provide an interface between multimode optical fields and arrays of single-mode waveguides, making them promising components for modal filtering, wavefront sensing, and high-contrast astronomical instrumentation. We present the design, simulation, two-photon-polymerization fabrication, and free-space characterization of a compact photonic lantern optimized for operation at $ 1050~\mathrm{nm} $. The device was designed to transform a multimode input into five nominally single-mode output waveguides. Eigenmode-expansion simulations in Ansys Lumerical MODE were used to optimize the lantern geometry while minimizing insertion loss and output-channel power nonuniformity. The optimized structure was fabricated using a Nanoscribe Photonic Professional GT2 two-photon-polymerization system and developed as a standalone polymer-waveguide component. The fabricated lantern was characterized using a free-space optical setup consisting of a $ 635~\mathrm{nm} $ laser for preliminary characterization, collimation and focusing optics, and camera-based imaging of the transmitted fields. Measurements were used to assess optical throughput, output intensity distribution, and light-guiding performance. Differences between simulated and measured results may arise from the wavelength mismatch, fabrication tolerances, material and surface-scattering losses, alignment errors, and deviations from the idealized material and geometric parameters used in simulation. These results demonstrate a compact, additively manufactured photonic-lantern platform and establish a pathway toward free-space-coupled astrophotonic systems for future high-contrast exoplanet-imaging instrumentation.

We introduce AREX, a training-free sampler for pretrained flow matching models that uses the target mean and covariance to capture an analytically tractable part of the sampling dynamics. We show that the velocity field of the moment-matched Gaussian target is the $L^2$-optimal affine approximation to the marginal velocity field. This motivates decomposition of the learned dynamics into an affine component over the whole sampling path, determined by the first two target moments, and a neural residual term. AREX keeps the affine component and integrates it using an explicit matrix-valued propagator. In turn, we only require to integrate over the residual term. This differs from scalar exponential integrators, which analytically handle only isotropic linear dynamics. Across image and text-to-image generation tasks, AREX consistently improves sample fidelity in the few-step sampling regime without retraining the underlying model.

Hallucination detection is particularly important for medical language models, but repeated-sampling approaches are computationally expensive. A faster alternative is a single-pass uncertainty head that predicts hallucination risk from a frozen generator's internal signals. Existing uncertainty heads consume backbone-specific features and tokenization, motivating adaptation when the backbone or language changes. We study two Persian medical models, Gaokerena-V and Gaokerena-R, on a 168-question Iranian medical entrance examination. Across five generations per question, Gaokerena-V produces the same option on only 14 questions and Gaokerena-R on 37, compared with 168 for Med-Gemma, indicating substantial response variability in the Gaokerena models. We therefore adapt the LLM Uncertainty Head (LUH) framework to these models and construct two paired claim-level hallucination datasets directly in Persian, with 1,600 responses per backbone. Lightweight heads are trained on frozen-backbone attention maps and token probabilities. On held-out test splits, the heads achieve PR-AUCs of 0.4820 and 0.4652, corresponding to 2.30 and 2.66 times their respective random baselines, and ROC-AUCs of 0.7852 and 0.7810. The resulting detectors require neither retrieval nor repeated sampling at inference.

Inverse game theory seeks to learn agents' unknown objectives from observed equilibrium behavior. Existing residual-based approaches can lead to non-convex problems and need not ensure strong monotonicity of the learned game, limiting reliable equilibrium prediction. We develop a tractable convex framework for learning static and dynamic non-cooperative games using first-order and Nikaido-Isoda (NI) loss. Specialized operator parameterizations, including a Helmholtz–Hodge decomposition in a reproducing kernel Hilbert space (RKHS), enforce strong monotonicity for quadratic, nonparametric, non-quadratic, and linear-quadratic dynamic games. We establish finite-sample out-of-sample prediction guarantees, using Rademacher complexity to match existing bounds for the non-quadratic setting. For noisy sequential data, we develop a robust receding-horizon learning scheme whose adaptive regularization admits a maximum a posteriori (MAP) interpretation and is computed using randomized trace estimation. Numerical experiments, including a stylized autonomous-vehicle collision-avoidance application, demonstrate predictive accuracy and robustness to measurement noise.

Post-training a large language model (LLM) often requires exploring trade-offs between multiple rewards, but retraining for each trade-off is expensive. Decoding-time policy composition allows these trade-offs to be adjusted by combining reward-specific policies at inference time. This composition targets a weighted product of the policies' probabilities over complete responses, but standard implementations combine their next-token probabilities, generally introducing sampling bias. We analyze a known iterative correction based on independence Metropolis-Hastings (MH). Our main result shows that, for every rollout budget, MH produces an output distribution at least as close to the target as sampling-importance-resampling (SIR) with the same budget, as measured by every convex f-divergence. We also derive a lower bound on MH's improvement over the uncorrected decoder in a consensus objective measuring agreement with the supplied policies. We further characterize the correction's sampling error in two asymptotic regimes: when the reward-specific policies approach agreement, and when the log ratio between target and uncorrected-decoder probabilities fluctuates increasingly widely, as can happen for long responses. We complement our analysis with experiments in enumerable and LLM-scale settings.

Henneaux-Teitelboim gravity is a diffeomorphism-invariant formulation of unimodular gravity that is locally equivalent to general relativity but includes an extra boundary variable, unimodular time, whose difference between hypersurfaces measures the enclosed 4-volume. In general, unimodular versions of quantum gravity can be expected to deviate from theories based on general relativity, but a discrete path-integral formulation for Henneaux-Teitelboim gravity has not yet been established. In this paper, we discretise Henneaux-Teitelboim gravity using the methods of Euclidean Regge calculus. Testing this framework in a symmetry-reduced model of Regge cosmology, we reproduce results in previous literature and demonstrate that the continuum limit can be naturally defined using unimodular time rather than proper time. Because unimodular time appears as boundary data as opposed to being a degree of freedom in the bulk, this approach allows for the comparison of general simplicial triangulations, beyond highly symmetric discretisations, to the continuum. Our work provides a first step towards a discrete path-integral formulation of Henneaux-Teitelboim gravity and adds a new perspective on time as a boundary variable in quantum gravity.

For any physical process, varying the initial distribution over its states will change the resulting expected entropy production (EP). An initial distribution that minimizes the EP of a particular process is called the prior of that process. Varying the microphysical details of the process will change its prior. We consider the following question: if an engineer wants to design a system to implement a given map, what prior should they design into the system to minimize the EP for the worst-case actual distribution? We refer to the resulting optimal worst-case value as the minimax EP, and investigate how it depends only on the dynamics of the process. We derive the closed-form solution to this minimax problem when the map is deterministic. We also show that for stochastic maps, a worst-case actual distribution can always be chosen to be a point mass on a single state, and that the associated minimax prior resembles a Boltzmann-Gibbs equation and can be found by a globally convergent numerical algorithm. We further show that the minimax EP is the maximum uncertainty about the input that remains after observing the output. Finally, we extend the analysis to the continuous-time regime, showing that the minimax instantaneous EP diverges, while the corresponding finite-time minimax EP has a universal short-time scaling set by the largest escape rate of the dynamics.

Given a graph $G$ and a positive integer $k$, a packing $k$-domatic coloring of $G$ is a function $f: V(G) \to \{1,\ldots,t\}$ such that (1) for any color $j \in \{1,\ldots, t\}$ and any two distinct vertices $u,v\in V(G)$ with $f(u)=f(v)=j$ we have $d_G(u,v)>j$, and (2) $V(G)$ admits a partition into $k$ sets $A_1,\ldots,A_k$ such that for any $v\in V(G)$ and any $i\in\{1,\ldots,k\}$ there exists a vertex $w\in A_i$ such that $d_G(v,w)\le f(w)$. The minimum integer $t$ such that $G$ admits a packing $k$-domatic coloring of $G$ using colors in $\{1,\ldots,t\}$ is denoted by $\chi_{\rho,k}(G)$. The condition (1) in the definition of a packing $k$-domatic coloring implies that $G$ is a packing coloring, hence $\chi_{\rho,k}(G)\ge \chi_\rho(G)$ holds for any graph $G$, where $\chi_\rho(G)$ is the packing chromatic number of $G$. On the other hand, the new concept also leads to a generalization of the domatic number of a graph due to which one can easily see that $\chi_{\rho,2}(G)=\chi_\rho(G)$ holds for any graph with no isolated vertices. One of the main result in this paper is that $\chi_{\rho,3}(G)=\chi_\rho(G)$ holds in any connected graph $G$ with minimum degree at least $2$, and the bound is best possible in two different senses. In addition, we provide several exact values and bounds on the new invariant in paths and cycles. We prove that $\chi_{\rho,k}(P_n)=k$ for any $k\in\{3,4,5\}$ as soon as $n\ge 8$, and, in contrast, $\chi_{\rho,k}(P_n)>k$ for any $n\ge k\ge 12$. We also prove the exact values of $\chi_{\rho,k}(P_\infty)$ when $k\in \{3,4,5\}$ for the two-way infinite path $P_\infty$, and exact values of $\chi_{\rho,k}(C_n)$ when $k\in\{3,4\}$ for all cycles $C_n$. We also consider a general framework of $S$-packing $k$-domatic colorings, where $S$ is an arbitrary sequence of non-negative integers, and present some basic results in this context.

Long-horizon mobile manipulation presents significant challenges due to compounding execution errors and capacity interference between locomotion and arm control. While recent Vision-Language-Action models excel at short-horizon tasks, they lack the hierarchical reasoning required for multi-stage objectives. Furthermore, existing hierarchical agents suffer from rigid sub-task mapping, inflexible replanning, and a lack of continuous learning. To address these limitations, we introduce MobiAgent, a dual-loop agentic framework that bridges robust deployment execution and recursive policy self-improvement. During deployment, the Inner Loop decouples high-level reasoning from low-level control through highly composable atomic skills. It employs Vision-Language models for receding-horizon planning and visual reflection, dynamically composing skills to ensure robust error recovery. These skills are executed by specialized flow-matching experts that share a unified VLM backbone, maximizing reusability while mitigating capacity interference. Concurrently, the Outer Loop drives automated lifelong learning by autonomously segmenting and verifying deployment rollouts, clustering them to discover atomic skills, and continuously fine-tuning the skill library without human annotations. Evaluations on RoboCasa, BEHAVIOR-1K, and real-world tasks demonstrate the effectiveness of MobiAgent. It outperforms $\pi_{0.5}$-TA by 22.5 percentage points on BEHAVIOR-1K and enables robust recovery from execution failures. Through autonomous data recycling, success improves from 7.50% to 27.50% on RoboCasa and from 32.5% to 57.5% on Astribot S1.

Many reinforcement-learning (RL) problems are non-stationary yet structured and can be decomposed into phases, each with its own transition probabilities and reward functions. When the phase sequence is known, the common solution augments the state with information to satisfy the Markovian property and applies standard RL techniques. However, prior work finds that the multi-policy approach for different phases can outperform a single state-augmented policy shared among the phases, for reasons that remain unclear. In this work, we first show that the shared policy can theoretically achieve performance of any multi-policy solution. However, whether a multi-policy solution can perform better than the corresponding single shared policy in practice depends on function approximation, learning and optimization processes, as well as, for multi-policy solutions, the sample efficiency and loss of continuity from one policy to another. We propose a regime-based phase decomposition method to identify which policy can provide better performance. The method is based on consideration of the duration of transient system dynamics relative to the duration of the quasi-stationary period. Numerical experiments are conducted with different non-stationary RL problems to validate our four major hypotheses: (a) longer phase durations favor multi-policies, (b) the heterogeneity between phases increases the burden on single policy, (c) multi-policies need sufficient data for each phase, and (d) environment-specific transition dynamics between phases can affect which policy is preferable.

Federated learning (FL) enables collaborative training of medical image segmentation models without sharing raw patient data, yet existing approaches assume a homogeneous compute budget across institutions, limiting participation of low-resource sites. We propose Fed-ADApt, a depth-adaptive federated framework for UNet-based segmentation that jointly addresses low-compute training and inference. Fed-ADApt integrates multi-depth supervision with hierarchical depth-wise aggregation, allowing each site to train according to its local compute budget while contributing to a global model that supports dynamic depth selection at deployment. We evaluated Fed-ADApt on multi-site 2D retinal fundus disc segmentation and 3D brain tumor segmentation. Across both tasks, federated collaboration substantially improves robustness under domain shift. Fed-ADApt matched the full-resource FedAvg performance in 3D and achieved competitive 2D performance with a 4.7% average Dice reduction, while reducing average inference cost by 19.5% in 3D and 34.5% in 2D and substantially reducing training cost by 98% at the most constrained sites. Importantly, Fed-ADApt enables low-resource institutions that cannot train full-capacity models to participate in federations while maintaining competitive global performance under a favorable accuracy to efficiency trade-off. By considering training and inference compute budgets, Fed-ADApt provides a practical and equitable solution for federated medical image segmentation across heterogeneous clinical and edge-enabled imaging environments.

We propose UniDynamics, a diffusion-based framework for future 4D dynamic scenes (RGB, depth, and optical flow) generation from a single event-RGB pair, without requiring long histories or control priors as in existing methods, while explicitly modeling future motion fields. The core idea is to leverage event streams to offer an alternative motion prior for single-RGB extrapolation, and to enforce geometric and motion constraints throughout generation via multimodal modeling. Specifically, we design an Event Latent Enhancement (ELE) module to align and enhance event latents into diffusion-injectable conditioning features, providing robust initial motion priors and reliable texture/structure cues. We further introduce a Perceptual Dynamics Space (PDS) embedded in the multi-scale U-Net, which decouples and adaptively interacts depth and flow while continuously feeding back constraints to appearance features, improving geometric-motion consistency for physically plausible and spatiotemporally coherent prediction. Experiments on VKitti2 and DSEC demonstrate state-of-the-art performance, producing high-quality, temporally coherent, and 4D-consistent future predictions, especially under challenging high-speed motion blur.

We present the first calculation of the third-order corrections to the rapidity anomalous dimension for jet-veto cross sections. This is a crucial ingredient for the resummation of these scattering observables in key processes such as colour-singlet and heavy-quark-pair production at hadron colliders. More precisely, our results enable the next-to-next-to-next-to-leading logarithmic (N$^3$LL) resummation of the jet-veto cross section for colour singlet production at the LHC, with immediate phenomenological relevance. The anomalous dimension is extracted from a calculation of the three-loop soft function in soft-collinear effective field theory, and is presented as a function of the jet radius $R$ for the clustering algorithms of the generalised-$k_t$ family. To handle the complexity associated with the clustering algorithm, we formulate a semi-numerical computational approach. This strategy is itself a result of the paper, and can be extended to the calculation of other anomalous dimensions and soft functions at three loops.

In the generalization of token graphs (or supertoken graphs), the vertices of a $k$-token graph of a graph $G$ correspond to $k$ distinguishable or indistinguishable tokens placed on $k$ different or equal vertices of $G$. In several cases, we provide the whole spectrum of a supertoken graph of a star by analyzing its regular partitions.

AI services increasingly rely on black-box security guardrails, yet privacy-preserving model auditing regimes often cannot measure how well these systems perform in both a human eyes-off production setting, which disallows human inspection of user input, and a machine eyes-off setting, which disallows model inspection of such input. We introduce CorrectGuard, an eyes-off correctness estimation framework for both settings, which involves an independent model-based evaluator predicting whether guardrail decisions on human- and machine-inaccessible inputs are correct using only labeled eyes-on data and without access to the guardrail's internals. We evaluate in-context learning, embedding, and finetuning-based correctness models under leave-one-dataset-out evaluation across 13 safety and security datasets spanning harmful content, jailbreaks, prompt injection, and extraction, and across open-weight guardrails treated uniformly as black boxes. Across both human and machine eyes-off settings (the latter implemented using privacy-preserving fingerprinting of inputs), in-context-learning-based correctness classifiers substantially improve error identification across guardrails, achieving up to a 25 percentage-point increase in macro accuracy, as do finetuning-based approaches which provide a nearly 15-point boost, although performance varies sharply across guardrails and held-out datasets. Correctness scores also support guardrail decision ranking and abstention: across 3 guardrails, the best correctness rankings reduce AURC from unranked baselines of 0.33-0.44 to 0.17-0.22, while the best operating points retain 37.5-52.0% of guardrail decisions at 15% observed risk. These results show that external correctness models can expose systematic failures and support guardrail decision abstention without privileged access to the guardrail.

The analysis of large data panels is important in econometrics and beyond. Prediction and inference methods for such data typically rely on simplifying model assumptions for the covariance structure of errors. One convenient assumption is what we call groupwise sphericity: that errors are uncorrelated across individuals and have constant variance within certain groups. While theoretically useful, in large panels groupwise sphericity is often too restrictive to apply in practice. We therefore develop new quantitative inference tools to test whether deviations from this model assumption are practically relevant. Our approach covers both large-dimensional data matrices and regression panels, in a regime where the cross-sectional dimension is proportional to the sample size. The theory is based on the analysis of extreme eigenvalues of the empirical covariance matrix and uses recent advances in random matrix theory. Numerical experiments demonstrate accurate size control and good power in finite samples.

Editable 3D models of field-grown crops support high-throughput phenotyping and in silico breeding trials, but building them from scanned point clouds requires organ-level segmentation and fitting. Procedural generators can turn an organ-level parameter set into an analysis-suitable 3D model, but obtaining that set requires hours of manual tuning per plant or segmentation models trained on species-specific labels. We present an automated pipeline that reconstructs procedural maize models from raw 3D point clouds without manual tuning or species-specific training data. A multimodal vision-language model (VLM) annotates leaf midlines in rendered orthographic views. Deterministic geometric algorithms back-project the annotations onto the point cloud, merge them into 3D leaves by cross-view consensus, and grow the midlines to full blades on an orientation-weighted surface graph. Measured organ parameters populate a plant descriptor for a Non-Uniform Rational B-Spline (NURBS)-based procedural model generator. Each leaf surface is then refined against its scan points by differentiable NURBS fitting. The pipeline reached a median whole-plant Chamfer distance of 5.4 mm on 100 genotypically diverse field-grown maize plants from the MaizeField3D dataset. The reconstructions were closer to the scans than those of an earlier semi-automated pipeline based on manual annotations. The pipeline recovered 1,017 of 1,023 (99.4%) curated reference leaves at an intersection-over-union of at least 0.5 without using those labels as input. These results show that VLM annotations become usable organ-level measurements when downstream geometric stages can correct them. This makes automated generation of editable 3D plant assets feasible at the scale of modern phenotyping experiments.

Accurate colon segmentation from CT images is essential for colorectal disease analysis, yet deep learning based methods often produce disconnected predictions due to complex anatomy. This study introduces a three-stage, topology-preserving segmentation pipeline to address this issue. The first stage performs initial deep learning-based segmentation, followed by centreline bridging to reconnect disjoint regions and a reconstruction stage to refine continuity. Evaluations on TotalSegmentator and RAOS datasets using overlap, distance and topology-based metrics demonstrate improved structural consistency while maintaining segmentation accuracy. The proposed method enhances topological integrity, enabling more reliable colon segmentation for clinical and research applications.

We introduce neckar, a public code for the one-loop matter and galaxy power spectrum, as well as correlation function, in the Eulerian Effective Field Theory of Large-Scale Structure (EFTofLSS). It is based on the FFTLog expansion, and is designed for fast and accurate parameter inference from large-scale structure data, making it a powerful tool for high-dimensional Bayesian analyses of current and upcoming galaxy surveys. neckar combines several numerical and analytical improvements, including the separation between pre-computable and cosmology-dependent contributions, a semi-analytic treatment of the Alcock-Paczynski effect for power spectrum multipoles, and an implementation of the symmetry-based bootstrap kernels, allowing straightforward applications to a broader class of cosmological models. The code also incorporates an improved infrared resummation scheme that corrects previous implementation inaccuracies, and which led to errors of the order of 1% for the quadrupole, and of 10% for the hexadecapole at scales $k \gtrsim 0.1 h \textrm{Mpc}^{-1}$, as well as an asymptotic treatment that extends the range of accurate predictions into mildly non-linear scales $k \sim 0.4 h \textrm{Mpc}^{-1}$. This leads to relevant corrections in the correlation function around the BAO peak. Taken altogether, these improvements render neckar up to two orders of magnitude faster than similar existing codes without relying on emulators, and at the same time improving numerical accuracy. The code is written in C and is distributed with a Python wrapper for convenience.

K-fold cross-validation (CV) is widely used as evidence of out-of-sample performance, although folds are neither independent experiments nor equally informative under heterogeneous data. Cross Upper-Bound Validation (CUBV) replaces point-wise CV accuracy by conservative upper bounds on true risk. Here we generalise CUBV through a single exponential framework in which the moment-generating function of the generalisation gap is controlled by a cumulant envelope gamma(lambda). This yields a family of risk bounds covering Hoeffding-, Bernstein-, dependency-aware, PAC-Bayesian, and heterogeneous source-fusion settings. For K-fold CV, dependence between fold-wise gaps is modelled through a joint sub-Gaussian proxy matrix. Under equicorrelation, this gives an effective number of folds, Keff = K/[1+(K-1)rho], showing that increasing K does not necessarily increase statistical evidence when folds are strongly dependent. The framework is also extended to posterior distributions over predictors and weighted multi-source fusion, where weights are selected by minimising an upper bound on future risk rather than empirical error alone. Experiments with trained linear classifiers on heterogeneous multimodal Gaussian mixtures compare K-fold CV with full-sample resubstitution plus risk correction. Bounds are evaluated by coverage and tightness. In low-dimensional small-sample settings, K-fold partitioning can increase uncertainty because individual folds under-represent minority modes, while corrected resubstitution can remain valid and tighter; this effect disappears as sample size increases. Overall, gamma-CUBV separates observed performance, uncertainty, dependence, model complexity, and confidence into explicit terms, providing a unified route from CV scores to risk statements and a principled validation criterion for heterogeneous small-sample applications such as neuroimaging.

We give a complete classification of Schur positivity for three-legged spiders. Every spider with at least two even legs is Schur positive, whereas every spider with three odd legs has a negative Schur coefficient. If $a$ is even and $b,c$ are odd, then the spider $S(a,b,c)$ is Schur positive if and only if $a\le 5b+5c+2$. Whenever Schur positivity fails, there is exactly one negative Schur coefficient, whose value we determine explicitly. These results extend those of Thibon and Wang for the families $S(a,2,1)$ and $S(a,4,1)$, and those of Wang and Wang for $S(a,b,2)$. The proof combines known Schur-positivity results for clique-spiders with Pieri's rule and simultaneous induction.

Neural quantum states based on modern deep learning architectures have emerged as powerful representations for quantum many-body systems. In particular, Transformer-based neural quantum states provide expressive models capable of capturing long-range correlations, and their empirical generalization performance has recently been demonstrated. However, a theoretical understanding of their generalization behavior remains largely unexplored. In this paper, we develop a theoretical framework to analyze the generalization properties of Transformer-based neural quantum states under in-context learning. We establish a rigorous inference-time generalization error bound in terms of mean squared error (MSE), showing that the pointwise prediction error decreases inversely with both the number of in-context examples and the depth of the Transformer. We further show that the Transformer depth required to achieve this guarantee scales only linearly with the system size–namely, the number of particles in continuous systems or the number of qudits in discrete systems. Building on this result, we extend our analysis to full quantum states formulated as rank-one density operators, and derive MSE-based generalization bounds over both continuous and discrete domains under physical constraints. Finally, numerical simulations corroborate our theoretical analysis.

Instanton theory provides a semiclassical approximation to nonadiabatic rate constants within a path-integral framework and captures nuclear quantum effects such as tunneling and zero-point energy. Although the simplest reactions proceed directly from reactants to products, a number of important nonadiabatic processes involve three electronic states and react via a concerted mechanism through a virtual bridge state, also referred to as bridge-mediated tunneling or superexchange. In previous work, we have derived an instanton theory to describe such reactions using a dominant tunneling trajectory that propagates on each of the three potential energy surfaces. However, this approach is only valid when the bridge state is sufficiently low in energy. In contrast, in the high-bridge regime, the trajectories on the bridge surface become infinitesimally short, which causes the previous theory to break down. In this work, we derive the appropriate asymptotic approximation for the high-bridge regime and find that the resulting theory reduces to a two-state golden-rule instanton with an effective coupling that describes a nonresonant hop to the virtual bridge state. We further develop a uniform asymptotic instanton theory that eliminates divergences and smoothly connects the high- and low-bridge regimes. In a companion paper, we apply the method to study the quintet-to-singlet transition (via a triplet bridge) of an iron(II) complex.

We establish a general framework for engineering unconventional magnetism using bichromatic driving. We identify a sharp hierarchy: for a bichromatic drive with a generic even commensurate frequency ratio, the leading continuum $q$-wave magnet generates components only up to order $q-2$, whereas lattice higher-gradient terms supply the missing $q-1$ and $q$ parities and complete the hierarchy through order $q$. We explicitly illustrate this new revised hierarchy on a $d$-wave altermagnet irradiated by a circularly-linearly polarized light, and show that the asymmetry of the driving field is transferred to the light-dressed electronic structure, producing momentum-asymmetric dispersions beyond the static and single-frequency limits. We further show that this band asymmetry is absent in the leading continuum expansion and originates from higher-gradient lattice terms that are converted by the bichromatic drive into odd-in-momentum contributions. Extending the analysis to higher-order unconventional magnets, we further obtain complete magnetic hierarchies for all $q$-parity unconventional magnets. Our results establish bichromatic Floquet driving as a general route for generating mixed-parity magnetic hierarchies and dynamically engineering unconventional magnetism.

For a matrix rank-metric code $\mathcal{C}$ and an integer $i$, the $i$-th subcode distance of $\mathcal{C}$ is the largest minimum rank distance of an $i$-dimensional subcode of $\mathcal{C}$. We study how subcode distances change under the Add-and-Remove construction, in which a subcode of codimension $\ell_s$ is kept and a space of dimension $\ell_a$ is added; this construction is used, with Gabidulin codes, in the $\mathsf{MIRANDA}$ signature scheme. For arbitrary matrix codes, we give inequalities between the subcode distances of the original and of the new code, and we show that Delsarte duality interchanges $\ell_s$ and $\ell_a$. For matrix Gabidulin codes, whose subcode distances are given by an explicit formula, we show that, if $\ell_s<\max\{m,n\}$, then within each block of indices $(a-1)\max\{m,n\}+1,\ldots,a\max\{m,n\}$ not exceeding $\dim_{\mathbb{F}_q}(\mathcal{C}_s)$, all but the last $\ell_s$ subcode distances are the same as for the Gabidulin code, and the remaining ones decrease by at most one; a small example shows that such a decrease can occur. We also express the minimum distance of the new code in terms of the rank distance between the added space and the common subcode. For $\mathsf{MIRANDA}$, the lower bound on the minimum distance of the dual public code used by the known distinguisher when $\ell_s=0$ is a special case of these results; for the proposed parameters, where $\ell_s>0$, the same bound holds for a subcode of codimension $\ell_s$ of the dual public code.

We present PopCWB, a Bayesian framework for the inference of the binary black hole (BBH) population based on the unmodeled search pipeline coherent WaveBurst (cWB). The standard population analysis takes an inverse approach by inferring the underlying population model parameters for a given set of detected events using the individual posterior samples. In PopCWB, we take a forward approach to population inference by varying population models to identify the most optimal one which describes the observed events. Rather than using event-level posterior samples, PopCWB uses a large set of simulated events reconstructed by cWB and their total mass, estimated with a machine-learning regression, to construct marginal probability distributions. These marginal probabilities are then used in the construction of the likelihood. We apply PopCWB to BBH events detected by cWB during the third observing run (O3) of the LIGO–Virgo–KAGRA detectors. We constrain an astrophysically motivated BBH population model that incorporates the effects of pulsational pair-instability supernovae and dynamical mergers. The analysis predicts a maximum black hole mass of $\mathbf{45.5^{+5.1}_{-6.1} M_{\odot}}$ from stellar evolution and an inferred local BBH merger rate of $\mathbf{23.0^{+16.6}_{-8.3} \, Gpc^{-3} yr^{-1}}$. We compare these results with the existing population models from the literature.

Post-training with verifiable rewards can induce reward hacking, motivating the use of monitors within the training objective rather than solely for offline auditing. We show that a low monitor readout does not identify whether such an intervention controls behavior. In a code-generation environment whose dominant exploit is available at the start of the reasoning trace, we train policies against three monitors that pass the same offline gate: an in-domain activation probe and two penalties conditioned on how early the policy commits to its own final answer. The probe score is at its numerical floor from the first recorded training step, and the trained-score median is zero for every prefix-trained run at the endpoint. These readouts estimate different quantities, and we do not compare their scales; within each monitor family, however, low values do not establish behavioral control. Within one fixed configuration, prefix-trained runs with the same zero-median trained score range, by seed alone, from a mixed regime with a low hacking share to near-pure reward hacking. All probe runs reach the hacking regime, but their floor-level readout reflects a mismatch between the position where the probe was validated and the position where it was read during training, not a second instance of this ambiguity. Text-level analysis identifies a prefix failure mode: generic planning and filler shells postpone the exploit past the cut without eliminating it from the final output. Low measured commitment therefore does not distinguish a low hacking share from delayed commitment to the exploit. Offline discrimination and low monitor-aligned readouts are insufficient evidence of behavioral control; an out-of-band behavioral check is required. We characterize the endpoint readout, not its evolution. Code is available at https://github.com/zhezhou1106/spoof-cost.